CHAPTER V. HEMATOCRIT ESTIMATION FROM TRANSDUCED
5.1 Review of Hematocrit and Previous Measurement Methods
Blood is made up of red blood cells (RBCs), white blood cells (WBCs), platelets, and plasma. The measure of the fractional level of red blood cells in the whole blood is expressed as hematocrit (HCT). For example, a hematocrit of 30% means that there are 30 milliliters of red blood cells in 100 milliliters of blood. The HCT is a very useful clinical indicator in surgical procedures and hemodialysis [78, 79]. It can affect the adenosine diphosphate-included aggregation of human platelets [2] and produce a decreased bleeding time [80]. An increased hematocrit can refer to an indicator of unfavorable outcome in the course of acute myocardial infarction [81].
In addition, many studies showed that hematocrit variations can significantly affect the accuracy of glucose measurements [3, 5, 8]. The glucose results are overestimated at lower hematocrit levels and underestimated at higher hematocrit levels. Therefore, the hematocrit estimation also plays an important role in improving performance of glucose meters.
5.1.1 Typical Methods for Measuring Hematocrit
The hematocrit can manually determined by centrifugation method. In which a capillary tube called micro-hematocrit tube is filled with blood. When the tube is centrifuged at 10,000RPM for five minutes, the blood is separated into layers. The RBCs with the greatest weight are forced to the bottom of the tube, the WBCs and platelets form a thin layer between the RBCs and the plasma that is the buffy coat, and the top layer is liquid plasma. The hematocrit is measured as the percent of the RBC column to the total blood column.
With modern lab equipment, the hematocrit is typically measured from a blood
by automated analyzer, which can make several other measurements at the same time.
In the automated machines, the hematocrit is not directly measured. It is calculated by multiplying the red cell count by the mean cell volume (number of red blood cells per liter):
HCT=Mean Corpuscular Volume x Red Blood Cell Count, (5.1)
The mean corpuscular volume (MCV) is measurement of the average RBC volume.
With anemia patients, it allows to identify whether they are microcytic anemia (MCV below normal range, <76fl) or macrocytic anemia (MCV above the normal range,
>100fl).
5.1.2 Hematocrit Determination from Impedance
There are also different methods for estimating hematocrit. In which Hanai’s model to blood could be used for hematocrit from impedance. With assumption of red blood cells to be non-conducting, the ratio of blood to plasma conductivities may be
(1 )3/ 2
blood plasma
δ HCT
δ = − . (5.2)
Let us denote Vc to be the internal cell volume located between the electrodes separated by a distance L, impedance is given by
2
blood c Z L
V δ
= . (5.3)
From (5.2) and (5.3) we have
2(1 ) 3
plasma c
L HCT
Z V δ
− −
= / 2 . (5.4)
At the start of dialysis, we have
2 3
0 (1 0)
plasma c 0
L HCT
Z V δ
− / 2
= − . (5.5)
If we assume that the plasma conductivity is constant that means
, then from (5.4) and (5.5) we have solution for HCT as
plasma plasma
δ =δ0
HCT=1-(1-HCT0)(Z0/Z)2/3. (5.6)
However, it showed that the plasma conductivity is not constant; it can be changed by protein concentration due to ultrafiltration. This variation is given by [82]
(1 )
plasma pw
δ =δ −αCp , (5.7)
where Cp in g/l is protein concentration, δpw is the conductivity of plasma water (mS/cm) and α=0.0022. In the absent of ionic transfer from/to the dialysate, Cp
increases at the same rate as hematocrit Cp=Cp0HCT/HCT0. Combining (5.4), (5.5) and (5.7), we have
32 0
0
0 0
1 1
1 x1 /
p p HCT αC
Z
Z HCT αC HCT HCT
− −
⎛ ⎞
= ⎜⎝ − ⎟⎠ − 0 . (5.8)
The iteration is required for resolving HCT. This method requires an initial hematocrit measurement by a classical method. It can be used only for continuous hematocrit monitoring.
5.1.3 Hematocrit Measurement by Dielectric Spectroscopy
The dielectric spectroscopy, which is also called impedance spectroscopy is a measurement of the dielectric properties of medium as a function of frequency. It is based on the interaction of an external field with the electric dipole moment of the sample, and often expressed as permittivity. Methods to measure hematocrit based on permittivity changes were proposed by researchers [9, 83]. It found that there is relationship between blood-dielectric-permittivity changes and hematocrit. There are three frequency-dependent phenomena characterizing the electric non-faradic passive properties of cell suspensions that are α, β, and γ dispersions [83]. Originally
proposed by Foster and Schwan [83], the relationship between β-dispersion and the permittivity change of a suspension of spherical particles covered by a dielectrically different membrane is given by
2 1 2
ε kP
Δ = P
⎛ + ⎞
⎜ ⎟
⎝ ⎠
, (5.9)
where ∆ε=εs-ε∞ is the permittivity β-dispersion change, εs and ε∞ are the low- frequency and high-frequency permittivity, respectively, P is the cell volume fraction (HCT/100), and k is the constant defined by
0 9
4
RCm
k= ε . (5.10)
Note that ε0=8.85x10-12 F/m is the vacuum permittivity, R is cell radius, and Cm is the cell membrane capacity.
Besides the nonlinear model shown in (5.9), Treo et al. [9] proposed a linear regression which can be used for estimating hematocrit from the permittivity β-
dispersion change as:
∆ε=a+bxHCT. (5.11) In addition, the multiple linear regressions among ∆ε, HCT, conductivity, and
osmolarity were also applied [9].
∆ε=a+bxHCT+cxπ+dxδ, (5.12)
where δ is conductivity and π is osmolarity. However, the results obtained from the multiple linear regressions are not significantly deviated from the linear regression and the best results on the correlation were obtained from the linear expression.