MATHEMATICAL MODEL OF BLOOD FLOW FOR DENGUE INFECTION - Kallista, Meta
Hematocrit value is one of the parameters to detect the severity of patients with Dengue infection. The significant change in hematocrit level is caused by the complex process immune defenses in the fight against the infection. During secondary infection, the immune release cytokine which makes blood vessels more permeable. Consequently, there is blood plasma that seeps out from the vessel wall. On the other hand, dengue infection has an effect on the decrease of platelet production which can lead to the increase of hematocrit. The increase of hematocrit level is proportional to the increase of blood viscosity. In this dissertation, mathematical model that represents the blood flow with a dengue infection phenomenon is built. A mathematical model, in which a hematocrit model and the blood flow equation coupled through blood viscosity variation, is proposed here. The process of hematocrit change during dengue infection in the bloodstream is accommodated through mathematical model of interaction between cells and viruses. We built a model of the relation between hematocrit and viscosity, therefore the viscosity value can specifically represent the blood viscosity in dengue patients. The viscosity changes due to dengue infection will be used in the blood flow model. Blood flow can be represented by the pulsatile flow model. In this model, the leakage phenomenon is neglected. Pulsatile flow model with perturbation on the viscosity and pressure difference is proposed as the novelty of this dissertation. A small perturbation in viscosity and pressure gradient to the equation is studied further by obtaining the analytical solution. Based on the analytical solution, the narrow vessels are more sensitive toward the perturbation. The decrease of velocity profile happens due to the perturbation. It will endanger the body because the oxygen and nutrients cannot be properly distributed by blood. Moreover, the blood flow model with the leakage phenomenon is captured by Stokes equation with low Reynolds number, due to the assumption that plasma leakage occurs in narrow vessels, especially in arterioles. A numerical approach is used to solve the Stokes equation. The weak formulation for the Stokes equation is constructed using the appropriate boundary conditions for with and without leakage will be discussed in more detail. A filtration boundary condition and modified natural boundary condition are used in this study to acquire plasma leakage through