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Colloid osmotic homeostasis in humans I. theoretical aspects and background
J. theor. Biol. (1970) 28, 1-14
Colloid Osmotic Homeostasis in Humans I. Theoretical Aspects and Background THEODORE R. REIFF Department of Internal Medicine, University of Nebraska College of Medicine, Veterans Administration Hospital, Omaha, Nebraska 68105, U.S.A. (Received 17 July 1969) The theoretical exploration of intravascular colloid osmotic pressureplasma volume relationships has been undertaken in an attempt to formulate meaningful physical parameters to describe the paths that may be taken when an individual has been subjected to colloid osmotic stress, i.e. changing colloid concentrations and/or total colloid mass within the vasculature. Colloid osmotic pressure-plasma volume diagrams have been constructed, and the formulae relating these two measurable quantities have been theoretically and semi-empirically derived. In addition to describing the path of oncotic adjustment, the P-V diagram has been utilized to visualize and calculate oncotic energy changes in traversing from an initial to a final P-V state. Thermodynamic analogy has allowed a comprehensive oncodynamic treatment of colloid osmotic pressure (P), colloid osmotic mass (M), and intravascular volume (V) in the derived relationship: P = AMV-1 + BMaVez (A, B constants). Utilizing a three-dimensional P, V, M plot, an oncodynamic surface has been constructed, the curvature of which is a function of partial differentials of measurable quantities.
1. Introduction The effects of the intravenous administration of oncotic material such as human serum albumin, Dextran and polyvinyl pyrrolidine, to human subjects, have been studied by others in the past. Parameters measured have
included: (1) concentration of the oncotic material; (2) selected hemodynamic properties, i.e. cardiac output, arterial and venous pressures, intravascular volume; (3) renal function. However, largely due to the difficulty and tediousness of multiple determinations of oncotic pressure, little study has been made of the effect of administered
oncotically
active material
upon the oncotic pressure of the intravascular fluid. Most of those studies that have included oncotic pressure have used empirical formulae to calculate 1 T.B.
2
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R.
REIFF
the oncotic pressure from the serum protein concentrations. That these formulae are inadequate was shown by Armstrong, Kark, Schoenberger, Shatkin & Sights (1954). Starling (1895-96) made some of the earliest studies on the importance of colloid osmotic pressure in transcapillary fluid exchange, and pointed out the basic mechanisms underlying the dynamics of “passive” water transport. Chinard, Lauson, Eder & Grief (1954) studied plasma volume changes following the administration of albumin in two patients with the nephrotic syndrome. The change in plasma volume per unit of albumin was less than would have been obtained had the response been “iso-osmotic “(increase in plasma volume to keep osmotic pressure constant). Results suggested that an increase in capillary hydrostatic pressure prevented the maximal isoosmotic response. In these studies Chinard did not measure protein osmotic pressure, but calculated it from measurement of albumin and total globulin concentrations and use of a modified formula developed by Scatchard (1946). In an editorial, Hyman & Steinfeld (1967) discussed regulation of plasma volume and pointed out some of the remaining problems involved in volume regulation. Weston et al. (1960) have discussed in detail the search for the so-called “volume regulator”. Reeve & Guyton (1967) have compiled the thoughts of a number of recent investigators concerned with the role of oncotic pressure in transcapillary fluid transport including analog computer simulation studies of water balance. Wiederhielm (1968) has also contributed an analog computer simulation of fluid balance at the capillary level. 2. Approach
The purpose of these studies is the theoretical and experimental exploration of intravascular colloid osmotic-plasma volume relationships and to formulate meaningful physical parameters to describe these relationships. From preliminary experimental data and, independently, from purely thermodynamic considerations involving colloid osmotic pressure and plasma volume, a description has been formulated of the possible paths from an initial state to a final state, that an individual might take when subjected to colloid osmotic stress, i.e. changing colloid concentrations and/or total colloid mass within the vasculature. Experimentally induced oncotic stress in human and/or other subjects can be produced by the following: (1) Concentration of oncotic mass. Judicious intravenous induced diuresis (ethacrynic acid, etc.).
COLLOID
OSMOTIC
HOMEOSTASIS
IN
HUMANS
3
(2) Dilution of oncotic mass. Rapid intravenous infusion of physiological saline. (3) Increase in total oncotic mass. Rapid intravenous infusion of salt poor human serum albumin or the subject’s own plasma. (4) Decrease in total oncotic mass. Plasmapheresis and/or phlebotomy. From experimental data it is possible to construct oncotic pressure-plasma volume (P-V) curves (“iso-oncomols”) by plotting simultaneous values for serum oncotic pressure and plasma volume that describe the oncotic adjustment of a subject to varying oncotic stresses.
i.e. lines of constant total amount of Parallel curves are “is0-oncomols”, intravascular oncotic mass. The iso-oncomols demonstrate the manner in which oncotic pressure varies with changes in concentration of the oncotic material. Line AB describes the path taken when the subject’s intravascular oncotic mass has been concentrated (e.g. diuresis or dehydration). Line AC describes the path taken when the subject’s intravascular oncotic mass has been diluted (e.g. intravenous administration of physiological saline). Individuals who undergo a change in their total oncotic mass could have the following responses: (1) Increase in total oncotic mass (e.g. intravenous salt free human serum albumin or plasma). (a) Line AD would describe a purely iso-oncotic response, i.e. an increase in volume with oncotic pressure constant. This would be accomplished by transfer of solvent from extravascular spaces into the vasculature.
4
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(b) Line AE would describe a purely iso-volumetric response, i.e. an increase in serum oncotic pressure with no change in plasma volume. (2) Decrease in total oncotic mass (e.g. plasmapheresis or phlebotomy). (a) Line AF would describe a purely iso-oncotic response, i.e. no extravascular solvent would transfer into the intravascular compartment to maintain intravascular volume. (b) Line AG would describe a purely iso-volumetric response, i.e. transfer of extrasvacular solvent into the vasculature would take place in an attempt to maintain plasma volume. In actuality the path taken by a given subject would be along line yAx, i.e. an intermediate response somewhere between iso-oncotic and isovolumetric. Because of vascular distensibility it might be expected that line Ax would be more towards an iso-volumetric response than Ay since the vasculature would become less distensible with increase in plasma volume. In fact, the slope of yAx, dP/dV, should vary inversely with vascular distensibility, capacitance or compliance. 3. Methods (A)
SERUM
ONCOTIC
PRESSURE
This is determined in an automatic semi-micro colloid osmometer (Reiff & Yiengst, 1959). The serum is equilibrated against a buffered physiological saline solution at pH 7.4 across a suitable semi-permeable membrane (ultrafine very dense membrane, Carl Schleicher and Schuell, Inc., Keene, New Hampshire) at 37°C. (B)
PLASMA
VOLUME
The day prior to the experimental run, plasma volume is determined with a tracer dose of radio iodinated human serum albumin (RISA). Serial per cent changes in plasma volume following induced oncotic changes are determined by a modification of the method of Abrams, Everson, Fields & Kaplan (1957) utilizing the RISA injected the day previously, and determining the deviations of specific activity of consecutive serum samples from the previously determined in vivo RISA specific activity decay curve for each subject. Absolute plasma volume changes can be calculated from per cent changes. 4. Calculations
From preliminary data the P-Y iso-oncomol curves have shown close agreement with theoretically derived formulae. The empirical relationship
COLLOID
OSMOTIC
HOMEOSTASIS
IN
HUMANS
between oncotic pressure and plasma volume fits the expression: P = av-‘+bV-2, P = serum oncotic pressure (dynes/cm’), V = plasma volume (cm3), Q = constant, b = constant. From thermodynamic considerations the theoretically derived formula for colloid osmotic pressure can be represented as: P +...
I n:iiRT = n2RTV-’ - ___ v-2+. . ., 2 P = colloid osmotic pressure (dynes/cm’), Y = volume of solution (cm’), n, = moles colloid, C = partial molal volume of solvent (cm3/mole), T = absolute temperature (“K), R = 8.3144 x IO’ (ergs/mole “K). The above formula is comparable to the empirical relationship it can be seen that: a = n,RT
from which
b=+!?. From experimental data the constants a and b can be calculated by least squares and from these values the number of moles of colloid osmotic material in the circulation (n2) can be determined. Since the concentration of oncotic mass can be determined [serum protein concentration (g/cm3)] and the volume (v) and total number of moles (n2) have been calculated, the number average molecular weight of serum protein can be determined. V (mol. wt) = serum protein concn x -. n2 The partial molal volume (Is) of serum solvent can also be calculated once n2 has been determined. -2b fi=n$RT’
6
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By substituting M/(m.w.) for n2, M = total colloid osmotic mass, = CV [total intravascular oncotic mass (g)] C = intravascular oncotic mass concentration (g/cm3) (m.w.) = mean number molecular weight of solute (protein), mass can be introduced into the formula for oncotic pressure so that p =.m
Ml,
since a
=
M
-!!T.
(m.w.) i?RT ..__. 2(m.w.)2
b = -ML by defining new constants (A and B) *=lLT (m.w.) then n=AM BE.---
CRT
2(m.w.)*
then b=BM”
we arrive at P = AMV-‘+BMZV-2.
In addition to describing the path of oncotic adjustment, the P-V diagram can also be utilized to visualize “oncotic energy” since the area difference under the P-V curve in traversing from an initial P-V state to a final P-V state is the difference in oncotic energy between the two states. Oncotic energy is a function that describes the total oncotic activity of a fixed amount of oncotic material (mass). It might be thought that the total oncotic activity of a given amount of solution could be expressed in terms of grams or even mols (oncomols) of oncotic mass. However, this leads to problems because the oncotic pressure of serum protein, as well as a number of other colloids, is not a linear function of its concentration. Therefore, the total number of oncomols of oncotic activity of a given amount of protein is not constant but is a function of its concentration. To circumvent this difficulty we have formulated the total amount of oncotic activity of a given solution in terms of “total oncotic energy”.
COLLOID
OSMOTIC
HOMEOSTASIS
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7
Oncotic pressure is usually expressed in units of “mm H,O”. By denoting the pressure in terms of dynes/cm2 (alternatively in ergs/cm3) the total oncotic energy of a given colloidal system can be calculated as the product of the oncotic pressure (dynes/cm2) and the volume (cm3) of the system. This gives the oncotic energy of the system in dyne cm (ergs). This has been conceptualized as the total potential oncotic energy of the system at a given concentration. If, in going from an initial P-V state to a final P- Vstate and then returning to the initial P-V state, a hysteresis loop is described, the area within that loop would represent oncotic work utilized in the process. Since the relationship between P and V has been derived and the constants A and B experimentally determined, it has been possible to integrate the formula for oncotic energy in terms of the known values (see Appendix A). 5. Discussion The foregoing provides the theoretical and experimental basis upon which further study of plasma volume-colloid osmotic pressure relationships is being performed. The importance of these studies may lie in several areas : (a) A theoretical understanding of plasma volume-colloid osmotic pressure relationships, and the role that colloid osmotic pressure plays in maintaining plasma volume under varying conditions (i.e. disease states such as heart failure, nephrotic syndrome hepatic cirrhosis, starvation and kwashiorkor, hypo- and an-albuminemia, “idiopathic” periodic edema, etc.). (b) The importance of colloid osmotic pressure in relation to plasma volume regulation under conditions of varying gravitational potential (i.e. positional changes such as prolonged bed rest and postural hypotension, space flight with prolonged exposure to gravity states different than those found on earth). On the basis of pilot studies we have been able to calculate that approximately 40 to 50% of the intravascular colloid osmotic energy is required to balance gravitational hydrostatic forces. In addition it seems that the postural hypotension reported in returning astronauts and cosmonauts whose cardiovascular reflexes had been previously well trained could be explained by changes in total intravascular colloid osmotic energy. Furthermore, on the basis of theoretical considerations, it can be demonstrated that a period of cardiovascular stress due to unbalanced colloid osmotic forces could lead to significant increase in plasma volume when going from the gravitational potential found on earth to gravity states significantly less.
8
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(c) The possible use of small calculated dosages of oncotic material in the treatment of pulmonary edema. Relatively small amounts of hyperoncotic albumin given as a bolus intravenously could produce an enormous colloid osmotic gradient in passing through the pulmonary circulation. It should be possible to accurately measure the transcapillary water flux by measuring oncotic pressure of plasma before and after passage through the pulmonary circulation. The small amounts of colloid needed to produce a significant oncotic gradient should not be large enough to overload the systemic circulation and could be accompanied by simultaneous phlebotomy, if necessary. (d) Colloid osmotic pressure-plasma volume curves should provide some index of intravascular capacitance and volume elasticity. The PV adjustment curves during changes in amount of intravascular colloid may provide information on vascular distensibility. (e) The PV iso-oncomol curves may be utilized precisely to determine relative changes in plasma volume, when there is no change in the total amount of colloid within the vasculature, by monitoring changes in colloid osmotic pressure (i.e. during renal dialysis, I.V. hydration, diuresis, etc.). Note added in proof. Sincethis paper wasprepared,Ladegaard-Pedersen (Stand. J. clin. Lab. Invest. 23, 153-158,1969)has reported the resultsof his experimental studies on plasma volume and plasma colloid osmotic pressurerelationships. In his calculationsan empiricalmodification of the Van’t Hoff formula for osmotic pressureis utilized. His empirical equation revealsa definedrelationship between plasma oncotic pressureand plasma volume that might apply only to limited pressureranges.Since he utilizes cm Ha0 as the pressuredimension, the calculation of oncotic energy is not apparentfrom the pressurevolume product.
REFERENCES ABRAMS, B., EVERSON, T. C., FIELDS, T. & KAPLAN, A. (1957). J. Lab. clin. Med. 49, 494. ARM~~ONO, S. H., KARK, R. M., SCHOENBERGER, J. A., SHATKIN, J. & SIGHTS, R. (1954).
J. clin. Invest. 33, 291. CHINARD, F. P., LAUSON, H. D., EDER, H. A. & GREIF, R. L. (1954). J. clin. Invest. 33, 629. HYMAN, C. & STEINFELD, J. L. (1967). Am. Heart J. 74,436. REEVE, E. B. & GUYTON, A. C. (eds) (1967). Physical Bases of Circulatory Transport: Regulation and Exchange. Philadelphia, Pa.: W. B. Saunders Co. REIFF, T. R. & YIENGST, M. (1959). J. Lab. clin. Med. 53 (2), 291. SCATCHARD, G. (1946). J. Am. them. Sot. 68,2315. STARLING, E. (1895-1896). J. Physiol., Lond. 19, 312. WESTON. R. E.. GROSSMAN. J.. ESSIG. A.. ISAAC& M. C.. HANENSON. I. B. & Ho~owrrz. H. B. ‘(196O).‘Metabolis& 9; 157. ’ WIEDERIUELM, C. A. (1968). Dynamics of Transcapillary Fluid Exchange. Biological Interfaces: Flows and Exchanges, pp. 29-63. Proceedings of a Symposium Sponsored by the New York Heart Association. Boston: Little Brown & Co.
COLLOID
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Appendix A (PV)z E,-E,
=a;E=TdE= 1 d(PV)=~VdP+j.PdV 1 El WV)1 P = AMV-‘+BMZV-2
dP = -MV-2(A+2BMV-1)
dV
-A’-2BP
-A+-zzzzz
JA=+ 2.
dP 4BP
2
V dP = i - MV-‘(A+2BMV-‘) 1
I 1
=44,++~BM2 2 i 1
1
dV
c 1 ;m-; 2
1
2
P dV =
1
dV
MV-‘(A+BMV-‘) 1
44+$M2 1
@=jPdV+jVdP=BM’ 1
[ 1 +-;
1
= &- ‘;’ [JA2+4BPz
2
- &iZ+4BPl]
in terms of V
1
in terms of P.
An oncodynamic description of the intravascular oncotic state has been formulated in terms of the following variables, one of which is intensive, two of which are extensive. P V M
colloid osmotic pressure (dyne cme2), plasma volume (cm3), colloid osmotic mass (g).
From these primary variables several derived quantities can be described: C = M/V concentration of oncotic mass (g cme3), E = PV total oncotic energy (ergs), S = E/M = PV/M specific oncotic energy (ergs g-l),
10
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P, V and C are quantities that can be experimentally M, E and S can be calculated. f(P,V,M)=O=PV2-AMV-BMZ P = AMv-'+BM2V-2
determined,
v=34i:JA2+4BP)
An oncotic surface can now be fully described, the curvature of which is a function of the forthcoming partial differentials. The following three-dimensional PVA4 surface was constructed by plotting P-F’ curves for varying total intravascular colloid osmotic masses on a Colloid
osmotic
mass 4
5
(g x10’) 6
7
8
9
IO
GAE FAD BAC yAx P=AMV-I
+B/h-2
Iso volumetric lso oncotic Iso oncomolic Actual poth of oncotic adjustment
COLLOID
OSMOTIC
HOMEOSTASIS
IN
11
HUMANS
Cal-Comp 1627 plotter with data programmed from a 1620 IBM computer into which had been fed the formula P = AMV-‘+BM2Vw2 utilizing average values for the A and B constants and varying volume by increments of 100 ml. In addition to the integration of the oncotic pressure formulations, partial differentials have been solved in terms of the three primary variables (P, V, M) = -MV34$2BMV3 -A’-2BP -A
ap = (3aM Y
iso-oncomolic
*JA2+4BP
V-‘(Af2BMV-9 V JA2 +4BP
iso-volumetric
iso-oncotic
These partial differential equations permit a precise characterization of the homeostatic variation and the solution of the exact differentials of the primary oncotic variables P, V and AL
= -MV-2(A+2BMV-1) dV=(g)*dP+(&)pdM
dV+V-‘(A+2BMV-‘)
dM
12
In addition
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to the partial differentials of the three primary variables differentials have been solved in terms of the derived
(P, F’, M), partial variable E.
f(E,Vi,P)=O=E-PV E=PV V=EP-’ P=EV-’
iso-volumetric
iso-oncotic
iso-energetic
dE = (;)vdP+(g),dV = VdPfPdV dV = (!$,dt+(fZ),dP = P-‘dE-EP-‘dP dP = ($),dE+(g>,d” = V-‘dE-EV-‘dV f(E,V,M)=O=E-AM-BMZV-’ E = AM+BM’V-’
COLLOID v=
OSMOTIC
HOMEOSTASIS
IN
HUMANS
BM2
E-AM M = -AV&A2V2+4BEV 2B = A+2BMv-’ s+-~
V --= JA2 V2 + 4BEV
iso-volumetric
iso-oncomolic
iso-energetic
dE = (g)vdM+@MdV = (A+2BMV-‘)dM-BM’V-‘dv dV = (;),dM+(g),dE 2BME - ABM’ = -(Z-AM)~
BM2 dM - (E-AM)2
dM = &vdE+(;$)EdV
--__ f(E,P,M)=O=E-~(A~JA2+4BP) E = r(AfJA2+4BP)
dE
13
14
T. p=--
R.
REIFF
E2-AME BM2
M = .~ ?“m ~- .. A&A2 +4BP
iso-oncotic
I
BM M= -~-+x/A
+4BP
iso-oncomolic
ME2 - 2E2 + AME BM3
&o-energetic
T2BE (A2f2BP)JA2+4BP_+A(A2+4BP)
I
dE -___ +(A_+JA2+4BP)dM dP
-.B&-- dp -t - &i’+ 4BP
(igMdE+(LiJEdM dE + ME’-2E2++4F --~. -~~~ BM3
= 2E;ti;!!
dM
dM = (g)pdE+(g)EdP 2 = A+ JA2 + 4BP
dE f 2BE (A2+2BP)\:A2+4BP+A(.4Z-+4BP)
~~ dP
Colloid Osmotic Homeostasis in Humans I. Theoretical Aspects and Background THEODORE R. REIFF Department of Internal Medicine, University of Nebraska College of Medicine, Veterans Administration Hospital, Omaha, Nebraska 68105, U.S.A. (Received 17 July 1969) The theoretical exploration of intravascular colloid osmotic pressureplasma volume relationships has been undertaken in an attempt to formulate meaningful physical parameters to describe the paths that may be taken when an individual has been subjected to colloid osmotic stress, i.e. changing colloid concentrations and/or total colloid mass within the vasculature. Colloid osmotic pressure-plasma volume diagrams have been constructed, and the formulae relating these two measurable quantities have been theoretically and semi-empirically derived. In addition to describing the path of oncotic adjustment, the P-V diagram has been utilized to visualize and calculate oncotic energy changes in traversing from an initial to a final P-V state. Thermodynamic analogy has allowed a comprehensive oncodynamic treatment of colloid osmotic pressure (P), colloid osmotic mass (M), and intravascular volume (V) in the derived relationship: P = AMV-1 + BMaVez (A, B constants). Utilizing a three-dimensional P, V, M plot, an oncodynamic surface has been constructed, the curvature of which is a function of partial differentials of measurable quantities.
1. Introduction The effects of the intravenous administration of oncotic material such as human serum albumin, Dextran and polyvinyl pyrrolidine, to human subjects, have been studied by others in the past. Parameters measured have
included: (1) concentration of the oncotic material; (2) selected hemodynamic properties, i.e. cardiac output, arterial and venous pressures, intravascular volume; (3) renal function. However, largely due to the difficulty and tediousness of multiple determinations of oncotic pressure, little study has been made of the effect of administered
oncotically
active material
upon the oncotic pressure of the intravascular fluid. Most of those studies that have included oncotic pressure have used empirical formulae to calculate 1 T.B.
2
T.
R.
REIFF
the oncotic pressure from the serum protein concentrations. That these formulae are inadequate was shown by Armstrong, Kark, Schoenberger, Shatkin & Sights (1954). Starling (1895-96) made some of the earliest studies on the importance of colloid osmotic pressure in transcapillary fluid exchange, and pointed out the basic mechanisms underlying the dynamics of “passive” water transport. Chinard, Lauson, Eder & Grief (1954) studied plasma volume changes following the administration of albumin in two patients with the nephrotic syndrome. The change in plasma volume per unit of albumin was less than would have been obtained had the response been “iso-osmotic “(increase in plasma volume to keep osmotic pressure constant). Results suggested that an increase in capillary hydrostatic pressure prevented the maximal isoosmotic response. In these studies Chinard did not measure protein osmotic pressure, but calculated it from measurement of albumin and total globulin concentrations and use of a modified formula developed by Scatchard (1946). In an editorial, Hyman & Steinfeld (1967) discussed regulation of plasma volume and pointed out some of the remaining problems involved in volume regulation. Weston et al. (1960) have discussed in detail the search for the so-called “volume regulator”. Reeve & Guyton (1967) have compiled the thoughts of a number of recent investigators concerned with the role of oncotic pressure in transcapillary fluid transport including analog computer simulation studies of water balance. Wiederhielm (1968) has also contributed an analog computer simulation of fluid balance at the capillary level. 2. Approach
The purpose of these studies is the theoretical and experimental exploration of intravascular colloid osmotic-plasma volume relationships and to formulate meaningful physical parameters to describe these relationships. From preliminary experimental data and, independently, from purely thermodynamic considerations involving colloid osmotic pressure and plasma volume, a description has been formulated of the possible paths from an initial state to a final state, that an individual might take when subjected to colloid osmotic stress, i.e. changing colloid concentrations and/or total colloid mass within the vasculature. Experimentally induced oncotic stress in human and/or other subjects can be produced by the following: (1) Concentration of oncotic mass. Judicious intravenous induced diuresis (ethacrynic acid, etc.).
COLLOID
OSMOTIC
HOMEOSTASIS
IN
HUMANS
3
(2) Dilution of oncotic mass. Rapid intravenous infusion of physiological saline. (3) Increase in total oncotic mass. Rapid intravenous infusion of salt poor human serum albumin or the subject’s own plasma. (4) Decrease in total oncotic mass. Plasmapheresis and/or phlebotomy. From experimental data it is possible to construct oncotic pressure-plasma volume (P-V) curves (“iso-oncomols”) by plotting simultaneous values for serum oncotic pressure and plasma volume that describe the oncotic adjustment of a subject to varying oncotic stresses.
i.e. lines of constant total amount of Parallel curves are “is0-oncomols”, intravascular oncotic mass. The iso-oncomols demonstrate the manner in which oncotic pressure varies with changes in concentration of the oncotic material. Line AB describes the path taken when the subject’s intravascular oncotic mass has been concentrated (e.g. diuresis or dehydration). Line AC describes the path taken when the subject’s intravascular oncotic mass has been diluted (e.g. intravenous administration of physiological saline). Individuals who undergo a change in their total oncotic mass could have the following responses: (1) Increase in total oncotic mass (e.g. intravenous salt free human serum albumin or plasma). (a) Line AD would describe a purely iso-oncotic response, i.e. an increase in volume with oncotic pressure constant. This would be accomplished by transfer of solvent from extravascular spaces into the vasculature.
4
T.
R.
REIFF
(b) Line AE would describe a purely iso-volumetric response, i.e. an increase in serum oncotic pressure with no change in plasma volume. (2) Decrease in total oncotic mass (e.g. plasmapheresis or phlebotomy). (a) Line AF would describe a purely iso-oncotic response, i.e. no extravascular solvent would transfer into the intravascular compartment to maintain intravascular volume. (b) Line AG would describe a purely iso-volumetric response, i.e. transfer of extrasvacular solvent into the vasculature would take place in an attempt to maintain plasma volume. In actuality the path taken by a given subject would be along line yAx, i.e. an intermediate response somewhere between iso-oncotic and isovolumetric. Because of vascular distensibility it might be expected that line Ax would be more towards an iso-volumetric response than Ay since the vasculature would become less distensible with increase in plasma volume. In fact, the slope of yAx, dP/dV, should vary inversely with vascular distensibility, capacitance or compliance. 3. Methods (A)
SERUM
ONCOTIC
PRESSURE
This is determined in an automatic semi-micro colloid osmometer (Reiff & Yiengst, 1959). The serum is equilibrated against a buffered physiological saline solution at pH 7.4 across a suitable semi-permeable membrane (ultrafine very dense membrane, Carl Schleicher and Schuell, Inc., Keene, New Hampshire) at 37°C. (B)
PLASMA
VOLUME
The day prior to the experimental run, plasma volume is determined with a tracer dose of radio iodinated human serum albumin (RISA). Serial per cent changes in plasma volume following induced oncotic changes are determined by a modification of the method of Abrams, Everson, Fields & Kaplan (1957) utilizing the RISA injected the day previously, and determining the deviations of specific activity of consecutive serum samples from the previously determined in vivo RISA specific activity decay curve for each subject. Absolute plasma volume changes can be calculated from per cent changes. 4. Calculations
From preliminary data the P-Y iso-oncomol curves have shown close agreement with theoretically derived formulae. The empirical relationship
COLLOID
OSMOTIC
HOMEOSTASIS
IN
HUMANS
between oncotic pressure and plasma volume fits the expression: P = av-‘+bV-2, P = serum oncotic pressure (dynes/cm’), V = plasma volume (cm3), Q = constant, b = constant. From thermodynamic considerations the theoretically derived formula for colloid osmotic pressure can be represented as: P +...
I n:iiRT = n2RTV-’ - ___ v-2+. . ., 2 P = colloid osmotic pressure (dynes/cm’), Y = volume of solution (cm’), n, = moles colloid, C = partial molal volume of solvent (cm3/mole), T = absolute temperature (“K), R = 8.3144 x IO’ (ergs/mole “K). The above formula is comparable to the empirical relationship it can be seen that: a = n,RT
from which
b=+!?. From experimental data the constants a and b can be calculated by least squares and from these values the number of moles of colloid osmotic material in the circulation (n2) can be determined. Since the concentration of oncotic mass can be determined [serum protein concentration (g/cm3)] and the volume (v) and total number of moles (n2) have been calculated, the number average molecular weight of serum protein can be determined. V (mol. wt) = serum protein concn x -. n2 The partial molal volume (Is) of serum solvent can also be calculated once n2 has been determined. -2b fi=n$RT’
6
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By substituting M/(m.w.) for n2, M = total colloid osmotic mass, = CV [total intravascular oncotic mass (g)] C = intravascular oncotic mass concentration (g/cm3) (m.w.) = mean number molecular weight of solute (protein), mass can be introduced into the formula for oncotic pressure so that p =.m
Ml,
since a
=
M
-!!T.
(m.w.) i?RT ..__. 2(m.w.)2
b = -ML by defining new constants (A and B) *=lLT (m.w.) then n=AM BE.---
CRT
2(m.w.)*
then b=BM”
we arrive at P = AMV-‘+BMZV-2.
In addition to describing the path of oncotic adjustment, the P-V diagram can also be utilized to visualize “oncotic energy” since the area difference under the P-V curve in traversing from an initial P-V state to a final P-V state is the difference in oncotic energy between the two states. Oncotic energy is a function that describes the total oncotic activity of a fixed amount of oncotic material (mass). It might be thought that the total oncotic activity of a given amount of solution could be expressed in terms of grams or even mols (oncomols) of oncotic mass. However, this leads to problems because the oncotic pressure of serum protein, as well as a number of other colloids, is not a linear function of its concentration. Therefore, the total number of oncomols of oncotic activity of a given amount of protein is not constant but is a function of its concentration. To circumvent this difficulty we have formulated the total amount of oncotic activity of a given solution in terms of “total oncotic energy”.
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Oncotic pressure is usually expressed in units of “mm H,O”. By denoting the pressure in terms of dynes/cm2 (alternatively in ergs/cm3) the total oncotic energy of a given colloidal system can be calculated as the product of the oncotic pressure (dynes/cm2) and the volume (cm3) of the system. This gives the oncotic energy of the system in dyne cm (ergs). This has been conceptualized as the total potential oncotic energy of the system at a given concentration. If, in going from an initial P-V state to a final P- Vstate and then returning to the initial P-V state, a hysteresis loop is described, the area within that loop would represent oncotic work utilized in the process. Since the relationship between P and V has been derived and the constants A and B experimentally determined, it has been possible to integrate the formula for oncotic energy in terms of the known values (see Appendix A). 5. Discussion The foregoing provides the theoretical and experimental basis upon which further study of plasma volume-colloid osmotic pressure relationships is being performed. The importance of these studies may lie in several areas : (a) A theoretical understanding of plasma volume-colloid osmotic pressure relationships, and the role that colloid osmotic pressure plays in maintaining plasma volume under varying conditions (i.e. disease states such as heart failure, nephrotic syndrome hepatic cirrhosis, starvation and kwashiorkor, hypo- and an-albuminemia, “idiopathic” periodic edema, etc.). (b) The importance of colloid osmotic pressure in relation to plasma volume regulation under conditions of varying gravitational potential (i.e. positional changes such as prolonged bed rest and postural hypotension, space flight with prolonged exposure to gravity states different than those found on earth). On the basis of pilot studies we have been able to calculate that approximately 40 to 50% of the intravascular colloid osmotic energy is required to balance gravitational hydrostatic forces. In addition it seems that the postural hypotension reported in returning astronauts and cosmonauts whose cardiovascular reflexes had been previously well trained could be explained by changes in total intravascular colloid osmotic energy. Furthermore, on the basis of theoretical considerations, it can be demonstrated that a period of cardiovascular stress due to unbalanced colloid osmotic forces could lead to significant increase in plasma volume when going from the gravitational potential found on earth to gravity states significantly less.
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(c) The possible use of small calculated dosages of oncotic material in the treatment of pulmonary edema. Relatively small amounts of hyperoncotic albumin given as a bolus intravenously could produce an enormous colloid osmotic gradient in passing through the pulmonary circulation. It should be possible to accurately measure the transcapillary water flux by measuring oncotic pressure of plasma before and after passage through the pulmonary circulation. The small amounts of colloid needed to produce a significant oncotic gradient should not be large enough to overload the systemic circulation and could be accompanied by simultaneous phlebotomy, if necessary. (d) Colloid osmotic pressure-plasma volume curves should provide some index of intravascular capacitance and volume elasticity. The PV adjustment curves during changes in amount of intravascular colloid may provide information on vascular distensibility. (e) The PV iso-oncomol curves may be utilized precisely to determine relative changes in plasma volume, when there is no change in the total amount of colloid within the vasculature, by monitoring changes in colloid osmotic pressure (i.e. during renal dialysis, I.V. hydration, diuresis, etc.). Note added in proof. Sincethis paper wasprepared,Ladegaard-Pedersen (Stand. J. clin. Lab. Invest. 23, 153-158,1969)has reported the resultsof his experimental studies on plasma volume and plasma colloid osmotic pressurerelationships. In his calculationsan empiricalmodification of the Van’t Hoff formula for osmotic pressureis utilized. His empirical equation revealsa definedrelationship between plasma oncotic pressureand plasma volume that might apply only to limited pressureranges.Since he utilizes cm Ha0 as the pressuredimension, the calculation of oncotic energy is not apparentfrom the pressurevolume product.
REFERENCES ABRAMS, B., EVERSON, T. C., FIELDS, T. & KAPLAN, A. (1957). J. Lab. clin. Med. 49, 494. ARM~~ONO, S. H., KARK, R. M., SCHOENBERGER, J. A., SHATKIN, J. & SIGHTS, R. (1954).
J. clin. Invest. 33, 291. CHINARD, F. P., LAUSON, H. D., EDER, H. A. & GREIF, R. L. (1954). J. clin. Invest. 33, 629. HYMAN, C. & STEINFELD, J. L. (1967). Am. Heart J. 74,436. REEVE, E. B. & GUYTON, A. C. (eds) (1967). Physical Bases of Circulatory Transport: Regulation and Exchange. Philadelphia, Pa.: W. B. Saunders Co. REIFF, T. R. & YIENGST, M. (1959). J. Lab. clin. Med. 53 (2), 291. SCATCHARD, G. (1946). J. Am. them. Sot. 68,2315. STARLING, E. (1895-1896). J. Physiol., Lond. 19, 312. WESTON. R. E.. GROSSMAN. J.. ESSIG. A.. ISAAC& M. C.. HANENSON. I. B. & Ho~owrrz. H. B. ‘(196O).‘Metabolis& 9; 157. ’ WIEDERIUELM, C. A. (1968). Dynamics of Transcapillary Fluid Exchange. Biological Interfaces: Flows and Exchanges, pp. 29-63. Proceedings of a Symposium Sponsored by the New York Heart Association. Boston: Little Brown & Co.
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Appendix A (PV)z E,-E,
=a;E=TdE= 1 d(PV)=~VdP+j.PdV 1 El WV)1 P = AMV-‘+BMZV-2
dP = -MV-2(A+2BMV-1)
dV
-A’-2BP
-A+-zzzzz
JA=+ 2.
dP 4BP
2
V dP = i - MV-‘(A+2BMV-‘) 1
I 1
=44,++~BM2 2 i 1
1
dV
c 1 ;m-; 2
1
2
P dV =
1
dV
MV-‘(A+BMV-‘) 1
44+$M2 1
@=jPdV+jVdP=BM’ 1
[ 1 +-;
1
= &- ‘;’ [JA2+4BPz
2
- &iZ+4BPl]
in terms of V
1
in terms of P.
An oncodynamic description of the intravascular oncotic state has been formulated in terms of the following variables, one of which is intensive, two of which are extensive. P V M
colloid osmotic pressure (dyne cme2), plasma volume (cm3), colloid osmotic mass (g).
From these primary variables several derived quantities can be described: C = M/V concentration of oncotic mass (g cme3), E = PV total oncotic energy (ergs), S = E/M = PV/M specific oncotic energy (ergs g-l),
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P, V and C are quantities that can be experimentally M, E and S can be calculated. f(P,V,M)=O=PV2-AMV-BMZ P = AMv-'+BM2V-2
determined,
v=34i:JA2+4BP)
An oncotic surface can now be fully described, the curvature of which is a function of the forthcoming partial differentials. The following three-dimensional PVA4 surface was constructed by plotting P-F’ curves for varying total intravascular colloid osmotic masses on a Colloid
osmotic
mass 4
5
(g x10’) 6
7
8
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IO
GAE FAD BAC yAx P=AMV-I
+B/h-2
Iso volumetric lso oncotic Iso oncomolic Actual poth of oncotic adjustment
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Cal-Comp 1627 plotter with data programmed from a 1620 IBM computer into which had been fed the formula P = AMV-‘+BM2Vw2 utilizing average values for the A and B constants and varying volume by increments of 100 ml. In addition to the integration of the oncotic pressure formulations, partial differentials have been solved in terms of the three primary variables (P, V, M) = -MV34$2BMV3 -A’-2BP -A
ap = (3aM Y
iso-oncomolic
*JA2+4BP
V-‘(Af2BMV-9 V JA2 +4BP
iso-volumetric
iso-oncotic
These partial differential equations permit a precise characterization of the homeostatic variation and the solution of the exact differentials of the primary oncotic variables P, V and AL
= -MV-2(A+2BMV-1) dV=(g)*dP+(&)pdM
dV+V-‘(A+2BMV-‘)
dM
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In addition
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to the partial differentials of the three primary variables differentials have been solved in terms of the derived
(P, F’, M), partial variable E.
f(E,Vi,P)=O=E-PV E=PV V=EP-’ P=EV-’
iso-volumetric
iso-oncotic
iso-energetic
dE = (;)vdP+(g),dV = VdPfPdV dV = (!$,dt+(fZ),dP = P-‘dE-EP-‘dP dP = ($),dE+(g>,d” = V-‘dE-EV-‘dV f(E,V,M)=O=E-AM-BMZV-’ E = AM+BM’V-’
COLLOID v=
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BM2
E-AM M = -AV&A2V2+4BEV 2B = A+2BMv-’ s+-~
V --= JA2 V2 + 4BEV
iso-volumetric
iso-oncomolic
iso-energetic
dE = (g)vdM+@MdV = (A+2BMV-‘)dM-BM’V-‘dv dV = (;),dM+(g),dE 2BME - ABM’ = -(Z-AM)~
BM2 dM - (E-AM)2
dM = &vdE+(;$)EdV
--__ f(E,P,M)=O=E-~(A~JA2+4BP) E = r(AfJA2+4BP)
dE
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E2-AME BM2
M = .~ ?“m ~- .. A&A2 +4BP
iso-oncotic
I
BM M= -~-+x/A
+4BP
iso-oncomolic
ME2 - 2E2 + AME BM3
&o-energetic
T2BE (A2f2BP)JA2+4BP_+A(A2+4BP)
I
dE -___ +(A_+JA2+4BP)dM dP
-.B&-- dp -t - &i’+ 4BP
(igMdE+(LiJEdM dE + ME’-2E2++4F --~. -~~~ BM3
= 2E;ti;!!
dM
dM = (g)pdE+(g)EdP 2 = A+ JA2 + 4BP
dE f 2BE (A2+2BP)\:A2+4BP+A(.4Z-+4BP)
~~ dP