CHAPTER 18 



Circulation times and the theory of indicator- 

 dilution methods for determining blood flow 

 and volume 



KENNETH L. ZIERLER 



Department of Medicine, The Johns Hopkins University 

 School of Medicine, Baltimore, Maryland 



CHAPTER CONTENTS 



Measurement of Flow and Volume in Well-Defined Systems 



Measurement of Flow 



Measurement of Volume 



Relationship Between Equations for Sudden- and Constant- 

 Injection 

 Effects of Violation of the Assumptions: Relation of the Model 

 to Real Vascular Systems 



The System Is not Closed 



The System Is Nonstationary 



Flow or Volume, or Both, not Constant 



Flow of Indicator Particles Is not Representative of Flow of 

 Total Fluid 

 Inhomogeneity of Blood and Significance of Venous Hematocrit 

 Recirculation 



Summary of Treatment of Recirculation 

 Effect of Injection Which Is Neither Sudden nor Constant 



Sudden-Injection Which Is not Truly Instantaneous 



Injection at Constant Acceleration 

 Effect of Collecting Catheter 

 Formal Expressions for the Distribution Function 



Empirical Expressions 

 Theoretical Approaches 



Laminar Flow Through Straight Tubes and More About 

 Catheters 



Random Walk and Other Probability Functions 

 Washout From a Mixing Chamber 

 Models Concerned Only With the Heart 

 Summary 



AMONG THE METHODS by which the flow and \olumc 

 of fluids, particularly blood, are measured are those 

 based on the indicator-dilution principle. An indi- 



cator, in the sense used here, is a substance which 

 permits observation of some element of volutne of 

 the fluid under study. The indicator shows the posi- 

 tion of the element of volume in space and with 

 respect to time, and distinguishes the indicated ele- 

 ment from all other elements of volume. 



In this chapter we shall develop the fundamental 

 equations which make the indicator-dilution prin- 

 ciple useful. We shall examine the assumptions under- 

 lying the principle and some effects of violation of 

 these assumptions. We shall then inquire into some 

 applications of the indicator-dilution principle. 



MEASUREMENT OF FLOW AND VOLUME IN 

 WELL-DEFINED SYSTEMS 



Indicator-dilution methods for measurement of 

 blood flow and volume arose from a century-old 

 technique for measurement of '"velocity" of flowing 

 blood within the cardiovascular system, where 

 velocity is defined as distance traversed per unit time 

 in contrast to flow which is volume displaced through 

 some arbitrary reference plane per unit time. In its 

 original application by Hering (14), potassium ferro- 

 cyanide was injected intravenously and blood was 

 collected at timed intervals from the corresponding 

 contralateral vein. Hering tested for ferrocyanide by 

 adding ferric chloride to serum. The first sample 

 giving the Prussian blue reaction was, therefore, 

 blood which had made one complete circuit from 



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