EXCHANGE OF SUBSTANCES THROUGH CAPILLARY WALLS 



1021 



capillary oxygen pressures may be extremely low in 

 brain (64) despite normal oxygen pressures in cerebral 

 venous blood. The critical venous oxygen pressure at 

 which brain suffers a decrease in oxygen consumption 

 is 20 to 25 mm Hg (269); presumably, under these 

 conditions, oxygen pressure is zero in regions most 

 remote from the capillaries. 



These observations suggest that the gradient of 

 oxygen pressure from capillary blood to tissues is 

 greater than predicted from the simplified model 

 proposed by Krogh. One factor neglected by Krogh's 

 treatment of the problem is the rate at which oxygen 

 can be released from red cells during their brief expo- 

 sure to the tissues in capillary blood. Roughton & 

 Forster (306) and Forster (108) have recently dis- 

 cussed evidence that chemical reaction velocity and 

 diffusion in the red cell account for almost one-half 

 the total resistance to transfer of oxygen between 

 alveolar gas and blood. The rate of dissociation of 

 oxygen from hemoglobin is slower than its rate of 

 combination and recent measurements by Niesel et al. 

 (261) and Thews (356) indicate that the intracapil- 

 lary component of oxygen diffusion may be a major 

 factor limiting the rate at which oxygen can be sup- 

 plied to adjoining tissues. This factor could be evalu- 

 ated experimentally and deserves attention in future 

 studies of the blood-tissue exchange of gases. Scho- 

 lander's recent demonstration of facilitated diffusion 

 of oxygen through thin films of hemoglobin or myo- 

 globin (32 1 ) may also be of significance for diffusion 

 of oxygen in muscle, especially cardiac muscle. 



B. Blood- Tissue Exchange of Small, 

 Xonmctabolized Molecules or Ions 



A simple model of blood-tissue exchange has been 

 employed by Renkin (299, 300) to describe diffusion 

 kinetics of urea, antipyrine, sucrose, and K 42 in perfused 

 muscle. This model is particularly useful for illus- 

 trating the relative effects of permeability and blood 

 flow on diffusion kinetics in uniformly perfused tissue. 

 In its simplest form the model assumes two compart- 

 ments representing total blood volume, V\ , and extra- 

 vascular distribution volume, V 2 ■ The compartments 

 are separated by a barrier of virtual area A m and per- 

 meability coefficient, P. V\ is allowed to flow past the 

 barrier at rate, Q. V% is assumed to be homogeneous 

 with respect to concentration of diffusing materials. 

 The mathematical solution for this model (300) is 

 given bv 



d/i-e « J (12.1) 



v.v, 



(v, + v 2 ) 



where C = clearance from the blood compartment, 

 V 1 , ml per min, and X = slope of the exponential 

 disappearance curve from the blood compartment, 

 min -1 . In perfused preparations the rate of blood flow- 

 may be varied over a wide range by simple adjustment 

 of perfusion pressure. Clearance, C, from the perfu- 

 sion reservoir can be measured accurately. It is there- 

 fore possible to determine over-all permeability, P X 

 A m , of barriers separating blood from the final distri- 

 bution volume, provided the original assumption of 

 uniform distribution in extravascular space is correct. 

 For many substances this assumption will not be valid 

 and in such cases PA m must be considered as a virtual 

 permeability which includes the effects of nonuniform 

 distribution in extravascular space. 



Figure 12.3 shows capillary clearances of anti- 

 pyrine, K 42 and urea as a function of blood flow in 

 widely dilated blood vessels of mammalian muscle. 

 The changes in blood flow were produced by change 

 of arterial perfusion pressure and presumably reflect 

 changes in flow velocity through a constant capillary 

 surface as required by the model. Comparison of the 

 results with theoretical curves drawn from equation 

 1 2. 1, suggest blood-tissue permeabilities (PA m ) of 

 about 3 and 10 ml per min per 100 g muscle for urea 

 and K 42 , respectively. For antipyrine the observed 

 capillary clearances were equal to blood flow, indi- 

 cating that for this (lipid-soluble) substance perme- 

 ability (PA m ) was large with respect to blood flow. 



Blood-tissue permeabilities estimated by equation 

 1 2. 1 from measurements of blood flow and clearances 

 are compared in table 12.1, with capillary permeabil- 

 ity estimated from osmotic transients and the theory 

 of restricted diffusion. In the case of sucrose the blood- 

 tissue permeability is 30 to 60 per cent of capillary 

 permeability. Sucrose distributes primarily in inter- 

 stitial fluid and the only barriers to diffusion are 

 capillary walls and interstitial fluid volume. From 

 the available data (table 12.1) it appears that in 

 muscle about one-half the total resistance to distribu- 

 tion is located in the capillary wall. Cotlove (46) 

 has shown that distribution rates of NaCl, sucrose, and 

 inulin into connective tissue spaces of extremities are 

 limited by the long path length for diffusion along 

 fascial planes and by retardation of diffusion in the 

 interstitial matrix. Recent measurements by Ogston & 

 Sherman (266) indicate that diffusion of molecules as 

 small as glucose may be appreciably restricted in 

 dilute gels formed by hyaluronic acid and the action 

 of hvaluronidase in reducing resistance to flow- 

 through connective tissue has been described by Day 

 (6 9 )- 



