Plasma protein osmotic pressure equations for humans

The following is the abstract of the article discussed in the subsequent letter:

	ABSTRACT

Yamada, S., M. K. Grady, V. Licko, and N. C. Staub Plasma protein osmotic pressure equations and nomogram for sheep. J Appl Physiol 71: 481-487, 1991.The equations developed by Landis and Pappenheimer (Handbook of Physiology. Circulation, 1963, p. 961-1034) for calculating the protein osmotic pressure of human plasma proteins have been frequently used for other animal species without regard to the fractional albumin concentration or correction for protein-protein interaction. Using an electronic osmometer, we remeasured the protein osmotic pressure of purified sheep albumin and sheep plasma partially depleted of albumin. We measured protein osmotic pressures of serial dilutions over the concentration range 0-180 g/l for albumin and 0-100 g/l for the albumin-depleted proteins at room temperature (26°C). Using a nonlinear least squares parameter-fitting computer program, we obtained the equation of best fit for purified albumin, and then we used that equation together with the measured albumin fraction to obtain the best-fit equation for the nonalbumin proteins. The equation for albumin is II_cmH2O,39°C = 0.382C + 0.0028C² + 0.000013C³, where C is albumin concentration in g/l. The equation for the nonalbumin fraction is II_cmH2O,39°C = 0.119C + 0.0016C². Up to 200- and 100-g/l protein concentration, respectively, these equations give the least standard error of the estimate for each of the virial coefficients. The computed number-average molecular weight for the nonalbumin proteins is 222,000. Using the new equations, we constructed a nomogram, based on the one of Nitta and co-workers (Tohoku J. Exp. Med. 135: 43-49, 1981). We tested the nomogram using 144 random samples of sheep plasma and lymph from 31 sheep. We obtained a correlation coefficient of 0.99 between the measured and nomogram estimates of protein osmotic pressure.

	LETTER

To the Editor: In clinical work, little attention has been paid to high plasma colloid osmotic pressure (_plasma). Which method for calculating  from plasma proteins (1, 2, 5) would be the best one at high protein levels?

Landis and Pappenheimer (1) formulated equations for calculation of  from total plasma protein (TP), albumin, and globulin. In each equation, a first-order term represented van't Hoff's law, square and cubic terms deviations from that law caused by Donnan effects, and protein-protein interactions (1). The albumin-to-globulin ratio was not included.

Nitta et al. (2) combined and corrected the equations to include albumin and nonalbumin fractions. Into their equation, I have introduced calculations of the fractions from albumin (alb) and TP (represented by C in equations, both in g/dl), with _Nitta,mmHg multiplied by 1.36 giving _Nitta,cmH2O

(1)

Yamada et al. (5) derived Eq. 2 for sheep. IgG accounts for nearly one-half of the nonalbumin fraction in sheep (5), as it does in human diseases of interest in this context. Hence, Eq. 2 may apply to humans, and it was recommended for casual studies, even in studies involving Starling pressures where errors of 1 cmH₂O could be serious (5). In Eq. 2, the unit for TP (represented by C, biuret method) and albumin (alb, bromcresol green) concentrations is grams per liter (g/l) (5). The fractions are calculated as in Eq. 1

(2)

A cubic term was not used for the nonalbumin fraction because it influenced  very little, except at high (>80 g/l) protein levels (5). I compared _Nitta and _Yamada in Table 1.

View this table: [in this window] [in a new window]   Table 1.   Colloid osmotic pressure calculated from total protein and albumin according to Nitta et al. (2) and Yamada et al. (5), and their difference

At moderate and high nonalbumin protein ("globulin") fractions, _Nitta is higher than _Yamada and the difference increases with increases of TP. At 85 g/l TP and 45 g/l albumin, _Nitta is 43.8 and _Yamada 42.3 cmH₂O, with the difference being 1.5 cmH₂O. At the same TP and 30 g/l albumin, the difference is 2.3 cmH₂O; in analbuminemia (compare with Ref. 1), the difference is 3.8 cmH₂O.

The protein fractions undergo change during the course of many human diseases, for example, rheumatoid arthritis. In phases of mild joint activity, the average level of albumin (TP  globulin) was shown to be 47 g/l and that of globulin was 27 g/l (4). In severe joint activity, albumin dropped by 8 g/l and globulin increased by 10 g/l (4), but the calculated drop of _Nitta (from 38 cmH₂O, by 2 cmH₂O) and _Yamada (from 37.5 cmH₂O, by 2.5 cmH₂O) remained moderate.

A two-pore theory (3) revived my interest in _plasma. At low filtration rates, the plasma  tissue  differences () draw low-protein fluid into plasma through small (radius of ~4.5 nm) endothelial pores, whereas hydrostatic pressure differences almost unopposed by drive high-protein fluid through sparse large (radius of 25-30 nm) pores (3). Testing of the proposal that -correlating recirculation increases protein clearance from plasma (3), and presumably protein mass (?) in tissues, and testing of the authors' (3) early conjecture that this mechanism might participate in the regulation of _plasma calls for a reliable and cheap (compare with Ref. 5) method for calculation of _plasma.

The early globulin equation (1) was misleading (2, 5). Lacking a mathematical mind, I kindly ask Yamada et al. (5) to tell me whether a nonalbumin fraction cubic term would improve the usefulness of Eq. 2 at the high globulin levels often met in clinical practice.

	REFERENCES

1.   Landis, EM, and Pappenheimer JR. Exchange of substances through the capillary walls. In: Handbook of Physiology. Circulation. Washington, DC: Am Physiol Soc, 1963, vol. II, p. 961-1043, sect. 2, chapt. 29.

2.   Nitta, S, Ohnuki T, Ohkuda K, Nakada T, and Staub NC. The corrected protein equation to estimate plasma colloid osmotic pressure and its development on a nomogram. Tohoku J Exp Med 135: 43-49, 1981[ISI][Medline].

3.   Rippe, B, and Haraldsson B. Transport of macromolecules across microvascular walls: the two-pore theory. Physiol Rev 74: 163-219, 1994[Abstract/Free Full Text].

4.   Ropes, M, and Bauer W. Synovial Fluid Changes in Joint Disease. Cambridge, MA: Harvard Univ. Press, 1952.

5.   Yamada, S, Grady MK, Licko V, and Staub NC. Plasma protein osmotic pressure equations and nomogram for sheep. J Appl Physiol 71: 481-487, 1991[Abstract/Free Full Text].

Johan Ahlqvist 25830 Västanfjärd, Finland. E-mail: johan.ahlqvist{at}kolumbus.fi

	REPLY

To the Editor: I was delighted when I was asked to reply to Dr. Ahlqvist's letter concerning plasma protein osmotic pressure. First, it reminded my wife and me of our memorable trip to Finland for the International Physiology Congress in 1989. Second, in a world gone mad with molecular biological hype, Dr. Ahlqvist's interest in applied physiology is a ray of sanity.

Dr. Ahlqvist's direct question is whether a cubic term for the nonalbumin portion of Eq. 2 would improve its usefulness. The simple answer is, No. In the 1991 paper by Yamada et al. (2), a cubic equation was a statistically better fit for the albumin osmotic pressure, according to our collaborator, Dr. Licko, a fine mathematician and statistician. However, the same could not be said for the nonalbumin portion of the equation. There was too much variation among the data to require a cubic term; the problem Dr. Ahlqvist poses is essentially insoluble in the real world.

If this answer is not sufficient, readers may want to look up my 1987 review paper (1). In terms of pulmonary liquid and protein exchange, my associates and I have found strong evidence for various types of microvascular inhomogeneity in addition to two or more pores. We obtained evidence over the years for the following inhomogeneities: vertical (top to bottom of lung), longitudinal (arterial, capillary, venous), and parallel (side by side). Each type is discussed with references in the article.

My advice is not to push theoretical calculations too far; they contain many simplifying assumptions, not necessarily made explicit. In my opinion, the best clinical approach is to use data obtained from real osmotic pressure measurements. This is especially true in clinical care, where, for example, access to serial plasma samples and pulmonary edema liquid by deep lung suction is most likely available. Perhaps, Dr. Ahlqvist may consider setting up this endeavor in his hospital.

If the reader must rely on calculations, then choose the one that seems most reasonable. As Dr. Ahlqvist showed by calculation in his letter, the variations are of the order of ±10-15%, which in the real world of whole animal physiology is good agreement. To let the other shoe drop, any calculation one applies to plasma osmotic pressure also applies to interstitial osmotic pressure; therefore, the effective differences may be even less than those calculated using plasma alone.

And so it goes.

	FOOTNOTES

10.1152/japplphysiol.00694.2002

	REFERENCES

1.   Staub, NC. Lung liquid and protein exchange: the four inhomogeneities. Ann Biomed Eng 15: 115-26, 1987[ISI][Medline].

2.   Yamada, S, Grady MK, Licko V, and Staub NC. Plasma protein osmotic pressure equations and nomogram for sheep. J Appl Physiol 71: 481-487, 1991.

Norman C. Staub, Sr. Professor of Physiology (emeritus) University of California San Francisco, California 94143