| Summary: | 碩士 === 國立中央大學 === 數學系 === 103 === Liver diseases are always on the list of the top 10 causes of death in Taiwan. Generally speaking, the progression of liver disease can be classified into three stages, including liver fibrosis, liver cirrhosis, and liver cancer. Recently, using the noninvasive Dynamic Contrast Enhanced MRI (DCE-MRI) technique for the early detection of chronic liver disease is quite promising. The research focus for clinical application is to define some index related to the relative signal enhancement in a liver to identify the degree of liver fibrosis. In reach the goal, we build both of the mathematical models for blood flows through the liver and the relative signal enhancement scanned by MRI varied with respect to time. Under assumptions that liver is a kind of porous medium, and the blood flow is Newtonian, Laminar, in steady state, the governing equations consist of the Darcy equation weakly coupled with unsteady convective-diffusive equation. The stabilized finite element Darcy solver together with time-dependent convective-diffusive solver are verified by a case with analytical solution and the mathematical models are validated by the experiment of fluid flow through the sponge. In addition, our numerical result is consistent with the clinical data. Finally, we find the porosity is potentially to be a good index to identify the degree of liver fibrosis.
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