HK1179346B - Biosensor system with signal adjustment - Google Patents

Description

Biosensor system with signal conditioning function

The present application is a divisional application of patent application No. 200980149014.7 entitled "biosensor system having signal conditioning function" on the filing date of 2009, 12/8.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. provisional patent application 61/120,525 entitled "complete indextfunctions" filed on 8.12.2008, which is hereby incorporated by reference in its entirety.

Background

Biosensor systems provide for the analysis of biological fluids such as whole blood, serum, plasma, urine, saliva, interstitial or intracellular fluids, and the like. Typically, the system includes a measurement device that analyzes the sample in contact with the test sensor. The sample is typically present in liquid form and may be, in addition to a biological fluid, a derivative of a biological fluid such as an extract, a dilution, a filtrate or a reconstituted precipitate. The analysis performed by the biosensor system may determine the presence and/or concentration of one or more analytes in the biological fluid, such as alcohol, glucose, uric acid, lactate, cholesterol, bilirubin, free fatty acids, triglycerides, proteins, ketones, phenylalanine, or enzymes. The above analysis can be used for diagnosis and treatment of physiological dysfunction. For example, a diabetic patient may use a biosensor to determine the glucose level in whole blood in order to regulate diet and/or medication.

The biosensor system may be designed for analyzing more than one analyte, and may use different volumes of biological fluid. Some systems may analyze a drop of whole blood, such as in a volume of 0.25-15 microliters (μ L). Biosensor systems may be implemented using bench-top (bench-top), portable, and similar measurement devices. The portable measuring device may be hand-held and may perform qualitative and/or quantitative detection of more than one analyte in a sample. Examples of portable measurement systems include Ascensia of Bayer healthcare, Inc. of Tarrytown, New York, TallownTypes anda type meter; while an example of a bench-top measurement system includes an electrochemical workstation available from CH instruments of Austin, Texas.

The biosensor system may analyze the biological fluid using optical and/or electrochemical methods. In some optical systems, analyte concentration is determined by measuring light that interacts with or is absorbed by a light-distinguishable substance, such as an analyte or a reactant or a product formed by a reaction of a chemical indicator with the analyte. In other optical systems, a chemical indicator fluoresces or emits light in response to an analyte when illuminated with an excitation beam. Light can be converted into an electrical output signal, such as a current or potential, which can be processed similarly to the output signal obtained by electrochemical methods. In either optical system, the system measures light and correlates the light to the analyte concentration of the sample.

In light-absorbing optical systems, chemical indicators produce light-absorbing reaction products. Chemical indicators such as tetrazolium salts may be used in conjunction with enzymes such as diaphorase. Tetrazolium salts typically form formazans in response to redox reactions of analytes(a chromogen). An incident input beam from a light source is directed to a sample. The light source may be a laser or a light emitting diode, etc. The incident light beam may be selected to have a wavelength that facilitates absorption of the reaction products. When an incident light beam passes through the sample, the reaction products absorb a portion of the incident light beam, thereby attenuating or reducing the intensity of the incident light beam. The incident beam may be reflected back to the detector by the sample or transmitted through the sample to the detector. The detector collects and measures the attenuated incident beam (output signal). The amount of light attenuated by the reaction product is indicative of the analyte concentration in the sample.

In optical systems that generate light, the chemical indicator fluoresces or emits light in response to an analyte redox reaction. The detector collects and measures the light generated (output signal). The amount of light produced by the chemical indicator is indicative of the analyte concentration in the sample.

In electrochemical biosensor systems, analyte concentration is determined from an electrical signal generated by an oxidation/reduction reaction or a redox reaction of an analyte or a substance responsive to the analyte when an input signal is applied to a sample. The input signal may be a potential or a current, and may be constant, varying, or a combination thereof (e.g., when an AC signal with a DC signal offset is applied). The input signal may be applied in the form of a single or multiple pulses, sequences or periods. An enzyme or similar substance may be added to the sample in order to enhance the transport of electrons from the first substance to the second substance in a redox reaction. An enzyme or similar substance may react with a single analyte to provide specificity to a portion of the output signal generated. Mediators can be used to maintain the oxidation state of the enzyme.

Electrochemical biosensor systems typically include a measuring device having electrical contacts that connect with electrical conductors in a test sensor. The electrical conductor may be made of an electrically conductive material such as solid metal, metal paste, conductive carbon paste, conductive polymer, and the like. The electrical conductors are typically connected to a working electrode, a counter electrode, a reference electrode, and/or other electrodes that extend to the sample reservoir. One or more electrical conductors may also extend into the reservoir to provide functions not provided by the electrodes described above.

The measuring device applies an input signal to the electrical conductor of the detection sensor via the electrical contacts. An electrical conductor passes the input signal through the electrodes to a sample located in a sample reservoir. The redox reaction of the analyte generates an electrical output signal in response to the input signal. The electrical output signal from the sensor strip may be a current (e.g., generated by amperometry (amperometry) or voltammetry (voltmetry)), a potential (e.g., generated by potentiometry/amperometry (galvometry)), or an accumulated charge (e.g., generated by coulometry). The measurement device may have processing capabilities to measure and correlate the output signal with the presence and/or concentration of one or more analytes in the biological fluid.

In coulometry, a potential is applied to the sample to completely oxidize or reduce the analyte. A biosensor system using coulometry is described in U.S. patent No. 6,120,676. In amperometry, when the measured output signal is a current, an electric signal of a constant potential (voltage) is applied to the electric conductor of the detection sensor. Biosensor systems using amperometry are described in U.S. patent nos. 5,620,579, 5,653,863, 6,153,069 and 6,413,411. In voltammetry, a varying potential is applied to a biological fluid sample. In gated amperometry (gated amperometry) and gated voltammetry (gated voltammetry), pulsed input may be used as described in WO2007/013915 and WO2007/040913, respectively.

In many biosensor systems, the detection sensor may be adapted for use outside, in vivo, or partially within a living organism. When used outside a living organism, a sample of biological fluid may be introduced into the reservoir of the test sensor. The detection sensor may be placed in the measurement device for analysis before, after, or during introduction of the sample. The detection sensor may be continuously immersed in the sample while in or partially in the living organism, or the sample may be intermittently introduced to the sensor strip. The detection sensor may include a reservoir that may be partially separated from or in communication with a volume of sample. When in communication with the sample, the sensor strip may take the form of an optical fiber or other structure disposed in contact with the biological fluid. Similarly, the sample may continuously flow through the sensor strip (e.g., continuous monitoring) or be interrupted (e.g., interrupted monitoring) for analysis.

The biosensor system may provide an output signal containing one or more errors in the analysis of the biological fluid. These errors may be reflected in an abnormal output signal, for example, when one or more portions of the output signal or the entire output signal do not respond or do not respond properly to the analyte concentration of the sample. These errors may arise from one or more factors, such as the physical characteristics of the sample, the environmental conditions of the sample, the operating conditions of the system, interfering substances, and the like. The physical characteristics of the sample include hematocrit (red blood cell) concentration, and the like. The environmental conditions of the sample include temperature, etc.

The measurement performance of a biosensor system is defined by accuracy and/or precision. The measurement performance of the system can be improved and the deviation reduced by increasing the accuracy and/or precision. Accuracy can be represented by the deviation of the analyte reading of the sensor system compared to a reference analyte reading, with a larger deviation value indicating lower accuracy. Accuracy can be represented by the distribution or variance of the deviation between the plurality of analyte readings and the mean. The deviation is the difference between one or more values determined by the biosensor system and one or more acceptable reference values for the analyte concentration in the biological fluid. Thus, one or more errors in the analysis can result in a deviation in the analyte concentration determined at the biosensor system.

The deviation can be expressed by "absolute deviation" or "percent deviation". Absolute deviations are expressed in units of measure, such as mg/dL; and the deviation percentage is expressed as a percentage of the absolute deviation value to the reference value. Under the ISO standard, absolute deviation is used to indicate the error at glucose concentrations less than 75mg/dL, while percent deviation is used to indicate the error at glucose concentrations above 75 mg/dL. The term "combined bias" (expressed as bias/% -bias) represents the absolute bias for glucose concentrations less than 75mg/dL and the percent bias for glucose concentrations above 75 mg/dL. A reference value for an acceptable analyte concentration may be obtained from a reference instrument, such as YSI2300STATPLUS available from YSI of gold springs (Yellow springs), Ohio^TM。

Hematocrit bias refers to the difference between a reference glucose concentration obtained with a reference instrument and the glucose readings of tests obtained from biosensor systems containing samples of different hematocrit levels. The difference between the reference value and the value obtained from the above system is caused by different hematocrit levels between the particular whole blood samples, and the difference can be expressed as a percentage by the following equation: % Hct-bias ═ 100% × (G)_m-G_ref)/G_refWherein G is_mAnd G_refA measured glucose concentration reading and a reference glucose concentration reading, respectively, of any hematocrit level. The greater the absolute value of% Hct-bias, the higher the hematocrit level of the sample (expressed as% Hct: volume of red blood cells/volume of sample), thereby reducing the accuracy and/or precision of the determined glucose concentration. For example, if a whole blood sample containing the same glucose concentration but having different hematocrit levels of 20%, 40%, and 60% is analyzed, the system reports three different glucose readings according to a set of calibration constants (e.g., a 40% hematocrit slope and intercept for the whole blood containing sample). "hematocrit sensitivity" is the blood representing the sampleThe degree of influence of the change in hematocrit level on the bias value used for the analysis. Hematocrit sensitivity may be defined as the value of the combined bias per percent hematocrit, i.e., bias/% -bias per% Hct.

Temperature drift refers to the difference between the analyte concentration obtained at a reference temperature and the analyte concentration obtained at a different test temperature for the same sample. The difference between the analyte concentration obtained at the reference temperature and the analyte concentration obtained at the different test temperatures can generally be expressed as a percentage by the following equation: % Temp-bias is 100% × (A)_mTemp-A_RefTemp)/A_RefTemPWherein A is_mTempAnd A_RefTempThe analyte concentration of the sample at the test temperature and the reference temperature, respectively. The greater the absolute value of% Temp-bias, the greater the temperature difference, thereby reducing the accuracy and/or precision of the glucose concentration determined at different test temperatures. The "temperature sensitivity" indicates the degree of influence of a change in temperature on the bias value used for analysis when the analysis is performed. Temperature sensitivity may be defined as the value of the combined deviation per degree celsius, i.e.,% -bias/° c. Temperature sensitivity can also be defined as the slope deviation per degree Celsius, i.e., Δ S/deg.C.

Many biosensor systems include one or more methods of correcting errors associated with the analysis. Concentration values obtained from an analysis with errors may be inaccurate. Thus, the ability to modify these analyses may improve the accuracy and/or precision of the concentration values obtained. The error correction system may compensate for one or more errors, such as a sample temperature different from a reference temperature, a sample hematocrit level different from a reference hematocrit value.

Some biosensor systems have an error correction system for compensating for different hematocrit concentrations in the sample. In order to reduce the influence of the bias of hematocrit on glucose at the time of measurement, various methods and techniques have been proposed. Some methods use the current ratio of the forward and reverse potential pulses to compensate for the hematocrit effect. Other methods have been proposed to reduce the effects of hematocrit bias, including filtering red blood cells from the electrode surface with silica particles or using a wide electrode spacing in conjunction with a mesh layer to distribute the blood throughout the detection sensor.

Some biosensor systems have an error correction system that compensates for temperature. Such error correction systems typically change the analyte concentration determined for a particular reference temperature in response to the instrument temperature or sample temperature. Many biosensor systems compensate for temperature errors by correcting the output signal before calculating the analyte concentration using the correlation equation. Other biosensor systems compensate for temperature errors by correcting the analyte concentration calculated by the correlation equation. Generally, conventional methods of temperature compensation focus on the effect of temperature on specific parameters, rather than the overall effect of temperature error on the deviation of the analysis. Biosensor systems having error detection and/or compensation systems for sample temperature are described in U.S. patent No. 4,431,004; 4,750,496 No; 5,366,609 No; U.S. Pat. No. 5,395,504; 5,508,171 No; 6,391,645 th and 6,576,117 th.

Some biosensor systems have error correction systems for compensating for interference and other factors. These error correction systems typically use electrodes that lack one or more working electrode reagents in order to remove background interfering signals from the working electrode signal.

While conventional error compensation systems balance different advantages and disadvantages, they are not ideal. Conventional systems are typically directed to detecting and responding to certain types of errors, such as temperature or hematocrit. These systems typically do not have the ability to compensate for multiple error sources. These systems also typically lack the ability to vary the error compensation based on the output signal of a particular sample. Thus, conventional biosensor systems may provide analytical results with measured analyte concentration values that are outside of the desired performance range.

For this reason, there is a continuing need for improved biosensor systems, particularly those that may provide increasingly accurate and/or precise detection of analyte concentrations from a sample. The systems, devices, and methods of the present invention overcome at least one of the disadvantages associated with conventional biosensor systems.

Disclosure of Invention

The present invention provides a biosensor system that is capable of adjusting a correlation used to determine an analyte concentration in a biological sample from an output signal based on one or more complex exponential functions that are responsive to one or more errors that are capable of biasing the determined analyte concentration. The deviation may be expressed as a slope deviation Δ S value derived from one or more error parameters and a standard slope deviation. The Δ S value represents the slope deviation determined using one or more complex exponential functions of the error parameter. The complex exponential function includes at least two terms modified by the weighting coefficients. The term may include an error parameter taken from the output signal or independent of the output signal.

In a method of determining the concentration of an analyte in a sample, an output signal value is generated that is responsive to the concentration of the analyte in the sample. At least one Δ S value from at least one error parameter is determined, and the at least one output signal value is compensated with at least one reference correlation and the at least one Δ S value to determine an analyte concentration in the sample. The at least one Δ S value may be determined by a prediction function i (predictor). The f (predictor) comprises an exponential function and relates at least one error parameter to Δ S. The reaction may be an electrochemical redox reaction.

In a method of determining a complex exponential function from error parameters, at least one error parameter is determined that is responsive to a percentage of deviation of a determined analyte concentration in a sample. The at least one error parameter is associated with at least one Δ S value by at least one complex exponential function, the at least one Δ S value representing a slope difference between a slope from the reference correlation and an assumed slope of a line capable of providing an output signal value of the sample analyte concentration without deviation. The complex exponential function includes at least one error parameter incorporated as a term multiplied by a weighting factor.

In a method of selecting terms for inclusion in a complex exponential function, a plurality of error parameters are selected as terms that may be included in the complex exponential function. A first exclusion value is determined for each selected item. Applying one or more exclusion tests to the exclusion values to identify one or more terms removed from the complex exponential function. After removing at least one item, a second exclusion value is determined for the retained item. If the second exclusion value does not identify a retention term to be removed from the composite exponential function in one or more exclusion tests, then the retention term is included in the composite exponential function.

In a method of determining a complex exponential function from a hematocrit-adjusted donor blood sample for use in a measurement device, a plurality of test sensors are used to determine a test glucose concentration of the hematocrit-adjusted blood sample having a known reference glucose concentration under a variety of environmental conditions. The slope and intercept of the reference correlation of the plurality of detection sensors is determined from the determined glucose concentration and the known glucose concentration at the reference temperature and the reference% Hct. A reference glucose concentration is determined for a plurality of donor blood samples. The plurality of hematocrit-adjusted blood sample glucose concentration data may be combined with the plurality of donor blood sample glucose concentration data. A plurality of terms is selected from the data of one or more output signal values. These items may also be selected for one or more physical characteristics, environmental conditions, concentration values, and the like. Not only are arbitrary coefficients taken into account, but also the weighting coefficients of these terms are determined. A complex exponential function is determined by a combination of the selected items, the corresponding weighting coefficients, and any constant.

A biosensor system for determining the concentration of an analyte in a sample includes a measurement device and a detection sensor. The measurement device has a processor coupled to a sensor interface and a storage medium. The detection sensor has a sample interface adjacent to a reservoir formed by the sensor. The processor determines an output signal value responsive to an analyte concentration in the sample from the sensor interface. The processor determines at least one Δ S value from the error parameter and compensates the output signal value with the at least one Δ S value and at least one reference correlation present in the storage medium.

The biosensor system adjusts a correlation between the analyte concentration and the output signal using at least one Δ S value in response to the error parameter. The processor determines an analyte concentration from an output signal from the sample interface using the slope adjusted correlation.

In another method for determining the concentration of an analyte in a sample, one or more output signals are generated from the sample. At least one complex exponential function is determined, wherein the complex exponential function is responsive to more than one error parameter. Determining an analyte concentration in the sample from the output signal in response to the at least one complex exponential function.

Other systems, methods, features and advantages of the invention will be, or will become, apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention, and be protected by the accompanying claims.

Drawings

The invention can be better understood with reference to the following drawings and description. The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.

FIG. 1A shows a method for determining the concentration of an analyte in a sample.

FIG. 1B illustrates a method for selecting terms contained in a complex exponential function.

FIG. 1C shows a method of determining a complex exponential function from a hematocrit-adjusted donor blood sample for use in a measurement device.

Fig. 2 depicts the dependence of% -bias on the exponential function based on the ratio parameter.

FIG. 3 depicts S_cal、S_hyp、ΔS、A_corr、A_calAnd Δ a.

Fig. 4 depicts a gated pulse sequence in which the input signal comprises a plurality of pulses.

FIG. 5A depicts a plot of the dependence of Δ S on the R4/3 index value.

FIG. 5B depicts a plot of the dependence of Δ S on composite index values.

FIG. 6A depicts a plot of the dependence of Δ S of blood samples on the R4/3 index value at 21 ℃.

Fig. 6B depicts a plot of the dependence of Δ S of blood samples at 21 ℃ on composite index values.

FIG. 6C depicts a plot of the dependence of Δ S of blood samples at 18 ℃ on the R4/3 index value.

Fig. 6D depicts a plot of the dependence of Δ S of blood samples at 18 ℃ on composite index values.

Figure 6E depicts a graph of hematocrit sensitivity in combined bias —% Hct.

Fig. 6F depicts a graph of the correlation of the combined bias with the uncompensated reference glucose concentration and the complex index compensation corrected analyte concentration.

Fig. 7 depicts a schematic diagram of a biosensor system for determining an analyte concentration in a biologic fluid sample.

Detailed Description

The biosensor system utilizes a complex exponential function extracted from an intermediate signal or other source of the output signal to adjust a correlation that is used to determine an analyte concentration in the biologic fluid sample from the output signal. The analyte may generate an output signal in response to a light-identifiable species or a redox reaction. The intermediate signal may be one or more portions of the output signal or the like. For one or more errors in the analysis, a prediction function comprising at least one complex exponential function adjusts a correlation used to determine an analyte concentration from the output signal. The prediction function including at least one complex exponential function may also be used to correct for analyte concentrations that include errors. Such errors can cause deviations, thereby reducing the accuracy and/or precision of the determined analyte concentration. When analyzing complex biological samples, the compensation system can be used to improve the performance of other types of analysis measurements, in addition to providing basic benefits.

The complex exponential function includes a combination of terms modified by the weighting coefficients. One or more exclusion tests may be used to select the terms included in the complex exponential function. The prediction function and/or the complex exponential function correspond to bias/% -bias in the correlation between analyte concentration and output signal caused by one or more errors in the analysis. The% -bias in the correlation may be represented by one or more Δ S values obtained from one or more error parameters. The Δ S value represents the slope deviation of the correlation between the analyte concentration and the measured output signal (from one or more error parameters). Therefore, the closer the prediction function or the complex index function is to Δ S (Δ S ═ f (cindex)), the better the error correction function in the analysis is.

The complex exponential function corresponding to the slope or slope change may be normalized to reduce the statistical impact of the output signal change, improve the variance of the output signal change, normalize a measure of the output signal, a combination of these, or the like. Since the slope deviation can be normalized, the complex exponential function can be expressed as Δ S/S ═ f (cindex). The adjusted correlation can be used to determine an analyte concentration of the sample from the output signal or can be used to correct the analyte concentration and can provide improved measurement performance compared to conventional biosensors. A more detailed process for error correction using an exponential function and a Δ S value can be found in international publication No. wo2009/108239 entitled "Slope-base compensation" filed on 12.6.2008.

FIG. 1A shows a method for determining the concentration of an analyte in a biological fluid sample. In step 102, the biosensor system generates an output signal in response to an oxidation/reduction (redox) reaction of an optically identifiable substance or an analyte in a biologic fluid sample. In step 104, the biosensor system measures the output signal. In step 106, the analyte concentration is determined according to a compensation equation that includes at least one complex exponential function and the output signal. In step 108, the analyte concentration is displayed and stored for future reference and/or for other calculations.

In step 102 of FIG. 1A, an output signal is generated in response to an oxidation/reduction (redox) reaction of an optically identifiable substance or an analyte in a biological fluid sample. Optical sensor systems, electrochemical sensor systems, and the like may be used to generate the output signal.

In step 104 of fig. 1A, the biosensor system measures an output signal generated by the analyte (e.g., generated by a redox reaction of the analyte) in response to an input signal applied to the sample. The system may measure the output signal continuously or intermittently. For example, the biosensor system may intermittently measure the output signal in pulses of the gated amperometric input signal, resulting in a plurality of current values recorded in each pulse. The system may display the output signal on a display and/or may store the output signal or a portion of the output signal in a storage device.

In step 106 of FIG. 1A, the analyte concentration of the sample may be determined according to a compensation equation that includes at least one complex exponential function and an output signal. The complex exponential function may form part of a prediction function. Fig. 2 depicts the correlation between the exponential function and% -bias based on the ratio parameter (R5/4). The ratio parameter R5/4 represents the relationship between the currents generated by the analyte in response to the fourth pulse and the fifth pulse, respectively, in a gated amperometric pulse sequence comprising 7 pulses. Other ratio parameters and exponential functions may be used. Thus,% bias of the analyte concentration measured in a biological fluid (e.g., glucose in whole blood) can be determined from or correlated with the output signal of an assay, such as an intermediate current generated by the analyte in response to a gated amperometric sequence.

The relationship between% bias and the prediction function can be expressed as follows:

percent-bias ═ f (predictor) (equation 1),

wherein% -bias equals (Δ A/A)_ref) 100%, and f (predictor) equals a₁*f(Index)+a₀. Δ A is the measured or calculated analyte concentration A_calWith reference analyte concentration A_ref(known analyte concentration in the biological sample), f (index) may be a single error parameter, a combination of error parameters, or other values. Thus, substituting the terms of equation 1 yields the following relationship between% -bias and the exponential function:

(ΔA/A_ref)*100％＝a₁*f(Index)+a₀(equation 2).

Rearranging the terms of equation 2 yields the following relationship:

ΔA＝A_ref*(a₁*f(Index)+a₀) 100 (equation 3).

The compensation can be expressed as:

A_corr＝A₀+ Δ A (equation 4).

Wherein A is_corrIs a corrected or compensated analyte concentration, and A₀Is the initial analyte value of the assay. Δ A can be obtained from equation 3, A in equation 3_refMay not be available during analysis of the biological sample. However, the initial analyte value A₀Can be used in place of A in the analysis_ref. Thus, equation 3 can be approximated by the following relationship:

(equation 5).

Finally, substituting equation 5 into equation 4 yields the following relationship:

A_corr＝A₀+A₀*(a₁*Index+a₀)/100＝A₀*[1+(a₁*Index+a₀)/100](equation 6).

Based on the initial analyte value A that may have a deviation due to one or more errors in the analysis, according to equation 6₀The difference Δ a between the measured analyte concentration and the reference analyte concentration is obtained. Thus, there is no reference point or value on which to base the measured analyte concentration compensation. These and other equations encompassed by this application and the claims may include an "═ mark" used to indicate equality, correlation, or prediction, etc.

The% -bias in the correlation of analyte concentration to output signal may also be represented by one or more slope deviations Δ S obtained from one or more error parameters. The error comprising part of the output signal is reflected by the deviation between the assumed slope of the output signal and the slope of the reference correlation. The measurement performance of the analysis may be enhanced by determining one or more Δ S values reflecting the slope deviation of one or more error parameters. One or more Δ S values for analysis may be determined from one or more error parameters. The relationship between the Δ S value and one or more error parameter values may be described by an exponential function. The exponential function may be predetermined and stored in the biosensor system in addition to the referenced correlation equation. The error parameter value may be determined before, during, or after the analysis.

The slope compensation equation uses the output signal value to provide a compensated analyte concentration. Other values may be used for the slope compensation equation. The slope compensation equation compensates for the error by adjusting the reference correlation between the output signal and the known analyte concentration to provide a compensated or corrected analyte concentration.

The slope compensation equation can be expressed as follows:

(equation 7) of the reaction mixture,

wherein A is_corrIs the corrected analyte concentration, i is the value of the output signal from the biosensor system, Int is the intercept of the reference correlation equation, S_calIs the slope of the reference correlation equation, and Δ S represents the slope S_calAssumed slope S of the and line_hypDeviation of slope between, assuming slope S_hypFor providing an error-free output signal value of the analyte concentration of the sample. Int and S in the reference correlation equation_calMay be embodied as a Program Number Assignment (PNA) table, or another look-up table, etc., in a biosensor system. Other slope compensation equations including at least one Δ S value and the output signal may be used.

Equation 7 represents a corrected analyte concentration determined using the slope deviation Δ S, where Δ S is substantially the total slope deviation that is substantially related to the total error associated with the analyte analysis. The total slope deviation may be generated by one or more error sources. Equation 7 may use a substantially linear line for analyte concentrationAny signal of sexual response. Equation 7 may use other signals, such as approximately linear or partially linear signals, and the like. When Δ S is responsive to one or more errors in the output signal, i represents an error that includes a portion of the output signal that is not responsive to the sample analyte concentration. Thus, S_hyp＝S_cal+ Δ S. For Int and S_calCan be stored in the biosensor system for comparison with the output signal i, in order to determine a of the sample_corr。

If the value of Δ S is experimentally measured from samples and substituted into equation 7, the deviation in the measured analyte concentration of these samples will be completely compensated. Alternatively, if a prediction function is substituted for Δ S, the ability of the compensation equation to correct for deviations in the measured analyte concentration depends on how much the value produced by the prediction function is related to Δ S. In equation 7, a prediction function f (predictor) may be used instead of Δ S. Therefore, equation 7 can be rewritten as follows:

(equation 8)

The prediction function f (predictor) may have the general formula: b₁*f(CIndex)+b₀Where f (CIndex) is a complex exponential function, other values or indices may be used in conjunction with f (CIndex) to provide f (predictor). For example, a complex exponential function may be provided with b₁Value b and₀one or both of the values may not be provided with b₁Value b and₀one or both of the values, providing a prediction function. F (predictor) may also be provided in conjunction with a plurality of complex exponential functions to obtain a corrected analyte concentration for the sample.

For the theoretical case where Δ S is completely correlated with the complex exponential function, b₁(representing the slope) and b₀(representing the intercept) are 1 and 0, respectively. When the prediction function is close to Δ S, if b₁1 ± 0.2, a theoretical value of 1 may be used instead of b₁(ii) a Preferably, when b is₁When 1 ± 0.15, the theoretical value 1 is used instead of b₁(ii) a And may be more preferred when b₁When 1 ± 0.1, the theoretical value 1 is used instead of b₁. When the prediction function is close to Δ S, if b₀0 ± 0.3, the theoretical value 0 may be used instead of b₀(ii) a Preferably, when b is₀When 0 ± 0.2, the theoretical value 0 is used instead of b₀(ii) a And may be more preferred when b₀When 0 ± 0.1, the theoretical value 0 is used instead of b₀. Other deviation data (deviationcut-off) may be used to determine when to use the theoretical value of b1 or b0 or b₁And b₀Both theoretical values. Except that b is replaced by theoretical values 1 and 0₁And/or b₀In addition, based on the same deviation data or other deviation data, a predetermined value in a lookup table or the like may be used instead of b₁And/or b₀。

In step 108 of FIG. 1A, the corrected analyte concentration value is displayed and stored for future reference and/or for other calculations.

FIG. 3 shows S_cal、S_hyp、ΔS、A_corr、A_calAnd Δ a. Line A represents a reference correlation having a slope S_calAnd correlating the output signal in the form of a current value from the biosensor system with an analyte concentration value obtained from the YSI or other reference instrument for the sample. When used by a biosensor system during analysis of a sample, the reference correlation-line a may include output signal current values having one or more errors that may provide inaccurate and/or imprecise analyte concentration values. Line B represents the error compensation correlation, which has a slope S_hypAnd correlating the current value obtained from the system with the sample analyte concentration value obtained from the reference instrument. The error compensation correlation is adjusted or modified to reduce or substantially remove one or more errors. Δ S is the slope difference between these correlation lines. Δ A is the uncompensated or uncorrected determined analyte concentration value (A)_cal) Error-compensated or corrected determined analyte concentration value (A)_corr) The difference between them.

Without compensation or correction, a particular output signal value will be provided corresponding to S_hypS different in error compensation line_calReference to the sample analyte concentration of the correlation line. Based on S_hypError compensation line derived A_corrThe values provide more accurate values of sample analyte concentration. Therefore, equation 7 uses Δ S to relate the current value, S_calAnd Int to a compensated analyte concentration value A_corr. In this way, the percent deviation can be linked into equation 7 by Δ S. The percent deviation can be pulled toward the center of the deviation distribution by the relationship of Δ S to percent deviation. Since Δ S responds to the deviation, changing Δ S affects the amount of deviation that is maintained in the compensated analyte concentration of the sample.

The response of Δ S to one or more errors in the analysis may be represented by a prediction function. Responsive to one or more errors (Δ S) for determining one or more prediction functions_cal) The slope deviation of the correlation equation of (a) can be determined from experimental data, for example, during factory calibration as follows:

(equation 9) of the process,

where i is the value of the output signal from the biosensor system, Int is the intercept of the reference correlation equation, A_refIs a sample reference analyte concentration, S, e.g. from a reference instrument_calIs the slope of a reference correlation equation, e.g. i ═ S_cal*A_ref+ Int. One or more Δ S may be determined at each analyte concentration_cal. In this manner, for a plurality of known analyte concentrations, output signal values can be obtained from the biosensor system to determine corresponding Δ S_calThe value is obtained. Δ S by employing equation 9_calValues and associates them with error parameters so that an initial prediction function can be determined.

The prediction function compensates the measured analyte concentration for one or more errors in the analyte concentration analysis. One or more prediction functions may be used. A prediction function that is perfectly correlated to the total slope deviation as will provide the final total error compensation for the analyte concentration. This hypothetical, perfectly correlated prediction function can be used to compensate for all errors in the analysis without having to know the exact cause of the total slope deviation (i.e., the deviation in the measured analyte concentration). The prediction function includes at least one exponential function, and one or more of the exponential functions may be complex functions. Preferably, the prediction function comprises at least one complex exponential function.

The exponential function is responsive to at least one error parameter. The exponential function may be a calculated number that is related to an error parameter (e.g., hematocrit or temperature) and represents the effect of the error parameter on the slope deviation Δ S. Thus, the error parameter may be any value responsive to one or more errors in the output signal. The exponential function can be experimentally determined as Δ S_calAnd a regression equation of the graph between the error parameters.

The exponential function may be determined using error parameter values from analysis of the analyte, such as from intermediate signals of the output signal, or from sources independent of the analyte output signal, such as thermocouples, additional electrodes, and the like. Thus, the error parameter may be taken directly or indirectly from the analyzed output signal and/or derived independently of the output signal. Any error parameters may be used to form those described in international publication No. wo2009/108239 entitled "Slope-base compensation" filed 12/6 2008.

Temperature may be considered an error parameter because errors in concentration values may be caused by analysis at temperatures other than those at which the reference correlation is determined. For example, temperature affects the oxidation and diffusion of glucose in whole blood samples and affects the diffusion of photoactive molecules. The temperature for analysis can be determined by any means such as thermocouples and computational evaluation. Therefore, f (index)_TempThe temperature is correlated to a slope deviation, which is the difference in slope between the slope of a reference correlation measured at a reference temperature and the hypothetical slope of the line providing the temperature-affected analyte concentration at the temperature at which the analysis is performed. Exponential function of temperature f (index)_TempMay be stored in the biosensor system along with the reference correlation equation.

Fig. 4 depicts a gated pulse sequence of an input signal comprising a plurality of pulses. The value of the output signal current resulting from the pulse is plotted on each pulse. The values of the intermediate signal currents described are depicted as dots. Each i value is a current value of the output signal in response to the input signal. The first number in the i-value index indicates the number of pulses and the second number in the index indicates the order in which the signals are output when the current value is recorded. For example, i_2,3A third current value representing the second pulse recording.

As previously mentioned, the exponential function may comprise a ratio taken from the intermediate output signal as shown in fig. 4. For example, several intermediate signal values may be compared within a single pulse signal decay period, e.g., the ratio R3 ═ i_3,3/i_3,1，R4＝i_4,3/i_4,1And the like. In another example, intermediate signal values within different pulse signal decay periods may be compared, such as the ratio R3/2 ═ i_3,3/i_2,3The ratio R4/3 ═ i_4,3/i_3,3And the like.

The exponential function may also include a combination of ratios taken from the output signals shown in fig. 4. In one example, the exponential function may include a Ratio of ratios, such as Ratio 3/2-R3/R2, Ratio 4/3-R4/R3, and so forth. In another example, the exponential function may include a combination of exponentials. For example, the combination Index-1 can be expressed as Index-1 ═ R4/3-Ratio 3/2. In another example, the combination Index, Index-2, may be expressed as Index-2 ═ (R4/3)^p-(Ratio3/2)^qWherein p and q are independently positive numbers.

When the function comprises a combination of weighting coefficients multiplied by terms, the exponential function is complex. The combination is preferably a linear combination, but other combining methods that provide weighting coefficients for the terms may be used. Each term may include one or more error parameters. An example of a complex exponential function is represented as follows:

f(CIndex)＝a₁+(a₂)(R3/2)+(a₃)(R4/3)+(a₄)(R5/4)+(a₅)(R3/2)(G_raw)+(a₆)(R4/3)(G_raw)+(a₇)(R3/2)(Temp)+(a₈)(R4/3)(Temp)+(a₉)(Temp)+(a₁₀)(G_raw) + … (equation 10),

wherein a is₁Is a constant number of times that the number of the first,a₂-a₁₀is a separate weight coefficient, G_rawIs the measured analyte concentration of the sample without compensation, and Temp is the temperature. Each weight coefficient (a)₂-a₁₀) Respectively, following the item with which it is associated.

There are at least three basic type terms in the complex exponential function represented by equation 10: (1) individual ratio indices taken from the output signal, such as R3/2 and R4/3, e.g., R3/2 and R4/3, (2) ratio index taken from the output signal to temperature or G_rawInter-interaction items, e.g. (R3/2) (G)_raw) And (R3/2) (Temp), etc., (3) temperature and G_raw. These terms may include inclusion of G in addition to the error parameter_rawThe value of (c). Other terms including, but not limited to, a combined exponential function as previously described may also be used. When these terms are replaced with appropriate values, the compound exponential function may be solved to provide a compound exponential value. The plurality of terms may be statistically processed to determine one or more constants and weighting coefficients. Statistical processing may be performed using a statistical software package including MINITAB (MINTAB, inc., stateclege, PA).

Constant a₁May be determined by regression or other mathematical means. When a single constant is shown in equation 10, no other constant is required; multiple constants may also be used and may be equal to 0. Thus, the complex exponential function may or may not include one or more constants. One or more constants (e.g., the constant b described above in relation to equation 8)₀) A prediction function may be formed in combination with the exponential function.

A term with a weight coefficient of 1 may be used, in which case the complex exponential function comprises at least two terms multiplied by the weight coefficient. The weight coefficient is a numerical value other than 1 or 0. Preferably, the terms including the error parameter are multiplied by a weight coefficient. More preferably, each non-constant term of the complex exponential function is multiplied by a weight coefficient. The weight coefficient may have a positive or negative value. The weighting factors may be determined by statistical processing of experimental data collected based on a combination of multiple analyte concentrations, different hematocrit levels, different temperatures, and the like.

Table 1 below lists the weight coefficients and p-values obtained by multivariate regression of data for glucose output signals (currents) obtained from capillary and venous blood samples at 21 ℃ and 18 ℃ for 52 donors subjected to the donor study. Two analyses of glucose in each blood sample from each donor were performed to give about 104 data points in the data population. The samples are analyzed using a gated amperometric input signal, wherein selected intermediate output signals are recorded from the pulses. Multivariate regression was performed using MINITAB version 14 software and selecting multivariate regression options for multivariate linear combinations. Other statistical analysis or regression options are also used to determine the weighting coefficients of the terms.

TABLE 1 results of multivariate regression

Item(s)	Weight coefficient	Standard error of coefficient	T	P
					Constant number	133.52	48.35	2.76	0.006
R3/2	204.96	71.03	2.89	0.004
					R4/3	-356.79	96.47	-3.70	0.000
(R3/2)(Graw)	-0.0408	0.1163	-0.35	0.726
					(R4/3)(Graw)	-0.0338	0.1812	-0.19	0.852
(Temp)(R3/2)	-12.237	3.704	-3.30	0.001
					(Temp)(R4/3)	15.565	5.115	3.04	0.002
Temp	-2.516	2.503	-1.01	0.315
					Graw	0.0827	0.09661	0.86	0.392

The resulting complex exponential function can be expressed as follows:

ΔS_RegA＝134+(205)(R3/2)-(357)(R4/3)-(0.041)(R3/2)(G_raw)-(0.034)(R4/3)(G_raw)-(12.2)(Temp)(R3/2)+(15.6)(Temp)(R4/3)-(2.52)(Temp)+(0.0827)(G_raw) (equation 11) of the process,

wherein, Delta S_RegAIs to describe Δ S_calDefining Δ S as a complex exponential function of_cal＝(i/A_ref)-S_calWherein, for example, A is as described above with reference to equation 7_refIs a reference analyte concentration value, S, obtained from a YSI reference instrument_calIs the slope in the reference correlation equation. R²The value reflects Δ S_RegATo what extent the output of the complex exponential function corresponds to 77.2% (R) of the Δ Scal value²100%). Thus, R²The value represents a complex exponential function and S_calThe correlation between them. R²The larger the value is, the more reflected in the description Δ S_calThe better the composite index.

FIG. 1B illustrates a method for selecting terms contained in a complex exponential function. In step 112, a plurality of error parameters are selected as terms that may be included in the complex exponential function. The error parameter may be directly or indirectly extracted from the output signal in response to the optically identifiable substance or from a redox reaction of the biological fluid sample analyte. The error parameter may also be derived independently of the output signal, for example from a thermocouple. These terms may include values other than error parameters. In step 114, a first exclusion value for each selected item is determined using one or more mathematical means. Mathematical means may include regression, multivariate regression, and the like. The exclusion value may be a p-value, etc. The mathematical means may also be provided with weighting coefficients, constants, and other values associated with the selected items.

In step 116, one or more exclusion tests are applied to the exclusion values to identify one or more terms to be excluded from the complex exponential function. At least one item was excluded under the test. In step 117, one or more mathematical approaches are repeated to identify a second exclusion value for the retained term. In step 118, if the second exclusion value does not identify a retention term to be excluded from the composite exponential function under one or more exclusion tests, then the retention term is included in the composite exponential function. In step 120, if the second exclusion value identifies a retained term to be excluded from the complex exponential function under one or more exclusion tests, one or more of the mathematical approaches in step 117 may be repeated to identify a third exclusion value for the retained term. These retention terms may be included in the composite exponential function, as shown in step 118, or the above process may be repeated in step 120 until the exclusion test fails to identify one or more terms to be excluded.

Table 1 above also lists the p-values of the various terms. The p-value represents the probability of affecting the correlation between the complex exponential function and Δ S when terms are removed from the complex exponential function. For example, a term having a p-value of 0.05 or more means that the probability of removing the term from the complex exponential function without reducing the correlation between the complex exponential function and Δ S is 5% or more. Thus, the p-value can be used as an exclusion value for an exclusion test to select terms that are likely to be excluded from the complex exponential function. The smaller the value p-value selected as the exclusion value, the more terms are excluded from the complex exponential function.

When the exclusion test uses a p-value as the exclusion value, the p-value is preferably from about 0.01 to about 0.10, and more preferably a value from about 0.03 to about 0.07. In addition to p-value based exclusion tests, other exclusion tests may be used to identify terms that may be excluded from the complex exponential function. Removing from the complex exponential function a term that does not affect the correlation between the complex exponential function and Δ S in an undesirable manner results in the desired correlation between the complex exponential function and Δ S. Thus, the desired improvement in measurement performance can be achieved by the compensation equation while providing a shorter analysis time. In addition, the accuracy of subsequent analysis using different biosensor systems and conditions can be improved by removing unwanted terms from the complex exponential function.

With respect to the entries in Table 1, entries with p-values greater than 0.05 may be selected to be removed from the complex exponential function. Thus, the term (R3/2) (G_raw)、(R4/3)(G_raw) Temp and G_rawTerms that can be suitably removed from the complex exponential function after being identified as a first multivariate regression. Due to (R4/3) (G_raw) The term shows the maximum p-value (0.852), removed and the variable regression repeated. This and third multivariate regression iterations identify Temp terms and G with second and third highest p-values_rawAn item. By removing (R4/3) (G)_raw) Item, Temp item and G_rawTerm, (R3/2) (G) was unexpectedly determined as shown in Table 2 below_raw) The p-value of the term is below the 0.05 exclusion value. Therefore, when (R3/2) (G)_raw) The ability of the complex exponential function to correlate with Δ S is facilitated by the term' S weighting coefficients being of small value (0.00799) relative to the other weighting coefficients. Preferably, an iterative process is repeated until the retained terms satisfy the trial, which is to select and remove the most undesirable terms that exclude the trial.

TABLE 2 results of multivariate regression with reduced term settings

Item(s)	Weight coefficient	Standard error of coefficient	T	P
					Constant number	95.463	3.930	24.29	0.000
R3/2	177.66	68.22	2.60	0.010
					R4/3	-289.31	70.91	-4.08	0.000
(R3/2)(Graw)	7.9899×10-3	7.575×10-4	10.55	0.000
					(Temp)(R3/2)	-11.221	3.550	-3.16	0.002
(Temp)(R4/3)	11.928	3.709	3.22	0.001

After removal of (R4/3) (G)_raw) Item, Temp item and G_rawAfter the term, the complex exponential function of equation 11 can be expressed as follows:

ΔS_RegB＝95.5+(178)(R3/2)-(289)(R4/3)+(0.00799)(R3/2)(G_raw) - (11.2) (Temp) (R3/2) + (11.9) (Temp) (R4/3) (equation 12).

R²The value reflects Δ S_RegBTo what extent the output of the equation is equivalent to S_calThe value was 77.1%. The removal of the exclusion term from equation 11 by exclusion testing does not produce a significant change in the ability of the complex exponential function of the simplified term to plot Δ S (0.1). Thus, the ability of the composite index of equation 12 to map errors in the data of table 1 is maintained, and the number of terms associated with equation 11 is advantageously reduced.

FIG. 5A is a graph of the dependence of Δ S on the R4/3 index value obtained from the data of the donor study discussed in Table 1 above. The "cap/21℃" data set represents correlation data from a capillary blood sample at about 21 deg.C, the "ven/18℃" data set represents correlation data from a venous blood sample at about 18 deg.C, and the "all" data set represents overall correlation data from both samples, as well as a capillary blood sample at about 18 deg.C and a venous blood sample at about 21 deg.C. Fig. 5B is a plot of Δ S correlation (as a function of the composite index value from equation 12) similar to the data of table 1. The difference between the overall correlation ("all") and the individual correlations at different temperatures is plotted against the complex exponential function (R) of FIG. 5B²0.77) compared to the R4/3 ratio exponential function of fig. 5A (R)²0.64) is much smaller. Despite these R²A difference of about 0.13 between the values is numerically small,but it shows that the correlation between Δ S and the complex exponential function is improved by 13% relative to the correlation between Δ S and the R4/3 ratio exponential function. Thus, the biosensor can compensate for four cases of capillary and venous blood samples at 21 ℃ and 18 ℃ using a single prediction function as represented by equation 13 below:

ΔS＝1.0043*ΔS_RegB+0.1308 (equation 13). In equation 13, the complex exponential function Δ S_RegBRepresented by equation 12, and the values 1.0043 and 0.1308 are, for example, b of equation 8 above₁And b₀(from the "all" data in FIG. 5B).

Using one or more complex exponential functions responsive to Δ S may reduce the range of deviation, which is measured by combining the standard deviations of the deviations. The smaller the standard deviation of the combined deviation, the smaller the deviation range and, thus, the more accurate and/or precise the analysis of the analyte in the sample. The effect of the compensation on improving the measurement performance of the analysis is directly related to the correlation between Δ S and one or more exponential functions, which directly affects the reduction of the Standard Deviation (SD) of the total number of deviations. The correlation between Δ S and one or more exponential functions or one or more prediction functions may be determined by a correlation coefficient R²And (6) measuring. Thus, R²The higher the value, the better the correlation between Δ S and one or more exponential functions or one or more prediction functions, the greater the reduction in SD values for the combined deviations, and the smaller the compensated deviation range. Preferably, the complex exponential function has an R of about 0.6 or greater with Δ S²The correlation value. More preferably, the complex exponential function has an R of about 0.7 or greater with Δ S²The correlation value. Preferably the exponential function or the predictive function provides an SD value of less than 5 for the combined deviation of the total number of data. Preferably, the prediction function comprising the complex exponential function provides an SD value of less than 4 for the combined deviation of the total number of data, more preferably an SD value of less than 3 for the combined deviation of the total number of data.

An empirical relationship between standard deviation and range of deviation can be seen in table 3 below. The mean of the combined deviations before and after R4/3+ Temp index compensation and composite index compensation, the SD of the combined deviations, and the percentage of concentration analysis (total number of data) that fall within the ± 10% combined deviation limit for the capillary blood samples used for glucose analysis at 21 ℃ and 18 ℃ described in table 1 above are listed. The abbreviation "R4/3 + Temp" is used to describe the compensation of the R4/3 exponential function and the temperature exponential function, as well as for "R4/3 + Temp" as described in Table 4.

TABLE 3 Compensation results using R4/3+ Temp and composite index

Determination of analyte concentration (G) by uncompensated_raw) The calculated mean values of the combined deviations show a negative deviation of the total number of data from zero deviations at 18 ℃ and 21 ℃. At 21 ℃, a combined deviation average of-1.03 is considered to be within the error range of the biosensor system. However, at 18 ℃, the combined mean deviation of-9.29 is considered to be due to temperature error. For data at temperatures below 18 ℃, values significantly above 9 indicate that the system uncompensated data is centered at the lower range of the ± 10 combined deviation limits and significantly away from the center of zero deviation. Therefore, about half of the total number of data is outside the range of the ± 10 combined deviation limit.

For the 21 ℃ data set, the R4/3+ Temp exponential function compensation provided a reduction in standard deviation of greater than two units (6.315-4.23 ═ 2.085). It is clear that on average, greater than two units of reduction, a standard deviation of 5 units or less will result in about 95% of the data being within the ± 10% combined deviation limits and about 63% of the data being within the ± 5% combined deviation limits. Thus, the R4/3+ Temp exponential function compensation places 98% of the data at 21 ℃ within the range of + -10% combined deviation limits and approximately 77% of the data within the range of + -5% combined deviation limits.

For the R4/3+ Temp exponential function compensation, the composite exponential function compensation reduces the standard deviation by about an additional 0.5 units. Thus, the compound index compensation places 99% of the data within the range of the + -10% combined deviation limit and approximately 88% of the data within the range of the + -5% combined deviation limit. For the data seen with the R4/3+ Temp exponential function compensation versus no compensation, the composite exponential compensation did not improve much relative to the R4/3+ Temp exponential function compensation, but the noise immunity of the system increased significantly when the data set was centered a small amount (larger mean of combined deviations).

Noise immunity can be considered as how the system provides accurate and/or precise analyte concentration values in the presence of errors in the analysis. Noise immunity is measured by subtracting twice the standard deviation from 10, thus providing a noise immunity indicator (PRI). For the total number of 21 ℃ data in Table 3, the PRI was 1.54 (i.e., 10-2 x 4.23) for R4/3+ Temp exponential function compensation; for the complex exponential function compensation, the PRI was 2.6 (i.e., 10-2 x 3.7). Since the uncompensated 21 ℃ data is substantially centered on the numerical mean 1, the composite exponential compensation increases the PRI by about 68% relative to the R4/3+ Temp exponential compensation, thereby adding an additional one percent of data to the range of the a + -10% combined deviation limit.

However, the advantage provided by the complex exponential compensation increases significantly when the system is disturbed by an error (which causes an uncorrected data range expansion), which can be observed by an increase in the value in the combined deviation average of the 18 ℃ data. For the perturbed 18 ℃ data, the standard deviation was reduced by 2.2 units by R4/3+ Temp exponential function compensation, and the standard deviation was further reduced by about 0.5 units by complex exponential function compensation. Thus, the composite exponential function compensation provides about 0.5 units SD reduction in standard deviation at both temperatures relative to the R4/3+ Temp exponential function compensation. This demonstrates that the composite exponential compensation has a greater ability to bring high deviation data into an acceptable range relative to the R4/3+ Temp exponential compensation.

When the PRI values were determined for the 18 ℃ data, the R4/3+ Temp exponential function offset provided a value of 0.58, while the complex exponential function offset provided a value of 1.64. It can be seen that the composite exponential function compensation increases by about 180% relative to the R4/3+ Temp exponential function compensation in PRI. The composite exponential function compensation provided a 68% increase in PRI that shifted an additional 1% of the 21 ℃ data (the data described above were tightly clustered) into the a ± 10% combined deviation limit, and the composite exponential function compensation provided a 180% increase in PRI that shifted an amount (3.4%) of more than three times the higher average (numerically) of the 18 ℃ data into the a ± 10% combined deviation limit. Therefore, the larger the error in the uncompensated data, the better the complex exponential function compensation, reducing the deviation to within a ± 10% of the combined deviation limit.

The compound exponential function compensates for an increase in the percentage of data points within the a + -10% combined deviation limit by about 17% (i.e., (99.1-84.9)/84.9 x 100%) at the higher 21 deg.C temperature relative to the uncompensated data points, and an increase in the percentage of data points within the a + -10% combined deviation limit by about 78% (i.e., (98.1-55.2)/55.2 x 100%) at the lower 18 deg.C temperature relative to the uncompensated data points. Although the difference between the R4/3+ Temp exponential function and the complex exponential function correction is not as large as for this substantially centered uncorrected data, the improvement provided by the complex exponential function correction is still crucial since there is rarely an analysis that falls outside the a ± 10% combined deviation limit. By reducing the number of readings outside the margin of deviation, more readings can be taken for accurate therapy of the patient (e.g., when monitoring glucose in the blood). In addition, the need for patients to abandon and repeat the analysis can be reduced.

FIG. 6A is a graph of the dependence of Δ S on the R4/3 index value at 21 ℃ for the capillary and venous blood samples described in Table 1 above. Fig. 6B is a plot of the correlation of Δ S for the same data with the composite index value of equation 12. R of the two figures²The values are 0.5998 and 0.7268, respectively, indicating an improvement of the dependence of the complex exponential function on Δ S of about 21% over the dependence of the R4/3 exponential function on Δ S (0.7269-0).5998)/0.5998). Similarly, fig. 6C and 6D plot the dependence of Δ S on the R4/3 index value (fig. 6C) and the dependence of Δ S on the composite index value of equation 12 (fig. 6D) for capillary and venous blood samples at 18 ℃. Comparing R4/3 index value with R of composite index function²Values (0.6307 and 0.7154, respectively) show that the dependence of the complex exponential function on Δ S is improved by about 13.5% over the dependence of the R4/3 exponential function on Δ S (0.7154-0.6307)/0.6307).

The slope deviation, Δ S, and/or associated complex exponential function may be normalized to represent% -bias of the correlation of analyte concentration to output signal. In the normalization process, the slope deviation, the exponential function or complex exponential function, or other parameters are adjusted (multiplied or divided, etc.) by variables to reduce statistical effects caused by parameter changes, improve differences caused by parameter changes, normalize parameter measurements, or combinations thereof.

Table 4 below compares the measured raw glucose concentration to the compensated glucose concentration resulting from R4/3+ Temp exponential function compensation and complex exponential function compensation including a temperature term. In addition to the Standard Deviation (SD) of the combined deviation of the total number of data, the percentage of data previously described for the donor study described in table 1 that fell within the ± 10%, ± 8% and ± 5% combined deviation limits was determined. The samples are analyzed using gated amperometric input signals, wherein selected intermediate output signals are recorded from the pulses.

TABLE 4 Compensation of R4/3+ Temp exponential function and Complex exponential function

Using a prediction function f (predictor) a₁*R4/3+a₀R4/3+ Temp exponential function compensation is performed and by comparing deltaS_cal(observed from recorded current values) and R4/3, where a₁And a₀Respectively, slope and intercept. Temperature control of dataSensitivity Δ S_TThe following relationship is also used to determine:

ΔS_T＝f(Index)_Temp＝c₁*T+c₀(equation 14) of the process,

wherein, f (index)_TempAs mentioned above, T is the temperature, c₁And c₀Respectively, slope and intercept.

The corrected glucose concentration is then determined using the following relationship:

G_corr＝(i-Int)/(S_cal+ΔS_T+ f (predictor)) (equation 15),

where i is the output signal value of the biosensor system, Int is the intercept in the reference correlation equation, and G_corrIs the corrected glucose concentration of the sample.

The percentage of data points falling within the combined deviation limits of + -10%, + -8% or + -5% (corrected glucose sample concentration) is given by the relation G_corr-G_ref(G of the sample)_refLess than 75mg per 1/10 liters of glucose (mg/dL)), where G_refIs the reference glucose concentration of the sample as determined by the YSI reference instrument. Relation 100% (G)_corr-G_ref)/G_refThe percent corrected glucose sample concentration that falls within the limits for data points greater than or equal to 75mg/dL is determined.

Using error parameters, temperature values, G determined from the intermediate current of the sample_rawComplex exponential compensation is performed by selecting terms, constants and weighting coefficients as previously described. The p-values are used to perform an exclusion test of terms to determine which terms are ultimately included in the composite exponential function f (CIndex). Then compares Δ S_calAnd f (CIndex) to obtain Δ S_cal＝b₁*f(CIndex)+b₀Wherein b is₁And b₀Respectively, slope and intercept. When b is₁About 1 and/or b₀About 0, f (CIndex) is about equal to Δ S without one or both of these modifications. Image needleThe percentage of data points (corrected glucose sample concentration for each sample) that fall within the combined deviation limits of + -10%, + -8%, or + -5% was determined as compensated for by the R4/3+ Temp index function above.

When considering the percentage of analyte concentration that falls within the narrowest ± 5% combined bias range, the R4/3+ Temp exponential function compensation brings about 72% of the total ("all") sample into that range, while the complex exponential function compensation brings about 82% of the total ("all") sample into that range. This represents an increase of approximately 14% (82-72)/72 x 100) in the total number of corrected analyte concentration values that fall within the narrowest ± 5% combined deviation limit. Although both methods include compensation for temperature differences, a significant enhancement of the measurement performance provided by the composite exponential function compensation over the R4/3+ Temp exponential function compensation can also be observed. Thus, at a measurement performance cutoff of ± 5% combined bias limit, the patient's analysis using the composite index function compensated glucose biosensor system required a reduction of approximately 14% over the same glucose biosensor system compensated using the R4/3+ Temp index function that was discarded and repeated. At the ± 5% combined deviation limit, the same glucose biosensor system without compensation would require about 56% of the glucose analysis to be discarded, making the uncompensated system practically useless for achieving measurement performance cut off at the ± 5% combined deviation limit. A significant reduction in the standard deviation of the deviation of each of the four individual data totals between the R4/3+ Temp exponential function compensation and the composite exponential function compensation was observed.

Figure 6E depicts a graph of hematocrit sensitivity of the combined bias —% Hct. For the uncompensated glucose concentration measurements, the complex exponential function compensation reduced the hematocrit sensitivity from about-1.11 (bias/% -bias)/% Hct to about-0.3 (bias/% -bias)/% Hct, a reduction of about 70%. Thus, the complex exponential function compensation substantially reduces the sensitivity of the analysis system to the reduction in measurement performance from hematocrit bias.

In addition to Δ S, the exponential function may be expressed as Δ S/S, i.e., a normalized form of the slope deviation. Thus, Δ S/S mayInstead of deltas. The normalization can be performed, for example, by the relation Δ S/S_calOr S/S_calTo be implemented. Thus, the slope deviation Δ S in equation 7 can be obtained by referring to the slope S of the correlation equation_calIs normalized to thereby obtain Δ S/S_calA compensating correlation with an exponential function.

In equation 7, Δ S is divided by S_calI.e. of the formula:

(equation 16).

ΔS/S_calMay be replaced by a prediction function f (predictor) which may include a complex exponential function and may be expressed as:

ΔS/S_cal＝f(predictor)＝c₁*f(CIndex)+c₀(equation 17).

The prediction function f (predictor) of equation 17 may be substituted into equation 16:

(equation 18).

Solving the slope deviation Δ S to obtain the following relation:

ΔS＝S_cal*f(predictor)＝S_cal*(c₁*f(CIndex)+c₀) (equation 19).

By S_calNormalization of the slope deviation Δ S may substantially eliminate S_calMay have an effect.

The slope deviation Δ S in equation 7 can also be obtained by multiplying by the normalized slope function S_NMLTo be normalized to obtain S_NMLA compensating correlation with a complex exponential function. Normalized slope function S_NMLWatch capable of showingShown below:

(equation 20)

Substituting equation 20 into equation 7 and replacing S with the prediction function f (predictor)_NMLThe following relationship is obtained:

(equation 21).

FIG. 1C shows a method for determining a complex exponential function based on the adjusted hematocrit and donor blood sample (as used in the measurement device). In step 122, a plurality of test sensors are utilized to determine a tentative glucose concentration for a plurality of hematocrit-adjusted blood samples having known reference glucose concentrations under a plurality of environmental conditions. A reference instrument can be used to determine a known analyte concentration. In step 123, the slope and intercept of the reference correlations of the plurality of detection sensors are determined from the determined and known glucose concentrations at the reference temperature and the reference% Hct. In step 124, reference glucose concentrations are determined for a plurality of donor blood samples. Donor blood samples may have varying glucose concentrations and hematocrit levels. The reference glucose concentration of a plurality of donor blood samples can be determined at a reference temperature. In step 125, the plurality of hematocrit-adjusted blood sample glucose concentration data is combined arbitrarily with the plurality of donor blood sample glucose concentration data. In step 126, terms for one or more output signal values are selected from the data. Items may also be selected for one or more physical characteristics, environmental conditions, concentration values, and the like. In step 127, the weighting coefficients and arbitrary constants for the terms are determined. In step 128, the terms contained in the complex exponential function, the corresponding weighting coefficients, and any constants are selected.

Table 5 below provides measured glucose concentration data for capillary and venous blood samples (about 106 samples) and samples with venous blood added to adjust the blood cell concentration content of the samples to about 20% Hct to about 60% Hct (about 60 samples). Thus, a hematocrit-adjusted blood sample is prepared, as generally described in step 122 of FIG. 1C. Unlike the previous determination of analyte concentrations from the donor study described previously with respect to table 1, the glucose concentrations of table 5 were determined by using a complex exponential function derived from different blood samples, rather than the blood sample used for the analysis of glucose. Therefore, the complex exponential function applied to the measuring device to correct the deviation in table 5 was determined in advance from the different present totals. The exclusion term in the complex exponential function was selected using a p-value exclusion test with an exclusion value of 0.05. After exclusion, the terms retained in the complex exponential function are: r4/3, R5/4, R5/4G_raw、R5/4*Temp、R4/3*Temp、R4/3*R5/4、R4/3*R5/4*G_rawR4/3R 5/4 Temp and Temp. The complex exponential function includes positive and negative weighting coefficients for the terms and an initial constant.

The compensation equation is used to determine a corrected glucose concentration for a blood sample having the general formula:

G_corr＝(i–Int)/(S_cal(1+ f) (predictor)) (equation 22),

wherein f (predictor) is b₁*f(CIndex)+b₀Δ S/S, i.e., a normalized version of the slope deviation.

When the prediction function is close to Δ S/S, if b₁1 ± 0.2, a theoretical value of 1 may be used instead of b₁(ii) a Preferably, when b is₁When 1 ± 0.15, the theoretical value 1 is used instead of b₁(ii) a And may be more preferred when b₁When 1 ± 0.1, the theoretical value 1 is used instead of b₁. When the prediction function is close to Δ S/S, if b₀0 ± 0.3, the theoretical value 0 may be used instead of b₀(ii) a Preferably, when b is₀When 0 ± 0.2, the theoretical value 0 is used instead of b₀(ii) a And may be more preferred when b₀When 0 ± 0.1, the theoretical value 0 is used instead of b₀. Can be used in₁Theoretical value of or b₀Theoretical value of (b)₁And b₀The theoretical values of both are measured using other deviation data. Except that b is replaced by theoretical values 1 and 0₁And/or b₀In addition, a predetermined value in a lookup table may be used instead of b according to the same deviation data or other deviation data₁And/or b₀。

For the total number of data, b₁Is 1.08, b₀And was 0.012. Thus, b₁Is estimated as 1, and b₀Is estimated to be 0. Elimination of b from the equation₁And b₀The following relationship is obtained:

G_corr＝(i-Int)/(S_cal(1+ f (cindex)) (equation 23).

Thus, the output current value responsive to the sample glucose concentration is converted to a modified glucose concentration for the sample using a complex exponential function representing Δ S/S. Alternatively, the corrected glucose concentration value may be determined from the uncorrected glucose concentration value using a complex exponential function and an equation having the general formula:

G_corr＝G_raw/(1+ f (CIndex)) (equation 24).

TABLE 5-f comparison of (CIndex) Compensation analysis with uncompensated analysis

For samples with an artificially expanded hematocrit range (from 30-50% to about 20-60%), the complex exponential function correction brought at least 96% of the measured analyte concentration within the ± 10% combined deviation limit and almost 94% of the measured analyte concentration within the ± 8% combined deviation limit. This is a significant improvement over the uncompensated analysis where only about 58% of the spiked vein samples fall within the ± 10% combined deviation limit: more than 60% ((96-58)/58 x 100). The standard deviation of the combined deviation for each of the four totals of data was also reduced by at least 1.5 units for the corrected density values relative to the uncorrected density values. The grouping in fig. 6F that is closer to the vicinity of the zero-combination bias line shows greater accuracy and precision of the compensated analyte concentration relative to the uncompensated analyte concentration. These results demonstrate that complex exponential functions can be transferred between different samples and can be determined in the laboratory for later use in a measurement device.

Fig. 7 depicts a schematic diagram of a biosensor system 700 for determining an analyte concentration in a biologic fluid sample. The biosensor system 700 includes a measurement device 702 and a detection sensor 704, which may be implemented as any analytical instrument in the form of a desktop device, a portable or handheld device, or the like. The measurement device 702 and the detection sensor 704 may be adapted to implement an electrochemical sensor system, an optical sensor system, a combination thereof, or the like. The biosensor system 700 uses at least one Δ S value to adjust the following correlations: the correlation is used to determine the analyte concentration from the output signal. This correlation of Δ S modulation may improve the measurement performance of the biosensor system 700 when determining the analyte concentration of a sample. The biosensor system 700 may be used to determine analyte concentrations, including those of glucose, uric acid, lactate, cholesterol, bilirubin, and the like. Although a particular configuration of the biosensor system 700 is shown, it may have other configurations, including configurations with other elements.

The detection sensor 704 has a base 706, the base 706 forming a reservoir 708 and a channel 710 with an opening 712. The reservoir 708 and channel 710 may be covered by a cap with a vent. The reservoir 708 defines a partially enclosed volume. The reservoir 708 may contain a component (e.g., a water-swellable polymer or porous polymer matrix) that helps retain the liquid sample. The reagent may be deposited in the reservoir 708 and/or the channel 710. The reagent may include one or more enzymes, binders, mediators, and the like. The reagent may comprise a chemical indicator for the optical system. The detection sensor 704 may also have a sample interface 714 disposed adjacent to the reservoir 708. The sample interface 714 may partially or completely surround the reservoir 708. The detection sensor 704 may have other configurations.

In an optical sensor system, the sample interface 714 has a light inlet or aperture for viewing the sample. The light inlet may be covered with a substantially transparent material. On both sides of the reservoir 708, the sample interface may have optical inlets.

In an electrochemical system, sample interface 714 has conductors that connect to the working electrode and the counter electrode. The electrodes may be located substantially in the same plane, or in multiple planes. The electrodes may be disposed on a surface of the base 706 that forms the reservoir 708. The electrodes may protrude or be inserted into the reservoir 708. The dielectric layer may partially cover the conductor and/or the electrode. Sample interface 714 may have other electrodes and conductors.

The measurement device 702 includes circuitry 716 connected to a sensor interface 718 and a display 720. The circuit 716 includes a processor 722 coupled to a signal generator 724, an optional temperature sensor 726, and a storage medium 728.

The signal generator 724 is responsive to the processor 722 to provide an electrical input signal to the sensor interface 718. In an optical system, the electrical input signal may be used to operate or control the detector and light source in sensor interface 718. In an electrochemical system, an electrical input signal may be transmitted by sensor interface 718 to sample interface 714, thereby applying the electrical input signal to a sample of biological fluid. The electrical input signal may be a potential or a current and may be constant, varying, or a combination thereof (e.g., applying an AC signal with a DC signal bias). The electrical input signal may be applied in the form of a single or multiple pulses, sequences or periods. The signal generator 724 may also record the output signal from the sensor interface as a generator-recorder.

An optional temperature sensor 726 measures the temperature of the sample in the reservoir of the detection sensor 704. The temperature of the sample may be measured, calculated from the output signal, or it may be assumed that the sample temperature is the same as or similar to the measured ambient temperature or the temperature of the device implementing the biosensor system. The temperature may be measured using a thermistor, thermometer, or other temperature sensing device. Other techniques may also be used to determine the sample temperature.

The storage medium 728 may be a magnetic, optical, or semiconductor memory, other storage device, or the like. The storage medium 728 may be a fixed storage device or a removable storage device such as a remotely accessed memory card.

Processor 722 performs analyte analysis and data processing using computer readable software code and data stored in storage medium 728. Processor 722 may initiate analyte analysis in response to detecting the presence of sensor 704 at sensor interface 718 and applying a sample to detection sensor 704, or in response to a user input or the like. Processor 722 instructs signal generator 724 to supply an electrical input signal to sensor interface 718. Processor 722 receives the sample temperature from temperature sensor 726. Processor 722 receives output signals from sensor interface 718. An output signal is generated in response to a reaction of an analyte in the sample. Optical systems, electrochemical systems, etc. may be used to generate the output signal. Processor 722 determines an analyte concentration compensated with Δ S from the output signal using the correlation equation described previously. The results of the analyte analysis may be output to the display 720 and may be stored in the storage medium 728.

The equation of correlation between analyte concentration and output signal can be represented graphically, mathematically, or a combination thereof. The correlation equation may include one or more exponential functions. The correlation equation may be represented by a Program Number Assignment (PNA) table, another look-up table, etc. stored in the storage medium 728. The constants and weighting coefficients may also be stored in the storage medium 728. The instructions for performing the analyte analysis may be provided by computer readable software code stored in the storage medium 728. The code described above may be object code or any other code that describes or manipulates the functionality described herein. The data from the analyte analysis may be subjected to one or more data processing in processor 722, including determining decay rates, K constants, ratios, and/or functions, and the like.

In an electrochemical system, the sensor interface 718 has contacts that connect or electrically communicate with conductors in the sample interface 714 of the detection sensor 704. Sensor interface 718 transmits the electrical input signal from signal generator 724 to a connector in sample interface 714 via these contacts. The sensor interface 718 also transmits output signals from the sample to the processor 722 and/or the signal generator 724 via these contacts.

In optical systems that absorb light and generate light, sensor interface 718 includes a detector that collects and measures light. The detector receives light from the liquid sensor via a light inlet in the sample interface 714. In an optical system that absorbs light, sensor interface 718 also includes a light source such as a laser, light emitting diode, or the like. The incident light beam may have a wavelength selected to facilitate absorption by the reaction products. Sensor interface 718 directs an incident light beam from a light source via a light inlet in sample interface 714. The detector may be positioned at an angle, such as 45 deg., to the light entrance to receive light reflected back from the sample. A detector may be disposed adjacent to the light inlet on the other side of the sample from the light source, receiving light transmitted through the sample. The detector may be located at another location to receive reflected and/or transmitted light.

The display 720 may be analog or digital. The display 720 may include an LCD display, LED display, OLED display, vacuum fluorescent display, or other display suitable for displaying numerical readings. Other displays may be used. The display 720 is in electrical communication with the processor 722. The display 720 may be separate from the measurement device 702, such as when the display 720 is in wireless communication with the processor 722. Alternatively, display 720 may be remote from measurement device 702, such as when measurement device 702 is in electrical communication with a remote computing device, an infusion pump, or the like.

In use, a liquid sample for analysis is transferred into the reservoir 708 by introducing liquid into the opening 712. The liquid sample flows into the reservoir 708 via the channel 710 and fills the reservoir 708 while venting the previously contained air. The liquid sample chemically reacts with reagents deposited in the channel 710 and/or reservoir 708.

The detection sensor 702 is disposed adjacent to the measurement device 702. The adjacent position includes a position where sample interface 714 is in electrical and/or optical communication with sensor interface 718. Electrical communication includes the transfer of input and/or output signals between contacts in sensor interface 718 and conductors in sample interface 714. Optical communication includes the transfer of light between an optical inlet in sample interface 714 and a detector in sensor interface 718. Optical communication also includes the transfer of light between the light inlet in sample interface 714 and the light source in sensor interface 718.

Processor 722 receives the sample temperature from temperature sensor 726. Processor 722 instructs signal generator 724 to provide an input signal to sensor interface 718. In the optical system, sensor interface 718 operates the detector and light source in response to the input signal. In an electrochemical system, sensor interface 718 provides the input signal to the sample through sample interface 714. Processor 722 receives output signals generated in response to the analyte redox reaction in the sample as previously described.

Processor 722 determines an analyte concentration of the sample. The measurement device adjusts the correlation between the analyte concentration and the output signal based on the at least one Δ S value. The analyte concentration is determined from the slope adjusted correlation and the output signal. As previously mentioned, normalization techniques may also be used.

While various embodiments of the invention have been described, it will be apparent to those of ordinary skill in the art that other embodiments and implementations are possible within the scope of the invention.

Claims (34)

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

generating at least one output signal value in response to the analyte concentration in the sample;

at least one deltas value is determined from at least one complex exponential function,

the at least one as value represents a slope difference between a slope of a reference correlation between the output signal and a known analyte concentration and an assumed slope of a line capable of providing an output signal value for the analyte concentration in the sample without deviation,

the complex exponential function comprises at least two terms, each of the at least two terms being multiplied by a weight coefficient, wherein the weight coefficient is a value other than 1 or 0, and at least two weight coefficients are independent of each other; and

determining an analyte concentration in the sample from a slope compensation equation comprising at least one complex exponential function and the output signal value,

wherein the slope compensation equation adjusts the slope of the reference correlation using the at least one Δ S value.

2. The method of claim 1, wherein the percent deviation of the determined analyte concentration is substantially linear with the at least one Δ S value.

3. The method of claim 1 or 2, wherein the at least one reference correlation is pre-determined using a reference instrument.

4. The method of claim 1 or 2, wherein the slope compensation equation is expressed as follows:

wherein A is_corrIs the determined analyte concentration, i is the value of the output signal generated by the biosensor system, Int is the intercept of the reference correlation, S_calIs a reference correlation and f (predictor) is a prediction function comprising said complex exponential function.

5. The method of claim 1 or 2, wherein the complex exponential function further comprises at least one constant not equal to zero.

6. The method of claim 1 or 2, wherein one of the at least two terms comprises a raw analyte concentration value of the sample.

7. The method of claim 1 or 2, wherein one of the at least two terms comprises temperature.

8. The method of claim 1 or 2, wherein one of the at least two terms comprises an error parameter responsive to% Hct of the sample.

9. The method of claim 1 or 2, wherein one of the at least two terms comprises an error parameter independently selected from an intermediate output signal value and a value other than the output signal value.

10. The method of claim 9, wherein the error parameter is responsive to an error source that varies the at least one output signal value.

11. The method of claim 9, wherein the error parameters are independently responsive to different error sources, andand has a value of and Δ S_calR of at least 0.3²Correlation, wherein said Δ S_calIs represented as follows:

wherein A is_refIs the reference analyte concentration, i is the output signal value generated by the biosensor system, Int is the intercept of the reference correlation, S_calIs the slope of the reference correlation.

12. The method according to claim 1 or 2, wherein the at least one Δ S value determined by the complex exponential function has a value corresponding to Δ S_calR of at least 0.6²Correlation, wherein said Δ S_calIs represented as follows:

wherein A is_refIs the reference analyte concentration, i is the output signal value generated by the biosensor system, Int is the intercept of the reference correlation, S_calIs the slope of the reference correlation.

13. The method of claim 1 or 2, wherein determining the analyte concentration in the sample further comprises determining the analyte concentration for a plurality of samples, and a complex exponential function provides the analyte concentration determined for the plurality of samples with a standard deviation value of less than 5 for the plurality of sample combined deviations.

14. The method of claim 13, wherein the determined analyte concentrations of the plurality of samples fall within a combined deviation limit of ± 10%, ± 8%, or ± 5%.

15. The method of claim 1 or 2, further comprising:

a second complex exponential function, wherein at least two Δ S values are obtained by transforming different error parameters through the complex exponential function and the second complex exponential function; or

An exponential function, wherein at least two Δ S values are derived by transforming different error parameters through the composite exponential function and the exponential function.

16. The method of claim 1 or 2, further comprising: normalizing at least one Δ S value, wherein the normalization is in response to a slope of a reference correlation equation or in response to a normalized slope function.

17. The method of claim 1 or 2, said at least two terms being selected by at least one exclusion test comprising:

selecting a plurality of error parameters as terms that may be included in the complex exponential function;

determining an exclusion value for each selected term;

applying at least one exclusion test to the exclusion values to identify one or more items excluded from the complex exponential function, and

excluding at least one item identified as excluded from the complex exponential function.

18. A biosensor system for determining the concentration of an analyte in a sample, the biosensor system comprising:

a detection sensor having a sample interface adjacent to a reservoir formed by a sensor strip; and

a measurement device having a processor connected to a sensor interface, the sensor interface in electrical communication with the sample interface, and the processor in electrical communication with a storage medium,

wherein at least one reference correlation between the output signal and the known analyte concentration is present in the storage medium,

wherein the processor determines an output signal value responsive to the concentration of the analyte in the sample from the sensor interface,

wherein the processor determines at least one Δ S value from at least one complex exponential function,

the at least one as value represents a slope difference between a slope of the at least one reference correlation and an assumed slope of a line capable of providing the output signal value of the analyte concentration in the sample without deviation,

the complex exponential function comprises at least two terms, wherein each of the at least two terms is multiplied by a weight coefficient, wherein the weight coefficient is a value other than 1 or 0, and at least two weight coefficients are independent of each other, and

wherein the processor determines the analyte concentration in the sample from a slope compensation equation comprising at least one complex exponential function and the output signal value,

wherein the slope compensation equation adjusts the slope of the reference correlation using the at least one Δ S value.

19. The system of claim 18, wherein the measurement device is portable.

20. The system of claim 18 or 19, the detection sensor arranged and configured to have a linear relationship between percent deviation of the determined analyte concentration and Δ S.

21. The system of claim 18 or 19, wherein the storage medium stores at least one reference correlation that is pre-determined using a reference instrument.

22. The system of claim 18 or 19, wherein the processor further compensates the output signal value using an intercept from the at least one reference correlation and a prediction function comprising the complex exponential function.

23. The system of claim 18 or 19, the complex exponential function further comprising at least one constant not equal to zero.

24. The system of claim 18 or 19, wherein one of the at least two terms comprises a raw analyte concentration value of the sample.

25. The system of claim 18 or 19, wherein one of the at least two terms comprises temperature.

26. The system of claim 18 or 19, wherein one of the at least two terms comprises an error parameter responsive to% Hct of the sample.

27. The system of claim 18 or 19, wherein one of the at least two terms comprises an error parameter independently selected from an intermediate output signal value and a value other than the output signal value.

28. The system of claim 27, wherein the error parameter is responsive to an error source that varies the at least one output signal value.

29. The system of claim 27, wherein the error parameters are independently responsive to different error sources and have a variance with as_calR of at least 0.3²Correlation, wherein said Δ S_calIs represented as follows:

wherein A is_refIs the reference analyte concentration, i is the output signal value generated by the biosensor system, Int is the intercept of the reference correlation, S_calIs the slope of the reference correlation.

30. The system of claim 18 or 19, wherein at least one Δ S value determined by the processor from the composite exponential function has a value corresponding to Δ S_calR of at least 0.6²Correlation of, whereinThe Δ S_calIs represented as follows:

wherein A is_refIs the reference analyte concentration, i is the output signal value generated by the biosensor system, Int is the intercept of the reference correlation, S_calIs the slope of the reference correlation.

31. The system of claim 18 or 19, wherein the processor further determines an analyte concentration in a plurality of samples, and the composite exponential function provides a standard deviation value for the determined analyte concentration of the plurality of samples of less than 5 for the combined deviation of the plurality of samples.

32. The system of claim 31, wherein the analyte concentration of the plurality of samples determined by the processor falls within a combined deviation limit of ± 10%, ± 8%, or ± 5%.

33. The system of claim 18 or 19, wherein the processor normalizes at least one Δ S value, wherein the normalization is in response to a slope of a reference correlation equation or in response to a normalized slope function.

34. The system of claim 18 or 19, the at least two terms being selected by at least one exclusion test comprising:

selecting a plurality of error parameters as terms that may be included in the complex exponential function;

determining an exclusion value for each selected term;

applying at least one exclusion test to the exclusion values to identify one or more items excluded from the complex exponential function, and

excluding at least one item identified as excluded from the complex exponential function.