Haematocrit and haemoglobin detection method and system

Abstract

A method of determining haematocrit or haemoglobin concentration of a blood sample, the method comprising: calculating first and second electrical properties based on one or more complex impedances of the blood sample; and determining the haematocrit or haemoglobin concentration of the blood sample using a relationship based on the first and second electrical properties, wherein the first electrical property is a complex capacitance or a real or imaginary component of a complex capacitance.

Description

[0001]Haematocrit and Haemoglobin Detection Method and System The present disclosure relates to methods of determining the haematocrit or haemoglobin concentration of a blood sample, a computer-readable medium comprising instructions for determining the same and a system for determining the same. Background Haematocrit is the ratio of erythrocytes to blood plasma in a blood sample. The current industry standard method for the electrochemical measurement of haematocrit comprises measuring the conductivity of a blood sample. The conductivity of blood decreases with increasing haematocrit due to the very low conductivity of the erythrocytes and the relatively high conductivity of the plasma the erythrocytes are suspended in. This is the fundamental principal that the Maxwell-Fricke equation is based upon, which describes the relationship between haematocrit and resistance of blood: ^^ = ^^ + 2^^ ^^^^ 2(1 − ^^)where Rs= resistance of blood / solution, Rp= resistance of plasma and ϕ = haematocrit. Haematocrit is a value which varies between 0 and 1 (optionally expressed as a percentage) for pure plasma and pure erythrocytes, respectively. To obtain the solution resistance, the simplest method is to measure the impedance of solution at a single high frequency to determine the solution resistance whilst reducing the effect of the double layer capacitive effect on the resistance measurement. The Maxwell-Frick method is reliant on an accurate value of plasma resistance to give an accurate haematocrit value, however, the value for plasma resistance depends on electrolyte content and concentration, which includes salts, colloidal electrolytes, proteins and anticoagulants. When these factors vary from normal values, through either clinical condition or clinical procedure, plasma resistance also varies. This can add significant error to the haematocrit value derived via the Maxwell-Fricke method. This reliance on an accurate value of plasma resistance for the Maxwell-Fricke method is an issue for point of care devices. These devices cannot get a plasma resistance measurement for each sample tested and instead use an internally stored average plasma resistance value that, if incorrect, will increase error in the point of care measurement. Therefore, improved methods of measuring haematocrit are needed. Haematocrit is closely correlated with blood haemoglobin concentration, and therefore improved methods of measuring haematocrit can also be used to measure haemoglobin concentration. Essentially, capacitance is charge stored at an interface due to an applied potential. Without wishing to be constrained by theory, when one electrode is in contact with a solution, interfacial capacitance is given by: wherein ^^^^is the relative static permittivity (generally referred to as the dielectric constant)of the liquid, ^^0 is the dielectric constant or dielectric permittivity of vacuum and ^^ is theinverse Debye length (LD = 1 / ^^), wherein ^^ is given by ^^ = [(2^^2^^) / ^^^^^^0^^^^^^)]1 / 2. ^^ is the molar concentration of any polarisable species in the solution, which means that there is a ^^ for each species and the total capacitance is generally the sum of the capacitance of all species. Capacitance is based on the charging / discharging process that can be caused by rearrangement of ions or oscillation of dipoles (in one species) at the electrode / solution interface. In other words, it is the accumulation of charge on the surface of an electrode. Electrode / electrolyte interfaces are complex with different processes resonating at different frequencies. Thus, the complex capacitance depends on the potential applied and the time of perturbation i.e. the frequency of the input signal in an electrochemical impedance spectroscopy (EIS) measurement, for example. Summary This summary introduces concepts that are described in more detail in the detailed description. It should not be used to identify essential features of the claimed subject matter, nor to limit the scope of the claimed subject matter. The inclusion of multiple statements in the same paragraph of the summary does not imply that there is a structural or functional relationship between such statements. In one aspect, there is provided a method of determining haematocrit or haemoglobin concentration of a blood sample. The method comprises: calculating first and second electrical properties based on one or more complex impedances of the blood sample; and determining the haematocrit or haemoglobin concentration of the blood sample using a relationship based on the first and second electrical properties. The first electrical property is a complex capacitance or a real or imaginary component of a complex capacitance. As demonstrated below, the method is found to show a higher accuracy for determining haematocrit and a decrease in sensitivity to blood salt concentration and other donor-to- donor variability compared to existing methods in the art, leading to improved haematocrit detection performance. The method may be performed on whole blood or lysed blood and / or may be a computer implemented method. The relationship based on the first and second electrical properties may be known as a calibration curve or mathematical relationship, such as a linear mathematical relationship, and may also be known as a multivariate relationship. The relationship may be determined using multivariate linear regression. Constants for the relationship may be determined using, for example, least squares fitting to training data. The second electrical property may be a complex impedance, real component of a complex impedance, imaginary component of a complex impedance, complex admittance, real component of a complex admittance, imaginary component of a complex admittance, complex capacitance, real component of a complex capacitance, imaginary component of a complex capacitance, or a phase shift. These terms (together with complex impedance, complex capacitance and real or imaginary component of complex capacitance) are familiar to the skilled person. Nonetheless, their mathematical relationship is explained in detail below. The first and / or second electrical properties may each be calculated based on the impedance of the blood sample at a plurality of different frequencies, as is common in impedance spectroscopy, for example. Alternatively, the first and / or second electrical properties may be a directly measured property of the blood sample derived from an impedance measurement at a single frequency only. When calculated from impedance of the blood sample at a plurality of different frequencies, the first electrical property or the second electrical property may be based on a frequency-dependent relationship determined from impedance data. In this case, the corresponding electrical property is then calculated using the frequency-dependent relationship based on a predetermined frequency. For example, a straight line or polynomial function may be fit to a real component of the complex capacitance derived from impedance data as a function of frequency (using, for example, least squares fitting; the electrical property does not need to be a component of complex capacitance). The value of the electrical property used to determine haematocrit or haemoglobin concentration is the value of the complex capacitance at a predetermined frequency value (such as 100 kHz, although any frequency value could be used) based on the frequency dependent relationship. As such, the method may further comprise: determining a frequency dependent relationship based on the complex impedance (or other electrical property) of the blood sample at a plurality of different frequencies; and determining the first or second electrical property using the frequency dependent relationship. Each of the plurality of different frequencies may be greater than 0.1 Hz, 1 kHz or 10 kHz and / or each of the plurality of frequencies is less than 100 kHz, 500 kHz or 1,000 kHz. Determining the first or second electrical property using the frequency dependent relationship may comprise determining the first or second electrical property at a predetermined frequency. Advantageously, using a frequency dependent relationship may reduce error by reducing the impact of outliers in the impedance data on the value of the electrical property. In a specific example, the first electrical property may be calculated based on a plurality of complex capacitance values of the blood sample and a complex capacitance at a predetermined imaginary component value, each of the plurality of complex capacitance values of the blood sample having a corresponding frequency. As would be understood, the complex capacitance values of the blood sample are derived from impedance values of the blood sample. Calculating a complex capacitance at a predetermined imaginary component value may comprise extrapolating from the plurality of complex capacitance values. Extrapolating may comprise 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 circular arc fitting is transformed to a weighted ordinary least squares fitting. The corresponding frequencies, f, may have a maximum value, fmax, and the circular arc is fit for the range of frequencies f ≤ fmax. Additionally or alternatively, the corresponding frequencies, f, may have a minimum value, fmin, and the circular arc is fit for the range of frequencies fmin ≤ f. The circular arc may be fit by applying an algorithm for least-squares estimation of nonlinear parameters. Each corresponding frequency of the plurality of complex capacitance values of the blood sample may be less than or equal to 1,000 kHz. Additionally or alternatively, each corresponding frequency of the plurality of complex capacitance values of the blood sample may be greater than or equal to 0.1 Hz. The predetermined imaginary component value may be less than or equal to 500 pF / mm2, preferably less than or equal to 200 pF / mm2, more preferably less than or equal to 100 pF / mm2, and yet more preferably substantially equal to or equal to zero. 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. The method may further comprise providing instructions to a potentiostat in order to determine the first and second complex impedances of the blood sample and / or may further comprise calculating the first and second complex impedances of the blood sample. The method is not limited to the use of only two electrical properties. Thus, determining the haematocrit or haemoglobin concentration of the blood sample using a relationship based on the first and second electrical properties may comprise determining the haematocrit or haemoglobin concentration of the blood sample using a relationship based on a plurality of electrical properties, the plurality of electrical properties comprising the first and second electrical properties and one or more additional electrical properties. In an example, the first electrical property may be the complex capacitance at a predetermined imaginary component value, the second electrical property may be an imaginary component of a complex impedance at a first frequency, and a third electrical property may be an imaginary component of a complex impedance at a second frequency different to the first frequency. As such, the first electrical property may be based on a plurality of complex capacitance values of the blood sample and a complex capacitance at a predetermined imaginary component value, each of the plurality of complex capacitance values of the blood sample having a corresponding frequency, and the second and third electrical properties may be based on a relationship between frequency and an imaginary component of a complex impedance, wherein the relationship is determined from a plurality of complex impedances of the blood sample at a plurality of different frequencies. In another aspect, a computer-readable medium comprises instructions which, when executed by one or more processors, causes the one or more processors to perform one of the methods above. In another aspect, there is provided a method of determining haematocrit or haemoglobin concentration of a blood sample. The method comprises: determining one or more complex impedance values of the blood sample, each of the plurality of complex impedance values having a corresponding frequency; and performing the method above using the complex impedance values, wherein the first and second electrical properties are based on the one or more complex impedance values. In another aspect, there is provided a system for determining haematocrit or haemoglobin concentration of a blood sample. The system comprises a cell configured to receive the blood sample; a device configured to determine one or more complex impedance values of the blood sample; a computer-readable medium as disclosed above; and a processor configured to execute the instructions of the computer-readable medium. 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: Figure 1 is a plot of complex capacitance data of two blood samples over a 90-200 kHz frequency sweep at 45% (squares) and 55% (triangles) haematocrit; Figure 2A is a flow diagram for a method for determining haematocrit of a blood sample; Figure 2B is a flow diagram for a method of determining an estimated intercept of the axis of the real component of the complex capacitance nearest to origin (CReal intercept) in capacitance space; Figure 2C is a flow diagram for a method of determining an imaginary component of a complex impedance at a predetermined frequency based on a frequency-dependent relationship (fitted ZImag); Figure 3 is a plot of imaginary capacitance values of two blood samples vs. frequency over a 90-200 kHz frequency sweep at 45% (squares) and 55% (triangles) haematocrit; Figure 4 is plot of real capacitance values of two blood samples vs. frequency over a 90- 200 kHz frequency sweep at 45% (squares) and 55% (triangles) haematocrit; Figure 5 is plot of imaginary impedance values of two blood samples vs. frequency over a 90-200 kHz frequency sweep at 45% (squares) and 55% (triangles) haematocrit; Figure 6 is plot of real impedance values of two blood samples vs. frequency over a 90- 200 kHz frequency sweep at 45% (squares) and 55% (triangles) haematocrit; Figure 7 is a plot of the estimated intercept of the axis of the real component of the complex capacitance (CReal intercept) values vs. haematocrit for a range of blood samples; Figures 8A-D are plots of the estimated real (fitted CReal) and imaginary (fitted CImag) components of the complex capacitance at 90 kHz and 200 kHz vs. haematocrit for a range of blood samples; Figures 9A-D are plots of the estimated real (fitted ZReal) and imaginary (fitted ZImag) components of the complex impedance at 90 kHz and 200 kHz vs. haematocrit for a range of blood samples; Figures 10A-D are plots of the real (CReal) and imaginary (CImag) components of the complex capacitance calculated directly from impedance measurements at 90 kHz and at 200 kHz vs. haematocrit for a range of blood samples; Figures 11A-D are plots of the real (ZReal) and imaginary (ZImag) components of the complex impedance calculated directly from impedance measurements at 90 kHz and at 200 kHz vs. haematocrit for a range of blood samples; Figure 12 is a plot of three-signal MLR recovered haematocrit vs. microhaematocrit recovered haematocrit for a range of blood samples; Figure 13 is a plot of recovery error = [three-signal MLR recovered haematocrit – microhaematocrit recovered haematocrit] vs. microhaematocrit recovered haematocrit; Figure 14 is a plot of CReal intercept recovered haematocrit vs. microhaematocrit recovered haematocrit for a range of blood samples; Figure 15 is a plot of recovery error = [CReal intercept recovered haematocrit – microhaematocrit recovered haematocrit] vs. microhaematocrit recovered haematocrit; Figure 16 is a plot of nine-signal MLR recovered haematocrit vs. microhaematocrit recovered haematocrit for a range of blood samples; Figure 17 is a plot of recovery error = [nine-signal MLR recovered haematocrit – microhaematocrit recovered haematocrit] vs. microhaematocrit recovered haematocrit; Figure 18 is a plot of eight-signal MLR recovered haematocrit vs. microhaematocrit recovered haematocrit for a range of blood samples; Figure 19 is a plot of recovery error = [eight-signal MLR recovered haematocrit – microhaematocrit recovered haematocrit] vs. microhaematocrit recovered haematocrit;; Figure 20 is a plot of recovered haematocrit using the real (CReal) and imaginary (CImag) components of the complex capacitance calculated directly from impedance measurements at 90 kHz for a range of blood samples (two-signal MLR); Figure 21 is a plot of recovery error = [two-signalMLR recovered haematocrit – microhaematocrit recovered haematocrit] vs. microhaematocrit recovered haematocrit; Figure 22 is a plot of recovered haematocrit using only the imaginary (CImag) component of the complex capacitance calculated directly from impedance measurements at 90 kHz for a range of blood samples; Figure 23 is a plot of recovery error = [ZImag@90 kHz recovered haematocrit – microhaematocrit recovered haematocrit] vs. microhaematocrit recovered haematocrit; Figure 24 is a plot of three-signal MLR recovered haematocrit vs. microhaematocrit recovered haematocrit for control and +10% NaCl spiked blood samples; Figure 25 is a plot of CReal Intercept recovered haematocrit vs. microhaematocrit recovered haematocrit for control and +10% NaCl spiked blood samples; Figure 26 is a plot of nine-signal MLR recovered haematocrit vs. microhaematocrit recovered haematocrit for control and +10% NaCl spiked blood samples; and Figure 27 is a diagram of a system for determining haematocrit of a blood sample. Detailed Description Figure 1 is a plot of complex capacitance data for blood samples with 45% haematocrit (squares) and 55% haematocrit (triangles). The vertical axis corresponds to the imaginary component of the complex capacitance, CImag, and the horizontal axis corresponds to the real component of the complex capacitance, CReal. The frequencies range from 200 kHz (left-most point for each blood sample) to 90 kHz (right-most point for each blood sample). The lowest frequency is termed the minimum frequency level, fmin. The highest frequency is termed the maximum frequency level, fmax. That is to say that each complex capacitance value has been derived from a complex impedance value of a blood sample measured at a specific frequency and therefore also has a corresponding frequency. Solid lines denote weighted least squares fitted arcs to the capacitance data, with stars indicating the fitted intercept of the axis of the real component of the complex capacitance, CReal intercept, nearest the origin (discussed further below). As noted, the capacitance data is derived from complex impedance data. Complex impedance, Z, is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. The resistance is also known as the real part, Z’, of the complex impedance. The reactance is also known as the imaginary part, Z’’, of the complex impedance. These terms are related by the following expression: ^^ = ^^′ + ^^^^′′Where j is the square root of -1. Complex impedances can be used to calculate real and imaginary components, C’ and C’’ of the complex capacitance, C, using the following formulae: Where f is the respective frequency and |Z| is the magnitude of the vector of the real and imaginary components of the complex impedance in the complex plane. The complex capacitance is related to its real and imaginary components by the following expression: ^^ = ^^′ + ^^^^′′Where j is the square root of -1. The following terms are used interchangeably herein: Z’ and ZReal; Z’’ and ZImag; C’ and CReal; C’’ and CImag. The impedance measurements for the data disclosed herein were performed using a conventional potentiostat (EMStat Pico, Palmsens BV, Houten, The Netherlands). The amplitude of the input signal was 10 mV about a potential of 0.0 V vs screen-printed carbon electrode (SPCE). The blood sample volume was around 2 µl and measurements were taken at room temperature. The dimensions of the flow cell were 2.0 mm by 6.0 mm by 225 µm. The electrodes were rectangular electrodes with dimensions of 3 mm by 2 mm with a separation of 0.3 mm. Each impedance measurement was taken at a specific frequency (i.e. at one of the above described plurality of frequencies). While the impedance measurements and electrical properties can be normalised for electrode area, this is not necessary and has not been done for the data presented herein. Figure 2A illustrates a method 100 of determining the haematocrit of a blood sample. The method comprises providing 101 instructions to a potentiostat in order to determine a plurality of complex impedance values of the blood sample, each complex impedance value have a corresponding frequency. That is to say that the potentiostat is instructed to apply a plurality of different input signals to the blood sample and measure the corresponding output signals (as would be understood by the skilled person), each signal having a corresponding frequency. Next, a plurality of complex impedance values of the blood sample are calculated 103, using the input and output signals. First, second and third electrical properties of the blood sample are then calculated 105 from the plurality of complex impedances. Finally, the haematocrit of the blood sample is determined 107 using a relationship based on the first, second and third electrical properties. Steps 105 and 107 for the present example will now be discussed in detail. Exemplary calculation of first electrical property First, we will discuss how the first electrical property is calculated 105. In the present example, the first electrical property is a real component of a complex capacitance at a predetermined imaginary component value (in complex capacitance space). With reference to Figure 2B, in the present example, the maximum frequency value, fmax, of the frequencies corresponding to the plurality of complex capacitance values is determined 109. The minimum frequency value, fmin, of the frequencies corresponding to the plurality of complex capacitance values is also determined 111. A circular arc is fitted 113 to the plurality of complex capacitance values in capacitance space for the range of frequencies fmin ≤ fmax. That is, for the range of frequencies fmin ≤ f ≤ fmax, the circular arc which satisfies: (^^′ − ^^)2 + (^^′′ − ^^)2 = ^^2is fitted 113, such that R > 0, A ≥ 0 and B ≤ 0. Initial guesses for A and B are the median of C’ and C’’, respectively. As an initial guess for R, half the Euclidean distance between the (C’, C’’) points at the minimum and maximum values of C’ is used. Let ^^ = ^^(^^) = [(^^′(^^)2 + ^^′′(^^)2)] − [^^2 − (^^2 + ^^2) + 2(^^^^′(^^) + ^^^^′′(^^))]represent a nonlinear cost function. Let represent a quadratic weighting function. The circular arc is fitted 113 by applying the iterative Levenberg-Marquardt nonlinear least squares algorithm (an algorithm for least-squares estimation of nonlinear parameters) to find optimal estimates for A, B and R which minimise the weighted sum of squares: The fitted circular arc is then extrapolated 115 to determine 117 the C’ intercept (“CReal”) nearest to the origin, which represents the theoretical capacitance as frequency tends towards +∞: That is, the predetermined imaginary component value in this example is 0 pF. Fitted and extrapolated arcs are shown in Figure 1 for a blood sample with 45% haematocrit (squares) and 55% haematocrit (triangles). Accordingly, it can be seen that the real component of a complex capacitance when CImag = 0 pF (“CReal Intercept”) of the first electrical property for the 55% haematocrit blood sample is approximately 0 pF, and for the 45% haematocrit blood sample it is approximately -8 pF. As would be understood, other predetermined imaginary component values close to 0 pF could also be used, and both the complex capacitance or a real component of the complex capacitance at this point could be used, since these will have similar values to the C’ intercept nearest to the origin and will therefore also positively correlate with haematocrit. Furthermore, an equivalent, unphysical estimator would be given by the ^^′ intercept furthest from the origin: In the present disclosure, only results from the physical estimator are presented, but identical recovery performance would be achieved using the unphysical estimator. The parameter B may be assumed to be equal to zero in order to simplify the fitting process, in which case B may be excluded from the equations above. Optionally, the circular arc fitting may be transformed to a weighted ordinary least squares fitting: For N complex capacitance values each with a real component C’ and imaginary component C’’ and corresponding frequency f, wherein fmaxis the maximum frequency of the frequencies corresponding to the N complex capacitance values, transformed variables X and Y, and fitting weights, W, are calculated: 5 10 Weighted ordinary least squares is then applied to estimate the maximum likelihood fit through (X, Y) subject to weights W: 15 ^̂^ =̅ ^̅ ̅^^̅^ − ^̅^ ^̅ ̅^^̅^20 Parameters A and R are then estimated using: 25 In this example, parameter B is set to zero. Advantageously, using this or a similar transformation may allow the C’ intercept to be 30 calculated using fewer computational resources or less powerful computational software. Calculation of the C’ intercept is also disclosed in international patent application WO2023012267 A1, published on 9 February 2023, which is incorporated herein by reference in its entirety. Exemplary calculation of second and third electrical properties Next we will discuss how the second and third electrical properties can be calculated 105. In the present example, the second electrical property is an imaginary component of a complex impedance at a first frequency, and a third electrical property is an imaginary component of a complex impedance at a second frequency different to the first frequency. Furthermore, the second and third electrical properties are based on a relationship between frequency and an imaginary component of a complex impedance, wherein the relationship is determined from a plurality of impedances of the blood sample at a plurality of different frequencies. Figures 1 and 3 to 6 are plots of electrical properties derived from the same impedance data for 45% and 55% haematocrit blood samples. In the present example, we will focus on Figure 5, which is a plot of the imaginary impedance values vs. frequency over a 90- 200 kHz frequency sweep for the 45% haematocrit blood sample (squares) and the 55% haematocrit blood sample (triangles). Specifically, we will focus on the 45% haematocrit data in this example. A solid line denotes a least squares linear fit to the data. Thus, the linear fit is a relationship between frequency and the imaginary component of the complex impedance of the corresponding blood sample. With reference to Figure 2C, the maximum frequency value, fmax, of the frequencies corresponding to the plurality of imaginary impedance values is determined 119 (200 kHz). The minimum frequency value, fmin, of the frequencies corresponding to the plurality of imaginary impedance values is also determined 121 (90 kHz). A straight line is fitted 123 to the plurality of imaginary impedance values for the range of frequencies fmin≤ fmax. ZImag at a predetermined frequency is then determined for each of the second and third electrical properties. The stars in Figure 5 indicate the fitted ZImag values at 90 kHz (second electrical property ≈ -340 Ω) and 200 kHz (third electrical property ≈ -70 Ω). Thus, the second electrical property is the imaginary component of complex impedance at 90 kHz (“Fitted ZImag @ 90 kHz”) based on the straight-line fit between frequency and the imaginary component of complex impedance, and the third electrical property is the imaginary component of complex impedance at 200 kHz (“Fitted ZImag @ 200 kHz”) based on the straight-line fit between frequency and the imaginary component of complex impedance. As stated above, the last step of the method 100 is to determine 107 the haematocrit of the blood sample using a relationship based on the first, second and third electrical properties. This relationship is determined using Multiple Linear Regression (MLR) based on training data. Here, the MLR recovered haematocrit = b0 + b1 (CReal Intercept) + b2 (Fitted ZImag @ 90 kHz) + b3 (Fitted ZImag @ 200 kHz), where constants b0, b1, b2 and b3 are estimated by least squares fitting to training data. In order to obtain training data, standard methods such as the microhaematocrit capillary method for determining haematocrit of a blood sample are known to the skilled person. For example, using this method, the blood sample is drawn into a capillary and centrifuged, and then the ratio of erythrocytes to blood plasma (i.e. haematocrit) can be measured and expressed as a decimal or percentage fraction. Blood samples with known haematocrit may be prepared by 1) measuring the haematocrit of a native sample; 2) centrifuging the blood sample; and 3) removing or adding plasma to adjust the haematocrit to the desired value. The blood samples are also probed using the impedance methods disclosed herein in order to obtain an MLR recovered haematocrit calibration curve based on the microhaematocrit derived haematocrit values. That is, theconstants of the curve are calculated in a conventional manner by determining the valuesof the respective variables for a plurality of blood samples with known haematocrit values. In other examples, haemoglobin concentration can be determined in a similar manner using a haemoglobin concentration calibration curve instead of a haematocrit calibration curve. A haemoglobin concentration calibration curve can be obtained by taking a blood sample with typical haemoglobin concentration (e.g.157 g / L) and removing or adding donor plasma to create a range of blood samples with different haemoglobin concentrations. The concentration of each adjusted blood sample is then measured, for example using a HemoCue Hb 201+ system. In other examples, the method 100 begins with complex impedance data and the step of providing 101 instructions to potentiostat to determine a plurality of complex impedance values of a blood sample and calculating 103 a plurality of complex impedance values of the blood sample are not necessary. In other examples, the first electrical property is a complex capacitance or imaginary component of a complex capacitance instead of a real component of a complex capacitance. In other examples, only two electrical properties are calculated, so long as the first electrical property is a complex capacitance, imaginary component of a complex capacitance or a real component of a complex capacitance. The second electrical property (and any further electrical properties) may be a complex impedance, real component of a complex impedance, imaginary component of a complex impedance, complex admittance, real component of a complex admittance, imaginary component of a complex admittance, complex capacitance, real component of a complex capacitance, imaginary component of a complex capacitance, or a phase shift. In other examples, only a single impedance value of the blood sample (i.e. not a plurality) is needed to calculate one or more of the electrical properties. Thus, an electrical property may be a directly measured property of the blood sample derived from an impedance measurement at a single given frequency. Furthermore, it is not necessary for the electrical properties to be based on a fitted frequency dependent relationship. As can be seen from, for example, Figure 5, there is not a large difference between the measured ZImag values and the fitted ZImag values. Thus, the fitting step can be left out and values measured at a predetermined frequency can be used as an electrical property for determining the haematocrit / haemoglobin concentration. That said, using a frequency dependent relationship generally improves the reliability of the method by minimising the error associated with a single experimental measure. When a frequency dependent relationship fitted to the relevant data is used, the fit may be a polynomial fit (instead of a linear fit as disclosed above). For example, a polynomial fit is used for the data shown in Figures 3 and 4. Figure 3 is a plot of imaginary capacitance measurements vs. frequency over a 90-200 kHz frequency sweep at 45% (squares) and 55% (triangles) haematocrit. Solid lines denote least squares fitted quadratic models, with stars indicating the fitted CImag values at 90 kHz and 200 kHz. Figure 4 is plot of real capacitance measurements vs. frequency over a 90-200 kHz frequency sweep at 45% (squares) and 55% (triangles) haematocrit. Solid lines denote least squares fitted quadratic models, with stars indicating the fitted CReal values at 90 kHz and 200 kHz. A polynomial model of order ^^ may be fitted using unweighted least squares such that: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ = ^^0 + ^^1^^^^^^^^^^^^^^^^^^ + ^^2^^^^^^^^^^^^^^^^^^2 + ⋯ + ^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^ if ^^^^^^^^^^^^^^^^^^^^^^^^ = 1,Where ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ = { ^^^^^^^^^^ if ^^^^^^^^^^^^^^^^^^^^^^^^ = 2,^^^^^^^^^^ if ^^^^^^^^^^^^^^^^^^^^^^^^ = 3,^^^^^^^^^^ if ^^^^^^^^^^^^^^^^^^^^^^^^ = 4,with the maximum likelihood estimate of ^^^^ for ^^ = 0, 1, … , ^^, respectively.The fitted signal is then set as: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ = ^^0 + ^^1 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + ⋯ + ^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Figure 6 is a plot of real impedance measurements vs. frequency over a 90-200 kHz frequency sweep at 45% (squares) and 55% (triangles) haematocrit. As for Figure 5, solid lines denote least squares fitted linear models, with stars indicating the fitted ZReal values at 90 kHz and 200 kHz. Figures 1 and 3 to 6 relates to data with a minimum frequency of 90 kHz and maximum frequency of 200 kHz, however, the data does not need to be limited to this range. In other examples, each of the plurality of different frequencies is greater than 0.1 Hz, 1 kHz or 10 kHz and / or each of the plurality of frequencies is less than 100 kHz, 500 kHz or 1,000 kHz. Exemplary performance data for method of determining haematocrit Figures 7 to 11 show: CReal intercept, fitted ZReal, ZImag, CReal, CImag at 90kHz and 200 kHz, and unfitted ZReal, ZImag, CReal, CImag at 90kHz and 200 kHz versus haematocrit measured via the microhaematocrit method for a range of blood samples with differing haematocrit. As explained above, the microhaematocrit method is a standard method for determining haematocrit known to the skilled person. In detail, Figure 7 is a plot of CReal intercept vs. haematocrit. Figures 8A-D are plots of fitted CReal @ 90 kHz, fitted CReal @ 200 kHz, fitted CImag @ 90 kHz and fitted CImag @ 200 kHz vs. haematocrit. Figures 9A-D are plots of fitted ZReal @ 90 kHz, fitted ZReal @ 200 kHz, fitted ZImag @ 90 kHz and fitted ZImag @ 200 kHz vs. haematocrit. Figures 10A-D are plots of (unfitted) CReal @ 90 kHz, (unfitted) CReal @ 200 kHz, (unfitted) CImag @ 90 kHz and (unfitted) CImag @ 200 kHz vs. haematocrit. Figures 11A-D are plots of (unfitted) ZReal @ 90 kHz, (unfitted) ZReal @ 200 kHz, (unfitted) ZImag @ 90 kHz and (unfitted) ZImag @ 200 kHz vs. haematocrit. The values of the electrical properties were all obtained under the same experimental conditions disclosed above for the data in Figure 1. The positive correlation between these electrical properties and haematocrit is self evident from these plots. It can also be seen that a positive correlation is obtained whether or not a fit is used. Figure 12 is a plot of Multiple Linear Regression (MLR) recovered haematocrit vs. microhaematocrit recovered haematocrit for the exemplary method disclosed above. As such, MLR recovered haematocrit = b0 + b1 (CReal Intercept) + b2 (Fitted ZImag @ 90 kHz) + b3 (Fitted ZImag @ 200 kHz) where b0, b1, b2 and b3 are estimated by least squares fitting to training data and have the following values in the present example: b0 = 64.1; b1 = 2.16; b2 = 0.00271; b3 = 0.0308. The equation of the fitted solid line shown in the plot is y = 0.994x + 0.454 with an R2of 0.994. Figure 13 is a plot of recovery error = MLR recovered haematocrit – microhaematocrit recovered haematocrit vs. microhaematocrit recovered haematocrit. The dashed line denotes y = 0. From the high R2value and low recovery error, it can be seen that the method disclosed herein is highly accurate. For comparison, Figure 14 is a plot of CReal intercept (only) recovered haematocrit vs. microhaematocrit recovered haematocrit. Here, recovered haematocrit = b0 + b1 (CReal Intercept) where b0 and b1 are estimated by least squares fitting to training data and have the following values in the present example: b0 = 55.5; b1 = 1.65. The equation of the fitted solid line shown in the plot is y = 0.979x + 0.899 with an R2of 0.979. Figure 15 is a plot of recovery error = CReal intercept recovered haematocrit – microhaematocrit recovered haematocrit vs. microhaematocrit recovered haematocrit. The dashed line denotes y = 0. Thus, it can be seen that the multivariate method disclosed herein improves the accuracy with which haematocrit can be determined. Figure 16 is a plot of nine-signal MLR recovered haematocrit vs. microhaematocrit recovered haematocrit. Here, nine-signal MLR recovered haematocrit = b0 + b1 (CReal Intercept) + b2 (Fitted ZImag @ 90 kHz) + b3 (Fitted ZImag @ 200 kHz) + b4 (Fitted ZReal @ 90 kHz) + b5 (Fitted ZReal @ 200 kHz) + b6 (Fitted CImag @ 90 kHz) + b7 (Fitted CImag @ 200 kHz) + b8 (Fitted CReal @ 90 kHz) + b9 (Fitted CReal @ 200 kHz), where b0,1,…,9 are estimated by least squares fitting to training data and have the following values in the present example: b0 = 7.85e+01; b1 = 1.51; b2 = 6.85e-02; b3 = - 7.08e-02; b4 = 1.34e-03; b5 = 5.44e-02; b6 = 9.90e-02; b7 = 5.10e-01; b8 = 7.81e-01; b9 = -1.69. The equation of the fitted line is y = 0.992x + 0.329 with an R2of 0.992. Figure 17 is a plot of recovery error = nine-signal MLR recovered haematocrit – microhaematocrit recovered haematocrit vs. microhaematocrit recovered haematocrit. The dashed line denotes y = 0. Thus, it can be seen that the presently disclosed method can be performed with additional electrical parameters, and that doing so may increase the accuracy of the method. Figure 18 is a plot of recovered haematocrit by combining all experimental terms (i.e. excluding a CReal Intercept term). Here, eight-signal MLR recovered haematocrit = b0 + b1 (ZReal@90 kHz) + b2 (ZReal@200 kHz) + b3 (ZImag@90 kHz) + b4 (ZImag@200 kHz) + b5 (CReal@90 kHz) + b6 (CReal@200 kHz) + b7 (CImag@90 kHz) + b8 (CImag@200 kHz), where b0,1,…,8 are estimated by least squares fitting to training data and have the following values in the present example: b0 = 105; b1 = 1.7; b2 = 0.0485; b3 = -0.0536; b4 = 0.00387; b5 = 0.0354; b6 = 0.201; b7 = -0.209; b8 = 0.454. The equation of the fitted line is y = 0.992 x + 0.337; R2= 0.992. Figure 19 is a plot of recovery error for recovered haematocrit by combining all experimental terms. The dashed line denotes y = 0. Thus, it can be seen that a CReal Intercept is not needed for the present method to be accurate. Figure 20 is a plot of recovered haematocrit using experimental (i.e. not fitted) CReal@90 kHz and ZImag@90 kHz. Here, two-signal MLR recovered haematocrit = b0 + b1 (CReal@90 kHz) + b2 (ZImag@90 kHz), where b0, b1 and b2 are estimated by least squares fitting to training data and have the following values in the present example: b0 = 57.2; b1 = -0.782; b2 = -0.0738. The equation of the fitted line is y = 0.938 x + 2.735; R2= 0.938. Figure 21 is a plot of recovery error = CReal@90 kHz + ZImag@90 kHz MLR recovered haematocrit – microhaematocrit recovered haematocrit vs. microhaematocrit recovered haematocrit. Figure 22 is a plot of recovered haematocrit using only experimental ZImag @ 90 kHz. The equation of the fitted line is y = 0.856 x + 6.316; R2= 0.856. Figure 23 is a plot of recovery error = ZImag@90 kHz recovered haematocrit – microhaematocrit recovered haematocrit vs. microhaematocrit recovered haematocrit. Figures 22 and 23 correspond to a conventional method of haematocrit determination using only a component of the complex impedance. Thus, comparison of these plots and R2values shows that the present method is more accurate than conventional methods of haematocrit determination based on impedance measurements. Figure 24 is a plot of MLR recovered haematocrit = b0 + b1 (CReal Intercept) + b2 (Fitted ZImag @ 90 kHz) + b3 (Fitted ZImag @ 200 kHz) vs. microhaematocrit recovered haematocrit for a control blood sample (circles, solid line y = 0.981x + 0.878) and +10% NaCl spiked blood sample (squares, dashed line y = 0.961x -1.058). As can be seen, the accuracy of the MLR recovered haematocrit remains high even when the sample is spiked with NaCl. This shows that the method is largely unaffected by blood plasma conductivity / ionic strength, which is a common issue with existing methods of haematocrit determination. Figure 25 is a plot of CReal Intercept (only) recovered haematocrit vs. microhaematocrit recovered haematocrit for a control blood sample (circles, solid line y = 0.907x + 4.276) and +10% NaCl spiked blood sample (squares, dashed line y = 0.741x + 8.194). As can be seen, this method is sensitive to the NaCl spike, demonstrating that the MLR method is superior to the CReal Intercept (only) recovered haematocrit method. Figure 26 is a plot of nine-signal MLR recovered haematocrit vs. microhaematocrit recovered haematocrit for a control blood sample (circles, solid line y = 0.986x + 0.619) and +10% NaCl spiked blood sample (squares, dashed line y = 0.953x -0.878). Nine- signal MLR recovered haematocrit = b0 + b1 (CReal Intercept) + b2 (Fitted ZImag @ 90 kHz) + b3 (Fitted ZImag @ 200 kHz) + b4 (Fitted ZReal @ 90 kHz) + b5 (Fitted ZReal @ 200 kHz) + b6 (Fitted CImag @ 90 kHz) + b7 (Fitted CImag @ 200 kHz) + b8 (Fitted CReal @ 90 kHz) + b9 (Fitted CReal @ 200 kHz). Thus, it can be seen that the MLR method remains largely unaffected by blood plasma conductivity / ionic strength when many electrical properties are included in the method. The disclosed methods may be implemented using computer executable instructions. A computer program product or computer readable medium may comprise or store the computer executable instructions. The computer program product or computer readable medium may 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 media in which information is stored for any duration (e.g. for extended time periods, permanently, brief instances, for temporarily buffering, and / or for caching of the information). A computer program may comprise the computer executable instructions. The computer readable medium may be a tangible or non-transitory computer readable medium. The term “computer readable” encompasses “machine readable”. Thus, in an aspect, there is provided a computer-readable medium comprising instructions which, when executed by one or more processors, causes the one or more processors to perform the method of Figure 2A and / or Figure 2B and / or Figure 2C. System for determining haematocrit of a blood sample Figure 27 is a diagram of a system 200 for determining haematocrit of a blood sample. The system 200 comprises a central bus structure; a cell 201 configured to receive a blood sample; a potentiostat 203 connected to the cell 201 and central bus structure and configured to determine a plurality of complex impedance values of the blood sample in the cell 201; data processing resources such as memory 205 connected to the central bus structure and storing the above-disclosed computer-readable medium; a processor 207 connected to the central bus structure and configured to execute the instructions of the computer-readable medium; and a display adapter 209, display device 211, one or more user-input device adapters 213, one or more user-input devices 215, such as a keyboard and / or a mouse, and one or more communications adapters 217, all connected to the central bus structure. The display device 211 has touch-input functionality and so also functions as a user-input device 215. The potentiostat may comprise or be in communication with a further processor and further data processing resources for processing measurement data, or may use the memory 205 and processor 207 of the system in order to measure and / or calculate impedance and capacitance data. The examples of the disclosure shown in the drawings and disclosed above are only examples and are not intended to limit the scope of the appended claims, including any equivalents as included within the scope of the claims. Various modifications are possible and will be readily apparent to the skilled person in the art. It is intended that any combination of non-mutually exclusive features disclosed herein are within the scope of the present disclosure. That is, features of the disclosed examples can be combined with any appropriate aspect disclosed above and optional features of any one aspect can be combined with any other appropriate aspect.

Claims

Claims 1. A method of determining haematocrit or haemoglobin concentration of a blood sample, the method comprising: calculating first and second electrical properties based on one or more complex impedances of the blood sample; and determining the haematocrit or haemoglobin concentration of the blood sample using a relationship based on the first and second electrical properties, wherein the first electrical property is a complex capacitance or a real or imaginary component of a complex capacitance.

2. A method according to claim 1, wherein the second electrical property is a complex impedance, real component of a complex impedance, imaginary component of a complex impedance, complex admittance, real component of a complex admittance, imaginary component of a complex admittance, complex capacitance, real component of a complex capacitance, imaginary component of a complex capacitance, or a phase shift.

3. A method according to any preceding claim, wherein the relationship based on the first and second electrical properties is a multivariate relationship.

4. A method according to any preceding claim, wherein the first and / or second electrical properties are each calculated based on the impedance of the blood sample at a plurality of different frequencies.

5. A method according to any preceding claim, wherein the first electrical property or the second electrical property is based on a frequency-dependent relationship determined from a plurality of impedances of the blood sample at a plurality of different frequencies.

6. A method according to claim 5, wherein each of the plurality of different frequencies is greater than 0.1 Hz, 1 kHz or 10 kHz and / or each of the plurality of frequencies is less than 100 kHz, 500 kHz or 1,000 kHz.

7. A method according to any preceding claim, wherein the first electrical property is calculated based on a plurality of complex capacitance values of the blood sample and a complex capacitance at a predetermined imaginary component value, each of the pluralityof complex capacitance values of the blood sample having a corresponding frequency.

8. A method according to claim 7, wherein calculating a complex capacitance at a predetermined imaginary component value comprises extrapolating from the plurality of complex capacitance values.

9. A method according to claim 8, 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 circular arc fitting is transformed to a weighted ordinary least squares fitting.

10. A method according to claim 9, wherein the corresponding frequencies, f, have a maximum value, fmax, and the circular arc is fit for the range of frequencies f ≤ fmax.

11. A method according to claim 9 or 10, wherein the corresponding frequencies, f, have a minimum value, fmin, and the circular arc is fit for the range of frequencies fmin ≤ f.

12. A method according to any of claims 9 to 11, wherein, wherein the circular arc is fit by applying an algorithm for least-squares estimation of nonlinear parameters.

13. A method according to any of claims 7 to 12, wherein each corresponding frequency of the plurality of complex capacitance values of the blood sample is less than or equal to 1,000 kHz.

14. A method according to any of claims 7 to 13, wherein each corresponding frequency of the plurality of complex capacitance values of the blood sample is greater than or equal to 0.1 Hz.

15. A method according to any of claims 7 to 14, wherein the predetermined imaginary component value is less than or equal to 500 pF / mm2, preferably less than or equal to 200 pF / mm2, more preferably less than or equal to 100 pF / mm2, and yet more preferably substantially equal to or equal to zero.

16. A method according to any of claims 7 to 15, 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.

17. A method according to any preceding claim, wherein determining the haematocrit or haemoglobin concentration of the blood sample using a relationship based on the first and second electrical properties comprises determining the haematocrit or haemoglobin concentration of the blood sample using a relationship based on a plurality of electrical properties, the plurality of electrical properties comprising the first and second electrical properties and one or more additional electrical properties.

18. A method according to any of claims 7 to 17, wherein the first electrical property is the complex capacitance at a predetermined imaginary component value, the second electrical property is an imaginary component of a complex impedance at a first frequency, and a third electrical property is an imaginary component of a complex impedance at a second frequency different to the first frequency.

19. A method according to claim 18, wherein the first electrical property is based on a plurality of complex capacitance values of the blood sample and a complex capacitance at a predetermined imaginary component value, each of the plurality of complex capacitance values of the blood sample having a corresponding frequency, and the second and third electrical properties are based on a relationship between frequency and an imaginary component of a complex impedance, wherein the relationships are determined from a plurality of impedances of the blood sample at a plurality of different frequencies.

20. A method according to any preceding claim, the method further comprising providing instructions to a potentiostat in order to determine the first and second complex impedances of the blood sample.

21. A method according to any preceding claim, the method further comprising calculating the first and second complex impedances of the blood sample.

22. A computer-readable medium comprising instructions which, when executed by one or more processors, causes the one or more processors to perform the method of any of claims 1 to 21.

23. A system for determining haematocrit or haemoglobin concentration of a blood sample, the system comprising: a cell configured to receive the blood sample;a device configured to determine one or more complex impedance values of the blood sample; a computer-readable medium according to claim 22; and a processor configured to execute the instructions of the computer-readable medium.

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