Interactive microprocessor graphics as aid in physiological modeling: two examples

Abstract

To dramatize the often counterintuitive dynamic effects of clamping (fixing, holding constant or tightly bounding or constraining) an endogenous physiological variable such as a hormonal secretion rate or level, we have used a microcomputer to display vector field portraits of system trajectories under a wide variety of initial conditions or perturbations, and under interactive (moving-cursor) control with a mouse. These graphic views of behavior illustrate the occasionally profound consequences of freezing out a degree of freedom in a dynamical system. Stability can change in surprising ways. Although the stability analysis can be done without graphical aids, nevertheless the computed displays seem unmistakably to increase comprehension and provide a feeling for the mathematized organism (model), particularly for nonmathematicians. As further demonstration of the potential usefulness of a graphical expression of nonlinear dynamics, we have explored the behavior of a minimal model of the glucose/insulin system. Because this model has been used in clinical diagnosis, it is important to explore its behaviors.

Neither physiological models nor microprocessors are new — yet the combination of the micro-processor technology with the needs of modeling physiological problems, though much discussed, still remains exploratory in most biological and clinical fields. This paper emphasizes applications in which the interactive feature of the graphics provides the attractiveness of the approach and its tutorial effectiveness.