WO2014072820A2 - Chronoamperometric methods and devices for electrochemical quantification of analytes - Google Patents

Abstract

Methods and devices disclosed herein relate to the use of a band electrode to create a two-component current in an electrochemical sensor, preferably for use with a blood glucose monitor. The dimensions of the band electrode are smaller than that of the solution deposited on it, hence one component of the current will result from planar diffusion and the second from edge diffusion. By analyzing the plotted currents, both the concentration and the diffusion coefficient of the target analyte can be determined simultaneously, which offers an improved accuracy over the art in concentration measurement. Methods and devices disclosed herein also relate to the use of multiple band electrodes of different widths to increase the speed of measurement without adversely affecting accuracy. Methods and devices disclosed herein further relate to the use of alternating pulse voltages to measure the concentration of an analyte, taking advantage of the faster recovery time for the concentration profile. The alternating pulses also tend to perturb the concentration profile in only a thin diffusion layer, allowing various layers of the sample to be interrogated.

Description

CHRONOAMPEROMETRIC METHODS AND DEVICES FOR ELECTROCHEMICAL QUANTIFICATION OF ANALYTES

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This non-provisional application claims priority from U.S. Provisional Application No. 61/724,265, filed on November 8, 2012, which is herein incorporated by reference in its entirety.

FIELD OF THE INVENTION

[0002] The invention disclosed herein generally relates to chronoamperometric methods and devices for measuring the concentration of an analyte. The invention also relates to the use of electrodes having an edge effect to measure the concentration and the diffusion coefficient of an analyte simultaneously. The invention further relates to the use of pulses and alternating pulse voltages to measure the concentration of an analyte.

BACKGROUND

[0003] All publications herein are incorporated by reference to the same extent as if each individual publication or patent application was specifically and individually indicated to be incorporated by reference. The following description includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art.

Conventional Electrochemical Sensor

[0004] In order to better manage their condition, many diabetics measure their blood glucose level on a daily basis. This is done using a disposable strip and a meter. One end of the strip is inserted into the meter and the blood is applied to the other end of the strip. The meter applies a voltage and measures a resulting current which is used to estimate the blood glucose concentration.

[0005] Such a system is called an electrochemical sensor. The meter applies the potential (typically between 200 and 400 mV, or 100 to 500 mV) between two or more electrodes which are exposed to the blood sample. [0006] Electrochemical systems of this sort are called amperometric systems. By applying the voltage between two electrodes they can oxidize (or reduce) an analyte of interest and use the resulting current to estimate its concentration.

[0007] Glucose cannot be directly oxidized electrochemically, so electrochemical blood glucose sensors use an enzyme to oxidize the glucose. In doing so the enzyme is itself reduced. This is then re-oxidized by a mediator, which is the oxidized species of a redox couple. A common example of a mediator is ferricyanide. In oxidizing the enzyme the e.g. ferricyanide is reduced to ferrocyanide. Sufficient ferricyanide is present that it is always in excess to the amount of ferrocyanide produced. The ferrocyanide is now oxidized at what is called the working electrode (W/E), which is at a positive voltage with respect to the other electrode, generating a current. This other electrode is called the counter electrode (C/E) and it completes the circuit, typically by converting ferricyanide to ferrocyanide. This is called mediated electron transfer. However the analyte of interest can sometimes be oxidized or reduced electrochemically directly, in which case it can be measured directly by direct electron transfer.

[0008] This system, which uses a W/E and a C/E is called a two electrode system. Sometimes it is desirable to have a more absolute knowledge of the potential of the W/E in which case a three electrode system is used. In this case the potential of the W/E is set relative to a reference electrode (R E) and the circuit is completed via a C/E. The R/E does not pass current. A three electrode system of this sort can also be used in the following invention. Alternatively a two electrode system can be used where the C/E does not use the redox couple to provide the C/E reaction - for instance Ag/ AgCl - as a sensor for an electrochemically oxidizable/ reducible analyte.

[0009] Ferrocyanide generated at the C/E can interfere with the estimation of the ferrocyanide produced by the enzyme at the working electrode, so the counter electrode is typically kept at a sufficient distance from the working electrode to ensure that it does not arrive there during the test and interfere with the working electrode.

[0010] So a strip typically contains two or more electrodes in contact with, or in the vicinity of, a mixture of an enzyme and an oxidized mediator (e.g. ferricyanide) and other substances, such as buffer. Typically the electrodes and reagent mix are contained within a cavity and the blood wicks into this and dissolves the reagents.

[0011] In a typical amperometric system the current is dependent on a variety of parameters other than the concentration of the analyte (C). These include time after the potential is applied (t), the area of the working electrode (A) and the diffusion coefficient (D), which is a measure of the mobility of the analyte in the solution. Usually, A and t are known, but C and D are both unknown. D can vary with factors such as temperature, viscosity of the solution, and haematocrit. In the past, an average value of D was assumed and used to calculate C, which however can result in significant inaccuracy in the measurement of C. Thus, there exists a need in the art to accurately determine D.

[0012] In certain situations D can be measured from the time dependent behavior of the current. For instance, the Verio system marketed by LifeScan has closely opposed electrodes, set an exact distance apart. As t increases there is an augmentation in current due to the diffusion of ferrocyanide from the counter electrode to the working electrode, allowing an estimation of D. In theory, adjacent electrodes can be used to interact in the same fashion, though practically speaking this is more difficult.

Chronoamperometry - Potential Step

[0013] Chronoamperometry is the name of the electrochemical technique in which the potential of the working electrode is stepped and the resulting current from faradaic processes occurring at the electrode (caused by the potential step) is monitored as a function of time. Alternate to stepping the potential the electrodes can be switched in at the desired voltage from open circuit.

[0014] Consider a two-electrode system. When the electrodes are immersed in an unstirred solution containing a redox couple (which is a reduced species and its corresponding oxidized form) and a potential is applied between the electrodes then oxidation of the reduced species takes place at the anode (the positive electrode), and reduction of the oxidized species takes place at the cathode (the negative electrode). For a sufficiently large voltage (around 0.3 volts for a reversible couple) the kinetics of oxidation and reduction become so rapid that the concentration of reduced species drops to zero at the anode surface, and that of the oxidized species drops at the cathode surface. This is said to be "mass- transfer-limited," or "diffusion-limited." In the case of electrochemical glucose sensors, a redox couple that is commonly used is ferro/ferricyanide (see below section Chemistry of Electrochemical Blood Glucose Sensors). Thus ferrocyanide is oxidized at the anode to ferricyanide, and ferricyanide is reduced at the cathode back to ferrocyanide. This redox couple is often referred to as an example throughout the specification, but one skilled in the art will recognize that any suitable redox couple can be used. [0015] Typically a supporting electrolyte is added to the solution to minimize solution resistance. This ensures that the voltage applied between the electrodes is primarily applied at the electrode interfaces and not across the solution between the electrodes.

[0016] Consider the anode only (in this case the anode is commonly called the working electrode (W/E) and the cathode is called the counter electrode (C/E) or reference electrode). Before the application of the potential between the electrodes (Figure 1 A, (t < 1 s) - the potential step in this example is arbitrarily set at t = 1 s), the concentration of ferrocyanide is uniform throughout the solution. Immediately after the application of a positive V (e.g. at t > 1 s) the ferrocyanide is oxidized to ferricyanide at the anode surface, its concentration drops to zero, and this generates a current. This consumption establishes a concentration gradient that produces a continuing flux of ferrocyanide to the anode. As it arrives it is immediately oxidized so the current at the anode is proportional to the concentration gradient at the electrode surface, dC/dx at x = 0, x being the distance from the electrode surface. The continued ferrocyanide flux causes the length of the diffusion layer to increase (the diffusion layer is the layer in which the ferrocyanide concentration is depleted with respect to the bulk concentration), so the slope of the concentration profile at the electrode surface decreases (Figure IB) and so does the current.

[0017] The current generated by the reduction or oxidation of a dissolved chemical substance at an electrode at time t is called the faradaic current (i_(t) Faradaic) where the subscript (t) shows it is time dependent (Figure 1C).

Planar (Shielded) Electrode (Cottr ell Behavior, No Edge Effects)

[0018] The simplest case to consider mathematically is that of diffusion in the region normal to the electrode surface in an unstirred solution of, for example, ferrocyanide of concentration C. This is the case where a disc electrode is inserted into a cylinder of the same internal dimensions as the disc. Such an electrode is known as a shielded electrode (SE). Diffusion to the electrode takes place though a zone which is normal to the electrode and of the same cross-sectional area. In this case a solution of the diffusion equation gives the current-time response:

i(t) Faradaic ⁼ nFAC(D^ t)°^'5 Equation 1 n = number of electrons involved in the redox process

F is the Faraday constant

A is the cross-sectional area of the electrode D is the diffusion coefficient.

[0019] This is known as the Cottrell Equation after Cottrell, who derived it in 1903. One can write:

i(t) Faradaic ⁼ i(t) Cottrell Equation 2

[0020] A plot of l(_t) Cottrell ^{vs tmie} is shown in Figure 1C.

[0021] Figure 2 A shows the variation of the diffusion layer as t increases for this shielded electrode (where Ϊ3 lt2-ti are in the ratio of 100:25: 1).

[0022] For a shielded planar electrode (the case considered above) the diffusion layer thickness (L_DL) is given by

LrjL ⁼ (TTDI)^0'5 Equation 3 i(t) Faradaic ⁼ nF ACD/L_DL Equation 4

Edge Effects (Unshielded Electrode)

[0023] Consider the case for an unshielded electrode, for example, a disc electrode mounted flush to a surrounding insulator in a cylinder whose diameter is much greater than that of the disc. Figure 2B shows the variation of the diffusion layer as t increases. One can write:

!(t) Faradaic ⁼ l(t) Cottrell ⁺ l(t) Edge Equation 5 where i_(t) Edge is the current caused by diffusion from the region non-normal to the electrode surface, for example, from the edges.

[0024] The length of the diffusion layer boundary for the edge effect increases with time, whereas that in the Cottrell region remains constant. It is therefore surmised from the diagram that the diffusion from the edges will contribute a progressively larger percentage of the faradaic current as t increases. Any electrode which has access to a solution from a cross-sectional area greater than that of the electrode will see edge effects. (Generally speaking, when the scale of the diffusion layer developed during the course of the measurement compares with the size of the electrode, the electrode is referred to as a microelectrode. Other terms are edge effect electrode, or unshielded electrode). Use of Chronoamperometry in Analysis

Chemistry of Electrochemical Blood Glucose Sensors

[0025] Electrochemical blood glucose sensors are discussed as examples, but one skilled in the art will understand that any solution based analyte can be determined using the same methodology.

[0026] The majority of electrochemical blood glucose sensors use Glucose dehydrogenase (GDH) to turn over D-glucose to D-glucono-l,5-lactone.

D-glucose + acceptor D-glucono-1 ,5 -lactone + reduced acceptor Equation 6

[0027] The most commonly used acceptor (or mediator) is ferricyanide. The enzyme reaction is a two electron reaction, which converts two ferricyanide ions to two ferrocyanide per molecule of D-glucose.

[0028] A complication is that in solution D-glucose converts to α:β-0- Glucopyranose in the ratio 36:64 and the GDH only acts on the β-D-Glucopyranose. Conversion of the a to β form in solution is relatively slow, so when the enzyme reaction has acted to completion it has produced 1.28 ferrocyanide ions for each molecule of glucose in the original solution. By measuring the concentration of this ferrocyanide the sensor estimates the original concentration of glucose.

Normal Cottrell (Measures C when D is Known)

[0029] From Equation 1 it is seen that the Cottrell current is proportional to the concentration of the analyte being oxidized, and various constants. All these constants can be measured, and hence the current at an electrode can be used to determine the concentration of an analyte. However, the diffusion coefficient is sensitive to factors such as the temperature of the solution and its composition. An average value of D can be used, but this is only useful if the variation in D is small compared to the accuracy desired. In the case of blood samples, for example, D varies significantly (approximately two times) for a haematocrit range (which is the volume percentage (%) of red blood cells in blood) of 20 to 70%, which can typically be encountered in samples of diabetic blood. Additionally D varies by approximately 3% per degree Celsius.

Interacting Opposing Electrodes - (Measure C and D Simultaneously)

[0030] Conventionally, for accurate measurement the Cottrell current, the anode and cathode are usually spaced far enough apart that they do not significantly interfere with each other during the course of the measurement. Until recently the need to use an assumed, or average, value of D was a significant limitation on sensor accuracy. In 1994 a system was developed which allowed the determination of D for the sample as the measurement was made. It works by having closely spaced opposed electrodes (a cathode and an anode- Figure 3 A). The solution consists of ferro and ferricyanide. There are no edge effects as the geometric electrodes cover both walls of a cavity, i.e., the available cross-sectional area is the same as the electrode areas. Ferrocyanide (produced by the enzyme reaction discussed above) is oxidized at the anode, and to complete the circuit ferricyanide is reduced to ferrocyanide at the cathode. Figure 3B shows the variation in concentration profile with time for a cell with thickness T = 100 μιη and D = 5X10^~6cm²s^_1. At short times - less than 0.5 sees - the current is entirely Cottrell. After approximately 0.5 sees the diffusion layers at the cathode and anode start to interact at the midpoint of the cell giving rise to an increased flux which results in a current additional to that resulting from normal Cottrell diffusion. This interference current increases with time and at around 3 sees a steady state current (iss) is achieved where the ferrocyanide concentration increases linearly from zero (at the anode) to twice the initial bulk concentration (at the cathode). The resulting current transient is shown in Figure 3C.

[0031] The expression for the end point current has long been known:

iss = [nFAC/T] * [2D₀D_R/(D₀ + D_R)] Equation 7

= nFADC/T where D = D₀ = D_R Equation 8

[0032] where C = total concentration of redox couple, Do and D_R are the diffusion coefficients for the oxidized and reduced species respectively and T is the thickness of the cell (S.J.Konopka, Anal Chem 1970 42 (14) ppl 741 - 1746). Whilst comparing the early Cottrell behavior with the end point current allows the determination of C and D, the time scales are relatively long for a blood glucose test, being of the order of 3 seconds for D = 5* 10^"6 cm²/sec and 13 seconds for D = 1 * 10^~6 cm²/sec (the typical range of D found in whole blood as the haematocrit increases).

[0033] An analytical solution to the diffusion equations describing this system has been determined It is represented by an infinite series of exponentials.

i(t) = i_ss[l +2∑ _ι= i ex (-4m½²Bt/T *)] Equation 9 where i_ss is the steady state current at the end of the transient given by

i_ss = 2nFADC/T Equation 10 where C is the concentration of ferrocyanide (compare Equation 8).

[0034] Of particular interest is the transitional region between Cottrell and Steady

State. As t increases, and l^) approaches l_ss, the higher m terms in the infinite sum of exponentials decrease in magnitude with respect to the m = 1 term. Setting the m = 2 term as 1% of the m = 1 term gives l(t) ⁼ 1 .43l_ss. So in the region l_ss < l(_t) < 1 .43l_ss.

ln[(i_(t) - i_ss)/(2 i_ss)] = -4n²Ot/T² Equation 11

(And for i_(t) > 1.43i_ss the Cottrell Equation is found to be accurate to better than 0.5%.)

[0035] Estimating l_ss and plotting the left hand side of Equation 11 vs t gives a straight line with slope

S = -4lA/T^2; Equation 12

[0036] Varying the estimate of i_ss and repeating the analysis until a best fit is obtained (e.g. via maximizing R², the coefficient of determination) gives the "optimal" value of l_ss. D is now calculated and used in Equation 10 to give C. Alternatively D can be used in an analysis of the Cottrell region to give C.

[0037] Note that the slope is proportional to the thickness of the cell squared and that analyzing the data requires estimating a value of i_ss.

[0038] Typically the data is analyzed in the time period corresponding to 1.43l_ss

≥ l(t)≥ l -051_ss. In this range the ratio of l(t) to the Cottrell current (i.e. the current if the electrodes were not interfering) is 1.003 to 1.14. That is, the excess current over Cottrell due to interaction of the electrodes is 0.3% to 14%.

[0039] Analyzing the data in this transitional region shortens the test time by approximately 1/3, to 2 to 9 seconds. However, this is still too long for a 5 second test. Reducing T significantly reduces the time of the test. However, 100 μιη is generally reckoned to be the minimum thickness that allows blood to fill the capillary in an acceptable time. For example, US8425759 states "capillaries with depths greater than or equal to 100 μιη have been found to allow fast fill of blood with haematocrit from 20 to 70% to reliable flow into the chamber." Thus, there exists a need in the field to develop a sensor system that is capable of measuring C and D of an analyte in a sample medium simultaneously within a short period, such as 5 seconds.

Interacting Planar (Adjacent) Electrodes

[0040] Closely spaced working and counter electrodes lying side by side (coplanar) start to interact when their relative diffusion layers extend "over" each other. The working electrode consumes ferrocyanide and generates ferricyanide, and the counter electrode does the opposite. Consequently a concentration profile builds up between them. However product generated at different points of the surface of one electrode takes differing times to arrive at the opposite electrode (transit time is proportional to distance squared), and some product escapes into the bulk of the solution. Consequently the deviation from Cottrell behavior is less, takes place over a longer timescale, and is harder to analyze than the interactive behavior of Interacting Opposing Electrodes (described above).

[0041] Such systems are described in the literature, usually in the form of interdigitated electrodes (Aoki et al. J. Electroanal. Chem., 266 (1989) 11 - 20, & 256 (1988) 269-282) (Figure 3D) and more recently in US patents, for example, US7276146 and US7276147. However, in US7276146 and US7276147 an analysis of the interactive behavior to give C and D has not been carried out, or attempted.

Analysis of Edge Effects on Non-interacting Electrodes

[0042] Oldham considers edge effects in planar unshielded electrodes in his paper Edge Effects in Semiinfinite Diffusion (J. Electroanal. Chem., 122 (1981) 1 -17). In that Oldham states essentially that: "Provided that the linear dimensions of the electrode are much greater than the diffusion layer thickness, the shape of the electrode is completely characterized by its area A and its perimeter length, P. In fact the current is the sum of an areal term, that depends on A but not on P, and a perimetric term, that depends on P but not on A."

i_(t) = nFACCD/π t)⁰-⁵ + nFCDP/2 Equation 13

[0043] Oldham states this is true of any geometry where the minimum dimension is greater than or equal to 4(Dt)^0'5, which is approximately the point at which C = 0.995C*. It can be seen in Figure IB that the concentration of C at x = L_DL is not C*, but approx 0.8C*, where C* is the concentration in the bulk solution, that is where it is unperturbed by either electrode process. In fact C = 0.99C* at x = 2L_DL. Nevertheless, it is a handy estimate of the diffusion layer thickness and its value represents the value obtained by extrapolating dC/dt at x=0 to C , making it useful in Equation 4.

SUMMARY OF THE INVENTION

[0044] Methods and composition described herein are provided by way of example and should not in any way limit the scope of the invention. [0045] In one aspect, a method for determining a concentration of an analyte in a medium is described. Particularly, the method comprises contacting the medium with one or more unshielded working electrode (W/E) and a counter electrode (C/E); wherein the W/E and C/E are non-interfering with each other; applying a voltage between the W/E and C/E; measuring a non-steady state current between the W/E and the C/E under the applied voltage over time (t), wherein the current is indicative of oxidation of a first species or reduction of a second species in the medium; plotting the measured current over 1/t^0'5 to produce a fitted straight line with a slope and a intercept; determining values of the slope and the intercept; and solving the concentration and diffusion coefficient of the first or second species of the redox couple simultaneously based on the determined values of the slope and the intercept.

[0046] In another aspect, a method for determining a profile of concentration change of an analyte in a medium is described. Particularly, the method comprises contacting the medium with at least two unshielded working electrodes (W/E) and a counter electrode (C/E), wherein the W/E and C/E are arranged to be non-interfering with each other; wherein the W/E comprise at least a band electrode (BE) and at least a microband electrode (MBE), wherein the BE is wider than the MBE; applying a voltage between the W/E and C/E; measuring a non-steady state current between each of the at least two W/E and the C/E under the applied voltage over time, wherein the current is indicative of oxidation of a first species or reduction of a second species in the medium; calculating a difference current over time by subtracting a fraction of the measured current between the BE and the C/E from the measured current between the MBE and the C/E; wherein the fraction is the ratio between an area of the MBE and an area of the BE; and generating a profile of the calculated difference current over time, the profile reflecting concentration change of the analyte over time.

[0047] In another aspect, a method for determining a profile of concentration change of an analyte in a medium is described. Particularly, the method comprises contacting the medium with a working electrode (W/E) and a counter electrode (C/E); wherein the W/E and C/E are non-interfering with each other; applying a train of alternating positive and negative voltage pulses between the W/E and the C/E; measuring a current between the W/E and the C/E at the end of each applied voltage pulse, wherein the current is indicative of oxidation or reduction of a first species in the medium; wherein a second species is present in excess to the first species in the medium; and wherein the first species and second species form a redox couple; calculating a difference current between the currents measured for each pair of successive positive and negative voltage pulses; estimating a concentration (C_t) of the analyte for each calculated difference current; and generating the profile of concentration change by tracking the estimated concentration (C_t) over time.

[0048] In another aspect, a device for electrochemical quantification of an analyte in a sample medium is described. Particularly, the device comprises one or more unshielded working electrode (W/E), a counter electrode (C/E), an insulating support, and a sensing meter. More particularly, the insulating support defines a cavity cell configured to receive the sample medium; the W/E and C/E are partially embedded in the insulating support such that each electrode exposes a surface to the cavity cell; the W/E and C/E are arranged to be non-interfering with each other; the W/E and C/E are capable of reversibly engaging with the sensing meter; and the sensing meter is configured to determine a concentration and a diffusion coefficient of the analyte simultaneously by applying a voltage between the W/E and C/E and monitoring the resulting current.

[0049] The present invention offers in several embodiments the advantage of measuring C and D independently and measuring C and D several times in a 5 second test, allowing measurement of the final concentration C_∞. The present invention also offers in several embodiments the advantage of using very small volume of cells and samples, down to < 100 nL and completing the test in very short time, for example, less than 5 seconds. Other advantages of the present invention include, but are not limited to, the ability to measure background electrochemical interferents, the ability to generate more accurate measurements than prior-existing methods and devices, and the ability to fabricate the device at a lower cost

[0050] The details of one or more embodiments of the disclosure are set forth in the accompanying drawings and the description below. Other features, objects, and advantages will be apparent from the description and drawings, and from the claims

BRIEF DESCRIPTION OF THE FIGURES

[0051] Those of skill in the art will understand that the drawings, described below, are for illustrative purposes only. The drawings are not intended to limit the scope of the present teachings in any way.

[0052] Figure 1 A depicts an exemplary voltage step applied between the working electrode and the counter electrode of the present invention.

[0053] Figure IB depicts exemplary concentration profiles following the application of a voltage step according to the present invention.

[0054] Figure 1 C depicts an exemplary current transient during the application of a voltage step according to the present invention. [0055] Figure 2A depicts the change in diffusion layer (the Cottrell behavior) with time for a shielded electrode according to the present invention.

[0056] Figure 2B depicts the change in diffusion layer (Cottrell behavior plus the Edge Effects) with time for an unshielded electrode according to the present invention.

[0057] Figure 3A depicts a diagrammatic representation of an opposing electrode cell according to the present invention.

[0058] Figure 3B depicts concentration profiles with time for a thin layer cell with opposing electrodes according to the present invention.

[0059] Figure 3C depicts i_(t) Faradaic for a thin layer cell (opposed electrodes) and a shielded planar electrode of the same dimensions according to the present invention.

[0060] Figure 3D depicts an exemplary interdigitated array according to the present invention.

[0061] Figure 4 A depicts the top view of a (Micro)Band Electrode according to the present invention. The counter electrode is not shown.

[0062] Figure 4B depicts the side view of a (Micro)Band Electrode according to the present invention.

[0063] Figure 5A depicts a i_(t) vs t plot showing the Cottrell behavior of a shielded planar electrode versus the Oldham behavior of the same electrode but unshielded (with edge effects) according to the present invention.

[0064] Figure 5B depicts a i_(t) vs 1/t^0'5 plot showing the Cottrell behavior of a shielded planar electrode versus the Oldham behavior of the same electrode but unshielded (with edge effects) according to the present invention.

[0065] Figure 6 depicts a i_(t) vs 1/t^0'5 plot showing the Cottrell behavior of a shielded planar electrode with different areas according to the present invention.

[0066] Figure 7 depicts a i_(t) vs 1/t^0'5 plot of band electrodes of different widths, same length, according to the present invention.

[0067] Figure 8 depicts diagrammatic representation of dual band electrode according to the present invention

[0068] Figure 8A depicts one possible variation of concentration with time according to the present invention.

[0069] Figure 8B depicts data from Figure 8A approximated as discrete changes according to the present invention

[0070] Figure 9 depicts multiple Microband Electrode without overlap of diffusion layers according to the present invention [0071] Figure 10 depicts a i_(t) vs 1/t^0'5 plot for Band Electrode, Microband Electrode and Multiple Microband Electrode according to the present invention

[0072] Figure 11 A depicts a possible low volume cell configuration according to the present invention.

[0073] Figure 11B depicts a possible low volume cell configuration according to the present invention.

[0074] Figure 11C depicts a complete strip from Figure 11A according to the present invention

[0075] Figure 12A depicts data plotted using t_zero as the Time of Application of the voltage pulse gathered from a Band Electrode of a width of 185 μιη, according to the present invention

[0076] Figure 12B depicts data plotted using optimized t_zero as 2.1 ms after the time of application of the voltage pulse gathered from a Band Electrode of a width of 185 μιη, according to the present invention. Data are plotted using the same data of Figure 12A

[0077] Figure 13A depicts data plotted using t_zero as the time of application of the voltage pulse gathered from a Band Electrode of a width of 268 μιη according to the present invention.

[0078] Figure 13B depicts C and D calculated from data presented in Figure 13 A. In each case the analysis is started at t = 0.01s and continued until the value of t_max shown on the x axis

[0079] Figure 14A depicts values of slope for successive pulses measured with different rest periods at O/C

[0080] Figure 14B depicts values of slope for successive pulses measured with different rest periods at 0V

[0081] Figure 15A depicts estimated concentration with time calculated using forward/ reverse pulses at +/- 0.3V. The pulses were applied as the solution entered the cavity.

[0082] Figure 15B depicts estimated concentration with time calculated using forward/ reverse pulses at +/- 0.3V. The pulses were applied 100 s after the solution entered the cavity.

DESCRIPTION OF THE INVENTION

[0083] All references cited herein are incorporated by reference in their entirety as though fully set forth. Also incorporated herein by reference in their entirety are: 1) A description of Interdigitated Electrodes Arrays as described in U.S. Patents 7276146 and 7276147; 2) A description of Microelectrode arrays of Circular Disks as described in U.S. Patent 8388821 and European Patent 2080023.

[0084] Unless defined otherwise, technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. One skilled in the art will recognize many methods and materials similar or equivalent to those described herein, which could be used in the practice of the present invention. Indeed, the present invention is in no way limited to the methods and materials described.

[0085] As used herein, the term "C/E" is an abbreviation of Counter Electrode.

[0086] As used herein, the term "W/E" is an abbreviation of Working Electrode.

[0087] As used herein, the symbol "i_(t) Faradaic" represents the total current generated by the reduction or oxidation of some chemical substance at an electrode. Such a chemical substance is in solution.

[0088] As used herein, the symbol '¾ cottreii" represents the current caused by diffusion from the region normal to the electrode surface.

[0089] As used herein, the symbol '¾ Edge or lEdge" represents the current caused by diffusion from the region non-normal to the electrode surface i.e. from the edges.

[0090] As used herein, the symbol '¾ oidham" represents i(_t) Cottrell+ lEdge (generally - but not exclusively - for a band electrode).

[0091] As used herein, the symbol "n" represents the number of electrons involved in the redox process.

[0092] As used herein, the symbol "F" represents the Faraday constant.

[0093] As used herein, the symbol "A" represents the cross-sectional area of the electrode.

[0094] As used herein, the symbol "C" represents concentration.

[0095] As used herein, the symbol "C*" represents the concentration in the bulk solution.

[0096] As used herein, the symbol "C_t" represents concentration of C at time t.

[0097] As used herein, the symbol "Cd" represents double layer capacitance, which term refers to the capacitance of the electrical double layer. "The whole array of charged species and orientated dipoles existing at the metal -solution interface is called the electrical double layer. At a given potential, the electrode-solution interface is characterized by a double layer capacitance, Cd, typically in the range of 10 to 40 μΕ/cm²." {Electrochemical Methods (Second Edition), Bard and Faulkner, page 12.)

[0098] As used herein, the symbol "D" represents diffusion coefficient.

[0099] As used herein, the symbol "D₀" represents diffusion coefficient for the oxidized species.

[0100] As used herein, the symbol "D_R" represents diffusion coefficient for the reduced species.

[0101] As used herein, the symbol "T" represents the thickness of a cell cavity.

[0102] As used herein, the symbol "t" represents time.

[0103] As used herein, the symbol "L_DL" represents the diffusion layer thickness, equals to (πϋί)°^'5, approximately the distance from the electrode at which C=0.8C*.

[0104] As used herein, the symbol "i_ss" represents steady state cell current.

[0105] As used herein, the symbol '¾" represents cell current at time t.

[0106] As used herein, the symbol "S" represents the slope of a line on a graph (generally of i_(t) vs 1/t^0'5).

[0107] As used herein, the symbol "I_nt" represents the intercept of a line on a graph (generally the y axis intercept of i_(t) vs 1/t^0'5).

[0108] As used herein, the symbol "W" represents the width of an electrode.

[0109] As used herein, the symbol "L" represents the length of an electrode.

[0110] As used herein, the symbol "P" represents the perimeter length of an electrode.

[0111] As used herein, the symbol "A" represents the area of an electrode (= L*W for a band electrode).

[0112] As used herein, the term "haematocrit" refers to the volume percentage (%) of red blood cells in blood.

[0113] As used herein, the term "chronoamperometry" refers to an electrochemical technique in which the potential of the working electrode is stepped against a counter electrode (or switched in from open circuit) and the resulting current from faradaic processes occurring at the electrode is monitored as a function of time.

[0114] As used herein, the term "redox couple" refers to a reduced species and its corresponding oxidized form.

[0115] As used herein, the term "BE" is an abbreviation of Band Electrode, which refers to a strip shaped electrode with substantially straight and parallel edges and a length that is greater than the width. For a BE width is understood to mean the average width over the length.

[0116] As used herein, the term "MBE" is an abbreviation of Microband Electrode.

[0117] As used herein, the term "VNBE" is an abbreviation of Very Narrow Band Electrode.

[0118] As used herein, the term "MDA" is an abbreviation of Microdisk Array.

[0119] As used herein, the term "EEE" is an abbreviation of Edge Effect Electrodes.

[0120] As used herein, the term "IOE" is an abbreviation of Interacting Opposed Electrodes.

[0121] As used herein, the term "non-interacting electrodes" refers to electrodes that are spaced sufficiently apart that there is insignificant diffusion of product from the C/E to the W/E within the timescale of a single determination of D and C. In other words, for non-interfering electrodes, there is insignificant overlap of the diffusion layers of any of the electrodes with each other.

[0122] As used herein, the term "interference between electrodes" refers to the diffusion of the product of one electrode and the reactant of the other electrode between the two electrodes in such a way that their concentration profiles interact.

[0123] As used herein, the term "O/C" is an abbreviation of open circuit.

[0124] As used herein, the symbol "t_p" represents the length of a voltage pulse.

[0125] As used herein, the term "bulk concentration" refers to the concentration which is unaffected by the diffusion profiles of the C/E and the W/E.

[0126] As disclosed herein, the present invention provides chronoamperometric methods and devices that use a single band electrode (BE). A BE has an edge which is substantially a straight line. (Substantially as there are manufacturing irregularities at the level of a few microns - see below). This substantial straightness of the edge of a BE allows the diffusion to be solved in 2 dimensions as opposed to the disk and sphere shaped electrode as known in the art, which are solved in 3 dimensions.

[0127] For a BE the short term data extrapolates to an intercept which is equivalent to a steady state current, and this is used in the determination of C and D. But it does not have an actual steady state current. The current tends to zero as t tends to infinity. A disc and sphere, on the other hand, have finite steady state currents which are approached as t tends to infinity. [0128] A BE has a two term approximation of the short time behavior that is accurate to 1% for t < 0.4W²/D. This is significantly wider range of time than the case for a microdisk where the equivalent short term approximation is accurate to 1% for t < 0.01d²/D. (W = width of band electrode and d = diameter of microdisk.)

[0129] If the term of diffusion layer thickness, L_DL, is compared, the BE expression is accurate for a ratio L_DL/W < approx 1.1, whereas the equivalent ratio (L_DL/d) for the microdisk is accurate up to < approx 0.35.

[0130] For a BE and MD of W = d = 100 μιη and D = 5xl0^"6cm²s^_1 the approximations are accurate (to 1%) for up to 8 sees and 0.2 sees respectively.

[0131] The edge of a BE is substantially straight. The realities of manufacturing mean that the edge is not entirely even. As with electrode surfaces there is some roughness. At very short times, when the diffusion layer thickness is around 100% or less of the dimensions of these edge irregularities, the edge as used in the equation increases from the geometric length towards the real length. Equally for short times the roughness of the electrode surface increases the area from the geometric towards the real area. This is handled by excluding data collected for the transient in the first 10 ms to 50 ms or so, or applying a correction factor. Manufacturing methods that are expected to give a roughness of the edges of the BE are e.g. the use of flex substrates/ substrates with rough surfaces, printing methods lacking edge definition, "scalloping" of the edge due to the laser using pulses, metal layer being uneven e.g. made up of overlapping grains.

[0132] A band electrode where W is e.g. > lOx the irregularities of the edges and surface will allow a good range to collect data - approx lOOx in time (W > 50 μιη). Small microdisks (d < 50 μιη) will have less time range to collect data in, especially given the limit on the approximation of t < 0.01d²/D.

[0133] A reasonably accurate estimate of intercept can be made for a BE where t > 0.0025 W²/D (in which case iEdge/i(t) Cottreii = approx 0.05, and L_DL = 0.05W).

[0134] The edges of a BE can be formed by etching, cutting, lasers etc. The ends can both be defined by an overlay, or one can be so defined and the other can be defined by a laser etc. Conveniently in manufacturing the ends of the BE can be formed by an overlay with a hole punched in it. In this case the accuracy of length is determined by the accuracy of the punch, a very well controlled dimension.

[0135] The possible range of dimensions of the band electrode and time are: 1 = 0.25 mm to 5 mm (could be greater), w = 10 to 500 μιη, t range = 0 to 0.1 - 8 sees. [0136] Denuault et al. {Journal of Electroanalytical Chemistry and Interfacial Electrochemistry Volume 308, Issues 1-2, 25 June 1991, Pages 27-38. Direct determination of diffusion coefficients by chronoamperometry at microdisk electrodes) have shown that C and D can be measured simultaneously using a microdisk electrode using chronoamperometry and comparing the transient behaviour with the steady state behaviour. This required measurement of the steady state current i_ss, normalising the current i_t with respect to this (=i_t/ i_ss), plotting this vs. 1/t^0'5 and measuring the slope, which gives D. This allows C to be calculated from i_ss. Electrodes were of 25 to 50 μιη diameter.

[0137] The behaviour of the microdisk cannot be solved mathematically (exactly) for all t. There are two approximations which hold to better than 1%. One for t < 0.04a²/D and one for t > a²/D, where a is the radius in and D is the diffusion coefficient.

[0138] Wang et al. (Journal of Electroanalytical Chemistry 585 (2005) 191-196. Direct determination of diffusion coefficient for borohydride anions in alkaline solutions using chronoamperometry with spherical Au electrodes.) used a spherical micro electrode (approx diameter 200 um) where there is an exact mathematical solution to the transient. This electrode is more complicated to make but it allowed them to measure the slope and intercept for the i_t vs. t^0'5 plot to determine C and D. Behavior of time periods longer than 1 second had to be rejected because of convection currents. ("In our case, the sphere electrodes were relatively large so that the convection influence was inevitable in long time.")

[0139] A common practice nowadays is to fit the entire transient from a microdisk to a multi-term equation (T Peilin Li, Martin C Henstridge, Linhongjia Xiong, Richard G. Compton. Electroanalysis 2013, Vol 25. 2268 - 2274. Rate and Extent of Carbon Dioxide Uptake In Room Temperature Ionic Liquids: A New Approach Using Microdisc Electrode Voltammetry).

[0140] The diffusion to a band electrode has been solved mathematically by e.g. Szabo et al. They do not teach the measurement of C and D from analyzing the transient (J. Electroanal. Chem., 217 (1987) 417-423. Chronoamperometric Current at Hemicylinder and Band Microelectrodes Theory and Experiment.).

[0141] US 7972487 B2 teaches the construction of a disposable sensor with band electrode in the cavity wall. There is no mathematical analysis of the transient and no teaching about using this to calculate C and D.

[0142] There is a family of patents including US7276146B2 and US7276147B2 which teach the use of interdigitated microband electrodes. This teaches the use of microband electrodes either interdigitated or not interdigitated. It does not teach the use of the transient at microband electrodes to measure C and D.

[0143] From the patent, in the case of non-interdigitated band electrodes: "In this case the width or diameter of the working electrode bands or disks should be of such a dimension as to allow for some degree of radial or spherical diffusion to the working electrode surfaces. Typically, this dimension should be in the range of 5 to 50 μιη, and most preferably 10 to 50 um."

[0144] This patent defines microelectrode as: electrodes can be considered a micro-electrode array, especially if the diffusion occurs predominantly (e.g., greater than 50%) according to a non-planar path, or if the size of the electrodes is less than 100 um, e.g., less than 50 μιη.

[0145] US8388821 teaches the use of microdisk electrodes to measure D by plotting i_t/ i_ss vs. 1/t^0'5 then using that to calculate C from i_ss. This requires the use of a plurality of microdisks, an overlay being used to define the whole perimeter of the each disk, using the long term approximation for microdisk electrodes and measuring i_ss. Diameters of the microdisks are 5 to 50 μιη.

[0146] Most existing designs of electrochemical glucose sensors consider only the situation where the W/E is large enough that diffusion can be considered as primarily planar. That is, either the electrode is of the same cross-sectional area as the solution it interacts, or diffusion from the edges is small enough to be ignored. These prior designs cannot determine both C and D of an analyte simultaneously through analysis of the current time behaviour.

[0147] Accordingly, in one aspect, the present invention provides a method and a device for determining C and D of an analyte in a medium simultaneously. In some embodiments, the simultaneous estimation of C and D is carried out using a W/E with a significant edge effect.

[0148] Particularly, in some embodiments, W/E of carefully controlled dimensions are placed in sufficient distance from each other so as to be non-interfering. Particularly, in some embodiments, electrodes of carefully controlled dimensions are spaced sufficiently apart to avoid interference (this is defined as non-interfering). For example, such electrodes can be a band electrode and a distal counter electrode. If the solution in contact with the electrode surface extends beyond the area normal to the electrode surface the diffusion region is said to have edges and the current i_(t) can considered to be made up of two components: one due to planar diffusion i_(t) cottreii and one due to edge diffusion i(_t)Ed_ge (see above Equation 5). [0149] An analysis of the current allows both C and D to be determined simultaneously. This offers a significant improvement in the accuracy with which C can be determined, representing an advantage for blood glucose sensors and also for the determination of C of other analytes. Additionally this will be useful for the manufacture of an implantable glucose sensor which continuously monitors the glucose in the body tissues. Or a sensor placed in contact with the skin measuring C and D of an analyte in the sweat. (Note that D can be measured, or rather estimated, in glucose sensors by other means, such as measuring the resistance of the solution or measuring the AC impedance at different frequencies, but direct electrochemical measurement offers significant improvement in accuracy of determining C).

[0150] In some embodiments, a band electrode (BE) of length L, width W, and area, A = WL (see Figure 4A) is used. In other embodiments, electrodes having an edge current in other configurations are used.

Band Electrode (BE) and Microband Electrode (MBE)

[0151] In some embodiments, a method and a device for accurately determining both C and D of an analyte in a medium simultaneously are provided. Particularly, in some embodiments, the method and device use one or more band electrodes as the W/E.

[0152] The terms Band Electrode and Microband electrode are to a large extent used interchangeably as described in this application. Sometimes in the art, microelectrodes are differentiated from (macro)electrodes based on the edge effect representing a "significant" proportion of the overall current/ diffusion to the electrode, or on L_DL being of "comparable" size to the minimum dimension of the electrode. MBE and BE are used in this application when discussing two band electrodes of different sizes, in which case it is convenient to call the smaller of the two "micro." In the case of confusion, both terms should be considered as being BE. The extent of the edge effect is covered in the math, not in the name.

[0153] Consider Oldham's analysis for the case of the Band Electrode of length L and width W (A = WL). An example of this is shown in Figures 4 A and 4B. In this case the BE is represented as a thin layer of metal of width W adhering to, and flush with, an underlying support. This support is of greater width than the BE. Both ends of this support are covered by an insulating overlay, and these define the length L of the band electrode. It can also be seen that this overlay shields the ends of the strip. A final overlay is normally placed on top of this, defining a cavity. The analyte solution, such as blood, is drawn laterally into the cavity by wicking action. However, some embodiments of the present invention do not require the use of a cavity. An option where the BE plus C/E etc. do not occupy the full width of the strip is to widen the connecting track to the BE below the cavity to reduce its resistance (the cricket bat shape, shown in Figures 4 A and 4B). This limits the voltage drop down the track due to the passage of the current (often known as iR drop), ensuring that the majority of the voltage applied to the connectors at the bottom of the strip is applied between the electrode interfaces when solution is introduced into the cavity. An approximate analytical solution to the amperometric behavior has been obtained by Szabo et al.{ J. Electro anal. Chem., 217 (1987) 417-423) based on the approach given by Oldham in Edge Effects in Semiinfinite Diffusion. The behavior at short times is given by:

i_(t) = nFACI D/π t)°-⁵+ (D/W)] Equation 14

= nFACCD/π t)°^'5 + nFAC(D/W) Equation 15

And as A = WL for a band electrode

= nFACCD/π t)^{0 5} + nFCDL Equation 16

⁼ i(t) Cottrell + ^Edge Equation 17

⁼ i(t) Oldham Equation 18

[0154] The term Oldham current (i_(t) oidham)) is used to distinguish it from the

Cottrell case. The subscript (t) for the edge current has been dropped as, in this approximation, the edge current is time independent.

[0155] The Cottrell current is dependent on A and 1/t^0'5 whereas the Edge Effect current is dependent on L and is time independent. Also:

lEdg t) Cottrell ⁼ (D7lt)^0'5/W Equation 19

= L_DL/W Equation 20 where L_DL is the diffusion layer thickness (Equation 3)

[0156] The Oldham current is proportional to concentration (for constant A, D and t):

i(t) Oldham d C Equation 21

[0157] Plots of i_(t) oidham vs t and 1/t^0'5 are shown in Figure 5A and 5B, along with that for i(t) cottrell from Equation 1. Values for n, F, C, A and D are assumed to be the same in both cases. It can be seen that the curve shapes and lines are identical for the Cottrell and Oldham cases, but i(_t) oidham is displaced upwards by a constant amount = i_Ed_ge. [0158] The Szabo reference gives a digital simulation based on which, Equation 14's accuracy is determined to be:

Better than 0.1% until t is approximately =0.16 W²/D (in which case iEdge i(t) Cottreii = approx 0.7 and L_DL = 0.7W)

Better than 1% until t is approximately =0.48 W²/D (in which case iEdge i(t) Cottreii = approx 1.2 and L_DL = 1.2 W)

[0159] These two points bracket the point at which the diffusion layer thickness approximates to W when t is approximately =0.32 W²/D (and iEd_ge i(t) Cottreii = approx 1 and L_DL = W). That is, the approximation holds well for L_DL <1).

[0160] For pure Cottreii behavior (shielded electrode) plotting i_(t) cottreii against 1/t^0'5 gives a straight line where:

Slope S = nFAC(D/7l)^0'5 Equation 22 and intercept I_nt = 0 Equation 23

[0161] This is shown in Figure 6 for electrodes of different area, the slopes being proportional to area. If D is known then C can be calculated, and vice versa.

[0162] Figure 7 is a plot of i(_t) oidham vs 1/t^0'5. In this case the Cottreii part of the current is the same, but all the lines are shifted up the y axis by lEdge- That is:

S = nF AC(D/7l)⁰-⁵ Equation 24

Int ⁼ lEdge ⁼ nFCDL Equation 25

[0163] That is, the intercept is independent of width for band electrodes where n,

F, C, D and L are the same. Therefore to determine the value of lEdge the value of W need not be known.

[0164] In this case C and D can both be calculated. From Equations 24 and 25: C = 7l/(I_ntnFL) * (S/W)² Equation 26

And D = (1/ 7l)*(I_ntW/S)² Equation 27

[0165] To determine C accurately I_nt, S, W and L must be measured accurately. Typically, the larger the slope with respect to the intercept, the less accurately the intercept can be determined as there is always some error in the estimation of the slope.

[0166] Consider an exemplary case, where the slope determined for a W = 500 μιη BE (band electrode) is 10X that determined for a MBE (microband electrode) of W = 50 μιη in absolute units. As the intercept is the same in both cases and it is determined by extrapolation of the slope, for the same range of t the intercept determined from the BE is expected to have lOx the error of that determined from the MBE. In this case that is 10% vs 1 %.

[0167] The most accurate estimation of intercept uses the smallest value of W. This is because the smaller the value of i_(t) cottreii is compared i_Ed_ge to the more accurately i_Ed_ge can be determined. (The condition L_DL <1 should also be maintained.)

[0168] Equation 14's accuracy has been determined to be:

Better than 0.1 % until t (= tL ie t lower) is approximately =0.16 W²/D (in which case iEd_ge/i(t) cottreii = approx 0.7 and L_DL = 0.7W)

Better than 1 % until t (= tu ie t upper) is approximately =0.48 W²/D (in which case iEd_ge/i(t) cottreii = approx 1.2 and L_DL = 1.2W)

(And iEd_ge i(t) Cottreii = approx 1 when t_M (= t middle) = 0.32 W²/D and L_DL = W).

[0169] So ideally the data should be collected up to the range t_L to tu. The table below gives an idea of how tu and t_L vary with W and D (with t_M lying between).

D (cmY¹) 5E-06 5E-06 3E-06 3E-06 1E-06 1E-06

W (cm) t_L tu t_L tu t_L tu

0.001 0.037 0.089 0.062 0.148 0.187 0.445

0.002 0.150 0.356 0.250 0.593 0.750 1.78

0.005 0.937 2.22 1.56 3.70 4.69 1 1.1

0.01 3.75 8.89 6.25 14.8 18.7 44.5

0.02 15.0 35.6 25.0 59.3 75.0 178

0.05 93.7 222 156 370 469 1 1 1 1

Table 1 Variation of the upper limits of t (in sec) that can be used in the MBE analysis (see text above) with D and W

[0170] It can be seen that to perform the analysis within an acceptable time period (less than around 1 second max) an MBE of width 20 microns (or less) will be used if this time, t, is to be kept in the range t_L < t < tu For a time of 0.2, using this argument, W = 10 μιη is preferred.

[0171] However, experiments have been carried out with BEs that show that collecting data up to t corresponding to lEdge/i(t) Cottreii ⁼ 0 1 to 0.25, or even to 0.05, allowed accurate estimation of iEdge- This occurs when L_DL = 0.1 to 0.25 W (or 0.05W). For t = 0.2 sec and D = 10^"6 cmV¹ this corresponds to a band of width of 32 to 80 μιη (or 160 μιη). This result is somewhat surprising and it indicates the robustness of the design and theory of band electrodes. [0172] The approach of using edge effects to determine C and D simultaneously was first used with a microelectrode made of a wire surrounded by insulating material and cut so as to expose the circular cross section of metal flush with the insulator surround (Guy Denuault, Michael V. Mirkin and Allen J. Bard Direct Determination of diffusion coefficients by chronoamperometry at microdisk electrodes J. Electroanal. Chem., 308 (1991) 27-38). However, this device is not of practical use for making disposable electrochemical strips.

[0173] U.S. patent US8388821 and European patent EP2080023 describe the use of microelectrode arrays where an overlay with openings is used to expose a plurality of microelectrodes to the solution. The prior invention differs from the present invention in using a plurality of microelectrodes and in necessitating the use of an overlay to define the electrode areas, and also in "measuring" the final steady state current (which exists for microdisk electrode, but does not for a band electrode). The mathematical approximation is less robust and the device is more complicated to make and is less robust in performance than the present invention.

Effect of Dimensional Errors in Accuracy of Band Electrode

[0174] As disclosed herein, inaccuracies in measuring W and L cause errors in calculating C and D. Dimensions of L of 1 mm or greater can be manufactured to 1% reliability or better. But if the width of an electrode can be determined to +/- 5 μιη, this is 1% on a 500 μιη wide band (BE), and 10% on a 50 μιη wide band (MBE). A 50 μιη track can be manufactured to a greater accuracy than +/- 10%> width. The use of this value should be seen as illustrative of a general point - that is, that as the width of the BE decreases there will be some point at which its accuracy and reproducibility is harder to maintain. Also if the tracks are manufactured on a smooth/ rigid substrate, such as silicon, rather than the flexible plastic substrates normally used in the manufacture of disposable sensors, then a 10 μιη track can be manufactured to 1% accuracy in width.

[0175] With these electrode widths it has already been estimated (see above) that for the same range of t, the intercept determined from the BE will have lOx the error of that determined from the MBE. [0176] Table 2 shows an estimate of the expected errors on the 4 measured parameters, I_nt , S, W and L.

W L S I„,

BE (W = 500 μιη, L = 1 mm) 1% 1% 1% 10%

MBE (W = 50 μιη, L = 1 mm) 10% 1% 1% 1%

Table 2 Comparison of Estimated Errors on Different types of Band Electrode

[0177] Given that the concentration is dependent on L, W², S² and I_nt, for these dimensions the BE will give a more accurate estimate of C than the MBE.

Comparison of Error caused by Dimensional Measurements for Opposing interacting electrodes and BE.

[0178] As disclosed herein, the opposing interacting electrodes strip has 3 dimension estimates used in the calculation of C: the length of the cavity, the width of the cavity and the thickness of the cavity. The BE also has 3 dimension estimates: the length of cavity and width of the BE twice (i.e. W²).

Microdisk Electrodes and Microelectrode Arrays (of Circular Disks)

[0179] In some embodiments, a method and a device for accurately determining both C and D of an analyte in a medium simultaneously are provided. Particularly, in some embodiments, the method and device use an electrode having a microdisk or alternatively other shape as the W/E.

[0180] Particularly, determining D and C simultaneously can be undertaken with a microdisk electrode (or other shapes). A multi-term solution for i_(t) at a microdisk has been determined for all values of t by Shoup et al. (J. Electroanal. Chem., 140 (1982) 237-245). For intermediate values of t the expression is an approximation, stated to be accurate to 0.6% (by comparison with digital simulation, a numerical solution to the underlying diffusion equation). Oldham gives a different equation containing multiple powers of t which he describes as "precise but complicated bipartite formulas." (Electrochemical Science and Technology, Keith B. Oldham, Jan C. Myland and Alan M. Bond, pub 2011 Wiley, page 246) There are simpler, two term solutions for short and long t. However, in the intermediate range both these approximations are inaccurate.

[0181] For longer times (t > r²/D) :

i(long t) = 4FCDr[ 1 + 2r/(7l³Dt)⁰-⁵] Equation 28 [0182] For short times (t< 0.04 r²/D):

i(short t) = 4FCDr[0.7854 + -⁵r/(4(Dt)^a5)] Equation 29 where r is the radius of the disk electrode.

[0183] Denuault et al. (Direct Determination of diffusion coefficients by chronoamperometry at microdisk electrodes J. Electroanal. Chem., 308 (1991) 27-38) suggested that a microdisk can be used to determine the diffusion coefficient without knowledge of the concentration, or alternatively, the concentration without knowledge of the diffusion coefficient.

[0184] The use of "a microelectrode array having a plurality of disk shaped microelectrodes" has been considered as an electrochemical glucose sensor in patents EP2080023 & US8388821. The authors cite the use of the long term solution to microdisks with electrodes of 5 to 50 μιη diameter, equation 28.

[0185] Electrodes of too small a diameter run into a problem described in a recent paper by Aoki et al. {Int. J. Electrochem. Sci., 7 (2012)). In this he reported "We compared the diameter of disk electrodes determined by the currents with those by a scanning electron microscope The diameters by both methods agreed when they were more than 10 μιη. When diameters ranged from 1 to 4 μιη, those by the currents from Saito's Equation were smaller than those by SEM."

[0186] Alternatively again "at all times it is possible to fit the experimental current ratio to the more exact term. However, this procedure requires a one dimensional non-linear regression which is more tedious than the linear approach using the approximate equation." (Y.Saito, Review of Polarography (Japan), 15, 1968, 177). Also Denuault et all found that such an approach resulted in less accuracy in the determination of D in their 1991 paper.

[0187] The fabrication of microdisks requires the use of an insulating layer around the whole perimeter of the electrodes. This must be continuous (i.e. have no pin holes) yet be thin enough that it does not interfere significantly with the diffusion condition that the electrode be flush with its surroundings. Whilst the condition of a shielded electrode transitioning to an unshielded electrode can be handled it represents a complication and requires knowledge of the insulating (shielding layer) thickness. Additionally r must be accurately known, to at least 1%. These requirements are not impossible, but are onerous for an electrode of radius < 50um. [0188] A variation on microelectrode arrays of circular disks is an "anti- microelectrode array of circular holes." That is, a planar electrode where circular areas are either covered with an insulator, or the metal (or other electrode material) is removed e.g. by a laser or by photo lith. This is covered by Equation 13 and can be analyzed in a similar fashion. Many of the construction problems are simplified i.e., there is no need for an insulator to define the electrodes which is one large electrode with holes. The holes need not be limited to circular shapes.

Dual Band Electrode (DBE)

[0189] In one aspect, the present invention provides a method and a device that are capable of increasing the speed of the test without adversely affecting accuracy in measurement. Particularly, in some embodiments, a method and a device that use two or more electrodes of different width are provided. In some embodiments, a narrow electrode allows a more rapid accurate determination of the value of the intercept. This value is independent of the width of the electrode, so the use of a narrower electrode, where W will be less accurately known, does not have any adverse effect. Such uncertainties however will affect the accuracy of the analysis of the slope, which is dependent on width. But the use of the wider electrode allows the area of the electrode to be accurately measured and therefore CD^0'5, which is calculated from the slope and area, can also be determined accurately. Accordingly, the use of two or more W/E of different widths allows accurate determination of C and D at shorter times than either electrode on its own. The wider and narrower BE can be of the same length, in which case they will have the same intercept, or different length in which case they will have different intercepts.

[0190] A DBE consists of two band electrodes of different widths. In the various discussions (below) of the use of the DBE it has been assumed that they are of the same length, but the two band electrodes of different lengths can be used and the maths modified in a straightforward way to take account of this.

[0191] A consideration of Table 2 shows an advantage in using the combination of a BE and an MBE to determine C more accurately than by using either individually. This consists of two working electrodes, the BE of e.g. W = 500 μιη and the MBE of e.g. W = 50 μιη, the electrodes being roughly parallel (though this is not necessary) and separated by e.g. a minimum of around 100 to 200 μιη, but preferably four times the maximum diffusion layer thickness (= 4L_DL) realized during the course of the electrochemical measurement. One configuration of a DBE is shown in Figure 8. In this case the BE, MBE and C/E are shown side by side, but they can also be in other configurations, such as on different sides of a cavity cell. The BE and MBE in a DBE are usually of the same length but the lengths can be different.

[0192] The BE is used to determine the slope (CD^0'5) and the MBE is used to determine intercept (CD). It will be noted from this analysis that the width of the MBE does not need to be known to determine the intercept.

[0193] The effect of this on accuracy is shown in Table 3 in row 3. This argument is exemplary rather than absolute. It is based on the fact that smaller widths can be less accurately manufactured and measured than larger widths.

W L S I„,

BE (W = 500 urn, L = 1 mm) 1 % 1 % 1 % 10%

MBE (W = 50 urn, L = 1 mm) 10% 1% 1% 1%

DBE (BE/ MBE combination) 1% 1% 1% 1%

Table 3 Comparison of Estimated Errors on Different types of Band Electrode

[0194] Both intercept and width are known (within this example) to 1% but the measurements are made at the shorter times determined by the width of the MBE, not the longer times required by the BE.

[0195] The estimation of the intercept from both BE allows further optimization. Clearly the values of I_nt should be the same for both BE so the estimates can be weighted statistically according to the errors expected on the slopes in order to give an average value. This helps in an accurate determination of C, and it is also a check on the validity of the test. Variation of the I_nt estimates from the BE and the MBE by more than a certain predetermined amount indicate an error. (This invariance of intercepts can be useful in detecting, and compensating for, changes in the concentration of analyte during the measurement. This is discussed below.)

[0196] It is not essential to use a BE to obtain the CD^0'5 behavior. Any electrode of accurately known area (and perimeter) can give the same data. Equally the method is not limited to using a single MBE to determine the CD behavior. Multiple MBEs or a backwards and forwards track (e.g. zigzag, or the U-shaped equivalent) can also be used. All that is required is to be able to accurately determine P, the perimeter length. The ease of determining the perimeter length of a band electrode is a major advantage. The perimeter length of a microdisk area can only be known, for instance, by knowing the diameters of the microdisks in a microdisk array. [0197] This analysis does not require that the larger of the two electrodes has any edge effect as only the slope (giving CD^0'5) is measured. However one advantage of having two band electrodes of different widths but the same length, is that plotting i_t against 1/t^0'5 gives the same intercept (although that from the narrower BE will be more accurate), a check of the validity of the analysis.

[0198] One skilled in the art will recognize that a plurality of BEs of different, or the same, widths can be used.

Calibration of MBE by BE

[0199] In some embodiments, the present invention provides a method for, and a device that is capable of, calibrating the width of the narrower MBE, thereby providing more accurate measurement of the concentration of an analyte in a media. Particularly, in some embodiments, a DBE system is configured to compare the slopes of the i_(t) vs. 1/t^0'5 curves generated using the BE and the MBE of the system, which comparison allows calibration of the MBE width value with respect to the BE width.

[0200] Particularly, the BE can be used to calibrate the MBE area more accurately as:

WMBE ⁼ (SMBE/SBE)*W_BE Equation 30

Where W_MBE, W_BE, S_MBE and S_BE are the widths and slopes of the MBE and the BE. In an initial measurement, this calibration allows the width of the MBE to be determined as accurately as that of the BE, in which case it can be used on its own in subsequent measurements to determine C and D, which can be carried out in a shorter time. A similar analysis can be carried out based on the areas of the BE and MBE if they are of different length.

[0201] Further calibration of the BE and the MBE can be done by measuring and comparing their double layer capacitances, or resistances (see below section Calibration of Electrode Width).

Difference Current for BE and MBE

[0202] In one aspect, the present invention provides a method and a device for tracking the concentration change of an analyte in a media. Particularly, in some embodiments, a fraction of the current due to the BE is subtracted from that due to the MBE. This difference current is time independent for constant C and proportional to C (lEdge = nFCDL). Hence, if C is changing with time, this difference current can be used to track the rate of the concentration change and to determine the end point concentration which will result after a relatively long time compared to that of the overall test (5 seconds for a typical blood glucose test), which situation can arise for example when:

1) C is increasing with time due to an enzyme reaction;

2) C is increasing with time due to diffusion from another region; or

3) C is increasing with time due to diffusion from one compartment to another, such as in the case where glucose diffuses out of blood cells and becomes available to enzyme to turnover and generate ferrocyanide.

[0203] The following discussion relates to the exemplary embodiment where the width of BE (W_BE) is 500 μιη and the width of MBE (W_MBE) is 50 μιη. However, a skilled person in the art will understand that the same principle can be also applied to other configurations.

[0204] Particularly, the difference current, i_Diff, is defined as:

!Diff ⁼ !(t) Oldham MBE - (WMBE W_BE) * i_(t) Oldham BE Equation 31

⁼ (l(t) Cottrell MBE + i(t) DL MBE + i(t) S MBE + ^Edge) ^" (W_MBE W_BE)

(i(t) Cottrell BE + i(t) DL BE + i(t) S BE+ ^Edge) Equation 32 where i_{(t) DL} and i_(t) s are the double layer charging current and the oxidation of surface groupings/ absorbed species i.e. the non-faradaic currents.

[0205] The Cottrell current, the double layer charging current and the surface oxidation current are proportional to the width of the MBE and BE (as they are the same length L and the area A = WL) so all these time dependent terms cancel giving

f ⁼ lEdge * [1 -(W_MBE/ W_BE)] Equation 33

= lEdge * (1 - Ratio) Equation 34 where

Ratio = W_MBE/ W_BE Equation 35

For a DBE where W_BE is 500 μιη and W_MBE is 50 μιη, Ratio = 0.1 and: iDiff ⁼ 0.9*lEdge Equation 36

[0206] This gives pure lEdge from t = 0 which can be used to track C changing with time. Alternatively, when C is constant, analysis of the difference current can provide accurate estimate of lEdge and also calibrate the width of the MBE. Particularly, the exact value of Ratio is unlikely to be known exactly because of uncertainties in the width of the BE and more particularly the MBE. This inexactness will manifest itself as a time dependence of the estimated ioi_ff. For an invariant C, by varying Ratio numerically the value can be determined which gives the most constant value of ioi_ff with time, and this gives the most accurate estimate of iEd_ge- For example, ioi_ff vs time can be graphed and the slope minimized (towards zero) or the mean and standard deviation of the individual estimates of ioi_ff at each time can be determined and the CV minimized (coefficient of variation = standard deviation/mean), both by varying Ratio. This also calibrates the width of the MBE which is then known to the same accuracy as the width of the BE. A similar analysis can be carried out based on the areas of the BE and MBE if they are of different length.

[0207] There are further analytical possibilities if the widths of the two electrodes are accurately known before the measurements relating to glucose are taken. These can be determined from manufacturing to a high accuracy, or from measurement of the double layer capacitance, or from measurement of the resistance of the electrodes before solution is added. Alternately the widths may be calibrated electrochemically by a measurement immediately after the solution is applied when there is very little glucose related current (this effect is even clearer if the enzyme is dried on the opposite side of the cell to the W/E). In this case the currents measured at short t are background currents, such as are discussed in Equation 32, and additionally electrochemical active interferents, such as ascorbic acid

Effect on DBE and Unshielded Cottrell of Varying Concentration of Analyte During the Time of the Test.

[0208] In one aspect, the present invention provides a method and a device for accurately measuring the concentration of an analyte in a medium while the concentration is changing during the course of measurement. Particularly, in some embodiments, the change in concentration is approximated as a series of discrete concentration changes, and each concentration increment is considered separately. In some embodiments, the current for each increment is calculated and summed vs. time, and the sum represents the current vs. time that is expected for that rate of concentration/time profile. Accordingly, C and D are determined based on the expected shape of the profile, even though C is changing during the course of measurement.

[0209] Particularly, in electrochemical glucose sensors at low temperatures and high glucose concentrations the glucose turnover by the enzyme is slowed. Additionally, whilst the glucose in plasma is relatively quickly turned over, glucose is also released from the red blood cells, slowing its availability for enzymic turnover. This effect is greater for high haematocrits, high glucose levels and low temperatures. This leads to the concentration of ferrocyanide varying (increasing) during its measurement.

[0210] Such a situation can be modeled if the rate of change of concentration is known. In general, because more ferrocyanide is being continuously produced by the enzyme next to the working electrode (and throughout the cell) the current increases progressively with time compared to what is expected if the ferrocyanide concentration does not change.

[0211] For the DBE both the best fit slopes of the BE and the MBE will also be decreased, and the intercepts will increase. A sensitive test for such a situation is that the estimates of intercept from the BE and MBE will be different.

[0212] Different i-t transients can be simulated mathematically or digitally for changes in C_t during the time of the transient. The shape of the transient as it deviates from the shapes expected for constant C can then be used to determine dC/dt. This allows the estimation of the "constant C" transient and therefore an estimation of D and the values of C_t throughout the measurement. This requires a relatively simple spreadsheet model, or alternatively digital simulation can be performed. This will allow the generation of look up correction factors e.g. if the concentration is estimated to vary by x% during the measurement period apply a correction of y% to the concentration estimate.

[0213] Two BEs of different widths will give a better fit as applying the correction for dC/dt to give the "undistorted" transients will give transients of different slopes but the same intercept. This sameness of intercept can be used to check if the transform is correct, as can the fact that the slopes from the two corrected transients will be in the same ratio as the areas of the edge effect electrodes, in this case the widths of the BEs as they have the same length.

[0214] The early part of the i vs 1/t^0'5 plot where the edge effect is small can be used to establish the relative widths of the two BEs.

[0215] Consider more carefully the case where C_t varies with time (Figure 8 A), finally settling at a steady concentration C_∞. This change can be approximated as a series of discrete concentration changes (Figure 8B). Here the concentration is Co =0 at to =0, then averages Ci at t₀ < t < t_ls then C₂, at t₂ < t < t₂ etc. Also:

Δί = tj - tj_i Equation 36a

AC[ = C - C _i Equation 36b [0216] Each concentration increment can be considered separately. Consider the Cottrell component of Equation 16 only. That is, the current

at time t_max for each A is given by:

( ar)* = FA ₍ - +Mpf* ^{Equation 36c}

[0217] To get the total current i_tmax at time t_max the increments is summed i.e.: hmax

Equation 36d

5

= UFA 1 ΙΓί-ι τ — . Equation 36e where t_n = t_max

[0218] A similar consideration of the edge effect current gives a simpler result. As each increment is time independent Equation 25 is simply modified by inserting C = C_t i.e.

lEdse ⁼ nFC_tDL Equation 36f

[0219] In the case where

C_t ⁼ C_∞f(t) Equation 36g where C_∞ is the final concentration as t tends to infinity and where f(t) is an analytical time dependent function which models the enzyme kinetics etc. In this case Equation 36e can be analytically solved. Alternatively digital simulation can be used. The time dependence can be determined from the time dependence of lEdge and comparison with the Cottrell behavior will allow D and C to be determined.

[0220] lEdge can be determined by using Equation 33. If the concentration is to be tracked in this fashion the ideal dimensions of the two BE will need to be determined. For instance, for a 5 second test, widths of 100 and 200 μιη could be used. In this case they can be manufactured with sufficient accuracy to allow the subtraction to leave only the edge current. Or the widths can be determined by resistance measurements. Or measuring the slopes at short times - e.g. 1 to 10 ms - when the edge current is a small percentage of the Cottrell current allows the relative slopes to be used to calibrate the widths. Or allowance for the increasing edge current allows the slopes over a larger time range to be used. [0221] Knowing that the time dependence of C_t is the same for both Cottrell and Edge currents the value of ratio used in Equation 34 can be adjusted for optimal fit. Now knowing both C_t and f(t), C_∞ can be calculated.

Two W/Es, second W/E predominantly measuring i_ss

[0222] Alternatively, the second working electrode can be one, such as a very narrow band electrode (VNBE) or a microdisk array (MDA), where the dimensions are sufficiently small that they predominantly give a pseudo steady state current during the period of measurement. In this case the second W/E will give a current that is largely proportional to concentration (that is, a situation where the current is constant if C does not change). In order to calculate the relative change in C with time it is not necessary to know the area of this electrode. This information can then be used to convert the "distorted" transient of the first working electrode (e.g. a BE) to the simple case where D can be accurately calculated.

[0223] In practice such a pseudo steady state current will still be decreasing slightly (in a constant concentration), but knowing that, it can be allowed for

Widely Spaced Multi-Microband Electrode (MMBE) (no Overlap of Diffusion Layers)

[0224] In some embodiments, a method and a device for accurately determining both C and D of an analyte in a medium simultaneously are provided. Particularly, in some embodiments, the method and device use multiple microband electrodes (multiple M_BE, MMBE) as the W/E.

[0225] The following discussion relates to the exemplary embodiment as shown in Figure 9, where ten MBE of W = 50 μιη are separ_ated by a gap of 200 μιη in between, which distance is far enough for the MBEs to be non-i_nterfering with each other during the course of measurement. However, a skilled person will understand that the same principle can be also applied to MMBE of different configurations.

[0226] Particularly, as shown in Figure 9, the current configuration leaves space for a C/E on one side, or one on both sides of the MBE. Alternatively, the C/E can be on the other side of the cavity opposing the MBEs.

[0227] For this exemplary configuration, the area of each MBE is:

A_MBE = WL Equation 37 [0228] If all the MBEs are connected as in the diagram, like fingers to the palm of a hand, then they will act as a band electrode of area:

A_MMBE = 10WL Equation 38 and length = 10L. In this case a plot of i_(t) oi_dham vs 1/t^0'5 is shown in Figure 10 (slope = S_MMBE) with a single MBE of the same dimensions (W = 50 μιη, slope = S_MBE) and a single BE of width 500 μιη and area = A_MMBE (slope = S_BE).

[0229] It can be seen that the intercepts of the individual MBE and the BE are I_nti and that of the MMBE is I_nt2 where in this case:

I_nt2 = 10*I_nti Equation 39

And:

SMMBE = S_BE = 10*S_MBE Equation 40

[0230] The earlier assumption was that the width of an MBE of 50 μιη was determinable to 10% respectively. In this case it is calculated that the MMBE will be known to 10%/10^0'5 = 3% - this assumption assume the 10% error on the width of the MBE is random, not systematic.

[0231] Row 4 of Table 4 shows a comparison of the errors expected for an MMBE with the previous three cases. This is open to further improvement if the determination of area can be improved. It is only one electrode to be measured electrochemically (compared to two for the DBE), and it is spread uniformly across a larger area ensuring it sees the average of the chemistry that is taking place.

BE (W = 500 urn, L = 1 mm) 1% 1% 1% 10%

MBE (W = 50 urn, L = 1 mm) 10% 1% 1% 1%

DBE (BE/ MBE combination) 1% 1% 1% 1%

MMBE 3% 1% 1% 1%

Table 4 Comparison of Estimated Errors on Different types of Band Electrode

Closely Spaced MMBE (Overlap of Diffusion Layers)

[0232] As disclosed herein, for a system having N multiple electrodes such as shown in Figure 9, but where the 50 μιη electrodes (W_MBE) are separated by 50 μιη gaps (Wo_ap). In this exemplary configuration, the diffusion layers will begin to overlap at relatively short times (when iEd_ge i(t) Cottreii = approx 0.5). At this point the behavior changes from N of MBE of width W_MBE and length L to one BE of width = N*W_MBE + (N-l)*W_GAP and length L. [0233] So the plot of i_(t) faradaic vs 1/t^0'5 will change from having a slope Si and intercept I_ntl

(Short t) Si a N*W_: MBE Equation 41

I_nti a NL Equation 42 to slope S₂ and intercept I_nt2

(Long t) S₂ a (N*W_MBE + (N-l)*W_Gap) Equation 43

I_nt2 a L Equation 44

And

S2/S1 = (N*W_MBE + (N-l)*WGap)/ N*WMBE (=1 .9 in for N = 10) Equation 45

WI_nti = 1/N (= 0.1 for N = 10) Equation 46

Possible Cell Configurations

[0234] As disclosed herein, a device for electrochemical quantification of an analyte is disclosed. In some embodiments, the device comprises one or more working electrode(s) (W/E) and one counter electrode (C/E), embedded within an insulating substrate. In some embodiments, the insulating substrate defines a cavity cell, in which the electrodes are exposed to an analyte. In some embodiments, the electrodes are connected to a sensing meter through a connector.

[0235] As disclosed herein, various configurations of the cavity cell provided. In some embodiments, the cavity cell assumes an open configuration. Particularly, in some embodiments, the insulating substrate defines the bottom and sides of the cavity cell. For example, in some embodiments, a base layer of the insulating substrate defines a bottom surface of the cavity cell and a cavity-defining layer of the insulating substrate is arranged on top of the base layer. The cavity-defining layer has a punch that defines the sides of the cavity cell. In some embodiments, the electrodes are mounted on the base layer and are exposed to the open space through an open face of the cavity. In some embodiments, the electrodes and/or cavity cell are exposed to a sample or sample fluid by filling the sample through the open face into the cavity cell. Alternatively, in other embodiments, the electrodes and/or cavity cell are exposed to a sample or sample fluid by placing the electrodes in direct contact with a sample surface through the open face of the cavity.

[0236] In some embodiments, the cavity cell assumes a closed configuration. Particularly, in some embodiments, the cavity cell is sealed within the body of the insulating substrate. For example, in some embodiments, a base layer of the insulating substrate defines a bottom surface of the cavity cell, a top layer of the insulating substrate defines a top surface of the cavity cell, and a cavity-defining layer placed in between the top and bottom layers has a punch that defines the sides of the cavity cell. In some embodiments, the electrodes are mounted on the base layer and are exposed to the space within the cavity. In some embodiments, the top or bottom layer of the cavity cell has a vent hole that allows filling of a sample or sample fluid into the cavity and becomes accessible to the electrodes.

[0237] In some embodiments, the cell uses either one or two BE (or BE plus MBE) or a plurality of BE and one counter electrode. The counter electrode (C/E) can be on the opposite side of the cavity as the working electrode (W/E) or on the same side as the working electrode (W/E). The same side offers a simplification in design and cost reduction. The electrodes are spaced far enough apart (approx 0.1 to 0.2 mm) not to interfere with each other during the course of the test.

[0238] For opposing electrodes W < T the BE measurement is preferably completed by the time L_DL≤ T/3, so that interference from the opposing C/E (the arrival of ferrocyanide) does not affect the accuracy of the measurement. For L_DL = T/3 the interacting opposing electrodes shows a 0.3% deviation from Cottrell behavior i.e. minimal interaction (see above section Interacting Opposing electrodes).

[0239] With opposing electrodes allows the cell volume to be smaller than for adjacent electrodes, and wider connecting tracks can be used {e.g. the whole of the top layer for the C/E), reducing iR drop.

[0240] Accordingly, for a band electrode of width W with an opposing C/E requires a cell thickness of T = W to ensure the opposite W/E does not significantly interact (assuming an opposite W/E). The 99% diffusion profile (Figure IB) extends to 0.7W on each side of the BE so a width of W on each side of the BE defines sufficient cell width. Assuming a BE length of 1 mm, the cell has volume 3W². For W =100 and 50 μιη the cell has a volume of 30 and 7.5 nL respectively. Preferably, such a small cavity does not extend the full width of the strip.

[0241] Figures 11 A - C show one possible strip configuration. This has a BE (W = ΙΟΟμιη) separated from the edge of the cavity by a gap (approx 200 μιη). Another gap separates the BE from the counter electrode/ fill detector. Alternately the C/E can be on the top of the cell (either patterned or occupying the whole width of the cavity), leaving the right hand metal strip as a fill detector only. A vent in the top overlay allows the air to be displaced from the cavity as the blood/ aqueous sample enters the cavity. [0242] The time to fill a capillary is given by the Washburn Equation:

·£·· . Equation 47

[0243] where t is the time for a liquid of dynamic viscosity η and surface tension γ to penetrate a distance L into the capillary whose pore diameter is d.

[0244] It is generally believed that a capillary cell cannot have a thickness of less than T = 100 μιη in order to have a "satisfactory" fill speed for approximately 5 second glucose test, but this is for cell lengths of several mm. A cell of a shorter path length fills in a similar time for much lower values of T. Such small values of path length can be realized with a single BE, or another edge effect type electrode, as described in this invention. Based on Equation 47, values of T as little as 25 μιη can be used.

[0245] A further advantage of having a thinner cell is that the enzyme/ mediator can be put on the opposite side of the cavity to the W/E. The W/E can now be used as soon as the liquid fills the cell (especially if it has a very small amount of ferricyanide dried on it) and the background interferences measured and subtracted, but due to the thinness of the cell the enzyme/ reduced mediator will rapidly diffuse to the W/E, allowing time related measurements of the ferrocyanide to track the enzyme reaction (plus diffusion of glucose from the blood cells) to end point.

[0246] In some embodiments, it is also possible to have BEs on each side of the cavity.

[0247] In some embodiments, an unshielded electrode is arranged coplanar with the surface of the insulating support where the electrode is mounted. Alternatively, in other embodiments, the unshielded electrode is not coplanar with the insulating support surface. Particularly, the electrode can assume any angle of between 0 to 180 degrees with the insulating support surface. In other words, the angle of edge effect (φ) can be 0 < φ < 180°, and for these configurations, the second term of Equation 13 is modified as (cp/90)nFCDP/2. Particularly, for the coplanar configuration, φ = 90.

[0248] For example, in some embodiments, the electrode is placed at the bottom of a cone with 45 degree sides, in which case the perimetric term is expected to be half that in Equation 13, as the angle of edge effect (φ) is defined as 45 degrees for the cone configuration.In other embodiments, the electrode is placed on the top of a Mesa like plateau (of height greater than the length of the diffusion layer), in which case the perimetric term is expected to be twice that of Equation 13, as the angle of edge effect (φ) is defined as 180 degrees for the plateau configuration. Calibration of Electrode Width

[0249] In one aspect, the present invention provides a method for, and a device that is capable of, calibrating the width of the electrode, thereby providing more accurate measurement of the concentration of an analyte in a media.

[0250] Particularly, in some embodiments, a DBE system is configured to compare the slopes of the i_(t) vs. 1/t^0'5 curves generated using the BE and the MBE of the system, which comparison allows calibration of the MBE width value with respect to the BE width (see also the above section "Calibration of MBE by BE".

[0251] In other embodiments, a DBE system is able to calibrate the width of the electrodes by measuring double layer capacitance once the cell is filled, as the double layer capacitance of an electrode in solution is proportional to its area. Hence, by measuring one electrode vs another, the relative area of the two electrodes can be determined. Electrodes can be measured in pairs to make up a circuit. Absolute area involves knowing the area of one electrode or knowing the capacitance per cm² for that type of electrode in that solution.

[0252] In other embodiments, a DBE system is built with tracks connecting to both ends of the working electrode(s) and to measure the resistance. This can be done as an absolute measurement of width if the metal layer is of a reproducible thickness and hence conductivity. However, given a more typical +/- 20% process variation across a production roll of metal coated support, it is preferable to make a relative measurement of the resistances of the MBE and BE (or of the C/E and the MBE) on the actual electrode immediately it is fitted into the connector of the accompanying meter. The calibration is of the MBE with respect to the BE (or the C/E) which is wider and therefore of a more accurately known width. The measurement includes the resistance(s) of the tracks to the working electrodes, but this can be allowed for.

[0253] Alternatively, in other embodiments, when only one BE or MBE is used in the system, the resistance of the C/E can be used to calibrate the width of the BE or MBE.

[0254] Alternatively, in other embodiments, a resistive track of accurately known width can be defined on the strip in a region remote from the cavity and not exposed to the sample to calibrate the width of the BE or MBE. This approach can be used, for example, when one BE or MBE is used, and if the C/E is opposing the BE or MBE (i.e. the C/E is placed on the opposite side of the cavity where the BE or MBE is placed).

[0255] One such configuration (one BE only) is shown in Figure 11 A. Measuring R between tracks 1 and 4 gives the resistance of the BE plus the wider tracks to both ends, just outside the cavity. Measuring R between tracks 3 and 4 gives the resistance of the calibration strip, which is of a width of 1 mm along its length, allowing accurate definition of its width.

[0256] It is to be expected that the relative variation of width of an MBE will be greater than that of a BE (as the BE is wider than the MBE). A test can be done during fabrication to reject strips that either had a break in the MBE (or BE) or had the (relative) resistance of the MBE move outside acceptable limits. A similar test can be performed on the strip just before the electrochemical test is carried out.

[0257] Measurements of tracks laser cut to a width of 1mm show a reproducibility of better than 1% when done on the same sheet of Au coated Mylar (thickness approximately 300 angstrom, 30 pairs of tracks compared).

[0258] iR drop down the tracks is a problem if the voltage across the electrode interface drops below that required to maintain the reaction in the diffusion limited region. A further advantage of measuring the resistance of the tracks is that the actual voltage across the working electrode/ counter electrode(s) interface(s) can be calculated. If this voltage needs to reach, for example, 200 mV for the reaction of the redox couple to become reversible (i.e. the concentration of e.g. ferrocyanide at the electrode surface to reach zero) then the time at which this is achieved can be set at t_zero in the data analysis (see below). Knowing the ohms per square (Ω/α) from the measurement of the BE plus track resistance and the geometry of the track to the counter electrode allows this voltage to be calculated.

[0259] In Figure 11 A it can be seen that the tracks to the BE and C/E are larger compared to the widths of the BE. It is the current at the BE which will determine that passed at the C/E. Consequently iR drop will be very limited in this design. If a C/E is used on the top of the cavity the whole of that surface can be used as either track or electrode, further reducing the iR drop down the tracks.

[0260] Alternatively, in other embodiments, one of the connectors to one side of the BE and C/E is used to supply current (i.e. tracks 1 and 2) and the other to measure the voltage across the electrode interface(s) (i.e. tracks 3 and 4).

[0261] Alternatively, in other embodiments, the voltage applied to the meter connectors is adjusted to be sufficient to ensure that the voltage across the electrode interface(s) was for example > +200 mV. Data Analysis

[0262] As disclosed herein, (i) In the analysis of the faradaic currents resulting from a constant concentration measured at an electrode, when the data is plotted in the form of i(t) vs 1/t^0'5 it is in the form of a straight line. In practice it is sometimes found that there is curvature at short times (< 0.1s), this being more pronounced the shorter the time. This is due to iR drop down the tracks, the high currents early in the transient resulting in an insufficient voltage between the W/E and the C/E to maintain the concentration of the reduced species (e.g., ferrocyanide) at the W/E surface at zero, as the theory assumes. This is shown in actual experimental data from a BE of W = approx 200 μιη in Figure 12 A. In such a case these "curved" points can be discarded from the analysis, limiting the analysis to t > 0.1s. Alternatively it is possible to apply an adjustment/ correction to the actual t = 0 point (t_zero), which is taken as the time when voltage across the electrode interface(s) is sufficient to maintain the concentration of the reduced species (e.g., ferrocyanide)at the W/E surface at zero. This correction is typically of the order of a few milliseconds, though when cricket bat shaped tracks were used to minimise the iR drop (see Figures 4A and 4B and related discussion) the correction required was less than 1 ms. This can be measured/ estimated (see above). However it has also been found that performing the analysis for t_zero = t +/- ηδί where 5t is e.g. 1 ms and n varies from e.g. 0 to 5, allows an estimate of t_zero by generating R² and using the maximum R² to determine the best t_zero. So if R² is maximum for n = -2 , t_corrected = t - 2 5t). This analysis can then be repeated for smaller increments of 5t if desired. This method of correction has been used on the data shown in Figure 12A to give the graph shown in Figure 12B. This has t_zero ⁼ 2.1 ms after the application of the pulse - 5t determined by maximizing R² for the data set. This extended the linearity of the analysis from 40 ms minimum to 7 ms minimum.

[0263] (ii) Measurement of the difference current (ioi_ff) between a BE and a MBE (see above section Difference Current for BE and MBE) will allow better estimates of lEdge, a calibration of the width of the BE, and an estimate of whether C is varying significantly during the measurement pulse.

[0264] (iii) Corrections for variation of concentration (C) during the time of measurement for DBE by checking that the BE and MBE have the same value for intercept when i t) is plotted vs 1/t^0'5. This is discussed in more detail in above section Effect on DBE and Unshielded Cottrell of Varying Concentration of Analyte During the Time of the Test.

[0265] (iv) If C varies (increases) during a measurement pulse this distorts the estimate. An advantage of the method of band electrodes described in this application is that measurement pulses can be of around 0.2 sees. If C varies by e.g. 50% in a 5 second test it varies by approximately 2% in a 0.2 second test. Such a limited variation has a limited distortion. With multiple pulses the different estimate of C from each pulse (even with distortion) allows an estimate of the variation of C throughout the test. This first estimate of the variation can be used to estimate the variation of C during the measurement pulse, and an analysis which takes account of this gives a more accurate estimate. The individual estimates can be extrapolated to a final value of C_∞ which may not be affected by such distortions (which decreases with successive pulses as the rate of production of ferrocyanide slows down).

[0266] (v) Varying C estimated from multiple pulses (even with distortion) allows estimate of variation of C during any single pulse which can be used to give a more accurate value and this can be iteratively minimized.

Pulses - General

[0267] As disclosed herein, if a solution has C present uniformly throughout (Equation 48), and a voltage pulse is applied to the W/E and current measurement taken, then the concentration of C can be estimated through a Cottrell analysis, either by measuring D or using an estimated value of D. If the concentration profile is allowed to recover to its pre- pulse distribution then the application of a second pulse gives a second estimate of concentration. D can be re-measured for the second pulse, or again, an estimated value can be used.

[0268] In the case where the concentration does not change then the repeat pulse allows a more accurate estimate.

[0269] In the case where C increases with time (as is the case with ferrocyanide being produced in an enzyme based glucose electrode) then the second estimate gives an estimate of the increase in concentration.

[0270] In summary, it is possible to use repeat voltage pulses to either more accurately determine a constant C, or to track a changing C. Accordingly, in one aspect, the present invention provides a method and a device for accurately measuring a constant concentration of an analyte in a medium using voltage pulses. In another aspect, the present invention provides a method and a device for tracking concentration change of an analyte in a medium using voltage pulses. Pulse Length Strategy Depending on Whether D and/or C Vary With Time

[0271] Particularly, as disclosed herein, in some embodiments, D is measured using a pulse of around 0.2 sec or greater. In some embodiments, the use of repeated pulses of this length allows repeated measurements of D.

[0272] Alternatively, in some embodiments, D does not vary while C varies. In these embodiments, D is measured once and the varying C is tracked with a multiple pulse train of shorter pulses. In some embodiments, pulses of 5 ms or shorter are used to track C by the measurement of one value only of i_(t). In other embodiments, more pulses are applied in any given time, giving more estimates of C.

[0273] In some embodiments, D is measured by applying a longer pulse to at the start or end of the pulse train, or at any time during it.

[0274] Alternatively, in some embodiments, D and C of an analyte in a medium are both changing. In these embodiments, D is measured at the beginning and end of the pulse train with shorter pulses between.

[0275] The majority of the following discussion will be limited to the consideration of electrodes without edge effect. However, a skilled person will understand that the discussion also applies to electrodes with edge effect, because the underlying principles of pulses are the same for both cases.

Recovery of the Concentration Profile Between Pulses

[0276] As disclosed herein, for the reaction where the application of a positive pulse to the W/E converts R to O:

R O + ne Equation 48

[0277] If the pulse is switched off, and the electrodes switched to O/C (open circuit) then given sufficient time the O diffuses away into the solution and the R diffuses back, giving the original unperturbed concentration distribution.

[0278] Alternatively, the electrode is switched to a potential where the reaction in Equation 48 is reversed and O is converted to R. In this case the concentration profile of R recovers more quickly.

Comparison of Recovery Periods at O/C and 0V

[0279] Recovery at O/C

[0280] As disclosed herein, typically the time required for a full recovery is very long. For instance, comparing the Cottrell slopes (S) determined from plotting i_(t) vs 1/t^0'5 for a pulse of length t_p separated by a times Nt_p at O/C, the following values of S_n/Si were determined for successive pulses, n being the number of the pulse. In this case t_p = 1 sec, the recovery periods were 4 sec, 9 sec and 19 sec (i.e. N varies from 4 to 19).

1 sec 1 sec 1 sec

Pulse no +0.3V, +0.3V, +0.3V,

(n) 19 sec O/C 9 sec O/CV 4 sec O/CV

1 1.00 1.00 1.00

2 0.91 0.84 0.74

3 0.90 0.76 0.64

4 0.74 0.58

5 0.72 0.55

6 0.51

7 0.52

8 0.51

9 0.51

10 0.52

Table 5 Values of S_n/Si for successive pulses. Rest periods O/C

[0281] The solution was 10 mM ferrocyanide/ lOOmM ferricyanide in 0.1M phosphate buffer (pH 7.4). The measurements were made with a band electrode of width 250 μιη so the recoveries are different to those observed for an electrode of sufficient width not to be seeing edge effects.

[0282] Recovery at 0V

As disclosed herein, for the solution above, which has both R and O in the bulk of the solution, the concentration profile is best recovered by applying a voltage of 0V (this is discussed in more detail in below section - Consideration of R only Present in Bulk of solution, and R Plus O Present in the Bulk of the Solution).

[0283] The effect of 0V in recovering the concentration profiles, and hence restoring the Cottrell current to the unperturbed value of the first pulse, can be seen below. The conditions are identical to Table 5, but the electrodes were held at 0V in the recovery periods instead of O/C. 1 sec 1 sec 1 sec

Pulse no +0.3V, +0.3V, +0.3V,

(n) 19 sec OV 9 sec OV 4 sec OV

1 1.00 1.00 1.00

2 0.98 0.98 0.97

3 0.97 0.97 0.96

4 0.97 0.96

5 0.96 0.95

6 0.94

7 0.94

8 0.94

9 0.94

10 0.94

Table 6 Values of S„/Si for successive pulses. Rest periods OV.

[0284] It can be seen that much faster recoveries were achieved.

[0285] In both these analyzes the Cottrell slope was obtained by plotting i_(t) vs 1/t^0'5, but single values of i_(t), typically taken at the end of the pulse, could have been used instead.

Concept of Calibration for Incomplete Recovery Period

[0286] Concentration of R Constant Throughout Test

[0287] As disclosed herein, the drop off in current response in the case of incomplete recovery can be allowed for in the use of a calibration factor = S_n/Si applied to each successive pulse. This calibration factor is a dimensionless number whose value depends only on N, the ratio of the recovery period at O/C (or 0V) to the length of the pulse. That is, it is independent of t_p, the length of the pulse, and D, the diffusion coefficient.

[0288] So for the first pulse (from Equation 1):

S _! = CnF Α(Ό/π)°^·5 Equation 49

[0289] And in the second pulse after a recovery period at O/C of 19t_p:

S₂ = 0.91 CnF Α(Ό/π)°^·5 Equation 50

[0290] As seen in Table 5 that:

S2/S1 = 0.91 Equation 51

[0291] This calibration factor can be determined experimentally, analytically, or by digital simulation. [0292] Concentration of R Increases Throughout Test

[0293] As disclosed herein, these ratios S_n/Si can be applied to the case where the concentration of R increases between pulses, provided it is produced uniformly across the bulk of the solution, or a region encompassing the diffusion layer produced during the pulse. In this case, however, it is necessary to apply the calibration factor according to when the reactant was produced.

[0294] For the first pulse the situation is described by Equation 49.

[0295] For the second pulse the situation is more complicated. Reactant which is present before the first pulse is at that point uniformly distributed (concentration = C_ti). However, after the first pulse it will not be uniformly distributed and a calibration factor is necessary to calculate C from the Cottrell slope. This slope is called S₂₍c_ti₎:

S 0.5

2_(Cti₎ = 0.91C_tl nFA(D/7r) Equation 52

[0296] However, new R which is produced after the first pulse and is uniformly distributed (this additional concentration = C_t2), so it will generate a Cottrell response which requires no calibration factor. This slope is called S₂₍c_t2):

s ^■2(Ct2) ^~~ C_t2 nF Α(Ό/π) 0.5

Equation 53 0297] These two responses can be summed to give the overall slope S₂:

Equation 54

Equation 55

= (0.91C_tl + C_t2) nFA(D/7i) Equation 56

m pulse:

Equation 57

Two-Electrode System Using a Redox Couple

[0299] As disclosed herein, the way the two electrode system comprising one W/E and one C/E works is that both members of a redox couple are present in the solution. For example, ferrocyanide in the presence of excess ferricyanide. When the reaction at the W/E is ferrocyanide being oxidized to ferricyanide, the opposite reaction takes place at the C/E. The potential between the electrodes is set such that the reactions at both electrodes are diffusion limited. In this case the reaction is limited by the concentration of ferrocyanide, as it is at the lower concentration. That is, for a W/E and a C/E of the same area, the ferrocyanide concentration at the W/E is zero and the concentration of the ferricyanide at the C/E is the bulk concentration of the ferricyanide minus the bulk concentration of the ferrocyanide. The bulk concentration is the concentration unaffected by the diffusion profiles of the C/E and the W/E.

[0300] Note that a system with two W/E held at the same potential with respect to a single C/E behaves as a 2 electrode system according to the above description.

[0301] As disclosed herein, a glucose sensor initially contains only ferricyanide and the enzyme. The enzyme turns over the glucose and in doing so mediates with the ferricyanide, generating ferrocyanide. The ferrocyanide is then available to be oxidized at the W/E. Enough ferricyanide is provided that it is always in excess. Measuring the ferrocyanide concentration can be used to determine the glucose concentration.

Forward/ Reverse Pulses of Equal and Opposite Potential and Equal Length

[0302] The following analysis is for electrodes without edge effects such as shielded electrodes. However, a skilled person in the art will understand that a similar analysis can be performed for electrodes with edge effect, either mathematically or by digital simulation.

Ferrocyanide only, three-electrode system

[0303] In order to understand the forward/ reverse pulses behave with the 2 electrode system described above, start by considering a three-electrode system with only ferrocyanide in solution. In this case the W/E is held at the appropriate potential with respect to the reference electrode such that the oxidation to ferricyanide is diffusion limiting. A remote C/E completes the reaction. This C/E can be any type as long as its electrochemical properties do not affect the behavior of the W/E.

[0304] If a pulse is applied at the W/E with respect to R/E for time = t_p the current follows the normal Cottrell Equation. The current at the end of the first pulse is given by: i(t) 1st pulse ⁼ nFAC D^ t_p)°^'5 Equation 58

[0305] If a reverse pulse of the same length t_p is now applied such that the reduction of ferricyanide is diffusion limiting the newly formed ferricyanide is converted to ferrocyanide. The current at the end of the reverse pulse is:

i(t) 2nd pulse = "0.293nF ΑΟ(Ό/π t_p)°^'5 Equation 59 [0306] This derivation is given in Bard and Faulkner {Electrochemical Methods, Second Edition), at page 210. Analysis of this diffusion behavior has been extended to continuous multiple forward and reverse pulses of equal length by Kambara (Polarographic Diffusion Current Observed with Square Wave Voltage by Tomihito Kambara Bull. Chem. Soc. Jpn., 27, 523 - 534). That is, each positive pulse is immediately followed by a negative pulse, and each negative pulse is immediately followed by a positive pulse, all pulses being of the same length t_p The general expression, true for all voltages, is given as Equation 7.3.29 in Bard and Faulkner {Electrochemical Methods, Second Edition), at page 295). For the case where the voltage pulses are to the forward and backward diffusion limiting regions of oxidation and reduction of the redox couple, this gives an expression for the sample current at the end of the m⁴ pulse is the current at time m*t_p (i_m*tp) which is the Cottrell Equation modified by a summation term:

im*tp =

+ I)*⁵)] Equation 60

The successive sums are (1, -0.293, 0.870, -0.370, 0.817, -0.409) and these oscillate around, and gradually converge on, the infinite limits of +/-0.605. This convergence is very slow, and the sum only approaches within 1% of the limit for m = 7,000.

[0307] This can be written as:

0.5

i_m*tp = K_mnFAC(D^ t_p) Equation 61 where K_m = 1, 0.870, 0.817 etc for the successive forward pulses (m = 1, 3, 5 etc.), and - 0.293, -0.370, -0.409 etc. for the reverse pulses (m = 2, 4, 6 etc.). The values of K_m are independent of the value of t_p, so the limit is approached in shorter times as t_p decreases in direct proportion to the shortening of t_p. The values of K_m are also independent of D, the diffusion coefficient. As stated earlier, these successive values converge very slowly on the infinite sum limit, only approaching within 1% for the 7,000 pulse, or 3,500th pulse pair.

[0308] When the difference current between successive forward and reverse pulses is taken, then it is found that:

Equation 62 where K_DIF(P) is the difference between K_m for a forward pulse and K_m+i for the following reverse pulse = 1.293, 1.240, 1.227 for the 1st, 2nd, 3rd pulse pair (P = 1, 2, 3 and m = 1, 3, 5 etc., that is P = (m+l)/2)) and this settles to within 1% of the infinite limit of 1.210 for the 6th pulse pair. This means that if the pulse pairs are applied at a frequency of e.g. 50Hz (t_p = 10 ms) over a 5 second test, a constant calibration factor of 1.210 can be used for all successive pulse pairs after 0.1s without appreciable loss of accuracy.

[0309] Such a system can be used as part of a three-electrode system, or a two-electrode system where the C/E does not use the redox couple to provide the C/E reaction (for instance Ag/ AgCl) as a sensor for an electrochemically oxidisable/ reducible analyte. Fixed concentrations can be measured or changing concentrations can be tracked.

Ferrocyanide in the Presence of an Equal Concentration of Ferricyanide, Two-electrode

System, W/E and C/E of the Same Area

[0310] In this section R is used for ferrocyanide, and O is used for ferricyanide as examples for the convenience of discussion. However, a skilled person in the art will understand that the same principle discussed herein can be applied for other redox couples.

[0311] This discussion relates to the case of the two-electrode system where W/E and the C/E are of the same size and the diffusion coefficient is the same for both O and R. Consider the case where both R and O are present uniformly in the bulk of the solution at equal concentrations. In this case, in the first pulse the reaction at the C/E is the opposite of that at the W/E. When a positive pulse is applied to the W/E, R is converted to O. The reaction at the C/E turns over an equivalent amount of O to R. i_(t) at the W/E in this first pulse is the standard Cottrell current as this is unaffected by the nature of the reaction at the C/E. When the negative pulse is applied to the first electrode then this corresponds to a positive pulse being applied to the second electrode. This now sees the R present in the bulk of the solution plus the additional R produced by the first pulse. The result is that the reverse current is the sum of the response to the R produced at the C/E in the forward pulse i.e. - 0.293i_(t) 1st pulse plus the response to the bulk concentration of R i.e. -i_(t) i_st _puise which adds up to -1. 293i_(t) ist puise- This relationship continues for successive pulses. That is, to obtain the total currents for each successive pulse/ reverse pulse two Equations 58 are summed, one with m and one with m- 1.

+∑£₂iC-!)^m/Csi - I +· I)⁸"⁵)]} Equation 63 where the second summation term = 0 for m = 1.

[0312] In this case the successive sums are (the sum of the terms in the curly brackets) for each half cycle are; 1, -1.293, 1.163, -1.240, 1.188, - 1.227... and the limit as m tends to infinity is +/- 1.205. The limit is approached much more rapidly than for the case when only R is present in bulk solution, with the m* term being within 1 % of the limit when m = 10. If the difference between the successive forward and reverse currents for each pulse pair is taken, it is found that the equivalent values of K_DIF(P) (Equation 62) in this case are 2.293, 2.404, 2.414 etc. and they approach the infinite limit of 2.420 almost immediately. The first term is within 5% of the infinite limit, and the second term is within 1 %. In this case, which is the case for the glucose sensor described above, a pulse train can be used to track changes in the concentration of ferrocyanide (R) with time without being concerned over changing K_DIF(P), the calibration factor, for each pulse.

[0313] The fact that the application of pulses in this fashion can rapidly give rise to the same value for the difference between the forward and reverse currents at the end of each successive pair of forward and reverse pulses is unexpected. It represents a major advantage over using (or analyzing) multiple forward pulses alone.

[0314] The case where the concentration of O is in excess of the concentration of R gives the same results as above as the limiting current is determined by the concentration of R.

[0315] When the concentration of R, [R], changes with time, changes in the difference current vs time will track the changes in [R] with time. Where the enzyme is present equally at both W/E and C/E [R] will change equally with time, and forward/ reverse pulses can be used to track the change of [R] with time.

[0316] Pulses as above can be used with shielded or unshielded electrodes (W/E and C/E) which are adjacent or opposite.

Ferrocyanide (R) Present at the W/E and an Excess of Ferricyanide (O) Present Across the

Cell W/E and C/E of the Same Area

[0317] Consider the hypothetical case where R is present uniformly in the half of the cell containing the W/E and it is absent in the other half of the cell, that containing the C/E. O is present in the bulk of the solution, and everywhere in the cell [O] > [R], which is to say the electrochemical reaction (below) is limited by [R].

[0318] When a positive pulse is applied to the W/E, R is converted to O. The reaction at the C/E turns over an equivalent amount of O to R. i_(t) at the W/E in this first pulse is the standard Cottrell current, the same as Equation 58 (assuming the part of the cell containing R is of thickness greater than the diffusion layer). [0319] When the negative pulse is applied to the first electrode then this corresponds to a positive pulse being applied to the second electrode. This now sees the R produced by the first pulse and the current is given by Equation 59.

[0320] The result of repeated forward and reverse pulses (+/-V, equal length) is the same as for the section entitled F err o cyanide Only, Three-Electrode System'^'' That is, Equations 60, 61 , and 62 58, 59 and 60 will hold. iDiF(t₎ will rapidly settle on 1.21 times the Cottrell current (Equation 62, K_DIF(P) = 1.21).

[0321] Now assume that R in the second half of the cell is raised to the same concentration as it was initially in the first half. The situation is now that in the section entitled "Ferrocyanide in the presence of an equal concentration of ferricyanide, two electrode system, W/E and C/E of the same area" Equation 62 will hold with K_DIF(P) = 2.42

[0322] The argument applies for R in the presence of excess O, and for O in the presence of excess R. Whichever species is at the lower concentration will be the limiting factor in the current generated (assuming W/E and C/E are equal).

[0323] The above arguments using forward/ reverse pulses (+/-V) of same length use C/E and W/E of the same area, but the analysis also applies for different areas. To complete circuit the W/E and the C/E pass the same current. If, for example, the C/E has half the area of the W/E the current density will be twice as high, but the same quantity of O will be turned over at the C/E as of R at the W/E, only over a smaller cross sectional area, giving a higher concentration profile. So in this case excess O will mean over twice the concentration of R.

[0324] Equally the forward and reverse pulses do not need to be of the same magnitude. +/-V could be +V₁/-V₂ where Vi need not be the same as V₂ and they can range between 0.2 volt and 0.5 volt. This voltage is sufficient to allow the oxidation/ reduction of R and O to be diffusion limited.

[0325] +V/ 0 volt would also work, giving a different value of K_DIF(P). Consider the situation discussed in paragraphs 0310, 031 1 and 0313 where [O] > [R] and both are present uniformly across the cell. The +V pulse would work as normally, consuming R at the W/E and generating it at the C/E. In the reverse pulse (at 0 volt) the two electrodes would attempt to restore the concentration profiles of R and O to their initial values i.e. being uniformly distributed across the cell. In this case it is as if only the electrochemically generated O at the first electrode is being reduced and the electrochemically generated R at the second electrode is being oxidised, so the reverse current would be described by Equation 59. In this case the value of K_DIF(_P) in Equation 62 would tend to 1.21. [0326] It will be clear to a skilled person in the art that the lengths of the first and second pulse in a pair of positive and negative pulses do not need to be equal, though the ratio between the pulse lengths of the first and second pulses should be constant among all the pairs. The series would be different, but the result would be the same. That is, the difference between the currents measured at the end of the forward and reverse pulses settles to a limit, (i.e. the same Equation 62 but with a different K_DIF(P).

Application to Glucose Sensors

[0327] Consider the situation with a glucose sensor before the sample is added which has enzyme and O dried on the W/E but not on the C/E. When the sample is added the reagents will dissolve. The enzyme has a low diffusion coefficient (lOx lower than a typical redox mediator) so it will essentially stay in the proximity of the W/E. The O will start to diffuse to the C/E. If it is present in sufficient concentration at the W/E, enough O will arrive at the C/E to complete the reaction when the first pulse at the W/E oxidises the R to O, thus converting an equivalent amount of O to R at the C/E. The reverse pulse will oxidise this electrochemically generated R only. This approximates to the situation above (" 'Ferrocyanide only, three electrode system. ") so with repeated forward and reverse pulses in Equation 62 K_DIF(P) = 1.21. (Obviously the situation will be more complicated as fresh R is being enzymically produced at the W/E as t progresses, and some of this R will diffuse to the C/E).

[0328] Eventually as R produced by the enzyme diffuses to the second electrode K_DIF(P) will increase as the enzymically produced R adds to the electrochemically produced R. As the test runs to completion and all the glucose is turned over producing R, this will achieve uniform distribution across the cell and K_DIF(P) ⁼ 2.42.

[0329] For a known separation of electrodes (such as opposed electrodes in a thin layer cell) the timing of this transition can be used to measure the diffusion coefficient of R.

[0330] Under the same pulse train as above, a glucose sensor with enzyme and "excess" O dried at both the W/E and the C/E will give I_DIF© according to Equation 62 with K_DIF(P) = 2.42 and this will track the rate at which R is generated and can be extrapolated to give an estimation of the total glucose in the cell.

[0331] Shorter pulses (see section Time Dependence of Whole Blood Test will probe shorter diffusion layers where the enzyme concentration is higher, and the turnover of glucose to give ferrocyanide is faster. Consequently a more accurate estimate of total glucose can result from the use of shorter pulses. Application of a Forward/ Reverse Pulse to a Band Electrode

[0332] In one aspect, the present invention provides a method and a device for tracking a concentration change of an analyte in a medium by applying alternating voltage pulses between the W/E and the C/E.

[0333] As disclosed herein, in some embodiments, a forward/ reverse pulse is applied to a band electrode to estimate D. In some embodiments, such an analysis is performed with digital simulation. In other embodiments, such an analysis is performed through a mathematical analysis, giving an exact or approximate solution. Such an analysis has been carried out for a microdisk electrode for a single forward/ reverse pulse pair (Haruko Ikeuchi , Mitsuhiro Kanakubo, Journal of Electro analytical Chemistry 493 (2000) 93-99, Determination of diffusion coefficients of the electrode reaction products by the double potential step chronoamperometry at small disk electrodes).

Time Dependence of Whole Blood Test

[0334] As described herein, the use of different frequencies of voltage pulse in a train of positive and negative pulses of equal length, allows different parts of the solution to be interrogated. This effect is true for all frequencies of pulsing (a forward/reverse pulse being considered as one cycle, the frequency being the number of cycles per second). It results in the concentration profile being perturbed in a thin diffusion layer. The higher the frequency, the thinner the layer. The thickness of this layer is proportional to 1/f², with f being the frequency in Hz. This means that different depths of the solution can be interrogated depending on frequency. With blood samples, where a layer of plasma separates next to the electrode surface, higher frequencies can allow analysis primarily in the plasma layer.

[0335] Particularly, using electrodes in blood samples where enzyme had turned over, or was in the process of turning over, the blood glucose to produce ferrocyanide was unexpectedly found to give anomalously high currents at short times. The results were consistent with a plasma layer of a few microns thickness forming at the electrode surface. Making measurements that sample within this time scale (where the diffusion layer extends only into this plasma layer) is a way of avoiding haematocrit effect. In this case the use of multiple pulses back and forward between the forward and reverse diffusion limiting regions maintains a thin diffusion layer for the length of the overall test. As an example, application of forward and reverse pulses of length 5 ms for 5 seconds overall maintains a diffusion layer thickness of < 10 μηι, whereas application of a fixed voltage for the whole test results in a diffusion layer thickness of up to 100 μηι.

[0336] Use of forward/ reverse pulses of different frequencies allows the solution to be sampled closer to, or farther away from, the electrode surfaces.

[0337] Timescales of less than 0.005 sec primarily probe the plasma layer, whereas longer pulses give time for the diffusion layer to extend into the region including blood cells. In this case measuring the current response with time gives information on the diffusion coefficient of both layers.

[0338] The analysis that involved using 2 BE of different widths and subtracting a multiple of the current at one from the current at the other to give the edge effect gives a current which is proportional to DC_t. (See above Section Effect on DBE and Unshielded Cottrell of Varying Concentration of Analyte During the Time of the Test.) This can be used with blood samples giving a diffusion coefficient for the plasma (short times) and the blood (longer times), allowing haematocrit to be determined.

Manufacturing Methods

[0339] In one aspect, the present invention provides methods for manufacturing a device for electrochemical quantification of analytes in a media.

[0340] As disclosed herein, the system consists of one C/E and 1 or more W/E(s). These can be adjacent or opposite, in any variation.

[0341] The electrodes can be metal, carbon, or semiconductor. Exemplary materials for the electrodes include but are not limited to platinum, gold, palladium, iridium or alloys of these, graphite, carbon pastes, and tin oxide.

[0342] The W/E and C/E can any one of a group of suitable materials, including the noble metals. In some embodiments, when it is desirable to reduce the amount of noble metal, such as for the purpose of reduce manufacturing costs, other materials, such as gold can be used in areas in contact with the test solution only. Typically disposable strips have the same material to make contacts with the meter, to make the electrodes and to make up the conducting strip that connects the two. For instance in Figure 4 A the connector, the connector track and the band electrode can all be formed from one material, such as gold. For example, a layer of gold can be sputtered onto an insulating substrate and the electrode, connector and connector track can be formed by laser cutting. Alternatively the material in the connector and/ or track area can be made from a second, lower cost conducting material, such as aluminium, and the band electrode from gold. For instance, if the material is coated on a roll made at right angles to the connector track in Figure 4A a stripe of aluminium can be sputtered in the region of the track and connector and a stripe of gold in the region of the electrodes. Some degree of overlap of the gold and aluminium layers is necessary to provide electrical contact between the two layers.

[0343] The electrode material can be formed in various forms, including but not limited to as an evaporated/ sputtered/ electrolessly deposited/ electroplated film on a flexible e.g. polymeric substrate or a rigid substrate such as silicon. Alternatively, an adhesive metal/ carbon film can be used, or a carbon layer can be printed (screen printing, offset printing etc), or a carbon/ metal film can be adhered to a substrate by an intermediate adhesive layer, or a carbon paste electrode.

[0344] For example, the electrodes can be formed into adjacent band electrodes, such as shown in Figure 8, , through the use of lasers, photolithography, sand blasting, water knives, or kiss cutting etc. In order to form two or more separate adjacent electrodes it is not necessary to remove all the conducting material between them. Two thin lines of electrode free material can define the edges of the electrodes, but the region between these edges of the two separate electrodes can still contain metal/carbon etc., so long as it is electrically isolated from each electrode.

[0345] In this case the tops and bottoms of the band electrodes can be defined by the use of an adhesive overlay, or an overlay with a hole punched through it, or two separate strips of overlay. This overlay can also form the body of a cavity, and a second overlay can be applied to the first, defining the top of a cavity. In this case opposing, though possibly laterally displaced, electrodes, can be formed on the underside of the second overlay, facing inwards.

[0346] One end of the covered band is necessary to make contact with a remote meter, but the other end can also be cut by e.g. a laser within the cavity (making 3 sides of the band defined by e.g. laser cutting and one by overlay).

[0347] Alternatively, a ribbed substrate can be used to deposit the e.g. metal film, leading to separate electrodes. Alternatively, a carbon paste material can be use to fill the troughs of such a ribbed substrate, defining a band electrode/ electrodes.

[0348] One such carbon paste is made from high purity graphite powder and a pasting liquid such as nujol.

[0349] A typical device will consist of a substrate with adjacent electrodes, separated distally (i.e. the electrodes are non-interfering), a second insulating layer which is adhered by adhesive (pressure sensitive, heat sensitive etc.). This, along with the lateral edges, defines the area of the electrodes, and exposes the connector to the meter (Figure 4A). Typically the length of the cavity will be defined by a punch. Then a third layer is applied to the second to define the top of the cavity. This third layer can be omitted.

[0350] The cavity can contain a mixture of reagents, such as an enzyme, mediator, buffer, supporting electrolyte etc., either on the electrodes, between them or on the opposite side of the cavity. This chemistry can be applied as a solution and dried in place. When test solution is applied to the lateral openings to the cavity it is drawn in and dissolves these reagents.

[0351] The substrates can be on for example either cards or rolls.

Method of Forming Electrodes

[0352] As disclosed herein, standard lithographic techniques can be used to form the electrodes or they can be formed on a single metal coated strip. In the latter case the metal can be left in place between the BE and C/E provided it was not in electrical contact. Techniques such as scribes, kiss-cuts, lasers, sand blasting, water knives etc. can be used.

[0353] If the tracks are manufactured on a smooth/ rigid substrate, such as silicon, a <10 μιη track can be manufactured to <1% accuracy. If the part of the sensor corresponding to the electrodes/ cavity is manufactured with such a substrate then this is cut & placed on the part of the sensor corresponding to the tracks. Calibration tracks can be included on the smooth/ rigid substrate in the non cavity region.

Sensing Meter

[0354] As disclosed herein, a sensing meter that is configured to cooperatively function with the electrodes is described. In some embodiments, the sensing meter is capable of reversible engaging with the electrodes. In some embodiments, the sensing meter is configured to apply a voltage between the W/E and C/E and measuring a current under the applied voltage. In other embodiments, the sensing meter is configured to apply a train of voltage pulses. In some embodiments, the frequency, pulse duration, and direction of the applied pulse train can be manipulated. Particularly, in some embodiments, the sensing meter is configured to apply a train of alternating positive and negative voltage pulses between the electrodes. In some embodiments, the sensing meter is configured to apply voltages and measure currents between multiple electrodes simultaneously. In some embodiments, the sensing meter is configured to perform various mathematical calculations, approximation and estimations based on the measured current. In some embodiments, the sensing meter comprises a processor or algorithm, and various functions of the sensing meter are programmed and controlled by the processor or algorithm. Those with ordinary skill in the art will recognize suitable algorithms that can be programed to realize the functions of the sensing meter.

[0355] In some embodiments, a meter can recognize that a strip has been inserted and switches on, prompting the addition of a sample fluid such as blood. The addition of sample fluid is detected by applying a voltage to the electrodes and measuring a resistance. Once the blood is detected the voltage may switch off until the test begins, or it may start the test. In some embodiments, the sensing meter is configured to measure the double layer capacitance to check that the electrodes are covered by the sample fluid and the filling is completed so as to avoid an underestimate of the analyte concentration.

[0356] In some embodiments, the sensing meter is configured to work with disposable consumables such as strips that are produced in batches and have different calibration methods or parameters for each batch. In some embodiments, the sensing meter is configured to provide a calibration number and prompt an end user to check whether the calibration number agrees with a batch number of the disposable consumables. In some embodiments, the sensing meter is configured to calibrate the device using a control solution. In some embodiments, the sensing meter can be any known amperometric or chronoamperometric device known to a person skilled in the art. A skilled person in the art will recognize that other embodiments are also possible for the sensing meter.

Advantages of the present invention as compared to prior-existing systems

Advantages of Edge Effect Electrodes (EEE) vs Interacting Opposed Electrodes (IOE)

[0357] As disclosed herein, various possible designs of the EEE offer many advantages. For example, because there is no need to control the thickness of the cavity cell of the device, the cavity cell can be made thicker to allow more rapid fill of the sample.

[0358] The manufacturing cost of the EEE device of the present invention is reduced compared to prior-existing devices. Particularly, the thickness of the cavity cell, i.e., of the insulator overlay, does not need to be precisely controlled during manufacture; also, metal parts can be put on only one side of the cavity; further, more standard connectors to meter can be used. These factors all contribute to simplify the manufacturing process and help to reduce the manufacturing cost of the device

[0359] D is determined more quickly for an EEE cell than for an IOE cell of the same dimensions. The width of the BE (MBE) can be reduced allowing shorter time scales to be probed than for an EEE cell of equivalent thickness. The EEE cells can use very narrow electrodes allowing the fabrication of narrow cells. Such narrow cells will fill quickly allowing thin cells of around 50 μηι to be used with acceptable filling times (Washburn Equation, Equation 47), resulting in a small cell volume.. This is useful where expensive reagents are used in the cell, or as part of a larger cell where blood is separated into plasma by lateral wicking through a membrane and only small volumes of plasma are available to the cell.

[0360] For EEE the CD^{0 5} and CD terms are determined over a shorter time period than for the IOE system. Consequently, changes in C and/ or D during the course of the measurement will cause less distortion for the EEE analysis.

Advantages of the Present Invention over Inter digitated Electrodes Arrays (US Patents

7276146 and 7276147)

[0361] As disclosed herein, interdigitated electrodes (IDEs) need to be manufactured to a high degree of accuracy. Small dimensions are necessary to get a test done in a reasonable time. Absolute knowledge of both electrode width and separation are needed. Electrodes varying in width will have an effect on accuracy as the gap between the electrodes will consequently vary. This is not the case for a band electrode where the only the average W needs be know, or for an MBE in a DBE format.

Advantages of the Present Invention Microelectrode arrays of Circular Disks (Patents

EP2080023 , US8388821)

[0362] As disclosed herein, microelectrode arrays of circular disks of small diameter can be used in a similar fashion. These are spaced sufficiently far apart to avoid overlap of diffusion layers during the course of the measurement. As stated in above section Microdisk Electrodes and Microelectrode Arrays (of Circular Disks), the analytical solution for microdisks is only accurate in the regions t< 0.04 r²/D and t > r²/D.

[0363] For a 5 second test it is stated that microelectrodes of 5 to 50 μιη are required. (U.S. Patent 8388821). The production of such microelectrodes presents significant difficulties. Typically a conducting film is defined into circular disks by the application of an overlayer which seals closely with the conducting material beneath but does not extend over the electrode surface. This gives problems, both in the reproducible definition of the size and shape, and in sealing the edges of the electrodes to prevent solution leaking below the overlay. This insulation has a minimum thickness of microns, resulting in the disks being recessed from the solution, complicating the diffusion situation, starting as shielded electrodes until the diffusion layer reaches the thickness of the overlay, then acting as essentially unschielded microdisks.. As the area of each electrode and its perimeter are small, a plurality is required to raise the signal to a magnitude that facilitates the measurement. It is necessary to accurately know the average diameter of the electrodes to analyze the signal and the variation must be small The technique of using the perimeter to give the CD term and a larger electrode to give the CD^0'5 term (see the section on DBE above) requires knowing the cumulative perimeter lengths of the microelectrodes. For the BE this is easily determined as the length of the band, whereas for the array of microelectrode disks it requires knowing the diameters of all the electrodes, or the average diameter if this is a tightly controlled parameter.

[0364] In summary, different aspects of the present invention include:

1. The use of an electrochemical cell made up of at least one (i.e. one or a plurality of) non-interacting working electrode in combination with a counter electrode, with electrode and cell dimensions/ geometry chosen to allow the use of edge current effects to determine D and C for an analyte in solution by the application of a voltage between the C/E ad the W/E and the measurement of the resulting current.

2. Optimization for measurements at short time scales.

3. The use of analyte that is the reduced or oxidized form of a redox couple (or any electrooxidisable / electroreducible reagent).

4. The use of reduced or oxidized form of a redox couple that is generated by an enzyme reaction. The use of this redox couple at the C/E to provide the C/E reaction.

5. The use of enzyme that is a glucose oxidizing or reducing enzyme.

6. The use of electrodes either enclosed within a cavity, or with unenclosed electrodes.

7. The use of a cavity which only extends part of the width of the strip.

8. The use of a vent hole to allow filling of a cavity which only extends part of the width of the strip.

9. The use of a vent hole to determine extent to which cavity fills.

10. The use of adjacent or opposed C/E

11. The use of band electrodes as the non-interacting electrodes.

12. The use a BE of width less than the thickness of the cell with an adjacent or opposite C/E.

13. Performing an analysis of the time dependence of current at a band electrode by plotting i(t) vs 1/t^0'5, giving a slope S and an intercept Ι_Ντ. Comparison of the two terms to give C and D (as the former depends on CD^0'5 and the area of the electrode, and the latter on CD and the length of the band, but not its width).

14. Varying the time t = 0 for the start of the analysis of i_(t) vs 1/t^0'5 to improve linearity of graph at shorter times.

15. The use of a cavity of narrow width (< 1mm) and narrow thickness (<100 um) which fills with blood over the desired range of haematocrits in short time scales (<1 sec).

16. Drying a mixture of reagents on or near the electrodes.

17. Drying the reagent mixture on one or more of the electrodes.

18. Drying different mixtures of reagent on the W/E and the C/E.

19. The use of a W/E opposed to a C/E where the C/E has a different loading for dried reagent to the C/E.

20. The use of narrow W/E and C/E compared to the width of the strip and using broader connecting tracks on the strip to reduce iR drop.

21. The application of one or more voltage pulses to determine C and D with a recovery period between (at O/C or close to 0V) to allow recovery of the concentration profiles.

22. The application of a reverse voltage pulse after each measurement pulse.

23. Following this reverse pulse with a recovery period between (O/C or close to 0V).

24. Analysis of the reverse pulse to give further information on the concentration e.g. reduced mediator and diffusion coefficient.

25. The use of calibration constants to allow calculation of C and D from pulses where incomplete recovery has taken place between successive pulses.

26. The application of multiple forward and reverse pulses.

27. The application of multiple forward and reverse pulses with recovery period between (O/C or close to 0V).

28. The use of repeat pulses to forward and reverse diffusion limiting regions of the redox reaction and the use of the different current between the forward and reverse pulses to track concentration changes.

29. The use of measurement pulses of different durations, longer ones which are used to measure C and D, and shorter ones which use more limited current measurements and the value of D obtained from the longer pulses to calculate C.

30. When C_t is time dependent, using the measurements of C determined from multiple pulses to calculate the final concentration C_∞.

31. When C is not time dependent, using the measurements of C determined from multiple pulses to more accurately determine C. 32. The use of multiple pulses to allow a first pass estimation of the variation of C with time, using this to estimate the variation in concentration during a measurement pulse, making a correction in the analysis of that measurement pulse to allow for this variation, resulting in a more accurate estimation of concentration in that measurement pulse. Repeating this iteratively as necessary.

33. The use of first pulse to determine concentration of background interferents (such as ascorbic acid) before significant reduced, or oxidized, part of a redox couple is generated by enzyme related activity.

34. DBE - using two BEs of different widths. Using the wider one primarily to determine slope and the narrower one primarily to determine intercept. The optimization of the width of the BEs to give the most accurate measurements within the desired timeframes and diffusion coefficients. Using the wider BE to give S and the narrower BE to give intercept, and calculating C and D without requiring accurate knowledge of the width of the narrower BE.

35. As with 34 but with more than 2 BEs.

36. Comparison of intercepts determined from both BE and MBE to check for variations in C during the measurement pulse.

37. The use of a comparison of the slopes determined with the BE and MBE to allow calibration of the width of the MBE.

38. DBE - subtraction of a fraction of the larger BE current from the smaller BE current. Varying this fraction until the resulting difference current is time independent. Using this as an improved estimate of intercept.

39. DBE - if the widths of the two BE electrodes are accurately known, multiplying the current from the wider BE by the ratio of the widths of the smaller to the larger BE, and subtracting this from the current at the smaller BE. If C and D are constant during the measurement pulse this difference current will be a time independent estimate of the intercept. If, on the contrary, this increases with time this can be used to determine if CD (=C assuming D is constant) is varying during the measurement, and this determination used to improve the transient analysis.

40. The measurement of track resistance to determine the width of the BE (before applying the blood sample) by having separate connecting tracks to each end of the BE.

41. The use of a wider track of more accurately known dimensions (in DBE use the wider BE, or the C/E, or a calibration track) to determine the film resistance, giving a more accurate estimate of the width of the smaller BE through measurement of its resistance. 42. The use of knowledge of the resistance of the tracks to the W/E and the C/E to calculate the iR drop down the tracks during the application.

43. Measurement of the voltage between the W/E and the C/E by using the tracks to one end to apply the voltage and measure the current, and the tracks at the other end to measure voltage only.

44. Manufacture electrodes and electrode tracks using lasers, photolithography etc.

45. The use of smooth substrates, such as silicon, to define the electrodes within the cavity region.

46. The use of electrode materials from noble metal group or carbon.

EXAMPLES

[0365] The following examples are provided to better illustrate the claimed invention and are not to be interpreted as limiting the scope of the invention. To the extent that specific materials are mentioned, it is merely for purposes of illustration and is not intended to limit the invention. One skilled in the art may develop equivalent means or reactants without the exercise of inventive capacity and without departing from the scope of the invention.

Example 1

Band electrode - scalpel cut

[0366] Electrode: Au film, Width = approx 181 μιη - scalpel cut, Length = 1.6 mm defined by adhesive tape.

[0367] Counter electrode: Au film

[0368] Solution: 10 mM ferro(CN)₆ in 100 mM ferri(CN)₆, 0.1M pH 7.4 phosphate buffer;

[0369] Applied voltage: +0.3V;

[0370] Plot i₍t₎ vs 1/t^0'5 (see Figure 12A) and use Equations 26 and 27 to estimates C and D:

[0371] C = 13.1 μιηο1/αη3

[0372] D = 4.84E-06 cmY¹

[0373] Note: the real concentration of the above solution has been determined to be approx 11 mM due to some of the 100 mM ferri(CN)6 existing in the ferro form.

[0374] In this case the width of electrode was only approximately determined due to the crude nature of the cut leading to an inaccuracy in the measured value of W. Example 2

Band electrode - laser cut + analysis

[0375] Working electrode: Au film, Width = approx 268 μιη - laser cut, Length = 1.51 mm defined by adhesive tape.

[0376] Counter electrode: Au film

[0377] Solution: 10 mM ferro(CN)₆ in 100 mM ferri(CN)₆, 0.1M pH 7.4 phosphate buffer;

[0378] Applied voltage: +0.3V, W/E and C/E are Au

[0379] Estimates of C and D (see Figure 13A):

[0380] C = 11.0 μιηοΐ/cm³

[0381] D = 6.10E-06 cmV¹

[0382] Analyzing the data for a series of time ranges between 0.01 sec and a varying t max (0.1 to 5 seconds) and calculating C for each time range and plotting these estimates vs. t_max gives the results as shown in Figure 13B.

[0383] The intercept(i_Ed_ge) can be accurately determined even the current i_tmax is many times larger. Expressing this the other way round shows that iEd_ge i(tmax) varies from 4.9% to 27% for t_max varies from 0.1 to 5s (see Table 7). Note, this method does not involve measuring the steady state current as many methods in the art requires (e.g., U.S. Patent 8388821 and European Patent 2080023).

0.5 · · j- t 1/t (tmax) Edge (tmax)

0.01 10.00 6.09E-05 1.6%

0.1 3.16 1.99E-05 4.9%

0.2 2.24 1.44E-05 6.8%

0.3 1.83 1.19E-05 8.2%

0.4 1.58 1.05E-05 9.4%

0.5 1.41 9.45E-06 10%

1 1.00 6.97E-06 14%

1.5 0.82 5.87E-06 17%

2 0.71 5.22E-06 19%

2.5 0.63 4.77E-06 21%

3 0.58 4.44E-06 22%

3.5 0.53 4.18E-06 23%

4 0.50 3.97E-06 25%

4.5 0.47 3.80E-06 26%

5 0.45 3.66E-06 27%

oo 0 9.79E-07 100%

Table 7 Values of i_Edge/i_(tmax for varying t_max. Example 3

Pulses O/C and OV (Band electrode, laser cut)

[0384] Working electrode: Au film, Width = approx 270 μιη - laser cut, Length = 1.51 mm defined by adhesive tape.

[0385] Counter electrode: Au film

[0386] Solution: 10 mM ferro(CN)₆ in 100 mM ferri(CN)₆, 0.1M pH 7.4 phosphate buffer, Applied voltage +0.3V, W/E and C/E are Au

[0387] These experiments used a series of 1 sec pulses which were applied with rest periods between the pulses at O/C. The rest period used were 4, 9 and 19 seconds. The slope was determined from a plot of i vs. 1/t^0'5 within each pulse(Figure 14A).

[0388] The same experiment was run but with the rest periods at 0V (Figure 14B). In this case it can be seen that there is less drop off in S with pulse number, even for the shorter recovery times.

Example 4

Pulses +/- 0.3 V, Opposing Electrodes (Verio Strip)

[0389] Electrodes: Unmodified Verio strip, electrode width 3.5 mm, electrode length 1.2 mm, opposing W/E Au & C/E Pd, separation 95 μιη.

[0390] Solution 10 mM ferro(CN)₆ in 100 mM ferri(CN)₆, 0.1M pH 7.4 phosphate buffer, Applied voltage +0.3V, W/E and C/E are Au

[0391] Solution was introduced into the cavity of a Verio strip and a pulse train of +/- 0.3V was immediately applied at a frequency of 100 Hz (forward and reverse pulses = 5ms). The currents were measured at the end of the pulses and converted to estimated concentrations using Equation 62 (K_DIF(P) =2.42) and a value of D. The value of D was determined from applying a fixed voltage to strips from the same batch using the same solution and analyzing the interaction of the opposing electrodes, comparing Cottrell behaviour to the steady state current.

[0392] Figure 15A shows estimated concentration with time calculated from the pulse method described in the above paragraph. The data is from two separate strips superimposed. The concentration estimate of 11.0 mM agrees well with the expected value.

[0393] The estimates of concentration for the first two seconds were low, and this was assumed to be due to the dissolving of the dried chemistry in the strip. To check this two more strips were tested as above but with a 100 second delay before the pulse train was applied. In this case 10 Hz was used (forward and reverse pulses = 50 ms). The concentration estimate of 12.0 mM is slightly high but this is due to some evaporation of the solutions from the edge of the cavity resulting in a concentration (Figure 15B).

[0394] It can be seen that the theory works equally well for 10 and 100 Hz. With repeated pulses the same current is repeatedly measured, giving the same estimate of concentration.

[0395] The various methods and techniques described above provide a number of ways to carry out the invention. Of course, it is to be understood that not necessarily all objectives or advantages described may be achieved in accordance with any particular embodiment described herein. Thus, for example, those skilled in the art will recognize that the methods can be performed in a manner that achieves or optimizes one advantage or group of advantages as taught herein without necessarily achieving other objectives or advantages as may be taught or suggested herein. A variety of advantageous and disadvantageous alternatives are mentioned herein. It is to be understood that some preferred embodiments specifically include one, another, or several advantageous features, while others specifically exclude one, another, or several disadvantageous features, while still others specifically mitigate a present disadvantageous feature by inclusion of one, another, or several advantageous features.

[0396] Furthermore, the skilled artisan will recognize the applicability of various features from different embodiments. Similarly, the various elements, features and steps discussed above, as well as other known equivalents for each such element, feature or step, can be mixed and matched by one of ordinary skill in this art to perform methods in accordance with principles described herein. Among the various elements, features, and steps some will be specifically included and others specifically excluded in diverse embodiments.

[0397] Although the invention has been disclosed in the context of certain embodiments and examples, it will be understood by those skilled in the art that the embodiments of the invention extend beyond the specifically disclosed embodiments to other alternative embodiments and/or uses and modifications and equivalents thereof.

[0398] Many variations and alternative elements have been disclosed in embodiments of the present invention. Still further variations and alternate elements will be apparent to one of skill in the art. Various embodiments of the invention can specifically include or exclude any of these variations or elements.

[0399] In some embodiments, the numbers expressing quantities of ingredients, properties such as molecular weight, reaction conditions, and so forth, used to describe and claim certain embodiments of the invention are to be understood as being modified in some instances by the term "about." Accordingly, in some embodiments, the numerical parameters set forth in the written description and attached claims are approximations that can vary depending upon the desired properties sought to be obtained by a particular embodiment. In some embodiments, the numerical parameters should be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. Notwithstanding that the numerical ranges and parameters setting forth the broad scope of some embodiments of the invention are approximations, the numerical values set forth in the specific examples are reported as precisely as practicable. The numerical values presented in some embodiments of the invention may contain certain errors necessarily resulting from the standard deviation found in their respective testing measurements.

[0400] In some embodiments, the terms "a" and "an" and "the" and similar references used in the context of describing a particular embodiment of the invention (especially in the context of certain of the following claims) can be construed to cover both the singular and the plural. The recitation of ranges of values herein is merely intended to serve as a shorthand method of referring individually to each separate value falling within the range. Unless otherwise indicated herein, each individual value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g. "such as") provided with respect to certain embodiments herein is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention otherwise claimed. No language in the specification should be construed as indicating any non-claimed element essential to the practice of the invention.

[0401] Groupings of alternative elements or embodiments of the invention disclosed herein are not to be construed as limitations. Each group member can be referred to and claimed individually or in any combination with other members of the group or other elements found herein. One or more members of a group can be included in, or deleted from, a group for reasons of convenience and/or patentability. When any such inclusion or deletion occurs, the specification is herein deemed to contain the group as modified thus fulfilling the written description of all Markush groups used in the appended claims.

[0402] Preferred embodiments of this invention are described herein, including the best mode known to the inventors for carrying out the invention. Variations on those preferred embodiments will become apparent to those of ordinary skill in the art upon reading the foregoing description. It is contemplated that skilled artisans can employ such variations as appropriate, and the invention can be practiced otherwise than specifically described herein. Accordingly, many embodiments of this invention include all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly contradicted by context.

[0403] All patents, patent applications, publications of patent applications, and other material, such as articles, books, specifications, publications, documents, things, and/or the like, referenced herein are hereby incorporated herein by this reference in their entirety for all purposes, excepting any prosecution file history associated with same, any of same that is inconsistent with or in conflict with the present document, or any of same that may have a limiting affect as to the broadest scope of the claims now or later associated with the present document. By way of example, should there be any inconsistency or conflict between the description, definition, and/or the use of a term associated with any of the incorporated material and that associated with the present document, the description, definition, and/or the use of the term in the present document shall prevail.

[0404] In closing, it is to be understood that the embodiments of the invention disclosed herein are illustrative of the principles of the present invention. Other modifications that can be employed can be within the scope of the invention. Thus, by way of example, but not of limitation, alternative configurations of the present invention can be utilized in accordance with the teachings herein. Accordingly, embodiments of the present invention are not limited to that precisely as shown and described.

[0405] Description of relevant art can be found in, for example, S.J.Konopka, Anal Chem 1970 42 (14) ppl741 - 1746; Aoki et al. J. Electroanal. Chem., 266 (1989) 11 - 20, & 256 (1988) 269-282; US7276146; US7276147; J. Electroanal. Chem., 122 (1981) 1 - 17; Szabo et al. J. Electroanal. Chem., 217 (1987) 417-423; David Shoup and Attila Szabo, J. Electroanal. Chem., 140 (1982) 237-245; Electrochemical Science and Technology, Keith B. Oldham, Jan C. Myland and Alan M. Bond, pub 2011 Wiley, page 246; Y.Saito, Review of Polar ography (Japan), 15, 1968, 177; Guy Denuault, Michael V. Mirkin and Allen J. Bard Direct Determination of diffusion coefficients by chronoamperometry at microdisk electrodes J. Electroanal. Chem., 308 (1991) 27-38; Koichi Aoki, Chun Ouyang, Chaofu Zhang, Jingyuan Chen, Toyohiko Nishiumi, Int. J. Electrochem. Sci., 7 (2012) 5880 - 5892 Comparison of Diameters of Disk Microelectrodes Obtained from Microscopes with Those Evaluated from Steady-State Currents; Polarographic Diffusion Current Observed with Square Wave Voltage by Tomihito Kambara Bull. Chem. Soc. Jpn., 27, 523 - 534. Electrochemical Methods (Second Edition), Bard and Faulkner, page 295. Haruko Ikeuchi, Mitsuhiro Kanakubo, Journal of Electroanalytical Chemistry 493 (2000) 93-99, Determination of diffusion coefficients of the electrode reaction products by the double potential step chronoamperometry at small disk electrodes; Journal of Electroanalytical Chemistry 585 (2005) 191-196. Direct determination of diffusion coefficient for borohydride anions in alkaline solutions using chronoamperometry with spherical Au electrodes; T Peilin Li, Martin C Henstridge, Linhongjia Xiong, Richard G. Compton. Electro analysis 2013, Vol 25. 2268 - 2274. Rate and Extent of Carbon Dioxide Uptake In Room Temperature Ionic Liquids: A New Approach Using Microdisc Electrode Voltammetry; each of which is hereby incorporated by reference in its entirety.

Claims

WHAT IS CLAIMED IS:

1. A method for determining a concentration of an analyte in a medium, comprising:

contacting the medium with one or more unshielded working electrode (W/E) and a counter electrode (C/E); wherein the W/E and C/E are non-interfering with each other;

applying a voltage between the W/E and C/E;

measuring a non-steady state current between the W/E and the C/E under the applied voltage over time (t), wherein the current is indicative of oxidation of a first species or reduction of a second species in the medium;

plotting the measured current over 1/t^0'5 to produce a fitted straight line with a slope and a intercept;

determining values of the slope and the intercept;

and solving the concentration and diffusion coefficient of the first or second species of the redox couple simultaneously based on the determined values of the slope and the intercept.

2. The method according to claim 1, wherein the analyte is the first species or the second species.

3. The method according to claim 1,

wherein the first or second species is generated by a chemical reaction of the analyte; and

wherein the method further comprises calculating the concentration of the analyte based on the concentration of the first or second species.

4. The method according to claim 1 wherein the W/E is a band electrode

5. The method according to any of claims 1-3,

wherein the one or more unshielded W/E comprise at least one band electrode (BE) and at least one microband electrode (MBE);

wherein a width of the BE is greater than a width of the MBE; and

wherein the determining is performed by determining the value of the slope based on the measured current between the BE and the C/E and determining the value of the intercept based on the measured current between the MBE and the C/E, thereby accelerating and improving accuracy of the method.

6. The method according to claim 5 further comprising calibrating the width of the MBE before the determining, thereby improving accuracy of the method.

7. The method according to claim 6, wherein the calibrating is performed by

determining the width of the BE;

determining a first value of slope based on the measured current between the BE and the C/E;

determining a second value of slope based on the measured current between the MBE and the C/E;

calculating a ratio between the first value and the second value; and

obtaining the width of the MBE based on the ratio and the width of the BE.

8. The method according to claim 6, wherein the calibrating is performed by

determining the width of the BE;

measuring a first resistance of the BE and a second resistance of the MBE;

calculating a ratio between the first resistance and the second resistance; and obtaining the width of the MBE based on the ratio and the width of the BE.

9. The method according to any of claims 1-8, wherein the plotting step further comprises selecting a suitable starting time for plotting the measured current over 1/t^0'5 to optimize linearity of the fitted line, thereby improving accuracy of the method.

10. A method for determining a profile of concentration change of an analyte in a medium, comprising

contacting the medium with at least two unshielded working electrodes (W/E) and a counter electrode (C/E), wherein the W/E and C/E are arranged to be non-interfering with each other; wherein the W/E comprise at least a band electrode (BE) and at least a microband electrode (MBE), wherein the BE is wider than the MBE;

applying a voltage between the W/E and C/E;

measuring a non-steady state current between each of the at least two W/E and the C/E under the applied voltage over time, wherein the current is indicative of oxidation of a first species or reduction of a second species in the medium; calculating a difference current over time by subtracting a fraction of the measured current between the BE and the C/E from the measured current between the MBE and the C/E; wherein the fraction is the ratio between an area of the MBE and an area of the BE; and generating a profile of the calculated difference current over time, the profile reflecting concentration change of the analyte over time.

11. The method according to any of claims 1-10, wherein the first species and the second species form a redox couple.

12. A method for determining a profile of concentration change of an analyte in a medium, comprising:

contacting the medium with a working electrode (W/E) and a counter electrode (C/E); wherein the W/E and C/E are non-interfering with each other;

applying a train of alternating positive and negative voltage pulses between the W/E and the C/E;

measuring a current between the W/E and the C/E at the end of each applied voltage pulse, wherein the current is indicative of oxidation or reduction of a first species in the medium; wherein a second species is present in excess to the first species in the medium; and wherein the first species and second species form a redox couple;

calculating a difference current between the currents measured for each pair of successive positive and negative voltage pulses;

estimating a concentration (C_t) of the analyte for each calculated difference current; and

generating the profile of concentration change by tracking the estimated concentration (C_t) over time.

13. The method of claim 12, further comprising estimating a final concentration C_∞ of the analyte based on the profile.

14. The method of claim 12 or 13, wherein the applying is performed by applying a train of alternating positive and negative voltage pulses between the W/E and the C/E at a suitable frequency (f) to interrogate the profile of concentration change of the analyte in a target layer of the medium.

15. The method of claim 14, wherein a thickness of the target layer to be interrogated is reverse proportional to f².

16. A chronoamperometric device for electrochemical quantification of an analyte in a sample medium, comprising one or more unshielded working electrode (W/E), a counter electrode (C/E), an insulating support, and a sensing meter,

wherein the insulating support defines a cavity cell configured to receive the sample medium;

wherein the W/E and C/E are partially embedded in the insulating support such that each electrode exposes a surface to the cavity cell;

wherein the W/E and C/E are arranged to be non-interfering with each other;

wherein the W/E and C/E are capable of reversibly engaging with the sensing meter; and

wherein the sensing meter is configured to determine a concentration and a diffusion coefficient of the analyte simultaneously by applying a voltage between the W/E and C/E and monitoring the resulting current.

17. The chronoamperometric device of claim 16, wherein the one or more unshielded W/E comprise at least one band electrode (BE) and at least one microband electrode (MBE); and wherein a width of the BE is greater than a width the MBE.

18. The chronoamperometric device of claim 16 or 17, wherein the W/E and C/E are arranged in an opposing configuration facing each other on opposite sides of the cavity cell or in a coplanar configuration adjacent to each other on a same side of the cavity cell.

19. The chronoamperometric device of any of claims 17-18, wherein the insulating support comprises a base layer and a cavity-defining layer,

wherein the base layer defines a bottom surface of the cavity cell and mounts the W/E and C/E; and

wherein the cavity-defining layer comprises a punch that defines edges of the cavity cell.

20. The chronoamperometric device of any of claims 17-19, wherein the insulating support further comprises a top layer, wherein the cavity-defining layer is arranged between the top layer and the base layer; and

wherein the top layer defines a top surface of the cavity cell and comprises a vent hole configured to allow filling of the sample medium into the cavity cell.

21. The chronoamperometric device of claim 19 or 20, wherein the W/E assumes an angle with the base layer of the insulating support, and wherein the angle is within a range of 45 to 180 degrees.

22. The chronoamperometric device of claim 19 or 20, wherein the base layer comprises a Mesa-like plateau and wherein the W/E is mounted on top of the plateau assuming a 180 degree angle with the insulating support.

23. The chronoamperometric device of claim 19 or 20, wherein the base layer comprises one or more connecting tracks configured to connect the W/E and C/E to the sensing meter.

24. The chronoamperometric device of any of claims 16-23, wherein the insulating support and the W/E and C/E form a disposable unit.

25. The chronoamperometric device of any of claims 17-24, further comprising pre-stored parameters for calibrating the width of the MBE.

26. The chronoamperometric device of any of claims 16-24, further comprising pre-loaded reagents on or near the W/E and C/E.

27. The chronoamperometric device of any of claims 16-26, wherein the W/E and C/E are made from a metal, a carbon material or a semiconductor material.

28. The chronoamperometric device of any of claims 16-27, wherein volume of the cavity cell is less than lOOnL.

29. The chronoamperometric device of any of claims 16-28, wherein volume of the cavity cell is less than lOnL.