ioio 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION II 



5 10 15 20 25 30 35 



MOLECULAR RADIUS, A 



FIG. Q.2. Restricted diffusion of lipid-insoluble molecules 

 from the capillaries of perfused cat hind limbs. Each point 

 represents the mean value of data from several experiments. 

 The curves are constructed from the theory of restricted diffu- 

 sion and filtration (equation 9.3) on the assumption that the 

 osmotic reflection coefficient is determined by equation 7.19. 

 The data fit theoretical restricted diffusion through pores of 

 radius 40-45 A in a membrane having the same filtration 

 fcoefficient as the capillaries in the hind limb. [Recalculated 

 rom the data of Pappenheimer et al. (281).] 



The upper panel of figure 9. 1 shows that for 

 rafnnose the restricted pore area per unit path 



cm 2 or less than 0.1 per cent of the total capillary 

 surface area in 100 g muscle. This conclusion is 

 consistent with the view that transcapillary ex- 

 changes of lipid-insoluble molecules take place at 

 junctional regions between endothelial cells and we 

 have already seen that pore areas of this magnitude 

 can provide a physiologically sufficient flow of small 

 molecules under the influence of small concentration 

 gradients (section 7 A). 



In the original analysis of Pappenheimer et al. (281) 

 the mean pore radius was estimated from combina- 

 tion of the capillary filtration coefficient with the 

 pore area per unit path length for a molecule the 

 size of water (equation 7.13). However, the latter 

 quantity was uncorrected for the osmotic reflection 

 coefficient and therefore cannot be employed for the 

 present analysis in which the osmotic reflection 

 coefficient is included as an unknown. In order to 

 solve for this additional unknown it is necessary to 

 introduce an additional equation relating osmotic 

 reflection coefficient to pore dimensions as suggested 

 by equation 7.19. This equation is cumbersome and 

 its use may not be entirely justified on the basis of 

 our present inadequate knowledge of factors de- 

 termining osmotic reflection coefficients. Neverthe- 

 less, it leads to a solution for capillary pore dimensions 

 which is more consistent with available data than the 

 dimensions originally proposed by Pappenheimer 

 et al. (281). Substitution of equations 7.19 and 9.2 in 

 equation 7.13 yields 



(,-^f[i- 2 ,0(^)+ 2 .09(^) 3 -0.95(±) 5 ] 



(,- f*ffziO&) + 2 .09(^-)-0.95(^ 



8 V K, An 

 D„[ RTD. * n 



(9.3) 



length, calculated from equation 9.2, was 0.38 ± .04 

 X io 6 cm. Results of similar measurements, made 

 with a variety of molecular species, are shown in 

 figure 9.2. It is seen that in capillaries, as in artificial 

 porous membranes (fig. 7.1), the restricted pore area 

 decreased as a function of molecular radius as pre- 

 dicted from the theory of restricted diffusion (equa- 

 tion 7.9). Extrapolation to zero molecular radius 

 suggests that the true pore area per unit path length 

 in the capillaries of 100 g muscle is approximately 

 0.6 X io 5 cm. Since the average thickness of the 

 capillary walls is less than io~ 4 cm (fig. 9.3), this 

 suggests that the total pore area available for diffusion 

 exchange of lipid-insoluble molecules is less than 6 



where 



j = mean capillary pore radius, A 

 a w = radius of water molecule = 1.5 A 

 a, = radius of test molecule, A 



= free diffusion coefficient of water = 3.4 X io -5 



cm 2 per sec -1 

 = free diffusion coefficient of test molecule 

 = viscosity of water = 0.007 dyne-sec-cm -2 at 37 C 

 K f = filtration coefficient of capillaries, average value 1.8 X 



io -7 cm 5 -dyne~'-sec~ l per 100 g 

 All = observed partial osmotic pressure, dynes-cm -2 at 



time, / 

 n = observed flux rate, mole-cm 3 at time, i 

 RT = 25 X io 9 dyne-cm-mol -1 at 37 C 



Study of equation 9.3 in relation to the experimental 



