INDICATOR SUBSTANCES AND FLOW ANALYSIS 



619 



importance and difficulty of data acquisition are 

 recognized, the present discussion will be chiefly 

 concerned with mathematical analysis and interpre- 

 tation of the data. 



CIRCULATORY FEATURES AFFECTING MIXING 

 AND DISTRIBUTION 



Anatomical 



Except those processes which involve the formed 

 elements of the blood and the blood vessel walls 

 directly, the exchange of materials between the 

 blood and the tissues occurs in the capillaries. In 

 this context the larger vessels may be regarded merely 

 as mixing chambers and as avenues for transportation. 

 Purely anatomical features which promote mixing 

 include the division of the circulating pathway into 

 the pulmonarv and the svstemic circulations, and 

 dififerences in the lengths of pathways to and within 

 the various organs. 



Normally all the venous blood has to traverse the 

 pulmonary circulation before returning to the 

 systemic circulation and, since in the pulmonary 

 circulation all but a small fraction of the blood passes 

 through a capillary bed, the effluent blood from a 

 given tissue is redistributed in the next cycle to the 

 other tissues according to the manner in which the 

 cardiac output is fractionated, with little or no 

 chance that preferred pathways, which would keep 

 the circulation of one tissue separated from that of 

 the others and delay mixing, can be maintained. 



The preceding statement must be modified when 

 substances, particularly gases, which may be quanti- 

 tatively removed in one passage through the lung 

 capillaries are under discussion. When this is the case 

 there is in effect no recirculation of the material in 

 the effluent blood from a given tissue. Except for the 

 gut-spleen-liver portion of the circulation, the tissues 

 served by the systemic circulation are arranged in 

 parallel with respect to each other, so that for some 

 purposes events in the lungs may be separated into 

 components related to each of the systemic tissues in a 

 relatively simple manner. Attempts to measure the 

 cardiac output by nitrogen elimination from the 

 tissues when the subject inhales pure oxygen have 

 been based on the above concept, but have not 

 been entirely satisfactory because the washout of 

 air in the lungs is not fast enough to avoid obscuring 

 the rapid components associated with tissues having 

 high blood perfusion rate factors (50). 



Because of variations in path lengths to and through 

 the tissues, both in the pulmonary and in the systemic 

 circulations (if these are not compensated for by 

 corresponding variations in flow rates), a concentra- 

 tion peak in the arterial blood emerges greatly 

 smeared, or prolonged, in the venous blood if the 

 substance under consideration remains intravascular. 



Dynamic 



INTRAVASCULAR MIXING. Although the cardiac output 

 is pulsed, the flow through the capillaries is practically 

 continuous and may usually be so regarded in the 

 analysis of tracer data. 



The role of anatomical factors in promoting mixing 

 is mentioned above. These factors are supplemented 

 by the effects of variations in flow rates and by the 

 nature of the flow. Flow within the circulation is 

 usually laminar, giving a longitudinal redistribution 

 of the blood's constituents, as is discussed by Zierler 

 (74). The occasional occurrence of turljulcnt flow 

 also produces some transverse mixing. 



These mechanical effects are so rapid and violent 

 relative to diffusion that the latter process plays only 

 a minor role in intravascular mixing. Diffusion 

 does play a much more important role in the transfer 

 and exchange of substances across the capillary 

 membranes. For some substances the transmembrane 

 diffusion rates are much faster than the blood per- 

 fusion rates, so that the rate of transfer of these 

 substances is flow-limited. Under some conditions, 

 differences in hydrostatic pressure result in bulk 

 flow. The effect of osmotic pressure differences is a 

 more controversial subject, however, and the relative 

 roles of diffusion and bulk flow are not clearly 

 delineated. 



EXTRAVASCUL.-\R DISTRIBUTION. The rapidity with 

 which the labeled form of a substance leaves the 

 circulation is also strongly influenced by the distribu- 

 tion of the natural form of that substance. 



Various labels of erythrocytes, iron, chromium, and 

 Ni=-labeled hemin, may remain in the circulation for 

 weeks, leaving essentially only when the red cells 

 themselves leave or are destroyed. P'-, which is also 

 useful as an erythrocyte label, is less firmly bound 

 to the cell. Although of little use in studying regional 

 blood flow rates, labeled red cells have given valuable 

 information on intravascular mixing times, uncompli- 

 cated by extravascular dilution. Kraintz et al. (39) 

 found that sequestration of red cells in the spleen 

 delays the achievement of uniform distribution of 



