Europ. J. Intensive Care Medicine 1,153-162 (1975) ©by Springer-Verlag 1975

The Changes in Blood Resistivity with Haematocrit and Temperature S. N. Mohapatra and D. W. Hill Research Department of Anaesthetics, The Royal College of Surgeons of England, Lincoln's Inn Fields, London, U.K.

Abstract. The temperature dependence of the resistivity of blood samples with haematocrits from 16 to 52.5% has been investigated over the temperature range of 22 ° to 40'°C at a frequency of 100 kHz. The resistivity of whole blood increased with an increase in haematocrit and a decrease in temperature. The data fitted the relationship: O

Pohm-cm = (6.272 Hct + 75.176) - (0.104 Hct+ 1.467) tC where Hct is the percentage haematocrit.

Key words: Blood resistivity.

Introduction The electrical impedance method of Kubicek et al. (1966), provides a convenient non-invasive technique for the monitoring of changes occurring in the stroke volume and cardiac output of patients with normal hearts. There has been an increasing tendency to use it during anaesthesia and intensive care, with outpatients and with pregnant women and for the study of the cardiovascular dynamics of normal subjects at rest and exercise. In order to calculate the stroke volume with this thoracic impedance method an accurate value of the patient's blood resistivity is required. This is particularly important in the monitoring of the cardiac output of patients on haemodialysis, where a wide range of haematocrits may be encountered (Hill and Thompson, 1975 b). Additionally, in order to be able to use the technique in hypothermic or hyperthermic patients, a knowledge of the relationship between the blood resistivity and body temperature is required. Although there is a considerable literature on the resistivity of blood (Fricke, 1927; Schwan, 1941 ; Okada and Schwan, 1960; Schwan, 1963; Geddes and Baker, 1967; Rosenthal and Tobias, 1948; Geddes and Sadler, 1973), very few investigators have used fresh human blood samples covering a range of haematocrits. In most cases the blood was reconstituted to obtain the desired mixture of plasma and erythrocytes and usually time-expired bank blood was employed for this purpose. Hill and Thompson (1975a) measured the resistivity of freshly

drawn human blood at 37 °C and 100 kHz over the haematocrit range 14-45%. Their values were consistently lower than those of Kubicek (personal communication) and Geddes and Sadler (1973), who all used time-expired bank blood. The difference between the values of Hill and Thompson (1975) and those of Geddes and Sadler (1973) was approximately 10 percent. For this reason, we decided to use individual blood samples obtained from patients whose haematocrits ranged from 16 to 52.5% and this avoided reconstituting cells and plasma to produce a range of haematocrits. This paper also reports data on the resistivity of fresh human blood samples of different haematocrits over the temperature range of 2 2 - 4 0 °C. Since the specific resistance (p) of blood increases with an increase in haematocrit and decreases with an increase in temperature a single composite equation has been proposed to account for the blood resistivity at a given temperature and for a given haematocrit over the temperature range 2 2 - 4 0 °C.

M e t h o d s and Materials

Measurement o f Blood Resistivity One of the major sources of error, in the measurement of the conductivity of an electrolyte using a two electrode conductivity cell is the presence of the electrode-electro-

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lyte interface impedance arising from the electrode polarisation. To represent the actual value of the electrolyte resistivity this interface impedance at the electrodes should be reduced to a minimum. The electrode separation variation technique of Fricke and Curtis (1934), is one of the many methods, summarised by Schwan (1963), designed to correct for the electrode polarisation contribution to the observed total impedance. Geddes (1973) has developed a variable-path-length cell, based on this principle, in order to measure the electrolyte resistivity conveniently and accurately without an electrode polarisation impedance error. Its use with blood has been reported by Geddes and Sadler (1973), and Hill and Thompson (1975 a). In our case, the volume of the blood samples available was strictly limited because low-haematocrit blood samples are relatively scarce. We were able to work with 5 ml as a minimum quantity of blood.

The Variable-Path-Length Conductivity Cell The cell (Fig. 1) of Hill and Thompson, was modified by the insertion of a thermocouple junction to measure the actual temperature of blood. The conductivity cell was constructed from a 5 ml disposable plastic hypodermic syringe barrel. A pair of circular polished, stainless-steel electrodes were arranged in parallel and could be moved forwards and backwards by turning a pair of threaded rods whose pitch was 40 threads/inch. Behind each stainless-steel disc was a rubber gasket, usually taken from the syringe plunger, which served as a water-tight seal. A pair of flexible connecting wires were soldered to the rear of the electrodes and brought out through the axial bores of the threaded rods. This avoided the twisting of the connecting wire when the threaded rods were rotated to move the electrodes along the bore of the cell. The thermocouple junction was inserted through a small hole in the lower side-arm to which a stopcock was also fitted. The blood sample was introduced into the cell via the upper side-arm. The interWATER IN

nal diameter of the cell was 12.7 mm (0.5 inch). The diameter of the electrodes was very slightly less than that of the bore of the syringe. The maximum possible separation of the electrodes was approximately 35 ram. The outer jacket of the cell was made of Perspex and was perfused with a flow of water from a thermostaticallycontrolled water bath. The Perspex jacket helped to visualise the presence of air bubbles in the sample. The complete cell assembly could be rocked at 2 - 5 Hz by means of an eccentric driven from a variable-speed electric motor in order to maintain the erythrocytes in suspension. The presence of the side arms had a negligible effect on the readings as the maximum amount of blood contained in them was only 0.3 ml.

Working Formulae Fig. 2 represents an equivalent circuit of a variable-pathlength conductivity cell, Geddes (1973). The resistors R 1 and R2, together with the capacitors C1 m d C2, constitute the electrode-electrolyte impedance, Warburg (1899, 1901). Rc is the resistance of the column of blood contained in the cell and Cd is the distributed shunt capacitance of the cell. If the ratio (L/d) of the electrode separation (L) to the electrode diameter (d) is kept large, then the reactance of "Cd" can be neglected. Under these conditions, the measured impedance Zm, between the terminals 1 and 2 is Zml = (R1 + 1/jwCl) + pL 1/A + (R 2 + 1/jwC2) CI

......................

C2

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THREADED ROD 40 t.p.i. SEAL s t a i n l e s s s t e e l electrode

Fig. 1. Variable-path-length conductivity cell (after Hill and Thompson, 1975 a)

S. N. Mohapatra and D. W. Hill: The Changes in Blood Resistivity with Haematocrit and Temperature Where "p" is the resistivity of the blood contained in the cell in ohm-cm; "L1" is the initial electrode separation in cm, "A" is the cross-sectional area (Trd2/4) of the column of the blood in cm 2 ; w = 27rf where "f" is the frequency in Hz. On decreasing L1 to L 2 by expelling some of the blood, the cell impedance falls from Zm 1 to Zm 2 . If the constancy of the electrode polarisation impedances maintained while the electrode spacing is varied, then Zmz is given by:

155

Zm 2 = (R 1 + 1/jwCi) + pL2/A + (R 2 + 1/jwC2)

R 3 and R 4 were non-inductive decade resistance boxes of 0.1% accuracy, the smallest increments being 0.1 ~2. C3 and C4 were measured in a component bridge as 1000 pF and Cs = 1000 pF. The bridge balance was detected with a frequency-selective detector (type 5710 by H. Tinsley & Co.). At cell electrode spacings of 25 mm or more, the measured impedance of the cell filled with blood was purely resistive and "Cd" was negligible. Thus in our case, two readings of Rc, one before and one after rotating either of the threaded rods through four turns were taken, such that

By subtraction:

(L 1 - L2) = 0.1 in = 0.254 cm

(Zml - Zm2) = p(LI - L,~)/A

Since A = 1.2668 cm 2,

The difference found in the measured impedance is solely a function o f the resistive component of the cell impedance, but is totally independent of the electrode polarisation impedance and the cell constant. The specific resistance o f the blood sample, can be determined by making two measurements with different electrode spacings. An inverted form of a Schering a.c. bridge (Fig. 3) energised at 100 kHz from a transistor oscillator was used to measure the impedance of the cell which formed one arm of this bridge. This allowed the provision of a constant electrode current density so that the constancy of the polarisation impedance was maintained as the electrode spacing was varied, because it is known that the electrode-electrolyte impedance depends on the current density, (Geddes, 1972). The two balance conditions for the bridge are:

p = 4.9873 ( R q - Rc2)

R c = (C4/C3)R 3 and Ca = (R4/R3) C3

.C3/

The temperature of the blood was measured by means of a thermocouple and a digital voltmeter. The thermocouple consisted of two junctions made from Alumel & Cromel metals. The reference junction was maintained at 0 °C inside a Dewar flask containing melting ice and the other junction was used to sense the blood temperature. The thermo-electric EMF was measured with a Solartron (LM 1440) digital voltmeter. It was verified that the high inpedance voltmeter did not shunt the Bridge. Prior to mounting the thermocouple inside the cell it was calibrated against a mercury thermometer inside a thermostatically controlled water bath.

Measurement of Haematocrit and E.S.R.

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Measurement of Blood Temperature

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The haematocrit of each blood sample was determined by centrifuging it at 12000 rev/min for five minutes in a Table 1

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resistivity measurement (after Hill and Thompson, 1975a)

Haematocrit %

E.S.R.

16 17.5 19 25 31 35 35 38.5 42 45 5O 52.5

26 26 21 t2 11 11 12 8 4 2 2 4

mm/h

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EuropeanJournal of Intensive Care Medicine, Vol. 1, No. 4 (1975) upper side arm and thus in the course of two or three readings, the concentration of red cells decreased. To eliminate the effects of sedimentation, the cell was emptied after each set of readings which were taken as quickly as possible. When the temperature of the water bath had reached the next desired temperature, the well mixed blood was replaced in the cell. Each blood sample was measured over the temperature range of 2 2 - 4 0 °C. Any further increase in temperature of the blood produced haemolysis. There was a marked increase in the measured resistivity, in contrast to the steady fall in cell resistivity which occurs as the temperature increases. This is shown in Fig. 4.

Hawksley micro-centrifuge. The mean value of three aliquots was taken. The erythrocyte sedimentation rate was measured by the method of Wintrobe and Landsburg (1935). As usual the bloods with the lower haematocrits were seen to have the higher E.S.R.'s (Table 1).

Experimental Procedure (sample handling) Each fresh sample of blood was collected in a plastic sample container with lithium-heparin as the anti-coagulant and was fully saturated with air. No significant difference in blood resistivity was found when ETDA was used instead of heparin as the avis coagulant. Initially, the cell electrodes were brought very close to each other with only sufficient spacing between them for the introduction of the needle of the filling syringe. Blood was then carefully introduced into the cell by pressing the plunger of the filling syringe with one hand and rotating one of the threaded rods simultaneously with the other. In this way, the maximum electrode spacing was filled with blood without introducing any air bubbles. Since the knobs at the end of each threaded rod could be aligned with a pair of fiduciary marks, each rod could be rotated through a definite number of complete turns. Particular difficulty was experienced with the low haematocrit bloods in maintaining the erythrocytes in suspension even by increasing the rocking frequency. In these circumstances~ if the electrodes were moved forward, instead of expelling blood, only plasma emerged from the

250

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In order to verify our method of measurement, at first, the resistivity of a 0.9% physiological saline sample was measured at 38 °C and 100 kHz. The value obtained was 49 ~2 cm which was comparable to the value of 50.5 g2 cm at 37 °C and 1 kHz quoted by Geddes and Baker (1967). Despite all precautions being taken, such as taking care to move the electrodes through exactly the same distance in each case and also to keep the blood cells in suspension by rocking, there was a scatter in the results when the blood resistivities were measured. The resistivity values were plotted against temperature for each blood sample and the least-squares best fit line determined, Figs. 5 to 8. The regression equations, correlation coefficients, haema-

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S. N. Mohapatra and D. W. Hill: The Changes in Blood Resistivity with Haematocrit and Temperature 250 -

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European Journal of Intensive Care Medicine, Vol. 1, No. 4 (1975) •

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S. N. Mohapatra and D. W. Hill: The Changes in Blood Resistivity with Haematocrit and Temperature tocrit values and the number of data points in each case are listed in Table 2. As was evident from the varying slopes of the resistivity versus temperature plots for different haematocrits, the resistivity of blood is a function of both the temperature and the red blood cell concentration. A multiple linear regression was carried out for the whole set of 312 data points to form a composite equation to account for both the variables. The final expression was of the following form: p = (6.272 (Hct) + 75.176) - (0.104 (Hct) + 1.467) t (1) where p is the blood resistivity in ohm-cm, Hct is the percentage haematocrit, and t is the temperature in °C. At a body temperature of 37 °C this equation reduces to

(2)

p = 2.424 ( H c t ) + 20.916

It can be seen from Eq. (1), that the blood resistivity has a negative temperature coefficient and a positive coefficient with haematocrit.

159

Discussion The scatter in the blood resistivity results was almost impossible to eliminate, although the blood was rocked to maintain its red cells in suspension, changes in its resistivity still occurred probably due to erythrocyte orientation, migration and sedimentation in the particulate suspension. These variations in blood resistivity for a given sample were also noted by Schwan (1941) and Hill and Thompson (1975). To obtain reproducible results Schwan specifically used settled-out blood in his technique. In our case the scatter was greater for low haematocrit blood samples (25, 19, 17.5, 16%), as would be expected from their high erythrocyte sedimentation rate values (Table 1). The resistivity values for bloods of various haematocrits found by Geddes and Sadler (1973), Hill and Thompson (1975 a) and Kubicek (personal communication) were compared with the values obtained at 37 °C from the composite equation given by this study. The comparison is shown in Table 3. It can be seen that the derived values are very close to those found for fresh blood by Hill and Thompson (1975 a).

Table 2. Resistivity versus temperature for blood samples of various haematocrits at 100 kHz Number of data points 20 43 27 18 21 21 26 38 16 23 21 38

Haematocrit

Correlation Coefficient

%

Resistivity (p) Simple linear regression form (p = naT + C) ohm-cm

16 17.5 19 25 31 35 35 38.5 42 45 50 52.5

-(3.55980) T + 193.15922 -(3.28944) T + 184.17059 -(3.09734) T + 181.66691 -(3.88972) T + 224.9779 -(4.52652) T + 263.2534 -(5.06944) T + 292.65703 -(5.18870) T + 296.94804 -(5.57395) T + 319.51029 -(6.21083) T + 350.35981 -(6.03909) T + 353.3072 -(6.66792) T + 389.5320 -(6.84432) T + 402.2298

-0.99310 -0.97512 -0.97712 -0.98712 -0.99535 -0.99382 -0.99519 -0.99263 -0.99807 -0.99815 -0.99773 -0.99891

Table 3. A comparison of the experimentally determined human blood resistivities at 37 °C for various haematocrits with those derived from the composite equation developed in this study Haematocrit

Resistivity at 37.5 °C and 100 kHz (Kubicek)

Resistivity at 37 °C and 25 kHz (Geddes & Sadler, 1973) p = 53.2 Exp (0.022 Hct)

Resistivity at 37 °C and 100 kHz (Hill & Thompson, 1975) p = 2.102 Hct+ 30.098

%

ohm-cm

ohm-cm

ohm-cm

Resistivity at 37 °C and 100 kHz derived from the composite equation (Mohapatra & Hill, 1975) p = 2.424 Hct + 20.916 ohm-cm

t0 15 20 25 30 35 40 45

89 94 102 116 121 133 148 168

66 74 83 92 103 115 128 143

51 62 72 83 93 104 114 125

45.156 57.276 69.396 81.516 93.636 105.756 117.876 129.996

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Euro ,ean Journal of Intensive Care Medicine, Vol. 1, No. 4 (1975)

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Fig. 10. A three dimensional plot of resistivity, temperature, and haematocrit. (Note the increase in resistivity with an increase in haematocdt and the decrease in resistivity with an increase in temperature)

S. N. Mohapatra and D. W. Hill: The Changes in Blood Resistivity with Haematocrit and Temperature Since the blood resistivity may be expressed as a linear function of the haematocrit (Eq. 2), the samples of pure plasma may be expected to have the lowest resistivity. In contrast, the plasma resistivities were found to range from 60 g2 cm to 63.5 g2 cm at 38 °C and moreover, it was interesting to note that the values were not consistent but dependent upon the centrifugation time. Such variations were also noted by previous workers (Rajewsky and Schwan, 1944; Hill and Thompson, 1975 a). The resistance of the serum of various blood samples varies only slightly, but decreases as the duration of centrifugation increases, according to a detailed investigation by Rajewsky and Schwan (1944). They quoted the typical values for the plasma resistivity of sheep blood as 88.1, 87.3, 86, 83.5, 80.2 and 78.1 ohm-cm corresponding to 1, 2, 3 and 4 hours of centrifugation time. Hence, in order to obtain reproducible results the time of centrifugation should be reduced as much as possible (Okada and Schwan, 1960). The effect of ageing of the blood sample on its resistivity was noted by Schwan (1941), who showed that the resistivity of defibrinated and washed sheep blood cells fell considerably after 7 - 8 hours at a rate of one percent per two hours. A typical value quoted was 500 g2 cm at 18 °C, which fell to 460 g2 cm at the end of 24 hours. In the light of these studies, one would expect the bank expired, reconstituted blood sample resistivities of Geddes and Sadler and Kubicek to be lower than ours which were obtained from fresh uncentrifuged blood samples. However, in practice, their values were consistently higher than ours.

Conclusions It has long been known that blood, like other electrolytes, has a negative temperature coefficient of resistivity. A two percent decrease in resistivity for each degree centigrade increase in temperature is often quoted whenever the frequency dependence is very small (Schwan, 1941 and t963). Sometimes to convert the blood resistivity from the temperature of measurement to the body temperature, the rate of decrease of saline resistivity is employed. For example, Burger and Van Milaan (1943) measured the blood resistivity at 18 °C and corrected the values by means of a factor of 1.45 times less, which was derived from saline measurements. Previous studies on the effect of temperature change on blood resistivity have been carried out with a.c. on sheep or rabbit blood (Schwan, 1941) or with d.c. (Burger and Van Milaan, 1943). The fall in blood resistivity with respect to an increase in temperature has also been noted for human blood samples by Geddes and Baker (1967) and Frewer (1972). However, their samples were from bank expired blood, so the question arises as to whether the - 2 % coefficient remains constant with variations of the haematocrit for different blood samples, and

161

whether the temperature coefficient for saline is identical with that for blood. This study has shown, that the rate of decrease of resistivity with temperature is not the same for all samples of human blood, as is evident from the varying slopes of the temperature versus resistivity plots. Fig. 9 compared the temperature dependance of plasma resistivity and saline resistivity. The slopes of the least-squares fit line were -1.316 and -0.932 for plasma and saline respectively. These values of slope indicated that the temperature coefficient for saline may be used for plasma but that it is not applicable to all samples of blood. The composite equation (1) linking haematocrit, temperature and resistivity may now be used to calculate the blood resistivity for blood samples with haematocrits in the range 16 to 52.5 percent and over a temperature range of 22 to 40 °C. The error between the calculated and experimental values is generally less than 3%, except for those samples with haematocrits of 16, 17.5, 19 and 25 where the error is 8% at the most. However, the mean percentage error for the whole data set is 0.22 and the standard deviation of the percentage error is 3. Apart from employing this equation in the impedance cardiograph technique, it may be useful in the electrical method of warming blood (Sher etal., 1965; Van Nierup, 1967) or determing its haematocrit (Okada and Schwan, 1960). Fig. 10 shows a three dimensional plot of resistivity, temperature and haematocrit which describes the increase in resistivity with an increase in haematocrit and the decrease in resistivity with an increase in temperature. Fresh blood does differ from reconstituted blood as far as its electrical properties are concerned. Consistently low resistivity values were found compared with those of Geddes and Sadler (1973) and Kubicek (personal communication), thus confirming the observations of Hill and Thompson (1975). Further studies are being persued on the ageing of whole blood and also on the effect of centrifugation on blood resistivity. These might explain why our resistivity values for fresh blood are consistently lower than those reported by others using time expired bank blood.

Acknowledgements. We are grateful to Dr. G. R. Graham of the Hospital for Sick Children, Great Ormond Street; Dr. C. Ogg of Guy's Hospital and to the clinical staff of the Research Department of Anaesthetics for the supply of blood samples. Thanks are also due to Mr. G. V. Devarajan and Dr. C. V. Subramanian, University of Salford for their advice on the computer analysis. One of us (SNM) wishes to acknowledge the financial support of the Vandervell Foundation. Professor L. Geddes and W. Kubicek have kindly provided useful information and encouragement.

References Burger, H. C., Van Milaan, J. B.: Measurements of the specific resistance of the human body to direct current. Acta. Med. Scand. 114,584 (1943)

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Frewer, R. A.: The effect of frequency changes on the electrical conductance of moving and stationary blood. Med. Biol. Engng. 10,734 (1972) Fricke, H.: The electric capacity of suspensions with special reference to blood. J. Gen. Physiol. 9, 137 (1927) Fricke, H., Curries, J. H. J.: The electrical impedance of haemolyzed suspensions of mammalian erythrocytes. J. Gen. Physiol. 18,821 (1934-1935) Geddes, L. A.: Electrodes and the measurement of bioelectric events, p. 228. New York: Wiley 1972 Geddes, L. A.: Measurement of electrolytic resistivity and electrode-electrolyte impedance with a variable-length conductivity cell. Chem. Instrum. 4, (3), 157 (1973) Geddes, L. A., Baker, L. E.: The specific resistance of biological material. Med. Biol. Engng. 5,271 (1967) Geddes, L. A., Sadler, C.: The specific resistance of blood at body temperature. Med. Biol. Engng. 11,336 (1973) Hill, D. W., Thompson, F. D.: The effect of haematocrit on the resistivity of human blood at 37 °C at 100 kHz. Med. Biol. Engng. 13,182 (1975a) Hill, D. W., Thompson. F. D.: The importance of blood resistivity in the measurement of cardiac output by the thoracic impedance method. Med. Biol. En~ng. 13, 187 (1975b) Kubicek, W. G., Karnegis, J. N., Patterson, R. P., Witsoe, D. A., Mattson, R. H.: Development and evaluation of an impedance cardiac output system. Aerospace Med. 37, 1208 (1966) Okada, R. H., Schwan, H. P.: An electrical method to determine haematocrits. IRE Trans. Med. Elect. ME-7, 188 (1960) Rajewsky, B., Schwan, H. P.: ~ber die individuellen Schwankungen des spezifischen Widerstandes yon Blut und Serum. Z. experim. Medizin. 113,553 (1944)

Rosenthal, R. L., Tobias, C. W.: Measurement of the electrical resistance of human blood; use in coagulation studies and cell volume determinations. J, Lab. Clin. Med. 13, 1110 (1948) Schwan, H. P.: 0ber die Niederfrequenz-Leitfiihigkeit von Blut und Blutserum bei verschiedenen Temperaturen. Zeits. f. d. ges. Exp. Med. 109, 531 (1941) Schwan, H. P.: Determination of biological impedance. In: Physical techniques in biological research. Ed. W. Nastuck, New York: Academic Press, VIB 1963 Sher, L. D., Schwan, H. P., Maczuk, J.: The electrical impedance of frozen blood and applications to electrical methods of thawing. Tokyo: Digest 6th I.C.M.E.B.E., p. 547, (1965) Stewart, G. N.: The conductivity of erythrocytes compared with that of serum. Ann. J. Physiol. 90, 194 (1929) Van Nierop, J. H.: Blood conductivity and R. F. heating. Biomed. Engng. 2, 446 (1967) Warburg, E.: ~lber das Verhalten sogenannter unpolarisierbarer Elektroden gegen Wechselstrom. Ann. Phys. Chem. 67,493 (1899) Warburg, E.: 0ber die Polarization compacitat des Platins, Ann. Phys. 6, 125 (1901) Wintrobe, M. M., Landsberg, J. W.: A standardised technique for the blood sedimentation test. Ann. J. Med. Sci. 189, 102 (1935) S. N. Mohapatra D. W. Hill Research Department of Anaethetics The Royal College of Surgeons of England Lincoln's Inn Fields London WC2A 3PN/England