EXCHANGE OF SUBSTANCES THROUGH CAPILLARY WALLS 



IOOg 



from the theory of restricted diffusion through pores 

 of radius 43 A (table 9.1). 



Arterial disappearance curves therefore provide a 

 method for quantitative studies of overall capillary 

 permeability to large molecules. It is not possible, 

 how ever, to extend this type of analysis to molecules 

 which diffuse rapidly through capillary walls. In 

 this case the mean concentration in capillary plasma 

 may be only a small fraction of that in arterial plasma, 

 particularly in early phases of the distribution process. 

 Application of equation 8. 1 to such data leads to 

 estimates of capillary permeability which are too low, 

 often by 1 or 2 orders of magnitude [see (281) and 

 (382) for critical review]. Factors which determine 

 mean concentration differences of small molecules 

 across capillary walls during diffusion include rate of 

 blood flow, diffusion rate, and the geometry and 

 volume of extravascular diffusion space. Several 

 interesting attempts have been made to take account 

 of these factors by mathematical techniques but the 

 solutions are complex and involve assumptions which 

 are difficult to evaluate experimentally (19, 319). 



Specialized experimental methods for estimating 

 capillary permeability to small molecules were 

 developed by Pappenheimer et al. (281) for the study 

 of molecular exchanges in the capillary circulation of 

 hind limbs of cats or dogs. Results obtained by these 

 methods lead to conclusions of general interest 

 relating capillary permeability to the number and 

 dimensions of capillary pores which would be re- 

 quired to explain observed transcapillary diffusion 

 rates of lipid-insoluble molecules ranging in size from 

 D 2 to hemoglobin. 



9. STRUCTURE OF MUSCLE CAPILLARIES AS DEDUCED FROM 

 PERMEABILITY MEASUREMENTS AND FROM ELECTRON 

 MICROSCOPY'. QUANTITATIVE ASPECTS OF 

 TRANSCAPILLARY DIFFUSION 



In isolated perfused tissues the rate of net trans- 

 capillary movement of test substances can be de- 

 termined from the product of blood flow and arterio- 

 venous concentration difference. Thus, 



(9.1) 



where Q is blood for plasma) flow and c a , c v are the 

 simultaneously measured concentrations of the test 

 substance in arterial and venous bloods (or plasma). 

 The driving force for diffusion (i.e., the mean 

 concentration difference across the capillary walls) 

 may be estimated from the partial osmotic pressure 



n= Q b (c a -cJ 



0.6 x 10 cm 



0.4 



A s RTo- h 



38 « 10* cm 



0.2 



mq /sec 

 per IOOg muscle 

 0.15 



0.10 



NET FLUX, 

 n = Q(C -C V ) 



0.05 



PARTIAL OSMOTIC PRESSURE 



DEVELOPED ACROSS 



CAPILLARY MEMBRANES 



10 



15 



20 



JlL 



30 



1 



MINUTES AFTER ADDITION OF RAFFINOSE 



no. 9. i . Diffusion of raffinose from the capillaries of a 

 perfused cat hind limb. At zero time 20 mM/liter raffinose was 

 added to the perfusion reservoir. The final distribution volume 

 of raffinose in perfused tissue was 19% of limb volume. The 

 capillary diffusion area per unit path length calculated for 

 raffinose was 0.38 X io 5 cm 2 ; this value was independent of 

 time, extravascular fluid volume, or of mechanically induced 

 changes of blood flow. [Adapted from Pappenheimer et al. 

 (281).] 



exerted by the test molecules during the diffusion 

 process. Figure 9. 1 illustrates a typical experiment 

 showing the simultaneous measurement of net flux 

 rate and partial osmotic pressure during the diffusion 

 of raffinose from the capillaries of a perfused cat 

 hind limb. The ratio of flux rate to partial osmotic 

 pressure is proportional to permeability and may be 

 related to the restricted pore area per unit path 

 length in the capillary wall by combining equations 

 7.6 and 7.1 7. 



Ax 



RTcr ft 

 D t * AIT 



(9.2) 



