6i4 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



the constant-injection curve is //F, and so provides a 

 measure of flow. The volume of the system tlirough 

 which indicator is distributed is always equal to the 

 flow multiplied by the mean transit time, providing 

 the assumptions are met. If recirculation occurs be- 

 fore the concentration has returned to zero (for 

 sudden-injection) or before the concentration has 

 reached a plateau (for constant-injection), the 

 problem may be handled in one of two ways. The 

 curve reflecting events of the first circulation may 

 be extrapolated in some arbitrary manner (say, by 

 assuming that it is exponential) if recirculation is 

 so late that the area under the curve (for sudden- 

 injection) is already almost qjF. If recirculation occurs 

 early, no arbitrary extrapolation is apt to be ac- 

 curate (although flow may be estimated in restricted 

 cases by empirical formulas) and the experiment 

 must be redesigned to include recirculation in the 

 theory and use one or another of the methods which 

 depend upon sampling from two sites or injecting 

 and sampling at two sites. 



Because sudden-injection is not really instan- 

 taneous, the mean transit time of indicator particles, 

 estimated from indicator concentration at outflow, 

 is an overestimate of that mean transit time which is 

 characteristic of the native fluid in the system vuider 



study. Therefore, volume is overestimated. If the 

 mean time of the injection process is a relatively 

 large part of the mean transit time through the 

 system the error may be important, as in the case of 

 measurement of plasma volume within the kidney. 

 Similarly, the mean time of the collecting device 

 may be long compared to the mean transit time 

 through the bed under study and so lead to over- 

 estimate of volume. Since mean times are additive, 

 the mean time of the injection process, measured, for 

 example, by replicate injection into a system of 

 known flow and volume and the mean time of the 

 collecting device, equated to its volume divided by 

 known flow through it, are simply subtracted from 

 the experimental mean time of the indicator con- 

 centration-time curve. If the true mean transit time 

 through the system proves to be, by this correction, a 

 small difference between two large numbers, the 

 result may be unreliable. 



It is not likely that any arbitrary distribution 

 function of transit times, stochastic or empirical, will 

 describe the distribution function as well as the 

 properly obtained indicator concentration-time curve. 

 The beauty of it is that with each experiment the 

 distribution of transit times through the bed under 

 studv is written for the investigator by the indicator- 

 dilution curve. 



REFERENCES 



1. .'\llen, C. M., and E. a. Tavlor. The salt velocity method 

 of water measurement. Mech. Engineering 46: 13, 1924. 



2. Andres, R., K.. L. Zierler, H. M. .\nderson, W. N. 

 Stainsbv, G. Cader, .\. S. Ghravyib, and J. L. 

 LiLiENTHAL, Jr. Measurement of blood flow and \olume 

 in the forearm of man; with notes on the theory of indicator- 

 dilution and on production of turbulence, hemolysis, and 

 vasodilatation by intra-vascular injection. ./. Clin. Invest. 33 : 

 482, 1954. 



3. Burger, H. C, Y. van der Peer, .\nd J. H. Douma. On 

 the theory of cardiac output measurement by the injection 

 method. Acta cardial. 1 1 : i, 1956. 



4. Cheesman, R. J., J. M. Gonzalez-Fernandez, and E. H. 

 Wood. Experimental studies on a new method of analysis 

 of indicator-dilution curves. Physiologist 2 (No. 3) : 23, 1959. 



5. Dow, P. Dimensional relationships in dye-dilution curves 

 from humans and dogs, with an empirical formula for 

 certain troublesome curves. J. Appl. Physiol. 7: 399, 1955. 



6. Dow, P., P. F. Hahn, and VV. F. Hamilton. The simul- 

 taneous transport of T-1824 and radioactive red cells 

 through the heart and lungs. Am. J. Physiol. 147: 493, 1946. 



7. Dow, P. Estimations of cardiac output and central blood 

 volume by dye dilution. Physiol. Rev. 36; 77, 1956. 



8. Einstein, .\. On the movement of small particles suspended 



in a stationary liquid demanded by the molecular-kinetic 

 theory of heat. Ann. der Physik 17:549, 1905. (English trans- 

 lation in: Einstein, A. Investigations on the theory of 

 Brownian movement. New York : Dover Publications, 



1956-) 

 9. Fries, E. D., J. R. St.\nton, and C. P. Emerson. Estima- 

 tion of relative velocities of plasma and red cells in the 

 circulation of man. Am. J. Physiol. 157: 153, 1949- 



10. Hamilton, VV. F., J. W. Moore, J. M. Kinsm.\n, and R. 

 G. Spurling. Simultaneous determination of the greater 

 and lesser circulation time, of the mean velocity of blood 

 flow through the heart and lungs, of the cardiac output and 

 an approximation of the amount of blood actively circu- 

 lating in the heart and lungs. Am. J. Physiol. 85: 377, 1928. 



1 1. Hamilton, \V. F., J. W. Moore, J. M. Kinsman, and R. G. 

 Spurling. Simultaneous determination of the pulmonary 

 and systemic circulation times in man and of a figure re- 

 lated to the cardiac output. Am. J. Physiol. 84: 338, 1928. 



12. H.AMiLTON, \V. F., J. \V. Moore, J. M. Kinsman, and R. 

 G. Spurling. Studies on the circulation. IV. Further 

 analysis of the injection method and of changes in hemo- 

 dynamics under physiological and pathological conditions. 

 Am. J. Physiol. 99: 534, 1932. 



13. Hamilton, \V. F., .\nd J. VV. Remington. Compaiison of 



