WO2014056951A1

WO2014056951A1 - Analytical method

Info

Publication number: WO2014056951A1
Application number: PCT/EP2013/070988
Authority: WO
Inventors: Piotr Garstecki; Mateusz TOMALA; Adam WARCHULSKI
Original assignee: PZ CORMAY SA
Current assignee: PZ CORMAY SA
Priority date: 2012-10-08
Filing date: 2013-10-08
Publication date: 2014-04-17
Anticipated expiration: 2015-04-08
Also published as: PL401098A1

Description

ANALYTICAL METHOD

The subject matter of the invention is an analytical method involving determining, with very high precision, small volumes of liquid samples in a microfluidic system. More specifically, the invention involves a method for determining small volumes of liquids using image analysis. The invention comprises specific sequence of experimental operations and measurements, and also includes a mathematical model allowing for calculation of droplet volume by measuring very accurately the length of the droplet.

The drive for miniaturisation of objects used in technology is related to the ability to create them, but also to creation of tools that allow for using them - in particular to measure, monitor and operate them. Pharmaceutical and pharmacological departments of research institutions and companies are trying to reduce the consumption of various substances (samples collected from patients and chemical reagents), which generates the demand for measurement systems miniaturised down to the microscale and results in the necessity of using measurement equipment adapted to that scale.

At present, the most popular method for measuring volume is precise dosing - a method relying on calibration of dosing system components so as to know indirectly the volume of the liquid measured out (for instance, if one knows the characteristics of a valve - the valve's opening time can be adapted to control the dosed volume; if one knows the characteristics of a syringe - one can mechanically put a limitation on the piston movement and so control the volume). This approach is implemented in robotic stations conducting reactions inside well plates that operate on reagent volumes in the range of single microliters or more, with frequencies in the range of tenths of a Hertz, or less. Likewise, robotic stations conducting reactions inside cuvettes operate on reaction volumes ranging from a few tens to a few hundred microliters. The rate of generation of reaction mixtures does not exceed a few dosing operations per second. In both techniques, the accuracy of dosing the volumes of solutions reaches the level of a few percent or better, with the best solutions reaching the precision of about 1%. These solutions require, however, technologically advanced fluid supply systems and fluid volume dispensing elements -very high operation reproducibility is a crucial point here. An example of such a device is the automatic pipetting station manufactured by Eppendorf^®. The volumes measured by these devices range from 5 μΙ up to ΙΟΟΟμΙ, single device, however, is able to measure a range of volumes comprising one decade only with a measurement error of 5% or better. For volumes less than a few microliters the devices are not suitable for precise applications.

Since recently, microfluidic techniques have been developed for handling smaller fluid volumes. A lab-on-a-chip enables to carry out experiments and operations on samples of a few microliters volume. Especially promising is the use of droplets generated in microchannels as miniaturised reactors, because of their very small volume, ranging from picoliters, through nanoliters up to microliters. Typically, droplet-based microsystems comprise a multiplicity of microfluidic channels, with their inlets and outlets, which may interconnect within the microfluidic chip, wherein, in particular, droplets of solutions surrounded by immiscible continuous phase are generated. Typically, the technique used for volume measurement is a copy of the precise dosing, and relies on the assumption that droplets produced with constant parameters of generation are of the same size (differing practically by 1-3% of the volume).

For a given microfluidic system with constant length and width (if square cross- section is assumed) of each channel, the size of droplets produced by the system is a function of a minimum of 7 parameters (flow rates of both phases, viscosities, densities and interfacial tension). A drawback of the method is that each of these parameters must be constantly controlled, which translates into an error in reproducibility of droplet volumes that for majority of the most advantageous cases is in the range 1-5% (Hao Gu, Michel H. G. Duits and Frieder Mugele, Int. J. Mol. Sci., 12, 2011, 2572-2597).

The diagram shown in Fig. 1 presents the percent change of the droplet's length in relation to the mean droplet's length for the entire series. The lengths were obtained for constant values of the seven parameters mentioned above, in a T-junction. The T-junction is a method for connecting channels at right angle and creating of a crossing - junction, characteristic for microfluidic techniques; the shape of the junction resembles the letter T. The main channel is usually used for supplying the dispersion medium to the junction, whereas the dispersed phase flows in the auxiliary channel. A T-junction has two inlets and one outlet (Thorsen PRL 2006, Garstecki LoC 2006).

Another method for generating droplets of predetermined volume is to use microfluidic valves. Typically, a valve is a device comprising a piston (or a membrane), enclosed in a housing with an inlet and an outlet for the liquid. The valve is electrically controlled - it changes its state upon application of voltage (depending on the configuration from closed to open or from open to closed) - as the piston or the membrane unblocks or blocks the stream, respectively, precise control over the valve allows for accurate dosing of liquid volume based on the liquid supply pressure at the valve and the valve opening time. An example of such a device is a microvalve manufactured by The Lee Company^® with the trade name INKA1202160D. These valves require constant flow monitoring and precise control.

The reproducibility of the volume of a liquid dosed by a given valve was examined in a test wherein the valve was opened for water flow for a specific period of time, and the mass of water that passed through the valve was recorded. The reproducibility of the mass of the sum of droplets obtained with constant valve opening time and pressure was in the most favourable case 0.5% (Table 1).

Table 1. Reproducibility measurements for generation of the mass of liquid flowing through a valve under given pressure and with given opening time

X - mean value, SD - standard deviation, RSD- relative error, i.e., SD/X*100%

In a summary, the existing methods for measuring mentioned above require significant expenditures to control the droplet's volume. In advantageous cases, from 3 (for valves: water pressure, opening time, closing time) to 7 (for microfluidic techniques) parameters must be controlled all the time droplets are generated, yielding the volume error for a single droplet of from 1 to 5%. In the state of the art there are no accurate methods for measuring volume of a droplet after it has been generated.

The method invented and disclosed in the present patent application allows for generation and subsequent precise volume determination of a single droplet of a liquid sample based on the length of the droplet as precisely calculated from droplet's images. The method for calculation uses 2 parameters only that need to be determined only once for a given geometry of the microfluidic system (chip), wherein the droplets are generated. The method allows for subsequent use of the measured droplet in an analytical assay to establish a concentration of an analyte in the liquid sample.

An analytical method allowing for the determination of a concentration of an analyte in a liquid sample according to the present invention comprises the steps of: i) generation and a very precise determination of volume of an aliquot of the liquid sample in the form of at least one droplet of the liquid sample surrounded by an immiscible carrier liquid and contained in a microfluidic channel of a microfluidic system, ii) introduction of said at least one droplet surrounded by said carrier liquid into a reservoir where it is mixed with a reagent comprising at least one ingredient which reacts specifically with the analyte in the liquid sample, iii) measurement of an analytical signal from the mixture resulting from step (ii), e.g. photometrically, iv) determining the concentration of the analyte in the liquid sample based on the analytical signal from step (iii) and the volume of the aliquot of the liquid sample from step (i).

Preferably, the liquid sample is a sample of a body fluid and the method allows for the determination of a concentration of one or more biochemical constituents thereof. Preferably, the very precise determination of volume of a droplet of a liquid sample in a microfluidic system in method step (i) is based on an analysis of an image obtained from a camera, in particular a digital camera, of the microfluidic system supplied with liquids from a dosing system, preferably a pump, and comprises the following steps: a) obtaining of a two-dimensional image of a channel of the microfluidic system containing a minimum of one droplet of the liquid sample, b) determination of the length of the droplet of the liquid sample by analysing the image, c) determination of the volume of the said droplet by employing a mathematical model relating the droplet's volume to its length in the image, in a given geometry of the microfluidic system.

Preferably, a camera is used, in particular a digital camera, installed over or under the microfluidic system.

Preferably, in step a) the image obtained from the camera is over-exposured, preferably for 7/8 of the maximum opening time of the shutter (exposure time) for given settings of the camera.

Preferably, series of droplets are used with a length of from 3 times larger than the width of the channel to 8 times larger than the width of the channel of the microfluidic system.

Preferably, microfluidic systems are used that generate droplets of fluid and comprise a T-junction and/or a flow focusing junction.

Preferably, in the microfluidic system, channels of square cross-section are used, preferably with sides from 0.1 mm to 2 mm , more preferably 0.2, 0.4 or 1 mm.

Preferably, a material from which the microfluidic system is fabricated and the carrier liquid are chosen such that the carrier liquid wets the walls of the microfluidic channel preferentially over the liquid sample, preferably the droplet of the liquid sample does not wet the walls of the microfluidic channel.

Preferably, step (c) employs a mathematical model based on the formula

V = aL - where: V means the droplet volume, L means the droplet length given in unit elements of the image (pixels), a is a coefficient characterizing the channel and the camera used, specifying the effective droplet volume per unit element of the image (pixel), and β is a correction to the droplet volume.

I n such a case, preferably, a and β constants are calculated from the formula :

. P

^{E L} _ ^q ~ tsr

tC H

where: EL means the sum of droplet lengths, tc means the total time of droplet generation, q means the flow of water, and tsr means the mean time of single droplet generation.

Preferably, in step b) two algorithms are used, wherein the first algorithm checks if the image comprises an entire droplet, and the second algorithm determines the front and rear boundaries of the said entire droplet in the image, and subsequently determines the length of the said droplet with a curve fitting method.

The first algorithm preferably analyses the image along a first line, running in the image inside the microfluidic channel and in parallel to the direction of flow, preferably the longitudina l axis of symmetry of the cha nnel. I n such case, the first algorithm uses intensity (or brightness) of pixels along said line as a function of their coordinate on a n axis parallel to the direction of flow to check whether two peaks of this function are present in the image, representing the front and rear boundary of a droplet, respectively. Preferably, the first algorithm performs a convolution of two functions: intensity (or brightness) of pixels along the said line in the image as a function of their coordinate on an axis pa rallel to the direction of flow and a polynomial function, preferably a polynomial of degree 3. The resulting function facilitates the determination of the said peaks and the values of their extremes.

Preferably, the first algorithm further ana lyses the image a long a second line, parallel to the first line and spaced apart therefrom, located inside the channel and preferably at the channel's periphery. I n such case, the first algorithm uses intensity (or brightness) of pixels along said second line as a function of their coordinate on an axis parallel to the direction of flow, or preferably a convolution of said function with a polynomial, preferably of degree 3, to determine two peaks representing the front and rear boundary of the droplet. The first algorithm preferably calculates the dista nces between the extremes of the two peaks for both said lines and checks whether the distance is smaller for the said second line than for the said first line.

Preferably, the second algorithm analyses the image along at least one line, running in the image across the droplet and in parallel to the direction of flow, preferably including the longitudinal axis of symmetry of the channel, preferably a maximum possible number of such lines. In such case the second algorithm preferably determines pixels in said line whose brightness is below a threshold, representing front and rear boundaries of the droplet, then preferably chooses the two outermost of said pixels, thus determining the coordinates on an axis parallel to the direction of flow of two points marking the front and rear boundaries of the droplet. The procedure is repeated for each analysed line in the image to generate a set of points in the image (two for each line analysed) which mark the front and rear boundaries of the droplet.

Preferably, the second algorithm fits curves, preferably in the form of polynomials, most preferably of degree 4, to points in the image which mark the front and rear boundaries of the droplet, then computes the extremes of the fitted functions and calculates the length of the droplet as the distance between these extremes.

In a preferred embodiment variant of the present invention, step b) is repeated for multiple different images of the same droplet, preferably using from 2 to 100 images, more preferably from 5 to 20 images, and the length of the droplet is calculated as the arithmetic mean of the values determined for each image.

The invention will now be explained in more detail in a preferred embodiment, with reference to the accompanying figures, wherein:

Fig. 1 (state of the art) shows a series of droplets and the ratio of the length of each droplet to the mean length of droplets from the whole series;

Fig. 2 shows a test stand, where 1- column, 2 - camera, 3 - plate, 4 - outlet of optical fibre, 5 - base;

Fig. 3 shows channel images obtained with a camera; left - image obtained with normal exposure time, right - over-exposured image; Fig. 4 shows an image with a droplet at the most preferable setting of the camera parameters; black horizontal line (A) (thickened for visibility) is a single image line; diagrams in the lower part of the Figure: right - diagram showing intensity of pixels along the marked horizontal line (A) as a function of their coordinate on an axis parallel to the direction of flow before convolution, left - diagram showing the function resulting from the convolution;

E L

Fig. 5 shows a plot of the slope tc as a function of the normalised droplet length; the slope (vertical axis) in units [pixel/ms], droplet length (horizontal axis) is given as a multiple of the channel width;

Fig. 6 shows a plot of the mean time of single droplet generation as a function of normalised droplet length; the mean time of single droplet generation (vertical axis) in units [ms], the droplet length (horizontal axis) is given as the multiple of the channel width, and

Fig. 7 shows a typical second polycarbonate plate with three microfluidic channels.

Detailed description of the invention

A test stand for studying droplet formation and forcing droplet flow in microfluidic systems has been designed and constructed. At the same time, new image-analysis based methods of detection and handling of droplets have been developed.

Description of test stand

The test stand shown in Fig. 2 is composed of a column 1 that is rigidly and perpendicularly fixed to the base 5. Plate 3 is installed in the base 5 by making use of four rods fixing the distance. The distance of the plate 3 from the base 5 is 125 mm, and the plate is installed in parallel to the base. The camera 2 is fixed to the column 1, placed directly over the observed part of the plate 3, and subsequently positioned so as to obtain a clear image. The output of the optical fibre 4 is installed under the plate 3 to allow for a better image exposure. White light from a 5 W LED is directed to the optical fibre 4 and focused with a 10 mm diameter lens. In other embodiments, an array of 64 white LEDs placed in rows containing 8 LEDs each was used as the light source instead of a single LED. In addition, in the embodiment with the LED-array a matt glass was used to provide uniform light intensity. The matrix of the camera 2 is at a distance approximately 185 mm from the plate 3, and the lens is positioned with spacer rings at a distance 60 mm from the camera, and 72 mm from the plate with channels.

Description of preparation of the stage

The camera recorded images of the channel after the T-junction where the droplets are generated (Fig. 3). The droplets were generated by appropriate matching of flows of two fluids, of which one (continuous phase) wetted the channel walls more than the other (droplet phase).

It was noticed during the experiments that if the boundary formed by the droplet surface was assumed to be the usable signal, and the droplet surrounding - to be the noise, then the most preferable result for a given embodiment was obtained, when the image was over-exposured for 7/8 of the maximum opening time of the shutter (exposure time) for given settings of the camera. To increase the accuracy of the readout of phase boundaries, the camera field of view was narrowed so that only the phase boundaries were present in a given scene. The height of the image was adjusted so that the channel occupies the possibly largest fraction of the image, and the width was set to the maximum obtainable with the camera used.

It was noticed during the tests that the information obtained from the image analysis could be used in a method for determining the droplet's volume. It is essential that the information contained in an image (which by definition describes two dimensions) could be used to describe a 3-dimensional object, a droplet. When treated as a structure in microfluidic channels and considered a body, the droplet can be preferably divided into two terminal sections with cross-sections strongly depending (varying) with X, where X means the spatial coordinate measured along the channel, and a middle section, where, the droplet cross-section is constant to a very good approximation (i.e., does not vary with X). The shape of the droplet's cross-section in the middle section depends on many parameters, including interfacial tension, phase viscosities, and the shape of the channel lumen [Wong, JFM], but for low capillary numbers that are typical for microfluidic systems and applications of the present invention, the cross-section is constant to a very good approximation. Therefore, it can be taken to a good approximation that the volume contained in the middle section of a droplet is proportional to the length of the section. In spite of their complexity and dependence on the shape of the channel's lumen, the shapes of the terminal sections are also approximately constant for a given channel geometry, viscosities of fluids, surface tension, and low capillary numbers. Therefore, the volume of the terminal sections is constant, and consequently the volume of the entire droplet (V) is the sum of the constant volumes of terminal sections (V_k0ncowe) and a volume that is proportional to the length of the middle section:

Because the shape of terminal sections is fixed, the length of the middle section (Lmiddie) can be written as: liddle- Ldroplet 2* -.terminal/ wherefrom, after transformation, the equation can be simplified to the formula 1. Since a and β are unknown numerical constants, the method requires that they are determined by calibration, and the length of droplet can be expressed in any convenient units, in a preferred embodiment in pixels (relating to the digital image of the droplet, e.g., on the screen). Under the assumption that determined will be the volume of a droplet situated in a microfluidic channel, wherein said microfluidic channel is characterised by geometrical dimensions of its cross-section (e.g., diameter for a circular cross-section, or width and height for a rectangular cross-section), and after taking into account the postulate, that the determination should be performed using an image analysis (which determines the type of available data), a mathematical model has been developed in the form of the following formula:

V = aL - (formula 1) where:

V - the droplet's volume, a - the coefficient describing the channel and the image detector (camera) used, specifying the effective droplet volume per unit image element (pixel), β - the correction to the droplet's volume (taking into account all losses in the droplet's volume due to a not entirely uniform cross-section, characteristic for a given channel geometry and properties of the substances flowing through the channel), and L - the droplet's length given in any units, preferably in unit image elements (pixels).

The model does not have to account for details of the droplet's shape, it is sufficient that the droplet's cross-section is to a very good approximation constant in the middle section.

In an embodiment of the present invention, two algorithms were used to measure the droplet's length. The first algorithm comprised the checking, if a given frame (image) comprised an entire droplet. The second algorithm was used to find the phase boundaries in the frames which comprised droplets and to calculate droplets' lengths based on these boundaries. The inventors of the present invention noticed that, if the frame contained a droplet, the brightness (opposite to intensity) of pixels in a single line of the image as a function of X comprised two minima corresponding to phase boundaries (Fig. 4), whereas the minimum marking the phase boundary located farther from the junction generating the droplets is deeper, that is the pixel intensities at that minimum are higher (darker) than those at the other minimum. The effect, which in simple terms can be identified with the observation that„the front of a droplet is darker than its rear", was used to find if an entire droplet is contained in the scene, rather than two parts of different droplets. To facilitate the interpretation of the position and the valley values, the inventors used a convolution of the brightness (or intensity) of pixels in a single line of the image as a function of X with a polynomial function, in the most preferable case with a polynomial of degree 3. To additionally check for the presence of a droplet in the image, two such pixel lines are determined, the first line arranged in the image, for example, in the channel's symmetry axis, in parallel to the direction of flow, and the second line - parallel to the first one and spaced therefrom by some distance, inside the channel and preferably at the periphery of the channel. Then, the distances between the valleys marking the beginning and the end of the droplet in both these lines are determined, and if the distance in the first line is greater than that in the second (extreme) line, then it is known that the droplet is present in a given scene.

The algorithm for calculating the length of a droplet in the case described here relies on accurate determination of the front and rear boundaries of the droplet (phase boundaries) and calculation of the distance between their extreme points. Firsty, rough phase boundaries are determined by searching, in a given image frame comprising the droplet, for points where the pixel brightness is below a certain threshold. For each pixel line of the image (running across a droplet and in parallel to the direction of flow), of all the pixels in the said pixel line whose brightness is below the threshold, said pixels representing the rough front and rear boundaries of the droplet, the two outermost pixels are chosen. The operation yields points in a two-dimensional space (two points, representing the said two outermost pixels, per pixel line of the image) that mark out the phase boundaries. The subsequent step is to fit curves, preferably polynomials, most preferably of degree 4, to the said points which mark the droplet's front and rear boundaries. The extremes of the fitted curves, representing accurate phase boundaries, are then calculated and the distance between them represents the droplet's length. In this way, the droplet's length can be calculated with an accuracy of 0.5 px (pixel). To refine the measurement, the lengths calculated for a number of frames for the same droplet are averaged. Preferably, droplet lengths calculated from a few to a few tens of different images of the same droplet are averaged. The averaging procedure allows for determination of the droplet's length with a relative accuracy in the per mill range. The constants a and β from the mathematical model (formula 1), used for volume calculation, are determined from two data sets, for droplets of different lengths. Having two series of droplets of different lengths, and knowing the volume of the sum of droplets for a given series, and the lengths of droplets from these series, we obtain two equations with two unknowns by substituting that data to the assumed mathematical model. The constants a and β are determined by solving these equations as a system of equations.

Preferred embodiments of the invention Example 1.

In an embodiment of the present invention a CCD ueye UI-1645LE camera with a Nikon Plan Ax/0.10 lens was used. A light source was a 64 LED array covered with a matt glass. Two polycarbonate plates were fabricated. A 0.4 mm cross-section channel with a T- junction was milled in the first plate. In the second polycarbonate plate, three microfluidic systems were produced to generate droplets of different sizes. The microfluidic systems were composed of square cross-section channels with sides 0.2, 0.4 and 1 mm, respectively. In the first system, the droplets were generated by a flow focusing junction, in the other ones - by a T-junction. The scene was prepared for each case so that in the frame seen by the program 100 pixels corresponded to the channel width. Constant flow was provided by two Harvard PHD Ultra pumps, wherein Hamilton glass syringes were installed. The flow rates were adjusted so that the droplet's length was three times the width of the channel, wherein they were generated (so called small droplets), and eight times the width of the channel, wherein they were generated (so called large droplets). The exact volume flowing through the system during a specific period of time was calibrated in a Sartorius laboratory balance. The algorithms for measuring the length of the droplets were developed in a LabView program. The program saved the results in Excel worksheets. Hexadecane with SPAN80^® surfactant was used as a continuous phase, and demineralised water as a dispersed (droplet) phase. In the testing of the first plate, the inventors tried to determine a and β constants used in the mathematical model. To determine the constants, 200 droplets were generated, each was measured and for each droplet the time of its generation was measured, and such a series was saved. 10 series of droplets of different lengths were generated with sizes ranging from three times the channel width to eight times the channel width. Efforts were made to obtain some diversity in creation of the droplet series, i.e., series with different droplet lengths were obtained by varying the flow rate of hexadecane oil. The flow rate of water was constant and equal to 120 μΙ/h, and the flow rate of hexadecane oil was varied in the following order: 190, 75, 175, 90, 160, 115, 135, 120 (data in μΙ/h). For each droplet series, diagrams were generated to present the sum of lengths of all generated droplets as a function of the droplet volume that should have flown through the system within a given period of time. The volume was represented by the time calculated from the difference between the time the generation of the last droplet in a given series was completed and the time the generation of droplets was started. If one knows the droplet flow rate, the volume is calculated from the total time. From the slope of the plot, which was constant for a series of droplets of a given volume, one can conclude on the linear dependence between the sum of lengths of droplets generated in a given series, EL, and the total time of droplet generation, tc. The formula describing the dependence is as follows: E L

tc a (formula 2) where:

EL means the sum of lengths of droplets, tc - the total time of droplet generation, q - the volumetric flow rate of water, and tsr - the mean time of single droplet generation.

From two series of droplets - knowing tsr and the slope of the EL/tc curve for each series, with the constant flow rate q - we obtain two equations, which combined into a system of equations allow for determination of a and β constants needed for the mathematical model used for volume determination.

The dependence of the slope of the curve on the droplet size is shown in the diagram in Fig. 5, and the mean time of single droplet generation as a function of droplet length is shown in the diagram in Fig. 6.

One can see that the diagrams shown in Fig. 5 and Fig. 6 confirm the validity of the assumed mathematical model. In addition, the reproducibility of the method was verified by generating 10 times the series with extreme droplet sizes (threefold channel width and eightfold channel width) and by checking deviations of the curve slopes and the mean times. The results are shown in Table 2.

Table 2. Verification of measurement reproducibility

From the two extreme series, after substitution to formula 2, a and β constants from the mathematical model were calculated. For that channel and for selected fluids they were as follows:

The volume of droplets can be calculated by substituting the data to formula 1. Droplet volumes so calculated are shown in Table 3.

Table 3. Droplet volumes for calculated droplet lengths and comparison with the volume of a cuboid with a length equal to the length of the droplet and the base area equal to that of the channel's cross-section.

Length [px] Calculated volume [nl] Cuboid volume [nl]

Large droplet 790 445.4248655 505

Small droplet 370 196.0930114 237 An exemplary second polycarbonate plate with three microfluidic channels of square cross-sections is shown in Fig. 7. The upper and the middle systems comprise T-junctions generating the droplets. The lower system is a droplet generating system comprising a flow focusing junction. Looking from the top, the channel widths are 1 mm, 0.4 mm, 0.2 mm, respectively.

The plate was typically fabricated to examine the applicability range of the invented method and the method correctness range for different system geometries and methods for droplet generation. The measurement results are shown in Tables 4 and 5 below.

Table 4. Results obtained with the plate with junctions of different cross-section areas.

Table 5. Calculated constant values

With a and β constants calculated, droplet volumes were determined from the lengths, then the volumes were summed up and compared with the volume determined from the flow after taking into account the total time of generation of a given series of droplets. The results are shown in Table 6.

Table 6. Results of volume determination

Table 7. Accuracy of length determination for a single moving droplet

Length readout from each iteration of the program for single droplet

Example 2. Photometric determination of lactate concentration in human plasma.

To the reaction chamber containing a defined volume of a biochemical reagent, the generated droplets of human plasma were added after their volume has been determined. In the next step, the reaction chamber was closed with adhesive tape and transferred to the centrifuge located in photometric system. The contents of the reaction chamber were mixed and the reaction chamber was placed in photometric position, where photometric measurement was performed.

The procedure was repeated three times, each time the volume of sample was increased by one droplet of human plasma. Each measurement was made in a separate cuvette.

Results of measurements are summarised in Table 8.

Table 8. Summary of results.

Lactate concentration in the reaction mixture (Cm) was determined by using the calibration curve, in a way known to persons skilled in the art. Lactate concentration in the original sample (Cs) was calculated from Cm, the known reagent volume and the determined droplet's volume, in a way known to persons skilled in the art.

Claims

1. An analytical method allowing for determination of a concentration of an analyte in a liquid sample, characterized in that it comprises the steps of: i) generation and determination of volume of an aliquot of the liquid sample in the form of at least one droplet of the liquid sample surrounded by an immiscible carrier liquid and contained in a microfluidic channel of a microfluidic system, ii) introduction of said at least one droplet surrounded by said carrier liquid into a reservoir where it is mixed with a reagent comprising at least one ingredient which reacts specifically with the analyte in the liquid sample, iii) measurement of an analytical signal from the mixture resulting from step (ii), e.g. photometrically, iv) determining the concentration of the analyte in the liquid sample based on the analytical signal from step (iii) and the volume of the aliquot of the liquid sample from step (i).

2. A method according to claim 1 characterized in that it comprises a diagnostic method for determination of a concentration of one or more biochemical constituents in a body fluid.

3. A method according to claim 1 or 2, characterised in that the determination of volume of a droplet of a liquid sample contained in a microfluidic system in step (i) is based on an analysis of an image obtained from a camera, in particular a digital camera, of the microfluidic system supplied with liquids from a dosing system, preferably a pump, and comprises the following steps: a) obtaining of a two-dimensional image of a channel of the microfluidic system containing a minimum of one droplet of the liquid sample, b) determination of the length of the droplet of the liquid sample by analysing the image, c) determination of the volume of the said droplet by employing a mathematical model relating the droplet's volume to its length in the image, in a given geometry of the microfluidic system.

4. A method according to claim 3, characterised in that a camera is used, in particular a digital camera, installed over or under the microfluidic system.

5. A method according to any of the preceding claims, characterised in that series of droplets are used in which a droplet's length is from 3 times larger than the width of the channel to 8 times larger than the width of the channel of the microfluidic system.

6. A method according to any of the preceding claims, characterised in that a microfluidic system is used that generates droplets of fluid and comprises a T-junction or a flow focusing junction.

7. A method according to any of the preceding claims, characterised in that in the microfluidic system, channels of square cross-section are used, preferably with the sides of from 0.1 mm to 2 mm, more preferably 0.2, 0.4 or 1 mm.

8. A method according to any of the preceding claims, characterised in that a material from which the microfluidic system is fabricated and the carrier liquid are chosen such that the carrier liquid wets the walls of the microfluidic channel preferentially over the liquid sample, preferably the droplet of the liquid sample does not wet the walls of the microfluidic channel.

9. A method according to any of claims from 3 to 8, characterised in that step (c) employs a mathematical model based on the formula

V = aL - where: V means the droplet's volume, L means the droplet's length given in unit elements of the image (pixels), a is a coefficient characterizing the channel and the camera used, specifying the effective droplet volume per unit element of the image (pixel), and β is a correction to the droplet volume.

10. A method according to claim 9, characterised in that a and β constants are calculated from the formula:

. p

^{E L} _ ^q ~ tsr

tC H

11. A method according to any of claims from 3 to 10, characterised in that in step b) two algorithms are used, whereas the first algorithm checks if the image comprises an entire droplet in the channel, and the second algorithm determines the front and rear boundaries of the said entire droplet in the image, and subsequently determines the length of the said droplet.

12. A method according to claim 11, characterised in that the first algorithm analyses the image along a first line, running in the image inside the microfluidic channel and in parallel to the direction of flow, preferably the longitudinal axis of symmetry of the channel.

13. A method according to claim 12, characterised in that the first algorithm further analyses the image along a second line, running in the image inside the microfluidic channel, in parallel to the said first line and spaced apa rt therefrom, preferably at the periphery of the microfluidic channel.

14. A method according to claim 12 or 13, characterised in that the first algorithm analyses peaks of intensity of pixels along the said line as a function of their coordinate on an axis parallel to the direction of flow.

15. A method according to claim 14, characterised in that the first algorithm performs a convolution of two functions: intensity of pixels along the said line as a function of their coordinate on an axis parallel to the direction of flow and a polynomial function, preferably a polynomial of degree 3, and analyses the peaks of the resulting function. .

16. A method according to any of claims from 11 to 15, characterised in that the second algorithm analyses the image along a plurality of lines, running in the image across the droplet and in parallel to the direction of flow, preferably a maximum possible number of such lines, and determines the two pixels in each line which mark the front and rea r boundary of the droplet, respectively, by finding the outermost of pixels whose brightness is below a threshold.

17. A method according to claim 16, characterised in that the second algorithm fits curves, preferably in the form of polynomials, most preferably of degree 4, to points in the image representing the said pixels which mark the front and the rear boundaries of the droplet, then computes the extremes of the fitted functions and calculates the length of the droplet as the distance between these extremes.

18. A method according to any of claims from 11 to 17, characterised in that step b) is repeated for multiple different images of the same droplet, preferably using from 2 to 100 images, more preferably from 5 to 20 images, and the length of the droplet is calculated as the arithmetic mean of the values determined for each image.

19. A method according to any of the preceding claims, characterised in that the precision of droplet's volume determination is at least 99%, preferably at least 99,9%.