where R is the universal gas constant and T is the absolute temperature. A widely accepted implication is that solute lowers the activity of the water in the solution by lowering the “Fugacity” of the water and that this explains why the chemical potential of the water is lessened an amount stated by this thermodynamic equation. As a matter of fact, this equation is nothing more than a definition of the term “activity of water in the solution”, as indicated by  between the two sides. It does not explain how the solute lowers the Fugacity or the activity or the chemical potential of the water in the solution.  Water activity is a dimensionless number greater than zero and less than or equal to one. Adding solute does lower the chemical potential of water so that the left side of the defining equation becomes negative.  Water activity, by definition, becomes less than one so that ln a becomes negative.  However, this account does not explain how the solute lowers the chemical potential or the activity of the water in the solution.

Another accepted implication of the Lewis account of osmosis is that the solute acts on the water and lowers its chemical potential at or near the semi-permeable membrane that separates pure liquid water from water in the solution.  The presumption is that water molecules diffuse from pure liquid water at a higher chemical potential through the semi-permeable membrane into the solution where the chemical potential of its water is less. Diffusion is said to continue until the rising pressure in the solution water increases the chemical potential of the water in the solution to equal the higher chemical potential of the pure liquid water beyond the semi permeable membrane.

2.       Hulett theory of osmosis.

Lewis ignored a valid and prior explanation of how solute alters the water in an aqueous solution. In 1903, Hulett ^6,7 correctly concluded that solute alters the internal tension in the force bonding the water molecules together in the liquid phase.  When  denotes the osmotic pressure of the water at a distensible boundary of the solution, Hullet recognized that the solute alters every partial molar property of the water in the solution just like the same molar property of pure liquid is altered by reducing the pressure applied to it by . Regarding the chemical potential,

. Likewise for the other molar properties, , where  is the vapor pressure. And

 ,

 ,

 ,

 ,

where , ,  and  are, respectively, the molar volume, molar internal energy, molar enthalpy and molar entropy.

By Hulett’s account of osmosis, the altered internal tension of the water in the solution pulls water through the semi-permeable membrane from the pure liquid water until the internal tensions in the water on both sides of the membrane become equal.

          3.       The water concentration theory, a modified Lewis theory, is disproved by the properties of solutions of NaF or MgSO4. 

Physiologists continue to reject Hulett’s account of osmosis and continue to accept a modified version of Lewis’s account^4,5. They do so based on a curious application of the process of diffusion.  In diffusion, a material in an aqueous solution at a high concentration moves by Brownian motion to an area of lower concentration.  Pure liquid water has a concentration of 55.50 moles per liter at 0° C; that is, the volume occupied by 55.50 moles of pure liquid water is one liter at 0° C.  When a solute, say, NaSO4, is added to one liter of pure liquid water, the volume of the resulting NaSO4 solution is greater than the volume of the pure water alone and the concentration of water in the NaSO4 solution falls below 55.50 moles per liter of solution. 

Physiologists claim that if the NaSO4 solution is separated from pure water by a semi-permeable membrane, the pure water will diffuse from the water with the higher water concentration (the pure water) to the water with the lower water concentration (the NaSO4 solution). As in Lewis’s theory, physiologists presume water molecules diffuse through the membrane until the increasing pressure in the water in the NaSO4 solution raises the chemical potential of the water in the solution to equal the chemical potential of the pure liquid water beyond the membrane.

If a single instance is found where the modified Lewis theory does not describe reality, the theory is disproved.  As illustrated by Figs. 3-5, the modified Lewis’s theory does not describe reality and hence is proved invalid because the properties of solutions 34 of NaF 28 and MgSO₄ 30 do not conform to the theory. As shown by Fig. 3, if NaF 28 or MgSO₄ 30 is added to pure water 32, the resulting solution 34 (Fig. 4) occupies less volume than did the pure water 32. In other words, when NaF 28 or MgSO₄ 30 is added to water 32, the concentration of water in the solution 34 increases, not decreases.  For example, for a NaF 28 solution 34 that is 1000 Osm/Kg water, the water concentration increases to 55.62 mols water per liter of solution at 0° C 34, an increase of 0.12 mols water per liter of solution at 0° C 34. 

The Physiologist’s modified Lewis theory predicts that such a solution would exert a negative osmotic pressure so that water would flow from the solution through a semi-permeable membrane and into adjacent pure water. Contrary to the modified Lewis theory prediction and as shown by Fig. 5, solutions 34 of NaF 28 or MgSO₄ 30 show a positive osmotic pressure 40.  Pure water 38 enters a solution 34 of NaF 28 or MgSO₄ 30 through a semi-permeable membrane 36 in about the same amount as would enter a comparable solution of NaSO₄ in which the water concentration in the solution is lower¹⁰.

The physiologist’s modification of the Lewis theory is therefore disproved and concentration and/or activity of water in a solution can not provide a mechanism for understanding osmosis.  Only Hulett’s mechanism provides a valid basis for understanding osmotic effects. 

B. Starling’s Hypothesis of Fluid Exchange between Plasma and Interstitial Fluid

In 1896, Starling³ performed an experiment in which he concluded that the colloid osmotic pressure of the proteins in plasma exert an osmotic force causing the return of interstitial fluid to the venous end of capillaries. In modern terminology, Starling’s hypothesis is expressed

as Starling’s equation, namely,

According to Starling’s hypothesis, four pressures determine whether fluid flows from plasma to interstitial fluid (“ISF”) or from ISF to plasma. Starling³ recognized that the hydrostatic pressure in the plasma () will normally exceed the hydrostatic pressure in ISF () outside the capillary endothelium along the entire length of the capillary. These differing pressures force the extravasation of fluid into the ISF at the arterial end of the capillary and they comprise the hydrostatic pressure term in the Starling equation.  Starling, and subsequent interpreters of Starling’s 1896 experiment, postulated another term consisting of the colloid osmotic pressure of plasma () and of the colloid osmotic pressure of ISF () at the same location along a capillary through which the plasma flows. These two COPs constitute the osmotic force in the Starling equation, where  is the volume of fluid filtering through the capillary in unit time and unit length at (x).   is the hydraulic conductivity of the capillary at (x).  S(x) is the circumference of the capillary.   is the reflection coefficient of the endothelium for the colloids.

The second Starling force or osmotic term, i.e., , states that since the protein concentration in the plasma exceeds the protein concentration in the ISF, this force will return fluid to the capillary when this osmotic force exceeds the hydrostatic force near the venous end of the capillary.

Interpreters of Starling’s equation assume that proteins in plasma lower the concentration of water in the plasma.  For this reason, they presume that interstitial fluid diffuses into the plasma at the venous end of the capillary where the hydrostatic pressure is least.  As noted above, water concentration does not and cannot cause osmotic effects.  As Hulett, recognized, the protein molecules in aqueous solution exert a pressure at a distensible boundary of the solution and alter the internal tension of the water in the solution as would lowering the external pressure applied to pure liquid water.  The protein molecules also alter the internal tension of the water in the solution and, thereby, lower the chemical potential of the water in the solution.  When plasma flows through the capillary at a constant rate (as in Starling’s hypothesis), the boundaries of the plasma are already distended by both the colloid pressure and by hydrostatic pressure.  That is, when flow is steady, the protein molecules no longer distend the wall of the capillary and have no other effect on fluid exchange between interstitial fluid and plasma.

The purpose of this background review has been: 1) to show that Starling’s hypothesis can not be valid and 2) to suggest another force that may be the most important osmotic force in determining the extravasation of fluid from plasma to ISF and in returning most of it from ISF to plasma within the capillary^{10,11,12,13,14}.

C.    The Osmotic Force that Accounts for the Return of ISF in Starling’s Experiment

           1.     The osmotic force in systemic tissue.

            a.   Changes in ion concentration and electroneutrality.

               For purposes of this application, “systemic tissue” 42 (Figs. 6,7) means all tissue of the body other than the alveolar tissue 22 of the lung (Figs. 8,9).

Cells of systemic tissues 42 produce CO2 44 as a waste product of metabolism.  The waste CO2 44 diffuses through the interstitial fluid 18 and is carried away in the blood plasma 24 in the form of bicarbonate ions () 26. When plasma 24 flows from the arterial end 6 to the venous end 8 of a capillary 2 in systemic tissue 42, the bicarbonate ion () 26 concentration of the plasma 24 increases from 27.5 to 29 millimols per liter (“mmol/liter”) of plasma in humans at rest¹⁵, an increase in the negative charge of the plasma of 1.5 mmol/liter.

To maintain electrical neutrality, the increase in negative charge of the plasma 24 caused by the increase in  ion 26 concentration must be offset by an equivalent increase in the strong ion difference (“SID”) of 1.5 mmol/liter.  SID is defined by the equation SID=[]-[].  The SID increases as the sodium ion concentration [] in the plasma increases and the chloride ion concentration [] decreases as the plasma flows from the arterial end 6 to the venous end 8 of the capillary 2.  The chloride ion concentration [] in plasma decreases because the chloride ions enter the red cells in exchange for bicarbonate ions 26.  The net effect is to increase the positive charge of the plasma 24 by 1.5 mmol/liter and thereby maintain electroneutrality.

b.              Changes in osmotic pressure corresponding to the changes in ion concentration.

          The increase in the bicarbonate ion concentration () 26 in the capillary 2 would increase the osmotic effect 16 of the water in plasma 24 by 29 Torr in the absence of other concentration changes.  The increase in osmotic effect 16 caused by the increase in concentration of  ions 26 is partially offset by a reduction in osmotic pressure caused by changes in the relative concentrations of Na+ and Cl-. The net increase in the osmotic effect 16 of the water in plasma 24 flowing from end to end (6,8) in a capillary 2 in systemic tissue 42 is about 33 Torr in humans at rest.  A Torr is equivalent to the pressure exerted by a column of elemental mercury 1 millimeter tall.

          c.       Mechanism of the change in osmotic pressure.

To state that a change in concentration of a solute changes the osmotic effect 16 of the water in the plasma  24 says nothing of the mechanism at work to create the change in osmotic effect 16.

As illustrated by Fig. 7, in capillaries 2 in systemic tissue 42, the primary source of the change in osmotic effect 16 is the diffusion of  ions 26 in the capillary 2 from the region of high  ion 26 concentration at the venous end 8 of the capillary 2 toward the region of low  ion 26 concentration at the arterial end 6 of the capillary 2. Diffusion of the HCO3- ions 26 is illustrated by arrow 46 on Fig. 7. 

As the  ions 26 diffuse from the venous end 8 toward the arterial end 6 of the capillary 2, the ions 26 drag on the plasma water 24 through which they diffuse 46 and alter the internal tension of the water in the plasma 24 just like the internal tension of pure liquid water is altered by lessening the pressure applied to it by 33 Torr.  The internal tension of the water in the plasma 24 is altered the most at the venous end 8 of the capillary 2.  The altered water in the plasma 24 pulls return fluid 11 from interstitial fluid 18 into the plasma 24 at the venous end 8 of the capillary 2 where the hydrostatic pressure 4 in plasma 24 is much less than 33 Torr. At the same time, the altered internal tension of the plasma water 24 retards the extravasation of fluid 10 from plasma 24 into the interstitial fluid 18 at the arterial end 6 of the capillary 2 where the hydrostatic pressure 4 exceeds 33 Torr. The net result is that extravasation of fluid 10 is reduced and most of the fluid 10 extravasated from plasma 24 into interstitial fluid 18 is returned as return fluid 11 to the plasma 24 at the venous end 8 of the capillary 2.

The osmotic effect 16 of diffusing bicarbonate ions 26 is also load dependent, i.e., as more  44 is produced in active systemic tissue 42 (e.g., muscle), more  ions 26 diffuse 46 upstream in the capillary 2 plasma 24 and have a greater osmotic effect 16 to pull return fluid 11 from interstitial fluid 18 to the plasma 24 at the venous end 8 of the capillary 2. 

2.       The osmotic force in pulmonary tissue.

As illustrated by figs. 8 and 9, in the alveoli 22 of the lung the osmotic effects of diffusing bicarbonate 26 and strong ions are reversed.  Plasma 24 laden with the metabolic waste product bicarbonate () 26 enters the arterial end 6 of the pulmonary capillary 2. The bicarbonate () 26 leaves the plasma 24 in the form of  44 and enters the alveoli 22 of the lung as the plasma 24 travels through the capillary 2. As a result, the  ion 26 concentration decreases as the plasma 24 flows from the arterial end 6 to the venous end 8 in the pulmonary capillaries 2. The concentrations of the strong ions  and  also change so as to maintain electroneutrality.  The HCO3- 26, the Na+ and the Cl- ions each diffuses from its area of higher concentration to its area of lower concentration within the plasma 24 within the capillary 2.  The diffusion of HCO3- ions 26 for alveolar tissue 22 is illustrated by arrow 48 of fig. 9.  The principal osmotic effect of these ions is the osmotic effect 16 created by the  ions 26 as they drag on the water in the plasma 24 through which they diffuse 48. In humans at rest, this osmotic effect 16 is about 33 torr at the arterial end 6 of the pulmonary capillary 2, where the osmotic effect 16 retards extravasation.  In humans in strenuous exercise,¹⁵ the plasma 24 osmolarity increases.  However, as plasma 24 flows from end to end 6,8 in a pulmonary capillary 2, its osmolarity may decrease as much as 27 milliosmol/liter due, in part, to a decrease in the  ion concentration from 33.2 milliosmol/liter to 23.7 milliosmol/liter, a decrease of 9.5 milliosmol/liter.  At rest, this decrease is only 1.5 milliosmol/liter.

In exercise, pulmonary arterial pressure 4 increases and more fluid 10 is extravasated from plasma 24 into adjacent alveolar fluid 18 of the lung. Note again that the osmotic effect 16 of diffusing hco3- ions 26 is load dependent in the pulmonary capillaries 2. That is, as more work is performed, more  ions 26 are formed, the ions diffuse 48 from arterial 6 to venous ends 8 of the pulmonary capillaries 2 at higher rate, and the osmotic effect 16 of the  ions 26 is as much as 184 torr, compared with 29 torr at rest.  As a result, less fluid 10 is extravasated into the alveolar fluid 18 and more return fluid 11 is removed from the alveolar fluid 18 at a higher rate, thereby avoiding pulmonary edema.

The diffusion 48 of bicarbonate ions 26 yields the primary osmotic effect 16 for prevention of pulmonary edema. Contrary to Starling’s hypothesis and equation and contrary to current accounts of the forces involved in plasma 24 -interstitial fluid 18 exchange, the role of the colloid osmotic pressure of plasma proteins is minor. Furthermore, Starling’s osmotic force is not load dependent; it is constant regardless of rate of work.       

D.       Minimizing HAPE

      Since diffusion of  ions 26 creates the necessary osmotic effect 16 to retard extravasation of fluid 10 from the capillaries 2 or to return extravasated fluid 18 to the capillaries 2, an adequate rate of production of  44 is essential for avoidance of pulmonary edema.  At high altitude, inspired  is insufficient to metabolize adequate carbon to  44 and hence to  ions 26 in the plasma 24. Food ingested by high altitude climbers can supply some of the required oxygen.

Food ingested by climbers should maximize the content of carbon and oxygen atoms (Figs. 10, 11).  Atoms that are metabolized to something other than CO2 should be minimized or eliminated from the diet. The food should minimize hydrogen content and should eliminate nitrogen atoms (Fig. 11). For these reasons, proteins (meat and legumes) should be eliminated from the food ingested at the highest elevations of the climb. Only digestible carbohydrates that yield the highest ratio of  and the highest ratio moles of  to moles of carbon, , should be ingested (Fig. 11). Pure glucose  and/or sucrose () is recommended. Glucose has sufficient oxygen to metabolize all of its hydrogen.  Metabolism of the carbon requires inspired oxygen. A digestible carbohydrate with less hydrogen would be better and fats are less desirable because the ratio  is less favorable.

REFERENCES

1) West, J.B., Mathieu-Costello, O. (1991) Stress failure in pulmonary capillaries: a mechanism for high altitude pulmonary edema. Hypoxia and Mountain Medicine. 7^th International Hypoxia  Symposium . Ed. Sutton, J. R. and Coates, G. pp 229-39.

2) Klocke, D. L., Decker, W. W., Stepenek, J. (1998) Altitude-related illnesses. Mayo Clin. Proc.  73: 988-93.

3) Starling, E. H. (1896) On the absorption of fluids from connective tissue spaces. J. Physiol. London,  19: 312-326.

4) Michel, C. C. (1996) One hundred years of Starling’s hypothesis. NIPS :11 229-237.

5) Taylor, A. E. and T. M. Moore. (1999) Capillary fluid exchange. Adv. Physiol. Ed. 22: S203-S210.

6) Hulett G. Beziehung zwischen negativem Druck und osmotischem Druck. Z.

Phys.Chem. 1903;  42: 353-368.

7) Hammel, H. T. (1994) How solute alters water in aqueous solutions. J.Phys.Chem. 98: 4196-204.

8) Mysels, K. J. (1978) Solvent tension or solvent concentration? J. Chem.Ed. 55: 21-22.

9) Lewis, G. N. (1908) The osmotic pressure of concentrated solutions, and the laws of the perfect solution. J. Am. Chem. Soc. 30: 668-683. 

10) Hammel, H. T. (1999) Evolving ideas about osmosis and capillary fluid exchange.   FASEB J. 13: 213-31.

11) Hammel, H. T. (1995) Role of colloidal molecules in Starling’s hypothesis and in returning interstitial fluid to the vasa recta. Am. J. Physiol. 268:H2133-44.

12) Hammel, H. T., Brecheu, W. F. (2000) Plasma-ISF fluid exchange in tissue is driven by diffusion of carbon dioxide and bicarbonate in presence of carbonic anhydrase. FASEB 14: Abstract 315.3.

13) Hammel, H. T. (2001) Osmotic effects on solvent of solute diffusing in solution. Advanced Research in Physical Chemistry. (In press).

14) Hammel, H. T., Brecheu, W. F. (2001) Causes of plasma-ISF exchange in fish, birds and mammals. FASEB, Abstract.

15)     McKenna, M.J., Heigenhauser, G.J.F, McKelvie, R.S., MacGougal, J.D. and Jones, N.L. (1997) Sprint training enhances ionic regulation during intense exercise in man. J. Physiol. 501:687-411. 

16) Porcelli, M. J., Gugelchuk, G. M. (1995) A trek to the top: a review of acute mountain sickness. J. Am. Osteopath. Assoc. 95: 718-20.

I Claim:

1.       A method for minimizing the incidence and effect of High Altitude Pulmonary Edema (“HAPE”) comprising the steps of:

a.               Ingesting foods selected so as to maximize the change in bicarbonate concentrations in the pulmonary arterial blood plasma;

b.               Refraining from ingesting said foods that reduce said bicarbonate concentration in said blood plasma.

2.               The method of Claim 1, said foods that maximize said change in bicarbonate concentration comprising a digestible carbohydrate selected so as to maximize a carbon content and selected so as to maximize an oxygen content per calorie per gram dry weight of said digestible carbohydrate.

3.               The method of Claim 2, said digestible carbohydrate further selected so as to minimize a hydrogen content of said food.

4.               The method of Claim 3, said digestible carbohydrate further selected so as to maximize a ratio of moles of said oxygen to moles of said carbon.

5.               The method of Claim 4, said digestible carbohydrate selected so as to minimize a content of fats as not maximizing the ratio of moles of said oxygen to moles of said carbon.

6.               The method of Claim 5, said digestible carbohydrate comprising glucose ().

7.               The method of Claim 5, said digestible carbohydrate comprising sucrose ().

8.               The method of Claim 1, said foods that reduce said bicarbonate concentrations further comprising said foods that contain nitrogen.

9.               The method of Claim 8 said foods containing nitrogen comprising meat and legumes.

ABSTRACT OF THE DISCLOSURE

          The invention comprises a method for reducing the incidence of High Altitude Pulmonary Edema (“HAPE”) based on a valid understanding of the process of osmosis.  Diffusion of bicarbonate ions through alveolar capillaries drags upon the water through which the ions diffuse in the same manner as if a reduced pressure were applied to the water.  The resulting osmotic effect present in the capillary as a result of the bicarbonate diffusion draws edemateous fluid from the alveoli into the capillary.  HAPE can be minimized through adjusting the diet to maximize bicarbonate ions in the plasma and hence to increase diffusion and the resulting osmotic effect.