Basic Concepts in the Determination of vascular Volumes by Indicator-Dilution Methods

Abstract

In this paper, we have considered some of the basic concepts underlying the measurement of vascular volumes by indicator-dilution methods. Granting the assumptions of stationary flow and homogeneous labeling of flowing blood, the classical Stewart-Hamilton prescription, V = Qt, provides a valid estimate of central volume. Although the boundaries of this volume can be precisely defined in terms of "time distances," the anatomic description is less definite. The classical treatment did not provide a theoretical model from which the form of the indicator-dilution curve could be deduced but a number of such models have now appeared. These include the mixing-chamber model of Newman and the stochastic models of Sheppard. The slope-volume based on Newman's model measures some fraction of the classical central volume, but precise anatomic boundaries probably cannot be assigned to it. We have attempted to show that so long as we deal with a linear system, the indicator-dilution problem, including recirculation, can be conveniently treated in terms of a block diagram-transfer function approach. Finally we have considered some of the theoretical and practical aspects of the measurement of ventricular volumes. In conclusion, it might be appropriate to say something about mathematical models in general. Every such model is an abstraction which deliberately neglects certain features of the prototype in order to make possible the rigorous treatment of others. We should therefore not be disappointed to find that "no thoroughly defined system can be expected to mimic completely all of the phenomena of physiological importance."⁵ What we should demand of a model is that it mimic enough of these phenomena to make it useful, and that it point the way to its own continuing improvement. If it does these things, it cannot help but be a contribution to the advancement of both theory and practice.