RATE OF EVAPORATION IN SERUM AS A MEASURE OF VAPOR PRESSURE, OSMOTIC PRESSURE, AND

CONCENTRATION OF SOLUTES*

BY ROBERT W. CULBERT, D. J. McCUNE, AND A. A. WEECH

(From the Babies Hospital and the Department of Diseases of Children, College of Physicians and Surgeons, Columbia University, New York)

(Received for publication, March 11, 1937)

In a previous communication (2) a method devised by Hill (3) for the measurement of vapor pressure of whole blood was described. The apparatus consists of a symmetrically wound thermopile so constructed that the solution under examination is permitted to evaporate from one face of the instrument while a standard solution (0.92 per cent of sodium chloride) simultaneously evaporates from the opposite face, the whole system being at con- stant temperature. The difference in rate of evaporation of the solutions produces an E.M.F. which is recorded on a galvanometer; thus, the unknown sample may be characterized in terms of the concentration of a solution of sodium chloride which possesses an identical rate of evaporation.

The application of this method to the measurement of vapor pressure in serum and in whole blood has met with some criticism, inasmuch as the pressure is not measured directly. What is measured is the rate of evaporation of the sample. Although with simple solutions of electrolytes strict proportionality exists between vapor pressure and rate of evaporation, it has been argued that in serum the formation of a film on the surface may retard the loss of moisture and that with whole blood the red cells may significantly alter the surface available for evaporation.

Modification of the rate of evaporation by such interfering phenomena might be expected to produce wide and unpredictable divergence between the results of duplicate determinations. It is

* A preliminary report (1) of this investigation was made at the meeting of the Society for Pediatric Research at Atlantic City, May 5, 1936.

589

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therefore important to note that the measurements are repro- ducible within a probable error of less than 0.5 per cent, a fact which at least indicates that some stable property of the blood is being measured. Reproducibility of results, while supporting, does not necessarily prove the contention that in serum or in whole blood the rate of evaporation is a measure of the vapor pressure. Because vapor pressure can be used for calculating osmotic pressure and because there is need of a method for esti- mating osmotic pressure in biological fluids which does not in- volve the extreme environmental conditions of freezing point determinations, it appeared worth while to secure additional data in support of the validity of determining vapor pressure by the thermoelectric method. These data were obtained with serum; the findings with whole blood which have been reported previ- ously still require critical examination.

In previous papers in which measurements made by the thermo- electric method were recorded (2, 4) and in which the validity of the method was not being examined, the results were regarded and spoken of as measures of vapor pressure or of osmotic pres- sure. For clarity in the ensuing discussion it is necessary to distinguish between vapor pressure and that measure of the rate of evaporation of a sample of serum which is given by the thermo- electric procedure; the term “equivalent vapor pressure” will be used to refer to the latter. The standard of reference in the thermoelectric method is a solution of sodium chloride of known concentration. When an unknown solution is measured against the standard of reference, the resulting deflection of the galva- nometer results from and is proportional to the difference between the rates at which the two solutions are evaporating. Equivalent vapor pressure is therefore conveniently expressed in terms of that concentration of a solution of sodium chloride which if it had been placed opposite to the standard would have produced an identical deflection of the galvanometer. If it can be shown that the equivalent vapor pressure of serum is a function of the same property which determines the true vapor pressure and the osmotic pressure, it will then be clear that there is a direct linear relationship between any two of the three properties: equivalent vapor pressure, osmotic pressure, and lowering of true vapor pressure from that of water; the relationship between these

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three properties and the absolute value of vapor pressure ex- pressed in pressure units is inverse.

Proof of the contention that the rate of evaporation of serum is a measure either of vapor pressure or of osmotic pressure would seem to be furnished if it were possible to determine quantitatively all of the separate constituents of serum, to calculate for each con- stituent its equivalent osmotic concentration, and finally to dem- onstrate that the sum of the calculated concentrations was equal to the observed equivalent vapor pressure of the serum. Ex- pressed as an equation the calculation would take the form

~[Nal + (n2Mgl + ‘p3LC.M + ... rp,lml = WI

where the various constituents are expressed in molecular or ionic concentrations, where the (o values represent osmotic ac- tivity coefficients, and where V is the equivalent vapor pressure. From the thermodynamic standpoint such a demonstration is impossible; moreover in this simple form it obviously could not express the relationship accurately, since it neglects the possi- bility of chemical combination between two or more constituents. An example of such a combination is the effect of protein on the ionization of calcium. In the present state of knowledge and with the limitations imposed by available analytic procedures, it is impossible to allow for all similar effects in a way which would inspire confidence in the result.

In view of the difficulty of effecting a comprehensive demonstra- tion such as that described, evidence for the significance of meas- urements of equivalent vapor pressure was sought in another way. In a group of sera the equivalent vapor pressure was meas- ured and a selected number of the osmotically active constituents were determined by chemical analysis; a relationship was then looked for between the results of all analyses and the equivalent vapor pressure. Instead, however, of assuming a theoretical os- motic effect for any constituent, the data were examined mathe- matically by the method of multiple correlation to determine the existence of any quantitative relationship between equivalent vapor pressure and chemical composition. This method of examination is based on the theory of least squares; it leads to the formulation of regression equations by means of which the equivalent vapor pressure can be predicted from the constituents

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592 Pressure Measurement in Serum

of serum in the best’ way that the data will permit. It was felt that such a study would support the assumption that equivalent vapor pressure is functionally related to osmotic pressure and vapor pressure, if two goals were realized: (1) that the agreement between predicted and determined values of equivalent vapor pressure was reasonably close; (2) that the regression equation assumed a form consistent with accepted concepts of the nature of osmotic pressure. To an extent which will appear both of these objectives have been reached.

In a preliminary investigation, in addition to measurement of equivalent vapor pressure, the sera were analyzed for the follow- ing constituents: total fixed base, non-protein nitrogen, protein, bicarbonate, chloride, and in a number of instances sugar. The preliminary study of correlation demonstrated the feasibility of this method of approach; it also showed that the inclusion of so many variables would have a negligible effect in improving the accuracy of predictions of equivalent vapor pressure. Moreover, justification for omission of some of the items can be adduced on theoretical grounds. The final study, which included 53 samples of serum, was therefore limited to measurements of equivalent vapor pressure, total fixed base, non-protein nitrogen, and protein.

It has been stated that one purpose in treating these analytic data by the method of multiple correlation was to learn whether the final regression equation would have a form consistent with ac- cepted concepts of the nature of osmotic pressure. It is easiest to visualize what this form should be by portraying the composition of serum diagrammatically (Fig. 1) in a manner similar to that origi- nated by Gamble (5). In the usual Gamble diagram the concen- trations of the various constituents of serum are expressed as milli-equivalents per liter; in Fig. 1 the concentrations are ex- pressed on a molal basis, that is as milli-equivalents per 1000 gm.

1 When regression equations with more than one independent variable are being computed, it is necessary to postulate linearity for all of the rela- tionships. For most of the simple solutes of serum it is known that vapor pressure and osmotic pressure vary in a linear manner with concentration throughout the range encountered in physiologic solutions. The word “best,” as we have used it, is valid only in so far as the assumption of linearity of regression is correct.

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Culbert, McCune, and Weech 593

of serum water. This distinction, is of no importance when it is desired merely to represent the balance between negative and positive electrolytes; it is, however, desirable in the present case, since osmotic pressure and vapor pressure are functions of molal concentration. It will be shown later that a relationship which is useful from the practical rather than theoretical standpoint emerges even when the distinction is not made. It is generally believed that the fixed base of serum exists for the most part in osmotically active form; only a small portion of the total base, namely the undissociated fractions of calcium and magnesium, is devoid of appreciable effect. The total base (represented by

M

B EM- I PI- FIG. 1. Diagrammatic representation of the chemical composition of

serum. B represents total base; Pr, osmotic effect of protein; B - Pr, osmotically active electrolyte; M, non-protein nitrogen.

B in Fig. 1) can be regarded as contributing positively to the os- motic pressure. On the anion side of the diagram the con- stituents of greatest importance are chloride (Cl-) and bicarbonate (HC03-); smaller contributions to the osmotic pressure are made by sulfate (S04=), phosphate (HPOd= and HzPOd-), and organic acids. Because of the large size of the molecule the osmotic effect of protein (Pr) is negligible. Since the sum of all the anions must equal the total base, the osmotically active anions are represented by B - Pr; it follows that the osmotically active electrolyte, both anions and cations, is represented by 2B - Pr. The usual Gamble diagram does not portray the non-electrolyte

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Pressure Measurement in Serum

constituents of serum; it is obvious that such constituents con- tribute to the osmotic pressure but unlikely that they rank in im- portance with the electrolyte. To measure by quantitative analysis all or even many of the non-electrolytes was impracti- cable. The single constituent of this group which may appear in large amounts in serum and which, because of its small molecular size, exerts an appreciable osmotic pressure is urea. Measure- ments of urea might well have been used in this study to provide a rough appraisal of the contribution of non-electrolytes to os- motic pressure. Actually the total non-protein nitrogen was selected rather than its urea fraction, because the quantity of serum was often limited and non-protein nitrogen estimations were always obtained in the process of determining protein. The difference here is probably of minor importance. It is clear that the final regression equation should include non-protein nitrogen (M) as a positive contributor.

The relationship to be expected from the foregoing concept can be approximate only; the exact value of the coefficients in the regression equation cannot be predicted in advance. How- ever, it can be seen that the equation should take the following form:

[VI = %CIB - CzPr + Cd4 + C;

Here C1, Cz ,Cs are constants which determine the exact values for the several coefficients and Cd is a constant which may be thought of as the average concentration of osmotically active constituents not otherwise represented in the equation. However, it is im- probable that Ca can have true physiologic significance, since it may be determined in part by mathematical considerations alone, such, for instance, as failure of linearity of regression in one of the independent variables. The important point to note, however, regarding the form of the equation is that the coefficients which introduce B and M are positive, whereas that which modifies Pr is negative.

Units of Measure-In the foregoing description the several constituents of serum are expressed in terms of molecular con- centration; it is assumed that the equivalent vapor pressure is to be predicted in terms of molecular concentration. Such a mode of expression is obviously impossible in the case of non-

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Culbert, McCune, and Weech 595

protein nitrogen. Moreover, since all of the variables in the regression equation will be modified by constants, it is clear that the use of any more convenient unit of measure for a con- stituent will result only in a change in the value of the respective constant. For this reason we have not been consistent in ex- pressing all constituents in the same units; the forms adopted are those which have become familiar by common usage. The units of measure as well as the symbols by which the various con- stituents will be designated in the equations are as follows:

Units and Abbreviations

V = equivalent vapor pressure in gm. NaCl per 100 gm. Hz0 b = total fixed base in m.-eq. per liter serum p = protein in gm. per 100 cc. serum n = non-protein nitrogen in mg. per 100 cc. serum

B = total fixed base in m.-eq. per 1000 gm. serum water P = protein in gm. per 100 gm. serum water N = non-protein nitrogen in mg. per 100 gm. serum water Water in 100 cc. serum = (99.0 --0.75~) gm. R = coefficient of multiple correlation P.E.(est.) = probable error of estimate

Methods

Samples of Serum-Blood was collected under liquid petro- Iatum, allowed to clot, and the serum separated by centrifuga- tion. After the s&urn had been transferred to another tube, no further attempt was made to prevent access of air. The majority of samples was obtained from healthy subjects; with the intention of securing wide variations in the various constit- uents to be studied, the remaining samples were taken from pa- tients with various illnesses. Several infants with intestinal intoxication yielded sera low in non-protein nitrogen; high values were obtained in severe renal insufficiency; the lowest and highest non-protein nitrogen values in the series were, respectively, 12.5 and 236.0 mg. per 100 cc. With total base, variations from the normal were obtained in infants with intestinal intoxication and in children with lobar pneumonia; the lowest and highest levels were 128 and 162 milli-equivalents per liter. Variations in serum protein were provided by patients with chronic malnutrition and by samples of serum from the veins of the foot in healthy subjects who had remained standing for from 20 to 30 minutes; the range

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596 Pressure Measurement in Serum

for serum protein was from 3.32 to 8.30 gm. per cent. The result- ing range for equivalent vapor pressure was from 0.7670 to 1.0859 gm. per cent of sodium chloride. Sera with pathologically high values for lipid or sugar were not included in the series.

Chemical Methods-The total fixed base of the serum was de- termined by Hald’s (6) microgravimetric modification of the benzidine method. Of the solution of ash, aliquots were taken which were equivalent to either 0.4 cc. or 0.8 cc. of serum and which yielded precipitates of about 8 mg. or 16 mg., respectively. The lighter precipitates were weighed with a microanalytic bal- ance. The following formula was used to convert the weight of precipitate into milli-equivalents of base per liter of serum: (1000 X weight of precipitate equivalent to 1.0 cc. of serum)/141 = milli-equivalents per liter (7). Nitrogen was measured as am- monia after micro-Kjeldahl digestion. With total nitrogen and the higher levels of non-protein nitrogen the ammonia was dis- tilled in steam into ~/70 hydrochloric acid and titrated back with N/70 sodium hydroxide. With the lower values for non- protein nitrogen the ammonia was determined by nesslerization and comparison with a standard in a calorimeter. Protein was calculated as 6.25 times the difference between total nitrogen and non-protein nitrogen. All chemical analyses were performed in duplicate.

Mathematical Aspects-The formula for computing the water content of serum, which is given in the list of units, was taken from McLean and Hastings (8). The formulas for calculating partial and multiple coefficients of correlation, regression equa- tions, and errors of estimate are given by Garrett (9). Correla- tions were made by the long method, that is without the use of scatter diagrams; through all computations an accuracy of six significant figures was maintained.

EXPERIMENTAL

Relationship in Serum between Equivalent Vapor Pressure and [Total Base, Non-Protein Nitrogen, and Protein]-The results of all 53 analyses are shown in Table I. When these data are cor- related with V as the dependent variable and with B, N, and P as independent variables, the following relationships emerge :

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Rv(B.N. P) = 0.9630 V = 0.003705B - 0.002978P + 0.001142N + 0.23745

P.E.(est. yj = 0.01042 (1)

The coefficient of multiple correlation, R, is so high as to leave little room for doubt that the relationship expressed by the re- gression equation is one of cause and effect. The probable error of estimate is 1.2 per cent of the mean value for determined equivalent vapor pressure. It may be concluded that the equiva- lent vapor pressure of serum gives a correct indication of the con- centration of its solutes. The agreement between predicted and determined values of the equivalent vapor pressure is shown in Fig. 2; the figure gives a graphic representation both of the co- efficient of multiple correlation and of the probable error of es- timate. The coefficients in the regression equation which modify B and N are positive; the coefficient which modifies P is negative. This form of the equation supports the assumption that the equivalent vapor pressure of serum is functionally related to its true vapor pressure and its osmotic pressure.

Relationship in Serum between Total Base and [Equivalent Vapor Pressure, Non-Protein Nitrogen, and Protein]-In view of the close interrelationship among the variables, the suggestion at once presents itself of reversing the process and attempting to predict total base from measurements of equivalent vapor pressure, non- protein nitrogen, and protein. It need scarcely be mentioned that regression equations are not simple algebraic equations and that the desired formula for predicting base cannot be obtained by solving Equation 1 for B. However, it is readily secured by the same process which led to Equation 1 when total base is treated as the dependent variable and vapor pressure, non-protein nitro- gen, and protein as independent variables. The following rela- tionships emerge :

RB(v,N. P) = 0.3531 B = 169.96V - 0.1936N + 1.481P + 11.65

b = (0.99 - 0.0075p)B ~.~.(e.t. b) = 2.096

(2) (3)

Equation 2 is used for predicting base in terms of milli-equiva- lents per 1000 gm. of serum water; Equation 3 is used for express- ing this result in the usual form of milli-equivalents per liter of

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598 Pressure Measurement in Serum

serum. The relationship between found and predicted values for total base is represented graphically in Fig. 3. In comparing R B(V.N.P) with RVW,N,P) it should be noted that the lower value of

TABLE I

Equivalent Vapor Pressure and Chemical Constituents in 65 Sera

The data are in ascending order of the values for equivalent vapor pressure.

1 0.7670 135.7 16.8 6.05 2 0.7932 139.3 14.9 3.32 3 0.7948 143.9 12.5 3.70 4 0.8068 143.3 20.4 7.23 5 0.8128 143.2 18.8 5.15 6 0.8208 145.8 31.0 6.03 7 0.8236 147.6 31.2 6.33 8 0.8248 147.4 20.6 5.72 9 0.8257 152.2 28.4 6.75

10 0.8311 151.8 31.2 6.80 11 0.8313 144.8 22.4 5.92 12 0.8314 127.6 116.8 5.45 13 0.8320 149.9 32.8 6.96 14 0.8357 149.9 29.6 7.08 15 0.8379 148.6 25.2 7.04 16 0 8384 156.0 29.6 6.69 17 0.8386 150.7 24.4 7.08 18 0.8388 151.3 25.2 6.65 19 0.8392 150.8 32.8 7.33 20 0 8413 149.9 36.9 8.05 21 0.8419 152.4 32.8 6.98 22 0.8428 150.5 33.2 6.83 23 0.8430 145.3 21.2 7.80 24 0.8438 148.4 24.4 7.75 25 0.8450 153 5 30.8 7.10 26 0.8454 148 0 27.2 7.62

!7m. pet cent n.-ep.

NaCL per 1.

NOlIT

proi?n Protein

gm. Pm 100 cc.

hmpl NO.

Non,-

proIP Protein

pz&t Tn.-eg. pw 1.

wn. per 100 cc.

27 0.8468 151.6 30.4 7.47 28 0.8469 151.8 37.6 9.10 29 0.8474 151.7 35.2 7.46 30 0.8479 150.7 26.4 7.60 31 0.8488 151.3 27.6 6.94 32 0.8503 149.7 28.4 6.94 33 0.8512 151.7 31.6 8.17 34 0.8539 155.8 19.7 5.24 35 0.8540 155.5 24.8 6.97 36 0.8554 151.8 30.4 6.57 37 0.8575 151.8 36.4 7.19 38 0.8578 153.2 27.2 6.80 39 0.8594 151.5 30.4 6.99 40 0.8594 153.5 32.8 7.65 41 0.8604 155.7 30.0 7.25 42 0.8620 149.3 28.3 7.54 43 0.8630 151.2 48.0 8.53 44 0.8790 152.7 37.8 6.74 45 0.8838 151.9 25.2 7.06 46 0.8910 157.7 28.1 6.80 47 0.8942 155.2 34.9 8.30 48 0.9112 155.7 52.3 5.44 49 0.9612 146.6 159.2 5.20 50 0.9695 144.9 108.8 8.06 51 0.9715 149.3 138.4 4.67 52 1.0735 161.9 182.4 5.33 53 1.0859 146.3 236.0 5.98

the former arises chiefly from the fact that the range of observa- tions was considerably less with B than with V. Still it can be shown that the error in predicting base is somewhat greater

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than in predicting equivalent vapor pressure. In the case of base the probable error of estimate is 1.40 per cent of the mean base value, whereas with equivalent vapor pressure the probable error is 1.21 per cent of the mean value.

Relationship in Serum between Equivalent Vapor Pressure and [Total Base and Non-Protein Nitrogen]-In order to simplify the procedure of obtaining estimates of equivalent vapor pressure a regression equation was calculated in which the least important

DETERMINED FIG. 2. Agreement of determined values of equivalent vapor pressure

with those predicted from total base, non-protein nitrogen, and protein by Equation 1. Thevalues are expressed as gm. per cent of sodium chloride.

FIG. 2. Agreement of determined values of equivalent vapor pressure with those predicted from total base, non-protein nitrogen, and protein by Equation 1. Thevalues are expressed as gm. per cent of sodium chloride.

of the variables, namely protein, was omitted. For further simplification and for reasons which will appear later the units selected for expressing the base and nitrogen values were those in common usage and not those which refer the concentrations to serum water; that is, total base was expressed as milli-equivalents per liter of serum and non-protein nitrogen as mg. per 100 cc. of serum. The argument for so simplifying the procedure follows: If a constant volume of serum is conceived as having a fixed con-

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600 Pressure Measurement in Serum

tent of total base and non-protein nitrogen, there are two theo- retical effects on osmotic pressure of varying the protein concen- tration. One effect results from the fact that increases in protein must be attended by decreases in serum water, so that no change in volume will occur; the decrease in serum water will increase the molal concentration of the other solutes and so lead to an increase in osmotic pressure. Another effect arises from the cir- cumstance that increases in protein must be associated with de-

Y 125 130 13.5 140 45

DfTERMl&D 150 I55

I 160

FIG. 3. Agreement of determined values of total base with those pre- dicted from equivalent vapor pressure, non-protein nitrogen, and protein by Equation 2. The values are expressed as milli-equivalents per liter.

creases in some of the osmotically active anions, chiefly chloride and bicarbonate, in order to maintain electrolyte balance; since the protein itself is osmotically inactive, this effect leads to a decrease in osmotic pressure. A further decrease in osmotic pres- sure results from the effect of protein on the ionization of calcium and magnesium. In our theoretical system there are, then, two effects from augmenting the protein, one tending to raise and the other to lower the osmotic pressure. To some extent

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at least the effects must cancel and to this same extent must the osmotic pressure be independent of variations in protein when the cation and non-electrolyte concentrations are given in rela- tion to volume of serum rather than gm. of serum water. The result of correlating the data in this way follows:

R V(b, n) = 0.9621 V = 0.004012b + 0.001194n + 0.20683

P.E.(est. v’) = 0.01055 (4)

It appears both from the coefficients of multiple correlation and from the probable errors of estimate that Equation 4 predicts the equivalent vapor pressure almost as accurately as .Equation 1. The agreement between determined values of equivalent vapor pressure and those predicted by Equation 4 is represented graph- ically in Fig. 4.

Relationship in Serum between Total Base and [Equivalent Vapor Pressure and Non-Protein Nitrogen]-When the procedure of the preceding paragraph is altered so that total base is treated as the dependent variable, the following relationships emerge:

&,(v.,,) = 0.8128 b = 164.34V - 0.1989n + 17.16

P.E.(eat. b) = 2.135 (5)

It is seen again that Equation 5 predicts the total base almost as accurately as Equations 2 and 3. The agreement between found and predicted values is shown in graph form in Fig. 5.

Comment

The relationship expressed by Equation 1 and represented graphically in Fig. 2 between the equivalent vapor pressure of serum and several of its solutes demonstrates conclusively that the rate of evaporation of serum under standard conditions of environment varies directly with the concentration of its solutes. The form of the equation, in which positive contributions to the equivalent vapor pressure are made by the total fixed base and the non- protein nitrogen and a negative effect is exerted by protein, strongly suggests that the same property of serum which deter- mines the vapor pressure and osmotic pressure also determines the equivalent vapor pressure. It is clear that there are no

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602 Pressure Measurement in Serum

large random variations in the equivalent vapor pressure which cannot be explained by fluctuations in the chemical composition of the sera. Much of the variation which was recorded is un- doubtedly traceable to the combined effect of errors of measure- ment. However, the method of statistical analysis does not and cannot exclude the possibility of some constant influence on the rate of evaporation of serum which would render all re- sults for equivalent vapor pressure consistently either too low

DETERMINED FIG. 4. Agreement of determined values of equivalent vapor pressure

with those predicted from total base and non-protein nitrogen by Equation 4. The values are expressed as gm. per cent of sodium chloride.

or too high when translated into terms of vapor pressure or osmotic pressure. Such an effect might conceivably result if the surface of the evaporating sample were always coated with a monomolecular layer of protein molecules; if a layer of this type interferes with the rate of evaporation, the interference will clearly be independent within wide limits of the concentration of protein in the serum. As yet no direct means of measuring the osmotic pressure of serum is available, nor does a method exist

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for direct determination of vapor pressure which is accurate enough to throw light on this point. For the time being, there- fore, it appears reasonable to think that the thermoelectric procedure measures that same property of serum which determines its osmotic pressure. In so far as this is true the equations which have been developed should prove useful when estimates of the osmotic pressure of sera are wanted. The estimates so obtained will be in the form of equivalent gm. per cent of sodium chloride,

V 125 I30 135 0 4

Di&l7rlINiD 5 150 155 I 0

FIG. 5. Agreement of determined values of total base with those pre- dicted from equivalent vapor pressure and non-protein nitrogen by Equa- tion 5. The values are expressed as milli-equivalents per liter.

which is to say that the osmotic pressure of the serum under inves- tigation is the same as that of a solution of sodium chloride of the estimated concentration. This result is easily expressed in the more conventional terms of mm. of mercury at 25” by multiplying by the factor 5901.2

2 Calculated in the manner outlined by Findlay (10). The value for the depression of freezing point used in computing the osmotic activity coeffi- cient of the standard 0.92 per cent solution of sodium chloride was taken

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The equations for predicting base are of limited value, since the apparatus for measuring equivalent vapor pressure is not widely distributed. They have, however, been serviceable in this clinic when with individual patients it was desired to construct rapidly a picture of the electrolyte partition of the serum. For this pur- pose measurement of specific gravity provides a rapid means of estimating the protein content (11). In an investigation pre- liminary to the present study a regression equation was calcu- lated for predicting total base from the sum of bicarbonate, chlo- ride, and protein ions. It is interesting that Equations 2 and 3 and Equation 5 predict the total base more accurately than was possible by the preliminary method. This is true in spite of the fact that sera with presumptively high values for undetermined acids were not included in either series.

It may be well to state that the values dealt with in this paper are not identical with that property of serum which renders it isotonic with respect to red blood corpuscles. Examination of the data in Table I indicates that marked elevation of equivalent vapor pressure occurs when the non-protein nitrogen of serum is high. Such sera do not cause shrinkage of red cells because the cell membranes are freely permeable to urea and probably to other molecules in the non-protein nitrogen complex. A question may be raised concerning the validity of regarding the osmotic pressure due to protein as negligible when the total osmotic pressure is being recorded. The so called colloid osmotic pressure of protein, as usually measured, is in the neighborhood of 0.5 per cent of the total pressure, hence within the error of measure- ment of equivalent vapor pressure. Moreover, it must be remem- bered that colloid osmotic pressure is always measured in a sys- tem in which a semipermeable membrane is utilized and that a part, about one-fifth (12), of the recorded pressure results from the Donnan effect in producing unequal distribution of the other ions. This portion of the colloid osmotic pressure does not exist as a property of protein under the conditions of measure- ment of equivalent vapor pressure.

from the “International critical tables,” volume 4. The coefficient is 1.355. Calculation of the factor involves the following steps: mm. of Hg osmotic pressure = V X 10 X 1.855 X 22.412 X 760 X (273 + 25) + 58.45 X 273 = 5901V.

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SUMMARY

The method devised by Hill for measuring the vapor pressure of whole blood is basically a measure of the rate of evaporation of the sample. Arguments against the validity of regarding such measurements as functionally related to vapor pressure and os- motic pressure are considered. To facilitate discussion, that con- centration of a solution of sodium chloride which evaporates at the same rate as an unknown sample of serum or blood is defined as the “equivalent vapor pressure.”

In 53 samples of human serum measurements were made of equivalent vapor pressure, and of the concentrations of total base, non-protein nitrogen, and protein. From the data the re- gression equation was computed which permits the prediction of equivalent vapor pressure from the three solutes. Both the accuracy of the predictions and the form of the equation lend support to the assumption that the rate of evaporation of serum is determined by the same property which also determines vapor pressure and osmotic pressure.

From the same data the regression equation was computed which permits the prediction of total fixed base from measure- ments of equivalent vapor pressure, non-protein nitrogen, and protein. The estimate of total base has a probable error of 4~2.1 milli-equivalents per liter.

Similar regression equations for predicting equivalent vapor pressure and total base were computed from the same data when one of the variables, protein, was omitted. By expressing the concentrations of total base and non-protein nitrogen in units which relate them to volume of serum rather than to gm. of serum water, some compensation was made for the loss in accuracy of prediction which would have resulted from simple omission of the protein variable.

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WeechRobert W. Culbert, D. J. McCune and A. A.

CONCENTRATION OF SOLUTESOSMOTIC PRESSURE, AND

A MEASURE OF VAPOR PRESSURE, RATE OF EVAPORATION IN SERUM AS

1937, 119:589-606.J. Biol. Chem. 

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