Interactive microprocessor graphics as aid in physiological modeling: two examples

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.