Mathematical Modeling and Sensitivity Analysis of Lumped-Parameter Model of the Human Cardiovascular System

In this thesis, a lumped-parameter model of the systemic circulation is developed and sensitivity analysis (local and global) is applied to quantify the impact of input parameters on output variables. The thesis is divided into two major parts, (1) cardiovascular (CV) modeling and (2) sensitivity analysis. In the CV modeling part, the major arteries of the systemic circulation are modeled explaining the elastic and the visco-elastic vessel walls behavior. In the sensitivity analysis part of the thesis, two local sensitivity analysis (LSA) and three variance-based global sensitivity analysis (GSA) methods are applied on a full and partial cardiovascular system (CVS). LSA is applied on a linear elastic model of arm arteries (with and without anastomosis). While GSA is applied on MACSim (Major Arterial Cardiovascular Simulator), visco-elastic model of the CVS and carotid bifurcation. The main aim of this research work is to provide a general framework of parameter estimation using sensitivity analysis. However, the objectives of this thesis are summarized as: • Formulate a reliable and clinically relevant model of the systemic circulation using the lumped-parameter approach (linear elastic and visco-elastic). • Identify and rank the most important CV parameters, which contribute most on the output uncertainty. Furthermore, these sensitive parameter can be accurately estimated from measurements. • Find the optimal measurement locations and optimal time regions in pressure and flow waves, which are very helpful in the parameter estimation. • Find a GSA method for multi-compartment lumped-parameter model of the CVS on the basis of computational cost, simplicity and straightforward implementation. • Discuss and explain the combine effect of vasodilation and vasoconstriction in linear elastic model of MACSim (Major Arterial Cardiovascular Simulator) by considering the sensitivity of the boundary resistance. • Study different levels of stenosis and aneurysm in visco-elastic model of the CVS. The study could benefit medical students and doctors to understand the dependence of hemodynamic variables on CV model parameters.

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