Capacitive Hematocrit and Hemoglobin Detection

Abstract

1. A method for determining a hematocrit or hemoglobin concentration of a blood sample, the method comprising: calculating a complex capacitance at a predetermined imaginary component value based on a plurality of complex capacitance values ​​of the blood sample, each of the plurality of complex capacitance values ​​of the blood sample having a corresponding frequency; and determining the hematocrit or hemoglobin concentration based on the calculated complex capacitance or a real component of the calculated complex capacitance.

Description

[Technical field]

[0001] The present disclosure relates to methods for determining the hematocrit or hemoglobin concentration of a blood sample, computer readable media comprising instructions for determining same, systems for determining same, and devices configured to determine same. [Background technology]

[0002] background Hematocrit is the ratio of red blood cells to plasma in a blood sample. The current industry standard method for the electrochemical measurement of hematocrit involves measuring the conductivity of a blood sample. Because red blood cells have a very low conductivity and the plasma in which they are suspended has a relatively high conductivity, the conductivity of blood decreases as hematocrit increases. This is the fundamental principle on which the Maxwell-Fricke equation is based, which describes the relationship between hematocrit and the resistivity of blood.

[0003]

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[0004] Here, R s = blood / solution resistance, R p = plasma resistance, φ = hematocrit. Hematocrit is a value (optionally expressed as a percentage) that varies between 0 and 1 for pure plasma and pure red blood cells, respectively. The simplest method to obtain solution resistance is to measure the impedance of the solution at a single high frequency to determine solution resistance, while reducing the influence of double layer capacitance effects on the resistance measurement. The Maxwell-Frick method relies on accurate plasma resistance values ​​to obtain accurate hematocrit values, but plasma resistance values ​​depend on electrolyte content and concentrations, including salts, colloidal electrolytes, proteins and anticoagulants. If these factors vary from normal values, either due to clinical conditions or clinical procedures, plasma resistance will also vary. This can add significant error to the hematocrit values ​​derived by the Maxwell-Fricke method. Relying on an accurate value of plasma resistance for the Maxwell-Fricke method is an issue for point-of-care devices. These devices cannot obtain plasma resistance measurements for each sample tested, but instead use an internally stored average plasma resistance value, which, if incorrect, increases the error of the point-of-care measurement. Thus, there is a need for an improved method of measuring hematocrit. Because hematocrit correlates closely with blood hemoglobin concentration, improved methods for measuring hematocrit can also be used to measure hemoglobin concentration.

[0005] Essentially, capacitance is the charge that accumulates at an interface due to an applied potential. Without wishing to be bound by theory, when one electrode is in contact with a solution, the interfacial capacitance is given by:

[0006]

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[0007] Here, ε r is the relative static permittivity of the liquid (commonly called the dielectric constant), ε0 is the dielectric constant of a vacuum, k is the inverse Debye length (LD = 1 / k), and k = [(2e 2 N) / ε r ε0k B T)]1 / 2 where N is the molar concentration of any polarizable species in the solution, which means that there are k of each species and the total capacitance is generally the sum of the capacitances of all species. The capacitance is based on a charge / discharge process that can be caused by ionic rearrangements or the vibration of dipoles (within one species) at the electrode / solution interface. In other words, the accumulation of charge on the electrode surface. The electrode / electrolyte interface is complicated by different processes that resonate at different frequencies. The complex capacitance therefore depends on the applied potential and the time of perturbation, i.e., the frequency of the input signal in, for example, electrochemical impedance spectroscopy (EIS) measurements. Summary of the Invention [Means for solving the problem]

[0008] overview This summary introduces concepts that are described in more detail in the detailed description. It is not intended to identify essential features of the claimed subject matter, nor should it be used to limit the scope of the claimed subject matter.

[0009] In one aspect, a method for determining a hematocrit of a blood sample may include calculating a complex capacitance at a predetermined imaginary component value based on a plurality of complex capacitance values ​​of the blood sample. As will be appreciated, each of the plurality of complex capacitance values ​​of the blood sample has a corresponding frequency. The corresponding frequency may be a frequency of an input signal used to measure the complex capacitance value. The method may further include determining a hematocrit based on the calculated complex capacitance or a real component of the calculated complex capacitance. The method may also be used, mutatis mutandis, to determine a hemoglobin concentration.

[0010] This method is sometimes referred to herein as the "capacitance" method, in contrast to conventional "impedance" methods, such as the Maxwell-Fricke method, which consider the resistive component of the impedance of a blood sample to determine hematocrit. Unlike the Maxwell-Fricke method, the capacitance method does not necessarily assume known plasma resistance. As demonstrated below, the capacitance method has been found to exhibit reduced sensitivity to salt and other inter-donor variability compared to the Maxwell-Fricke method, resulting in improved hematocrit detection performance.

[0011] Calculating the complex capacitance at a given imaginary component value may include extrapolating from a plurality of complex capacitance values. The extrapolation may include fitting a circular arc to the plurality of complex capacitance values ​​in a capacitance space and extrapolating the arc to calculate the complex capacitance at a given imaginary component value. The capacitance space is a plot of the real component of the complex capacitance versus the imaginary component of the complex capacitance. The circular arc fitting may be transformed into a weighted ordinary least squares fitting, and an example of the transformation operation is described below in the detailed description. When fitting an arc, the plurality of complex capacitance values ​​may be at least four complex capacitance values.

[0012] The corresponding frequency f is the maximum value f max and fitting the arcs is done for frequencies f≦f max Additionally or alternatively, the corresponding frequency f may include fitting an arc for a range of f min and the arc has frequency f minThe arcs are fitted to a range of ≦f. The arcs can be fitted by applying an algorithm for least-squares estimation of nonlinear parameters, such as the Levenberg-Marquardt algorithm or the damped least-squares method. The corresponding frequencies of the plurality of complex capacitance values ​​of the blood sample may be 1000 kHz or less, 500 kHz or less, 200 kHz or less, or 100 kHz or less. The corresponding frequencies of the plurality of complex capacitance values ​​of the blood sample may be 0.1 Hz or more, 10 Hz or more, or 1 kHz or more.

[0013] Determining the hematocrit based on the calculated complex capacitance or the real component of the calculated complex capacitance may include using a calibration curve. Optionally, the calibration curve is an inverted linear calibration curve;

[0014]

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[0015] where φ is the hematocrit, C is the calculated complex capacitance or the real component of the calculated complex capacitance, α is the intercept, and β is the slope.

[0016] The calculated complex capacitance or the real component of the calculated complex capacitance may correspond to the capacitance of the blood sample at frequencies tending towards infinity. As the frequency approaches infinity, the imaginary component of the complex capacitance becomes insignificant, and thus the calculated complex capacitance and the real component of the calculated complex capacitance are of substantially equal semantic value, and either value may be used to reliably determine the hematocrit. At frequencies tending towards infinity (e.g., frequencies above 100 or 1000 kHz, for example), there is no significant effect from the concentration of ions, and the effect of variable salt concentrations on the hematocrit measurement is reduced. The predetermined imaginary component value is 500 pF / mm 2 Less than 200 pF / mm 2 Less than or equal to 100 pF / mm 2Below that, it may be even more preferably substantially zero.

[0017] In another aspect, a method for determining a hematocrit or hemoglobin concentration of a blood sample includes determining a plurality of complex impedance values ​​of the blood sample, each of the plurality of complex impedance values ​​having a corresponding frequency, calculating a plurality of complex capacitance values ​​of the blood sample based on the plurality of complex impedance values, and performing the method as described above using the plurality of complex capacitance values. The method may be performed on whole blood or lysed blood.

[0018] In another aspect, a computer-readable medium comprises instructions that, when executed by one or more processors, cause the one or more processors to perform any of the methods previously described.

[0019] In another aspect, a system for determining a hematocrit or hemoglobin concentration of a blood sample comprises a cell configured to receive the blood sample, an apparatus configured to determine a plurality of complex impedance values ​​of the blood sample, a computer readable medium as described above, and a processor configured to execute instructions of the computer readable medium. As will be appreciated, execution of the instructions of the computer readable medium is based on the plurality of complex impedance values ​​from which a corresponding complex capacitance value is determined. The processor may be further configured to calculate a plurality of complex capacitance values ​​of the blood sample based on the plurality of complex impedance values.

[0020] In another embodiment, a device configured to determine the hematocrit or hemoglobin concentration of a blood sample comprises two electrodes. The distance between the electrodes may be 2 mm, 1 mm or 0.5 mm or less. The two electrodes may be arranged such that when the electrodes are immersed in the plasma, the solution resistance of the plasma may be less than 20 kΩ, less than 10 kΩ, or less than 5 kΩ. The track resistance of the track between one of the electrodes and the corresponding electrode contact may be less than 1 kΩ, 0.7 kΩ, or 0.5 kΩ. The electrodes may be in a cell configured to receive the blood sample. The device may further comprise electronics, such as a potentiostat, configured to determine the impedance of the blood sample at multiple frequencies. The device may comprise additional electrodes, such as a reference electrode. The cell may have an internal volume of 1-20 μL. The device may be for performing measurements in vitro, i.e. outside the human or animal body. The device may not be suitable for in vivo implantation. The device may be integrated into the system described above, and / or the cell of the system described above may have electrodes having the configuration described above.

[0021] BRIEF DESCRIPTION OF THE DRAWINGS Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which: [Brief description of the drawings]

[0022] [Figure 1] 1 shows a Nyquist plot of complex capacitance data for a blood sample of unknown hematocrit. [Figure 2a] 1 illustrates a method for determining the hematocrit of a blood sample. [Figure 2b] 1 illustrates a method for determining the hematocrit of a blood sample. [Diagram 3] 1 shows a system for determining the hematocrit of a blood sample. [Figure 4a] 1 shows capacitance data for plasma and whole blood at 65% hematocrit and is a Nyquist plot. [Figure 4b]1 shows capacitance data for plasma and whole blood at 65% hematocrit, which is a Bode plot of actual capacitance. [Figure 4c] 1 shows capacitance data for plasma and whole blood at 65% hematocrit, which is a Bode plot of imaginary capacitance. [Figure 5a] 13 shows hematocrit detection performance for a fixed sodium concentration; and FIG. 14 is a Nyquist plot of derived capacitance fit arcs for different hematocrit concentrations. [Figure 5b] FIG. 13 is a calibration plot showing the hematocrit detection performance for a fixed sodium concentration, showing the observed hematocrit φ versus the estimated intercept of the axis of the real component of the complex capacitance C'intercept, including the linear regression slope (black line) and 95% prediction interval (grey shading). [Figure 5c] 1 shows hematocrit detection performance for a fixed sodium concentration and is a plot of observed hematocrit φ versus hematocrit recovered using the Maxwell-Fricke method, including the linear regression slope (solid line) and the 1:1 line (dashed line). [Figure 5d] Figure 5C shows the hematocrit detection performance for a fixed sodium concentration. Similar to Figure 5C, except that the hematocrit φ is recovered by C'intercept calibration (capacitance method). [Figure 5e] FIG. 1 is a calibration plot showing observed hemoglobin concentration versus the estimated intercept of the axis of the real component of complex capacitance C'intercept, including the linear regression slope (black line) and 95% prediction interval (grey shading) for the determination of hemoglobin concentration. [Figure 5f] 1 is a plot of observed hemoglobin concentration versus hemoglobin concentration recovered by C'intercept calibration (capacitance method) including the linear regression slope (solid line) for the determination of hemoglobin concentration. [Figure 6a] 13 shows a hematocrit detection error analysis for a fixed sodium concentration; FIG. 13 is a series of histograms showing the distribution of hematocrit φ recovery error for the Maxwell-Fricke and C'intercept calibration (capacitance) methods. [Figure 6b] Hematocrit detection error analysis for fixed sodium concentration is shown, with observed hematocrit φ versus hematocrit φ recovery error from the Maxwell-Fricke method, with the mean error ±1.96 standard deviations shown alongside the p-value from the D'Agostino and Pearson normality test (dashed line). [Figure 6c] Shows hematocrit detection error analysis for a fixed sodium concentration, similar to Figure 6b, except that the recovered error of hematocrit φ is from C'intercept calibration (capacitance method). [Figure 7a] Same as Figures 5a-d, except for various Na+ concentration spikes. [Figure 7b] Same as Figures 5a-d, except for various Na+ concentration spikes. [Figure 7c] Same as Figures 5a-d, except for various Na+ concentration spikes. [Figure 7d] Same as Figures 5a-d, except for various Na+ concentration spikes. [Figure 8a] Same as Figures 6a-c, except for various Na+ concentration spikes. [Figure 8b] Same as Figures 6a-c, except for various Na+ concentration spikes. [Figure 8c] Same as Figures 6a-c, except for various Na+ concentration spikes. [Figure 9] 1 shows a cell for performing impedance measurements on blood samples. [Figure 10] 1 shows an apparatus configured to determine the hematocrit of a blood sample. [Figure 11a] 4 shows a calibration curve for the capacitance method using an electrode spacing of 2.4 mm. [Figure 11b] 1 shows the calibration curve of the capacitance method using the optimized cell design with an electrode spacing of 0.6 mm. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0023] Detailed Description FIG. 1 is a Nyquist plot (i.e., a plot in capacitance space) of complex capacitance data for a blood sample of unknown hematocrit. The vertical axis corresponds to the imaginary component of the complex capacitance C" and the horizontal axis corresponds to the real component of the complex capacitance C'.

[0024] Each complex capacitance value is derived from the complex impedance of the blood sample measured at a particular frequency, and therefore also has a corresponding frequency. In Figure 1, the frequencies range from 200 kHz (the left-most point for each blood sample) to 25 Hz (the right-most point for each blood sample), with 25 points per decade. The lowest frequency is the minimum frequency level f min It is called.

[0025] Impedance measurements were performed using a conventional potentiostat (EMStat Pico, Palmsens, Gauteng, The Netherlands). The amplitude of the input signal was 10 mV around a potential of 0.0 V versus a screen-printed carbon electrode (SPCE). The blood sample volume was 10 μl and measurements were performed at 30 °C. The flow cell dimensions were 2.4 mm × 9.7 mm × 225 μm. The electrodes were rectangular electrodes with dimensions of 0.3 mm × 2 mm with a spacing of 0.6 mm. In the figures, the capacitance is normalized to the electrode area, but this is not required. Each impedance measurement is performed at a specific frequency (i.e., at one of the multiple frequencies mentioned above). In the figures, the C' axis is rescaled by adding a constant (e.g., -1*minimum extrapolated C' for 0% hematocrit, as determined during calibration - see below) to normalize the data. This does not affect the final hematocrit result and is not a required part of the capacitance method.

[0026] The complex impedance measurement consists of two values: a real part Z' and an imaginary part Z". The complex impedance measurement is used to calculate the complex capacitances C' and C" using the following formula:

[0027]

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[0028]

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[0029] where f is the respective frequency and |Z| is the vector magnitude of the real and imaginary components of the complex impedance in the complex plane.

[0030] 2a illustrates a method for determining the hematocrit of a blood sample, the method including calculating 101 a complex capacitance at a predetermined imaginary component value based on a plurality of complex capacitance values ​​of the blood sample, each of the plurality of complex capacitance values ​​of the blood sample having a corresponding frequency as described above.

[0031] In this example, the complex capacitance values ​​of the blood sample are the complex capacitance values ​​of the points in FIG. 1. The predetermined imaginary component value is C"=0 pFmm -2 and is also known as the abscissa intercept or C' intercept.

[0032] The method of Figure 2a further includes determining 103 the hematocrit based on the calculated complex capacitance or the real component of the calculated complex capacitance, as described below. Alternatively or additionally, the hemoglobin concentration can be determined, as described below.

[0033] Referring to FIG. 3b, in this example, calculating 101 the complex capacitance at a given imaginary component value includes calculating a maximum frequency value f of frequencies corresponding to a plurality of complex capacitance values. max determining 105 a minimum frequency value f of the frequencies corresponding to the plurality of complex capacitance values; min 107 will also be decided.

[0034] The arc is at frequency f min ≦f≦f max, i.e., for a range of frequencies f min ≦f≦f max In the range of

[0035]

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[0036] The arcs that satisfy are fitted such that R>0, A>0 and B<0109.

[0037] The initial estimates for A and B are the medians of C' and C", respectively. As an initial estimate for R, half the Euclidean distance between the (C', C") points at the minimum and maximum of C' is used.

[0038]

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[0039] Let denote the nonlinear cost function.

[0040]

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[0041] Let denote the quadratic weighting function. The arcs are fitted by applying an iterative Levenberg-Marquardt nonlinear least-squares algorithm (an algorithm for least-squares estimation of nonlinear parameters)109 to find optimal estimates of A, B, and R that minimize the weighted sum of squares.

[0042]

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[0043] The fitted arc is extrapolated 111 to determine the C′ intercept closest to the origin 113, which represents the theoretical capacitance as the frequency trends towards +∞.

[0044]

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[0045] That is, the predetermined imaginary component value in this example is 0 pFmm -2 The fitted and extrapolated arcs are shown in Figure 1.

[0046] As can be seen, 0pFmm -2 Other predetermined imaginary component values ​​close to can also be used, and both the complex capacitance at this point or the real component of the complex capacitance can be used, since these have similar values ​​as the C' intercept closest to the origin.

[0047] Furthermore, an equivalent non-physical estimator is given by the C' intercept furthest from the origin.

[0048]

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[0049] In this disclosure, only results from physical estimators are presented, but identical recovery performance is achieved using non-physical estimators.

[0050] To simplify the fitting process, the parameter B can be assumed to be equal to 0, in which case B can be omitted from the above equation.

[0051] Optionally, the arc fitting may be transformed into a weighted ordinary least squares fitting.

[0052] For N complex capacitance values ​​each having a real component C' and an imaginary component C" and a corresponding frequency f, maxis the maximum frequency of frequencies corresponding to the N complex capacitance values, and the transformation variables X and Y, as well as the fitting weights W, are calculated.

[0053]

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[0054]

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[0055]

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[0056] Then, weighted ordinary least squares is applied to estimate the maximum likelihood fit through (X,Y) subject to the weights W.

[0057]

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[0058]

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[0059]

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[0060]

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[0061] The parameters A and R are then estimated using:

[0062]

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[0063]

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[0064] In this example, parameter B is set to 0. Advantageously, use of this or a similar transform may allow for the C' intercept to be calculated using fewer computational resources or less powerful computational software.

[0065] Referring back to FIG. 2a, in this example, determining 103 the hematocrit based on the calculated complex capacitance or the real component of the calculated complex capacitance includes using a hematocrit calibration curve, where the calibration curve is an inverted linear calibration curve.

[0066]

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[0067] where φ is the hematocrit, C is the C' intercept closest to the origin, α is the intercept, and β is the slope. Hemoglobin concentration can alternatively be determined using a hemoglobin concentration calibration curve.

[0068] The constants α and β are calculated in a conventional manner by determining the C' intercept values ​​of multiple blood samples with known hematocrit values ​​and calculating the corresponding α and β values ​​using a (linear) least squares best fit. The constants α and β for a hemoglobin concentration calibration curve can be determined in a similar manner. Figures 5a and 5b, described below, show sample data for creating a calibration curve from capacitance data of blood samples with known hematocrit, and the resulting calibration curve. The hemoglobin calibration curve is shown in Figure 5e.

[0069] Standard methods, such as the microhematocrit capillary method, for determining the hematocrit of blood samples are known to those skilled in the art.For example, this method is used to draw blood samples into capillary tubes, centrifuge, and then measure the ratio of red blood cells to plasma (i.e., hematocrit), which can be expressed as a decimal or percentage.Blood samples with known hematocrit can be prepared by 1) measuring the hematocrit of a natural sample, 2) centrifuging the blood sample, and 3) removing or adding plasma to adjust the hematocrit to a desired value.

[0070] A hemoglobin concentration calibration curve can be obtained by taking a blood sample with a typical hemoglobin concentration (e.g., 157 g / L) and removing or adding donor plasma to create a series of blood samples with various hemoglobin concentrations. The concentration of each adjusted blood sample is then measured, e.g., using a HemoCue Hb201+ system. The samples are then measured using a capacitance method and the C' intercept is plotted against the hemoglobin concentration, e.g., as shown in Figure 5e.

[0071] The described methods can be implemented using computer executable instructions. A computer program product or computer readable medium can comprise or store computer executable instructions. The computer program product or computer readable medium can comprise a hard disk drive, a flash memory, a read only memory (ROM), a CD, a DVD, a cache, a random access memory (RAM), and / or any other storage medium in which information is stored for any period of time (e.g., long term, permanent, short term, temporary buffering, and / or caching of information). A computer program can include computer executable instructions. A computer readable medium may be a tangible or non-transitory computer readable medium. The term "computer readable" encompasses "machine readable". Thus, in one aspect, a computer readable medium is provided that comprises instructions that, when executed by one or more processors, cause the one or more processors to perform the method of FIG. 2a and / or FIG. 2b.

[0072] 3 is a diagram of a system 200 for determining the hematocrit of a blood sample. The system 200 includes a central bus structure, a cell 201 configured to receive a blood sample, a potentiostat 203 connected to the cell 201 and the central bus structure and configured to determine a plurality of complex impedance values ​​of the blood sample in the cell 201, a data processing resource such as a memory 205 connected to the central bus structure and storing the computer readable medium described above, a processor 207 connected to the central bus structure and configured to execute instructions of the computer readable medium, a display adapter 209, a display device 211, one or more user input device adapters 213, one or more user input devices 215 such as a keyboard and / or mouse, and one or more communication adapters 217, all connected to the central bus structure. The display device 211 has touch input capabilities and therefore also functions as the user input device 215.

[0073] The potentiostat may include or be in communication with further processors and further data processing resources for processing the measurement data, or may use the system's memory 205 and processor 207 to measure and / or calculate impedance and capacitance data.

[0074] Performance data Figure 4a is a Nyquist plot of the impedance-derived capacitance of blood (65% hematocrit, square points) and pure serum / plasma (0% hematocrit, circular points). Figure 4a includes a close-up of the area near the origin. High frequency data points are on the left and low frequency measurements are on the right. Thus, it can be seen that the lower the frequency, the greater the capacitance due to the greater contribution to capacitance from ions in the plasma. It can also be seen that plasma has a higher capacitance than 65% hematocrit blood at a given frequency. This is because the blood cells themselves have a relatively small capacitance, while effectively reducing the ion concentration.

[0075] FIG. 4b) shows the corresponding Bode plot of the real capacitance C', and FIG. 4c) shows the corresponding Bode plot of the imaginary capacitance C'', where the relaxation R f The frequency is indicated by the minimum plateau of C″.

[0076] The frequency at which the charge and discharge harmonize with the potential oscillation is called the relaxation frequency R. f is known as the interfacial capacitance of the system, C i In this method, the relaxation frequency R f There is no need to ask for

[0077] The "semicircle" in the Nyquist plot in Figure 4a corresponds to the relaxation frequency R f (see also Figure 4c) and the graph ends exactly at the system interfacial capacitance C i In this plasma / blood cell system, C i is dominated by the charging and discharging of ions in the plasma, and R f is 10 2Hz and is considered to be a low frequency. Without being bound by theory, it is believed that a high frequency (e.g., 10 5 At frequencies above 100 Hz, the oscillations of the input signal are fast enough that no rearrangement of the ions occurs. Thus, the capacitance becomes dominated by the oscillations of the dipoles of the polarizable species. Thus, when measuring the capacitance of blood at high frequencies (frequencies that tend toward infinity), the contribution to the output signal from the ions and other ionic species becomes insignificant. Thus, the inventors have determined that by calculating the capacitance of a blood sample at high frequencies, which are relatively insensitive to the ionic strength of the blood, the hematocrit can be calculated with much less error caused by changes in the salt concentration of the blood. Note that at high frequencies, the capacitance signal increases with increasing hematocrit, as predicted by the following equation (see Figure 5b):

[0078]

number

[0079] where N is the molar concentration of red blood cells. Figures 5a-d show hematocrit detection performance for fixed sodium concentrations using the "capacitive" method described above and the conventional Maxwell-Fricke method. Figure 5a shows the hematocrit detection performance for blood samples with hematocrits of 0 and in the range of 20-65% without the addition of additional ions to the blood sample (i.e., Na, discussed further below). + (Spikes are at 0 mM) and Nyquist plot of capacitance fitted arcs at 5% increments. Similar to Figure 4a, at low frequencies, we can see that capacitance decreases as hematocrit increases, as expected.

[0080] Figure 5b shows the complex capacitance C', including the linear regression slope (black line) and the 95% prediction interval (gray shading). intercept FIG. 5B is a calibration plot (derived from the data in FIG. 5a) showing observed hematocrit φ versus the estimated intercept of the axis of the real component of φ.

[0081] FIG. 5c shows the known hematocrit φ versus the recovered hematocrit using the Maxwell-Fricke method for a range of blood samples, including the linear regression slope (solid line) and the 1:1 line (dashed line). FIG. 5d shows the relationship between the hematocrit φ and C' in FIG. 5b. intercept 5c is similar to FIG. 4c, except that it is recovered by calibration, i.e., using the capacitance method of the present disclosure. As can be seen from a comparison of FIG. 5c and FIG. 5d, the hematocrit accuracy at a fixed sodium concentration of the capacitance method is superior to the Maxwell-Fricke method. FIG. 5f shows the hematocrit accuracy of C', including the linear regression slope (solid line). intercept 1 is a plot of observed hemoglobin concentration versus hemoglobin concentration recovered by calibration (capacitance method). It can thus be seen that the capacitance method can also be used to determine hemoglobin concentration in blood with reasonable accuracy.

[0082] Figure 6a shows the Maxwell-Fricke (impedance) method and C' intercept 6 is a series of histograms showing the distribution of hematocrit φ recovery error for the calibration (capacitance) method. As can be seen, the error is much smaller when using the capacitance method. Fig. 6b shows the observed hematocrit φ against the hematocrit φ recovery error from the Maxwell-Fricke method, with the mean error ±1.96 standard deviations shown together with the p-value from the D'Agostino and Pearson normality test (dashed line). Fig. 6c shows the distribution of hematocrit φ recovery error against the C' intercept Similar to Figure 6b, except from the calibration method. Again, it can be seen that the error is much smaller when using the capacitance method.

[0083] Figures 7a to 7d show various Na + Similar to Figure 5, except for the concentration spike. Figure 7a shows the results for fixed hematocrit and Na of 0.0, 10.0 and 25.0 mM. + 1 shows capacitance data of blood with spikes.

[0084] Figures 8a to 8c show various Na +Similar to Figures 6a-c, except for the concentration spikes. As can be seen, the recovered hematocrit error is much lower when the capacitance method is used instead of the impedance method. Therefore, the capacitance method is less sensitive to variations in plasma conductivity / ionic strength than the impedance method.

[0085] Hematocrit Sensor FIG. 9 shows a cell 300 for performing impedance measurements on a blood sample.

[0086] The cell 300 comprises a chamber 301 for receiving a blood sample. The chamber 301 comprises two electrodes 303, 305. The electrodes may be made of platinum, gold, glassy carbon, or any other suitable electrode material. The chamber 301 may comprise more than two electrodes 303, 305, for example the chamber may comprise a reference electrode. The distance between the electrodes 303, 305 is 0.6 mm. When the two electrodes are immersed in plasma, the solution resistance of the plasma is less than 5 kΩ. The cell further comprises two electrode contacts 307, 309. Each electrode 303, 305 is connected to a respective one of the electrode contacts 307, 309 via a track (not shown). The resistance of each track is 0.7 kΩ.

[0087] Figure 10 shows an apparatus 400 configured to determine the hematocrit of a blood sample. The apparatus comprises the cell 300 of Figure 9 in electrical communication with a potentiostat 401 configured to determine a plurality of complex impedance values ​​of the blood sample in the cell 300. The cell 300 may also be incorporated into the system of Figure 3, i.e., by replacing the cell 201.

[0088] Conventional hematocrit sensor designs for resistance-based systems, such as the Maxwell-Frick system, use two parallel conductive electrodes optimized to have high solution resistance so that the signal difference between low and high blood resistance is large. The inventors have determined that this approach is not optimal for the capacitance method disclosed above, producing a calibration curve with a low slope response from the blood sample. Performance can be optimized by removing much of the resistance from the electrode design in terms of track resistance (e.g., by using tracks with larger cross-sectional areas) and solution resistance (e.g., by using electrodes with the closest possible spacing).

[0089] 11a and 11b show the effect of optimizing the cell for the capacitance method, most notably showing a roughly 2-fold improvement in the slope of the calibration curve which improves the separation between data points.

[0090] Figure 11a shows the calibration curve of the capacitance method using an electrode spacing of 2.4 mm. The equation of the line is y=0.311x-12.9, and the R^2 value is 0.9940. Figure 11b shows the calibration curve of the capacitance method using the optimized cell design with an electrode spacing of 0.6 mm. The equation of the line is y=0.609x-36.1, and the R^2 value is 0.9935.

[0091] The embodiments of the present invention shown in the drawings and described above are merely exemplary embodiments and are not intended to limit the scope of the appended claims, including any equivalents contained within the scope of the claims. Various modifications are possible and will be readily apparent to those skilled in the art. Any combination of non-mutually exclusive features described herein is intended to be within the scope of the present invention. That is, features of the described embodiments can be combined with any suitable aspect described above, and any feature of any one aspect can be combined with any other suitable aspect.

Claims

1. 1. A method for determining the hematocrit or hemoglobin concentration of a blood sample, comprising: calculating a complex capacitance at a predetermined imaginary component value based on a plurality of complex capacitance values of the blood sample, each of the plurality of complex capacitance values of the blood sample having a corresponding frequency; determining the hematocrit or hemoglobin concentration based on the calculated complex capacitance or a real component of the calculated complex capacitance.

2. The method of claim 1 , wherein calculating the complex capacitance at a given imaginary component value comprises extrapolating from the plurality of complex capacitance values.

3. 3. The method of claim 2, wherein extrapolating comprises fitting a circular arc to the plurality of complex capacitance values in capacitance space and extrapolating the arc to calculate the complex capacitance at the predetermined imaginary component value, optionally wherein the arc fitting is converted to a weighted ordinary least squares fitting.

4. The corresponding frequency f is the maximum value f max and the arc has a frequency f≦f max The method of claim 3, wherein the fitting is performed over a range of

5. The corresponding frequency f is the minimum value f min and the arc has a frequency f min The method of claim 3 or 4, wherein fitting is performed for a range of ≦f.

6. The method of claim 3 , wherein the arc is fitted by applying an algorithm for least-squares estimation of nonlinear parameters.

7. The method of claim 1 , wherein determining the hematocrit or hemoglobin concentration based on the calculated complex capacitance or a real component of the calculated complex capacitance comprises using a calibration curve.

8. 2. The method of claim 1, wherein the calculated complex capacitance or the real component of the calculated complex capacitance corresponds to the capacitance of the blood sample at frequencies tending towards infinity.

9. 2. The method of claim 1, wherein each corresponding frequency of the plurality of complex capacitance values of the blood sample is less than or equal to 1000 kHz.

10. 2. The method of claim 1, wherein each corresponding frequency of the plurality of complex capacitance values of the blood sample is greater than or equal to 0.1 Hz.

11. The predetermined imaginary component value is 500 pF / mm ２ Less than 200 pF / mm ２ Less than 100 pF / mm, more preferably ２ 2. The method of claim 1, wherein n is less than or equal to 0, and even more preferably substantially less than 0.

12. 1. A method for determining the hematocrit or hemoglobin concentration of a blood sample, comprising: determining a plurality of complex impedance values of the blood sample, each of the plurality of complex impedance values having a corresponding frequency; calculating a plurality of complex capacitance values of the blood sample based on the plurality of complex impedance values; and performing the method of claim 1 using the plurality of complex capacitance values.

13. 10. A computer-readable medium comprising instructions that, when executed by one or more processors, cause the one or more processors to perform the method of claim 1.

14. 1. A system for determining the hematocrit or hemoglobin concentration of a blood sample, comprising: a cell configured to receive the blood sample; an apparatus configured to determine a plurality of complex impedance values of the blood sample; A computer-readable medium according to claim 13; a processor configured to execute the instructions of the computer-readable medium.

15. A device for measuring the hematocrit of a blood sample, comprising two electrodes, the distance between the electrodes being 2 mm or less.

16. 16. The device of claim 15, wherein the two electrodes are positioned such that when the electrodes are immersed in plasma, the solution resistance of the plasma is less than 20 kΩ.

17. 17. The device of claim 15 or 16, wherein the track resistance of the track between one of the electrodes and the corresponding electrode contact is 1 kΩ or less.

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