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Talk Abstract
A Stochastic Biomathematical Model of the Male Reproductive
Hormone System

Daniel Keenan
Division of Statistics
Department of Mathematics
University of Virginia
Charlottesville, Va 22903-3199

Joint work with Johannes Veldhuis, M.D., University of Virginia.

A stochastic biomathematical model for the male reproductive hormone system (gonadotropin-releasing hormone, luteinizing hormone, and testosterone) is developed. Hormone secretion occurs as either a continuous release, a pulsatile release, or a combination thereof; in the latter two, hormone molecules are stored and later released. Each form of release is represented within the male system. The model begins at the cellular level of hormone synthesis, aggrandizes to the level of the gland and secretion, and finally to the level of elimination and circulation in the blood. The model consists of a system of stochastic integro-differential equations which describe the nonlinear time-delayed feedback from concentrations (of the various hormones) on their rates of hormone synthesis. A stochastic formulation is established, showing that the various imposed structures are consistent with one another.

Computer experiments are performed and compared to analogous clinical exper iments (where components are decoupled via pharmacological intervention) to show the dynamic range of the model and its potential usefulness (e.g., assessing the pathway of the circadian rhythm).

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  1998-1999 Mathematics in Biology