Quantitative Analyses of the CO2 Dissociation Curve of Oxygenated Blood and the Haldane Effect in Human Blood

Japanese Journal of Physiology, 33, 601-618, 1983 Quantitative Analyses of the CO2 Dissociation Curve of Oxygenated Blood and the Haldane Effect in Human Blood Hiroshi TAZAWA, Masaji MocHIZUKI, Masakazu TAMURA, and Tomoko KAGAWA Department of Physiology, Yamagata University School of Medicine, Yamagata, Yamagata, 990-23 Japan Abstract The theoretical equations for the C02 dissociation curve derived by MocHIZUKI et al. (1983) have made it possible to estimate the C02 contents in blood at any Pco2 by putting the intra- and extracellular bicarbonate contents at a certain Pco2 into them. Moreover, according to their Haldane effect equation, the carbamate and bicarbonate contributions are evaluated, when the Haldane effect and its plasma component are known along the PCo2 range. In order to accomplish the above calculation the water shifts due to the Pc02 and 02 saturation changes were measured as the changes of hematocrit. The hematocrit of oxygenated blood was linearly correlated to ph with a factor of -0.037, and the difference in hematocrit between oxygenated and deoxygenated bloods was 0.004 in terms of fractional hematocrit. The blood and plasma C02 contents measured at four different Pco2's were compared with the ones calculated by use of the intra- and extracellular bicarbonate contents at 42 Torr Pco2. The measured and calculated C02 contents coincided fairly well with each other. Using intra- and extracellular bicarbonate contents in oxygenated blood together with the Haldane effect and its plasma component, the carbamate contribution was then calculated. The carbamate content was about 1.2 mmol/liter blood over a Pcp2 range of 20 to 100 Torr, and its ratio to the total Haldane effect decreased from 50 to 40 %, as PC0, was increased. The ratio of the bicarbonate shift to the total bicarbonate change due to the Haldane effect, ranging from 0.82 to 0.66, was significantly greater than that measured by changing PCO2. Key Words: Henderson-Hasselbalch equation, C02 dissociation curve, hemoglobin buffer value, Haldane effect, carbamate content. Received for publication November 11, 1982 m, m f*n 1inJEl 601

602 H. TAZAWA, M. MOCHIZUKI, M. TAMURA, and T. KAGAWA In the preceding paper (MocHIzuK! et al., 1983) it was clarified that the C02 dissociation curve of blood could be evaluated by using two Henderson-Hasselbalch equations in the red cell and plasma compartments. When the intra- and extracellular bicarbonate contents at Pc02=Po are put in the respective equations, the bicarbonate concentration at any Pco2(x) are evaluated. Their equations are described as follows : to g x =(1 +6).4 HP+4pK ' p +logl + 4Ht P o p We ' Ht + (1 +a)(1--a)j9c (HC0. 4pHP 1 3 jc(po)/ht ' ( ) and where togp x a =4pHP+4pK'p+ l0g1-- yvp,(1_ht) 4Ht + {Qp+(1 +6)A,9c. Ht/(1-Ht)}4pHP (HC03~ Po 1-Ht) (2) 4pHc-(1+c) ' 4pHP, (3a) Q=-0.21 +0.05.4pHP. The notations are similar to those in the preceding paper (MocHizuKI et a!.,1983). The parameters relating to the above equations are summarized in Table 1, A. Let Po be the Pco2 close to 40 Torr. The C02 content in the blood, Cb(P0) has a close correlation to the curvature of the dissociation curve (MocHlzuKI et al., 1982), and in addition, the curvature is approximately determined by the buffer value of hemoglobin, /3c. Therefore, when the intra- and extracellular bicarbonate contents, (HC031c(Po) and (HC03-)p(P0) are measured, the buffer value is determined from the relation between the Cb(40) and /3c. The individual variations of the buffer value of plasma protein, 9p is fairly small, and in addition, the influence to the parameter values to be derived is not great. Therefore, the /3p was assumed to be 7.5 mmol/(liter plasma rn ph) (TAKIWAKI et al., 1983). Similarly, the water concentrations in the cell and plasma, We and Wp cause no significant errors, thus, they were assumed to be 0.715 and 0.94, respectively. The changes in water concentrations in the red cell and plasma which were effective, to some extent, to the Donnan ratio were put in forms of 4Ht/ We Ht and -4Ht/ Wp (1-Ht), respectively, as shown in Eqs. (1) and (2). As for the Pco2 or ph dependency of the hematocrit, however, no experimental data have yet been available, thus, in the present study its ph dependency was measured in order to make the calculation easier. The other parameter values to be derived from the equations are tabulated in Table 1A, together with the equations through which the determinations were carried out. MocHizuKI et al. (1983) also derived the simultaneous equations for the (3b) Japanese Journal of Physiology

ANALYSES OF CO2 CONTNET IN BLOOD 603 Table 1. A. Parameters to be given and derived from the dissociation curve equations. Haldane effect. Using their equations, the carbamate and bicarbonate contributions to the Haldane effect are evaluated from the intra- and extracellular bicarbonate contents of the oxygenated bloods, the Haldane effect and its plasma component. The equations are given by and -(1 --~Q) d p H P =l0 g 1-- + dht + (1-2')(HE-R) We Ht HC03- ox (4) - dphp=1o g 1 - W dht 1 - Ht + HC03 ~'(HE-R) ox ' (5) HEp=~'(HE-R). (6) The notations of the parameters have been described in the preceding paper (MocHIzuKI et al., 1983). When the Pco2 is changed, the hematocrit decreases as the ph increases. However, when the deoxygenation proceeds, the hematocrit increases with the ph. That is, the relation between the ph and hematocrit observed in the oxygenated blood does not hold in the Haldane effect. Thus, in the present study the hematocrit difference between the oxygenated and deoxygenated bloods was measured together with other parameter values. Besides the measurement of the ph- and 02 saturation-dependencies of the hematocrit, we attempted to validate the theoretical equations by comparing the C02 dissociation curves calculated with those measured. The C02 dissociation Vol. 33, No. 4, 1983

604 H. TAZAWA, M. MOCHIZUKI, M. TAMURA, and T. KAGAWA curves of blood and plasma were measured in both the oxygenated and deoxygenated bloods at 5 different PCO2's in a range of 5 to 100 Torr. From the intraand extracellular bicarbonate contents at 42 Torr, the blood and plasma CO2 contents at other four PCO2's were evaluated using Eqs. (1), (2), and (3). The close correlation was observed between the measured and calculated C02 content of the blood and their red cell and plasma components. Furthermore, the validity of the Haldane effect equation was checked by comparing the carbamate contribution and the Donnan ratio for bicarbonate in the oxygenated and deoxygenated bloods. From the average C02 dissociation curve of both the oxygenated and deoxygenated bloods, the Haldane effect, HE, and its plasma component, HEp, were calculated. Putting, then, the HE and HEp into Eqs. (4), (5), and (6) together with the intraand extracellular bicarbonate contents of the oxygenated blood, the carbamate and bicarbonate contributions were obtained. The parameters to be put in and to be derived from the equations are summarized in Table 1 B together with the relations connecting these parameters. The carbamate content was independent of the PC02 (FERGUSON and ROUGHTON (1934), FERGUSON (1936), and STADIE and O'BRIEN (1937) and showed 1.2 mmol/liter blood, on an average, which corresponded to the middle value between those of ROSSI-BERNARDI and ROUGHTON (1967) and BAUER and SCHRODER (1972). On the other hand, the calculated Donnan ratios for HC03- in the oxygenated and deoxygenated bloods coincided well with each other, as shown by FITZSIMONS and SENDROY (1961). Through such processes as above, the theoretical equations of the C02 dissociation curve and the Haldane effect were proved to be feasible. METHODS Venous blood of 20 ml was drawn into a heparinized syringe from 7 healthy male subjects at rest in the morning, 2 to 3 hr after breakfast. Blood samples were equally divided into 10 aliquots and stored in an ice bath before equilibration procedures. The equilibration was carried out at 37 C using a tonometer (IL-237). Ten gas mixtures were used for equilibration, five of which were 02-free, and the remainders contained about 25 % 02. The CO2 concentration was determined with a Scholander gas analyzer to the nearest 0.01 %, and the Pco2 was calculated referring to the barometric pressure. After 8 min equilibration, a blood sample of 0.15 ml was drawn in a Hamilton microsyringe-750cn whose dead space was flushed with the same gas mixture as used forr equilibration. A 0.08 ml sample in the syringe was introduced to a ph capillary electrode (IL-Meter 227), and a remainder was transferred under paraffin layer in a cone-shaped cuvette. The paraffin prevented the sample from contamination with air. The blood of 0.03 ml was sucked in a glass capillary of Natelson analyzer (NATELSON, 1951) for measuring C02 content and the rest of the blood was emptied into glass capillaries for hematocrit. In preliminary experiments using fresh dog blood, CO2 contents obtained from Japanese Journal of Physiology

ANALYSES OF CO2 CONTENT IN BLOOD 605 the Natelson analyzer were compared with those from a conventional Van Slyke analyzer. The following relation was obtained: CCO2(Van Slyke)=-0.55+ 1.12 CCo2(Natelson), (N=23, r=0.998), where Cco2 is the C02 content in vol %. According to the above equation the Cco2 measured with the Natelson was corrected. For the hematocrit measurement, the blood was spun down at 10,000 rpm for 8 min. The whole blood ph was determined in duplicate and the average value was taken. For separating true plasma, the tonometered blood was transferred under paraffin in the centrifuge tube and separated at 37 C and 1,600 g for 10 min. After separation, the true plasma was analyzed for ph and C02 content. The ph measurement was repeated in the plasma after equilibrating it with the same gas mixture for 5 min. There was no significant difference in ph between before and after the reequilibration, indicating no change in gas composition during separation. The water concentrations in the red cell and plasma were measured at a PCO2 level of about 42 Torr and a P02 level of about 190 Torr. A thin film of 0.2 ml red cells or plasma spread on a slide glass was dried at about 110 C. The water concentration in kg H20/liter RBC or kg H20/liter plasma was determined by measuring the sample weight before and after desiccation. The water in the red cell was, furthermore, corrected by assuming a plasma volume trapped in the intracellular space to be 3 % according to JACKSON and NUTT (1951). At other Pco2 levels (x), the water concentration was calculated from the hematocrits at PC02= 42 and x Torr, and the water concentration at PCO2=42 Torr as follows: and Wc(x) = ( Wc(42) Ht(42) --f - d Ht)/Ht(x), (7) Wp(x)=( Wp(42)(1-Ht(42))-4Ht)/(1-Ht(x)). (8) The calculation of the C02 dissociation curve was carried out through the simultaneous equations, Eqs. (1), (2), (3a), and (3b). In order to solve the above equations, (HC03-)c, (HC03-)p, and Sc at Po have to be put in the equations. Actually, the average C02 dissociation curves of the whole blood and true plasma of the oxygenated blood were measured. Then, (HC03-)p was evaluated by subtracting dissolved C02 from the C02 content in the plasma. The intracellular C02 content was evaluated from the C02 contents in the whole blood and true plasma by referring to the hematocrit. (HC03-)c was evaluated, by subtracting dissolved C02 and carbamate from the intracellular C02. Physically dissolved C02, in the red cell, was calculated by using 0.026 mmol/(liter RBC Torr) for C02 solubility (VAN SLYKE et al., 1928; BARTELS et a!., 1959). The carbamate fraction in the oxygenated blood was evaluated by assuming it to be about 40% of that in the Haldane effect, referring to the experimental data of BAYER and SCHRODER (1972). Since the carbamate fraction of the Haldane effect and its PC02 dependency were not evaluated without knowing the carbamate in the oxygenated blood, these Vol. 33, No. 4, 1983

606 H. TAZAWA, M. MOCHIZUKI, M. TAMURA, and T. KAGAWA fractions were estimated simultaneously through a trial and error method. As the result of it, the carbamate fraction in the oxygenated blood was estimated to be about 0.5 mmol/liter blood independently of Pco2, the details of which will be described later in this paper. Therefore, (HC03)c was evaluated by subtracting the dissolved CO2 and 0.5 mmol/liter blood of carbamate from the intracellular CO2 content. The CO2 dissociation curve of the oxygenated blood measured in the present study was given, on an average, by the following experimental equation : Cb=1.35 B-2.27.pco2B (vol %), (9) where B is a parameter with values in a range of 0.42 to 0.48 varying from subject to subject. The curvature of the dissociation curve of Eq. (9) is closely correlated with the B value. On the other hand, the curvature of the theoretical dissociation curve computed from Eqs. (1), (2), and (3) is mainly determined by the 8c. In the preceding paper (MocHIzuKI et al., 1983) a simulation method was elaborated to evaluate the relation between the ~3c and the CO2 content at Pco2=40 Torr, Cb(40). Thus, for convenience to obtain the /3c value in the individual subjects, the above relation was computed again from the new dissociation curve of Eq. (9), using the same technique as before. First, assuming the carbamate fraction in the oxygenated blood to be 0.5 mmol/liter blood and the ratio of (HC03-)c/(HCO3-)p to be 0.48, both the (HCO3-)c and (HCO3-)p were calculated at various Cb(40) values. Then, substituting these values into Eqs. (1) and (2) together with the measured Ht, 4Ht, Wc, and Wp values at Pco2=40 Torr, the j9c was determined, where /3p= 7.5 mmol/(liter plasma ph) was used (TAKIWAKI et a!., 1983). Finally, /3c-Cb(40) relationship was obtained, as shown in Fig. 1, from which the /3c of the individual subject was evaluated using their own Cb(40) values actually measured. The carbamate fraction in the Haldane effect was estimated from the three simultaneous equations (MocHIzuKI et a!., 1983), Eqs. (4), (5), and (6). (HC03-)c (ox) and (HCO3-)p(ox) in Eqs. (4) and (5) were obtained from the average CO2 dissociation curves of the whole blood and true plasma according to the procedure as already mentioned. HE and HE P were obtained from the CO2 dissociation curves measured under the oxygenated and deoxygenated states in the whole blood and true plasma, respectively. RESULTS (1) Hematocrit and water concentration The hematocrit and water concentration measured at P002=42 Torr are summarized in Table 2. The average values for water concentration in the red cell (Wc) and plasma (Wp) were 0.715 kg H20/liter RBC and 0.937 kg H20/liter plasma, showing good agreement with the previous data (SAVITZ et al., 1964; FUNDER and WIETH, 1966; SIGGAARD-ANDERSEN, 1974). ph dependency of the Japanese Journal of Physiology

ANALYSES OF CO2 CONTENT IN BLOOD 607 Fig. 1. Relation between the jlc and Cb (40). Fig. 2. Relation between the hematocrit and the ph obtained by varying PC02 in blood with the normal hematocrit. The solid and broken lines were obtained in the oxygenated and deoxygenated bloods, respectively. The plotted points are the averages and the arrows, the standard deviation. hematocrit obtained by changing PC02, is shown in Fig. 2. The open and closed circles were obtained in the oxygenated and deoxygenated bloods, respectively. In both cases a linear relation was observed. The gradient, 4Ht/4pH, in the oxygenated blood was distributed among subjects in a range of -0.055 and -0.028, and the average gradient was -0.037. Vol. 33, No. 4, 1983

608 H. TAZAWA, M. MOCHIZUKI, M. TAMURA, and T. KAGAWA The experimental equations for the hematocrit of oxygenated and deoxygenated bloods were expressed as follows Ht(ox)=0.439+0.51 x 103P02-0.24x 10-5Pco22, (10) and Ht(deox)=0.443+0.51 x 10-3Pco2--0.26 x 10-5Pco22. (11) The difference in hematocrit between the oxygenated and deoxygenated bloods, Table 2. Fractional hematocrit (Ht), hemoglobin concentration (Hb, g/dl), and water concentration in true plasma (kg H20/liter plasma) and red cells (kg H20/liter RBC), measured at P02=42 Torr. Fig. 3. Relation between the hematocrit (Ht), the water concentrations in plasma (Wp) and in the red cell (Wc) and the P002. The solid lines were obtained in the oxygenated blood and the broken, in the deoxygenated. Japanese Journal of Physiology

ANALYSES OF CO2 CONTENT IN BLOOD 609 4Ht=Ht(ox)--Ht(deox), was obtained from the difference between Eqs. (10) and (11) as ca. -0.004. The water concentrations in the red cell and plasma were evaluated by putting Ht(ox) and Ht(deox) of Eqs. (10) and (11) into Eqs. (7) and (8), respectively, and shown in Fig. 3 together with the hematocrit against the Pco 2 (2) Hemoglobin buffer value The buffer value of hemoglobin, f3c for each subject was obtained from the relation between the Cb(40) and 40c values in Fig. l. The evaluated,3c values are shown in Table 3. The average j3c value was 66.3 mmolf (liter RBC.pH), which was higher than the value measured by Siggaard-Andersen in blood sample with no Pco2. However, it was fairly compatible with the data of VAN SLYKE et al. (1923). In Table 3 the buffer value of true plasma (5tp) is also tabulated. The j3tp values were evaluated from (HC03-)p and ph values calculated from Eqs. (1) and (2) at two Pco2's of 25.0 and 62.5 Torr and also from those measured at the same Pco2's. Fairly good correlation was observed between the calculated and measured j3tp values. (3) C02 contents in whole blood, plasma, and red cell compartments The validities of Eqs. (1), (2), and (3) were appreciated by comparing the Cb, (O)c, and (HC03-)p values measured at P02=8, 25, 62, and 92 Torr with the calculated values at the same Pco2. The (C02)c and (HC03-)p values measured at 42 Torr (Table 4) were used together with the j3c (Table 3) as the initial values in the calculation. In Fig. 4 the measured and calculated blood C02 contents, Cb are depicted. The chain line is the regression line, which is given by, Cb(calc)= -0.310+1.003 x Cb(meas), Table 3. Cb(40) and the buffer values in the individual subjects. Vol. 33, No. 4, 1983

610 H. TAZAWA, M. MOCHIZUKI, M. TAMURA, and T. KAGAWA Table 4. PC02, (C02)c, and (HC03)p values used for the calculation of the CO2 content and bicarbonate concentrations at four other PCo2's, i.e., 8, 25, 62, and 96 Torr. where the correlation coefficient was 0.998. The (C02)c and (HC03)p values are shown in Figs. 5 and 6, respectively. The regression line of (5)c C2in Fig. 5 was given by (C02)c(calc)=-0.117+ 1.006 x (C02)c (meas), where the correlation coefficient was 0.981. The regression line of (HC03)p in Fig. 6 was given by, (HC03-)p(calc)=0.114+0.982 x (HC03)p (meas), Fig. 4. Calculated Cb values plotted against the measured Cb. sion line. The chain line is the regres- Japanese Journal of Physiology

ANALYSES OF CO2 CONTENT IN BLOOD 611 Fig. 5. Calculated intracellular bound CO2 plotted against the measured bound CO2. I I IV 6{J. ~1 IVV' /~ r r r rr r rvr /r./ vvv Fig. 6. Calculated bicarbonate content in plasma plotted against the measured bicarbonate. Vol. 33, No. 4, 1983

612 H. TAZAWA, M. MOCHIZUKI, M. TAMURA, and T. KAGAWA where the correlation coefficient was 0.997 good correlation was observed. In all the above three C02 quantities (4) Carbamate fraction in the Haldane effect The experimental equations for the average C02 dissociation curves in the oxygenated and deoxygenated bloods and true plasmas were expressed in the exponential form as follows : Cb(ox)=3.93 x Pco2o.435 (mmol/liter blood), Cb(deox)=5.10 x Pco2 400 (mmol/liter blood), Cp(ox)=3.78 x Pco2 35 (mmol/liter blood), and Cp(deox)=4.31 x P020335( mmol/liter blood). In Fig. 7 are shown the average experimental values and the theoretical dissociation curves derived from Eqs. (1) to (3). Good agreement is shown between the measured and calculated values in all the curves. From the differences between the oxygenated and deoxygenated curves the Haldane effect and its plasma component were calculated. The upper curve of Fig. 8 shows the Haldane effect, and the area denoted by HE P is the plasma component of the Haldane effect. The ph difference in plasma, dphp=php (ox)-ph P (deox), was calculated from (HC03-)p and Pco2, using the Henderson-Hasselbalch equation. dphp was given approximately by Fig. 7. CO2 dissociation curve of whole deoxygenated bloods. The solid and and deoxygenated bloods, respectively. values obtained in the 7 subjects. blood and true plasma of the oxygenated and broken lines were calculated in the oxygenated The plotted points along them are the average Japanese Journal of Physiology

ANALYSES OF CO2 CONTENT IN BLOOD 613 -dphp=0.076 x PCO2-o.i6' (12) and showed a gradual decrease around -0.04 as PC02 increased. Thus, using Eqs. (3a) and (3b), the relation between the intracellular and plasma ph changes Fig. 8. The measured Haldane effect (HE) and its plasma component (HEp), and the calculated carbamate fraction illustrated along the Pcc2. Fig. 9. Relations between the 2' and R/HE ratios and the Pco2. Vol. 33, No. 4, 1983

614 H. TAZAWA, M. MOCHIZUKI, M. TAMURA, and T. KAGAWA are given from Eq. (12). Subsequently, referring to the hematocrit values of Eqs. (10) and (11), and the water concentrations in Fig. 3, the carbamate fraction and A' value are evaluated from Eqs. (4), (5), and (6). The lower curve of Fig. 8 shows the calculated carbamate fraction. It gradually increases with increasing Pco2, reaching the maximum of about 1.24 mmol/ liter blood at a Pco2 range of 50 to 60 Torr, and then gradually decreasing at a higher Pco2 range. In Fig. 9 are shown the ratio of the carbamate to the Haldane effect, R/HE, and the A' value. The former decreases linearly from 0.5 to 0.4, as Pco2 increases. The A' value is generally higher than that observed when the Pco2 is changed (MocHlzuKI et al., 1983). It decreases exponentially in a range of 0.88 to 0.66, as the Pco2 increases. DISCUSSION The present analyses were carried out in order to validate the simultaneous equations for the C02 dissociation curve, Eqs. (1), (2), and (3), and tnose for the Haldane effect, Eqs. (4), (5), and (6). For the sake of the analyses the Pco2 dependencies of the hematocrit and water concentrations in the red cell and plasma were measured together with ph and C02 content. As shown in Fig. 2, a linear relation was found between the hematocrit and ph, where the coefficient, (4Ht/ dph) was -0.037. Then, the theoretical dissociation curve was obtained by putting this relation into Eqs. (1) and (2). In the preceding paper (MocHlzuK! et al., 1983) the Donnan ratio of the bound Fig. 10. Donnan ratio for CO2 plotted against ph in the plasma. The plotted points represent the experimental values obtained in the present measurement, whose regression line is illustrated by the chain line. The solid line is the theoretical one obtained in the preceding paper (Mocsuzuxi et a1.,1983) from the typical CO2 dissociation curve. Japanese Journal of Physiology

ANALYSES OF CO2 CONTENT IN BLOOD 615 CO2 was compared between two cases: in one of which a was given by Eq. (3b) and in the other a=0. When a=0, the ratio for the bound CO2 was almost constant, regardless of the PC02. On the other hand, when Eq. (3b) was used, the ratio decreased along with the Pcp2, as expected from the previous data on the ratio and ph P (FITZSIMONs and SENDROY, 1961). In Fig. 10, the actually measured ratios of (C i2) for individual subjects are plotted against ph. The solid line is the theoretical curve cited from the preceding paper, and the chain line is the regression line of the plotted points. The regression and theoretical lines are given respectively by, and r(c02)=-0.3 r(c;02)=-0.37 ph+2.96, ph+3.49. No statistical significance is observed in the difference between the above two lines, indicating an applicability of the a value of Eq. (3b). When Eq. (3b) is used for the a value, the j3c inevitably becomes a value in a range of 63 to 70 mmol/(liter RBC. ph), in order that Eqs. (1) and (2) satisfy the actual CO2 dissociation curve. Thus, it may be safe to say that the 15c value in a ragne of 63 to 70 mmol/(liter RBC.pH) is also valid. Fig. 11. Calculated Donnan ratio for HC03- plotted against ph in plasma. The intracellular bicarbonate of the oxygenated blood was estimated by subtracting the carbamate of 0.5 mmol/liter blood from (CU2)c evaluated from the data of Fig. 7. The (HCO3-)c of the deoxygenated blood was evaluated by referring to the data of Fig. 8. Vol. 33, No. 4, 1983

616 H. TAZAWA, M. MOCHIZUKI, M. TAMURA, and T. KAGAWA BAUER and SCHRODER (1972) estimated the carbamate content in the oxygenated blood to be about 40 % of the carbamate in the Haldane effect. In the present study, HE was about 3 mmol/liter blood and R/HE was in a range of 0.4 to 0.5 (Fig. 8). Based on these results and Bauer and Schroder's estimation, the Donnan ratio for HC03-, r(hc03-), was calculated for both the oxygenated and deoxygenated bloods. In Fig. 11, r(hc03) of the oxygenated and deoxygenated bloods are illustrated against ph by the open and closed circles, respectively. The Donnan ratio for the bound C02 is certainly higher in the deoxygenated blood than in the oxygenated (FITz5IMONS and SENDROY, 1961). For the r(hc03-), however, there was no difference between the oxygenated and deoxygenated bloods, as similarly observed in the data of Fitzsimons and Sendroy. They also measured r(c1) in both the oxygenated and deoxygenated bloods, in which the value in the deoxygenated blood was obviously higher than that in the oxygenated blood. BAUER and SCHRODER (1972) determined the carbamate fraction in the red cell by subtracting from the intracellular bound C02 the intracellular bicarbonate, which was estimated from the extracellular bicarbonate by assuming r(hc03^)=r(cl-). This assumption, however, seems invalid, referring to the data on r(cl j (HENDERSON, 1928; FITzsIMONS and SENDROY, 1961) and on r(hc03) (FITzsIMONS and SENDROY, 1961, and Fig. 11). The C02 contents in the whole blood at 40 Torr PC02, Cb(40), when plotted against (HCO3)p(40) 'in the same subject, are distributed along two-lower and upper--regression lines corresponding to the oxygenated and deoxygenated bloods, respectively, as shown in Fig. 12. The similar distribution has already been obtained in the previous study (MOcHIzuKI et al., 1982). The vertical distance Fig. 12. Relation between Cb (40) and (HCO3-)p in the oxygenated (open circles) and the deoxygenated (closed circles). Japanese Journal of Physiology

ANALYSES OF CO2 CONTENT IN BLOOD 617 between the two lines is about 1.8 vol %, as shown by the arrow. Since the carbamate contribution in the Haldane effect is as great as 40 to 50 % of the total effect of ca. 6 vol %, as shown in Figs. 8 and 9, the above vertical distance is expected to be in a range of 2.4 to 3.0 vol %. However, the actually measured distance is smaller than that predicted. This tendency will be explained by the high A' value in the Haldane effect. In general, the A value observed when the Pco2 changes, varies in a range of 0.5 to 0.6, depending on the Pco 2 range. On the other hand, the A' ratio in the Haldane effect is about 0.7, as illustrated in Fig. 9. Thus, it is possible that in the Haldane effect the (HCO3-)p increases more than (HC03-)c upon the deoxygenation. In consequence, the vertical distance shown in Fig. 12 becomes smaller than the carbamate content in the Haldane effect. In conclusion, it may be safe to say that the simultaneous equations for the CO2 dissociation curve, Eqs. (1) to (3), and the Haldane effect, Eqs. (4) to (6), are applicable to the analyses of the acid-base status in the red cell and plasma. The a value of Eq. (3b) and therefore, the jlc value ranging from 63 to 70 mmol/(liter RBC. ph) may also be valid for the blood with the normal hematocrit. This work was supported in part by a Grant-in-Aid for Scientific Research 56480086 from the Ministry of Education, Science and Culture of Japan. REFERENCES BARTELS, H., BUCHERL, E., HERTZ, C. W., RODEWALD, G., and SCHWAB, M. (1959) Lungenfunktionsprufungen, Springer Verlag, Berlin, pp. 305, 409. BAUER, C. and SCHRODER, E. (1972) Carbamino compounds of hemoglobin in human adult and fetal blood. J. Physiol. (Loud.), 227: 457-471. FERGUSON, J. K. W. and RoUGHTON, F. J. W. (1934) The chemical relationships and physiological importance of carbamino compounds of CO2 with hemoglobin. J. Physiol. (Loud.), 83: 87-102. FERGUSON, J. K. W. (1936) Carbamino compounds of CO2 with human hemoglobin and their role in the transport of CO2. J. Physiol. (Loud.), 88: 40-55. FITZSIMONS, E. J. and SENDROY, J., Jr. (1961) Distribution of electrolytes in human blood. J. Biol. Chem., 236:1595-1601. FUNDER, J. and WIETH, J. 0. (1966) Potassium, sodium and water in normal human red cells. Scand. J. Clin. Lab. Invest., 18: 167-180. GARBY, L. and MELDON, J. (1977) The Respiratory Functions of Blood, Plenum Medical Book Co., New York and London, pp. 114-141. HENDERSON, L. J. (1928) Blood. A Study in General Physiology, Yale University Press, New Haven, pp. 107-109. JACKSON, M. D, and NUTT, M. E. (1951) Intercellular plasma and its effect on the absolute red cell volume determination. J. Physiol. (Lond.),115: 196-205. MOCHIZUKI, M., TAKIWAKI, H., KAGAWA, T., and TAZAWA, H. (1983) Derivation of theoretical equations of the CO2 dissociation curve and the carbamate fraction in the Haldane effect. Jpn. J. Physiol., 33: 579-599. Mocnizuiu, M., TAZAWA, H., and TAMURA, M. (1982) Mathematical formulation of CO2 dissociation curve and buffer line of human blood at rest. Jpn. J. Physiol., 32: 231-244. Vol. 33, No. 4, 1983

618 H. TAZAWA, M. MOCHIZUKI, M. TAMURA, and T. KAGAWA NATELSON, S. (1951) Routine use of ultramicro method in the clinical laboratory. Am. J. Clin. Pathol., 21:1153-1172. ROSSI-BERNARDI, L, and ROUGHTON, F. J. W. (1967) The specific influence of carbon dioxide and carbamate compounds on the buffer power and Bohr effects in human hemoglobin solutions. J. Physiol. (Lond.), 189: 1-29. SAVITZ, D., SIDEL, V. W., and SOLOMON, A. K. (1964) Osmotic properties of human red cells. J. Gen. Physiol., 48: 79-94. SEVERINGHAUS, J. W., STUPFEL, M., and BRADLEY, A. (1956) Variations of serum carbonic acid pk' with ph and temperature. J. App!. Physiol., 9: 197-200. SIGGAARD-ANDERSEN, 0. (1974) The Acid-Base Status of the Blood, Munksgaard, Copenhagen, pp. 7-91. STADIE, W. C. and O'BRIEN, H. (1937) The carbamate equilibrium. II. The equilibrium of oxyhemoglobin and reduced hemoglobin. J. Biol. Chem., 117: 439-470. TAKIWAKI, H., MOCHIZUKI, M., and NIIZEKI, K. (1983) Relationship between hematocrit and CO2 contents in whole blood and true plasma. Jpn. J. Physiol., 33: 567-578. VAN SLYKE, D. D., SENDROY, J., Jr., HASTINGS, A. B., and NEIL, J. M. (1928) Studies of gas and electrolyte equilibria in blood. X. The solubility of carbon dioxide at 38 C in water, salt solution, serum and blood cells. J. Biol. Chem., 78: 765-799. VAN SLYKE, D. D., Wu, H., and MCLEAN, F. C. (1923) Studies of gas and electrolyte equilibria in the blood. V. Factors controlling the elctrolyte and water distribution in the blood. J. Biol. Chem., 106: 765-849. Japanese Journal of Physiology