Bifurcation theory in physiology

Physiology is dynamic in nature, as seen in circadian rhythms and numerous ultradian rhythms (of core body temperature, heart rate, hormonal levels, etc.). To capture these highly oscillatory processes, we need techniques for longitudinal observation with adequate spatiotemporal resolution. To make sense of these oscillatory processes, we need methods for analyzing time-dependent data as well as mathematical frameworks for characterizing qualitative changes in system behavior, such as the emergence of bistability and the emergence of oscillation. In dynamical systems theory, qualitative changes are modeled as bifurcations in the underlying solution structure, for example, the emergence of oscillatory behavior in a Hopf bifurcation. In this talk, I will share examples of Hopf bifurcation theory applied to cancer and renal physiology, to demonstrate how dynamical systems theory can shed light on the mathematical structure underlying the transition from health to disease. I will also highlight the utility of intravital two-photon microscopy in capturing cell-level metabolic dynamics and tissue-level fluid flow dynamics in vivo.