The Valsalva maneuver (VM) is a quick, noninvasive, clinical procedure with a variety of uses. In particular, the VM can aid in the diagnosis of autonomic nervous system dysfunction. The VM induces changes in blood pressure, which reflexively induces a neural signaling cascade to adjust heart rate, heart contractility, peripheral vascular resistance, and venous compliance. These neural signaling cascades are difficult to measure in vivo, becoming invasive procedures and increasing care and costs. Our collaborators are interested in having a clinically useful model of these neural signals to use in practice.

I use mathematical modeling to analyze patient data (electrocardiogram, blood pressure, intrathoracic pressure and heart rate) and predict these neural signals and their effects on the vasculature. This talk will discuss the development of the system of first-order, stiff, nonlinear, delay differential equations describing these neural pathways, its efficacy in predicting heart rate via parameter estimation methods, and a sensitivity analysis of the model formulation. We will also discuss the coupling of this model to a systemic cardiovascular model and its effectiveness in predicting behaviors of both healthy control and diseased subjects.