EXCHANGE OF SUBSTANCES THROUGH CAPILLARY WALLS 



IOig 



If the specific permeability of muscle capillaries for 

 oxygen were comparable with that of alveolar mem- 

 branes, then transcapillary oxygen pressure differ- 

 ences of 0.3 to 0.6 mm Hg and 3 to 8 mm Hg would 

 suffice to account for observed rates of tissue oxygen 

 consumption at rest and during maximal work, re- 

 spectively. For CO i the corresponding values are 20- 

 fold smaller owing to its greater solubility. It therefore 

 seems unlikely that capillary permeability is an im- 

 portant factor limiting the exchange rates of respira- 

 tory gases, except possibly during maximal muscular 

 activity. 



12. CAPILLARY PERMEABILITY AND BLOOD FLOW IN 

 RELATION TO EXCHANGE OF MATERIALS 

 BETWEEN BLOOD AND TISSUES 



In previous sections evidence was reviewed showing 

 that lipid-soluble molecules and small lipid-insoluble 

 molecules or ions diffuse back and forth across capil- 

 lary walls at rates which greatly exceed rates at which 

 these substances are brought to or from the tissues by 

 the blood. For such substances capillary permeability 

 is clearly not an essential factor determining net rates 

 of blood-tissue exchange. Other more essential factors 

 include the distribution and rate of flow of capillary 

 blood, the volume and permeability of extravascular 

 distribution compartments, and rates of chemical 

 reaction in the tissues. For molecules of intermediate 

 size, including products of intermediary metabolism, 

 capillary permeability may become more important 

 but is still only one of the several factors determining 

 over-all kinetics of the exchange process. Only in the 

 case of relatively large molecules (e.g., inulin in- 

 larger) can capillary permeability be considered as a 

 primary factor limiting exchange with well-perfused 

 tissues. 



Mathematical descriptions of diffusion kinetics in 

 the capillary circulation are included in papers by 

 Krogh (183), Hill (153, 154), Kety (173, 174), Opitz 

 & Schneider (269), Morales & Smith (256), Schmidt 

 (318, 319), Sangren & Sheppard (310), Renkin (300), 

 and Blum (19). Each of these mathematical descrip- 

 tions is based upon a particular model of capillary- 

 tissue geometry and each involves simplifying assump- 

 tions concerning permeability which do not apply to 

 all molecular species. Such models are nevertheless 

 useful, if only to provide a definite hypothesis with 

 which experimental results may be compared. Exam- 

 ples illustrating the use of such models are given 

 below. 



A. Blood- Tissue Transport of Oxygen 



The essential role of the capillaries in the blood- 

 tissue exchange of respiratory gases was considered by 

 Krogh (183) in terms of spatial distribution of blood 

 vessels relative to tissue metabolism. Krogh proposed a 

 simple model in which each capillary of radius, r, sup- 

 plied a cylinder of tissue of radius R. The intercapil- 

 lary distance was therefore iR and the number of 

 capillaries per cm 2 was (1/2R)-. It was assumed that 

 rate of tissue metabolism would be uniform through- 

 out the cylinder and that the diffusion coefficients 

 of gases through the cylinder would be uniform and 

 identical with values measured in dead tissues. The 

 mathematical solution for steady-state radial diffu- 

 sion under these conditions was derived for Krogh by 

 Erlang (183) and has formed the starting point for 

 many subsequent discussions of the blood-tissue ex- 

 change of gases [cf (174) for contemporary review]. 



Figure 12.1 is a graph of the Krogh-Erlang equa- 

 tion for capillaries of radius 4 ft; the equation is rela- 

 tively insensitive to values of r and for all practical 

 purposes the same graph applies to capillaries of radii 

 3 to 5 /j. This model suggests that as few as 25 open 

 capillaries per mm 2 would suffice to supply the oxygen 

 requirements of resting muscle without exceeding the 

 limiting diffusion pressure head set by oxygen in 

 venous blood (i.e., a finite oxygen pressure would 

 exist even in the outermost region of the diffusion 

 cylinder surrounding each capillary). The corre- 

 sponding figure for maximal muscular activity is 500 

 capillaries per mm 2 . Brain and liver would require 200 

 anc 100 capillaries per mm 2 , respectively. Estimates of 

 capillary density usually exceed these values by a wide 

 margin and suggest that the oxygen pressure head re- 

 quired to supply the diffusion cylinder around each 

 capillary is far less than that available in capillary 

 blood, even at maximal rates of tissue metabolism. 



Capillary counts on injected muscles from anesthetized 

 animals lead to estimates in the range 200 to 600 per mm 2 

 for resting muscle and 600 to 5000 per mm 2 for contracting 

 muscle (84, 143, 183, 22-j, 272, 284, 320, 335, 353). There is 

 considerable variation among skeletal muscle, heart (305), 

 and abdominal wall muscle (184) representing examples of 

 high and low density, respectively. In general, muscles from 

 small animals have a higher capillary density than from large 

 animals (320). In maximal vasodilatation there is often a 1 : 1 

 relation between number of capillaries and number of muscle 

 fibers, but maximum capillary density can be increased by 

 exposure to high altitudes or by daily physical exercise (358). 

 Capillary counts made on fixed preparations tend to be high 

 because of shrinkage artifact; in frozen sections the muscle 

 fibers are larger and estimated capillary densities smaller. 

 In the author's experience, 150-200 capillaries per mm 2 is 



