Analysis and Control of Cardiovascular Dynamic Models

Abstract

Lakshmi N Sridhar

Cardiovascular diseases (CVDs) is one of the leading causes of death in the world. It is very important to understand the dynamics of this disease and develop strategies to control it minimizing the damage as much as possible. This article involves analysis and control of two dynamic cardiovascular models. Bifurcation analysis is a powerful mathematical tool used to deal with the nonlinear dynamics of any process. Several factors must be considered, and multiple objectives must be met simultaneously. Bifurcation analysis and multi-objective nonlinear model predictive control (MNLMPC) calculations are performed on two cardiovascular dynamic models. The MATLAB program MATCONT was used to perform the bifurcation analysis. The MNLMPC calculations were performed using the optimization language PYOMO in conjunction with the state- of-the-art global optimization solvers IPOPT and BARON. The bifurcation analysis revealed the existence of branch points in both models. The branch points (which cause multiple steady-state solutions from a singular point) are very beneficial because they enable the Multiobjective nonlinear model predictive control calculations to converge to the Utopia point ( the best possible solution) in the models. It is proven (with computational validation) that the branch points were caused by the existence of two distinct separable functions in one of the equations in each dynamic model. A theorem was developed to demonstrate this fact for any dynamic model.

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