ANNALS OF BIOMEDICAL ENGINEERING 2, 307-320 (1974) A Dynamic System Model of Testosterone Transport and Metabolism in Normal Man MARLENE T. MAYEKAWA, JOSEPH J. DISTEFANO III, AND RONALD S. SWERDLOFF Biocybernetics Laboratory, Engineering Systems Department and Department of Medicine, University of California, Los .4 ngeles Received March 30, 1974 A nonlinear model is proposed for testosterone (T) transport and metabolism in the normal adult male. The model structure consists of 2 pools: one which includes plasma distribution, direct disposal, and the binding of T to three plasma proteins; and a second pool for distribution and other disposal of T. Nonlinearities in the model are manifest in the mass action law dynamics of binding to plasma proteins. A directed random search algorithm was employed to estimate model param- eters. The model was fitted to real data by minimization of the least squares output error. The real data consisted of discrete samples of radioactively labeled T in blood following a rapid, pulse injection of labeled T. A quadratic approximation for unbound T in terms of total T concentration was derived by application of the mass action principle to the multiple hormone-protein binding relationships. This approximation permitted the two model state variables to be expressed as total T concentration in each pool. This choice guarantees a linear measurement or output model. The model was completely quantified, including a relationship and estimate for the unmeasurable concentration of T in the lumped intracellular space. These results indicate that: (1) 98% of T is cleared directly from plasma; (2) the lumped phase boundary between the intra- and extravascular spaces is nearly isotropic to T; and (3) the average steady state intracellular total T concentration is only 30% of the corresponding plasma total T concentration in normal man. The predictive value of the model also was explored by performing three simulated experiments, each representing pathologic possibilities. When simulated T secretion was decreased by 75%, the plasma T decreased by 70%. When simulated protein concentrations were changed significantly, in opposite directions, the plasma T concentration fell well below the normal level; but the T concentra- tion in the outer pool remained normal. When the parameter representing transport of T to the outer pool was decreased, plasma T did not change, but the outer pool T decreased. Among other things, these results suggest that the plasma T concen- tration does not always reflect changes in distribution and disposal; and plasma total T concentration is not by itself a reliable indicator of system pathologies. Also, low plasma T concentration and normal T secretion can be consistent with normal concentrations of T in tissue and hence the target organs for testosterone action. I. INTRODUCTION Many important questions in the field of male sex hormone physiology con- cern the mechanism and dynamics of feedback control of testosterone secretion in the adult male. As is the case with all humoral regulation systems, an integral 307 Copyright 9 1974 by Academic Press, Inc. All rights of reproduction in any form reserved.