肝臟是人體的重要器官，負責許多生理所需功能，但近幾年肝臟疾病已躍升為前十大死亡因素。一般來說，慢性肝病可大致分為幾個漸進式階段: 纖維化、硬化、癌症。臨床上已發展出許多診斷與偵測的方式，伴隨著科技的發展，電腦輔助系統也逐漸在進步。研究上，我們傾向可以發展出非侵入性的偵測方法，以期應用於疾病之早期診斷。核磁共振造影是目前醫學影像上迅速進展的技術，在肝臟的掃描上通常會搭配顯影劑以提高準確度。本研究目標即運用數學建模的方式擬合動態顯影磁振造影之曲線，考慮血液為牛頓流體；組織為均質且各向同性，方程模型為達西方程式搭配與時間相關之擴散對流方程式，並在演算法中引用機
器學習相關概念來做效能評估。最後，我們將提出如何決定肝臟纖維化分期之方法，在早期診斷方面可達九成準確度。

The liver is an important organ of human beings, it supports many functional mechanisms. Hepatic diseases are listed as top 10 life-threatening in many Asian countries. Generally speaking, there are three common hepatopathies for liver diseases: fibrosis, cirrhosis,
cancer. Although a number of medical tests have developed, computer-aided diagnosis still keeps improving. We prefer to establish the non-invasive treatment of a diagnostic system for early detection. Magnetic Resonance Imaging (MRI) is a promising imaging
test nowadays. This technique provides an alternative with adding contrast agent can help to diagnose the liver diseases. The target of this research is to fit the signal enhancement curve of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) through mathematical modeling. Assume that the blood is Newtonian and viscous; tissue is treated as homogeneous, isotropic porous media and the governing equations are Darcy equation weakly coupled with unsteady convection-diffusion equation. The solution algorithm is proposed based on the concept of machine learning. As a result, we proposed an approach
to determine the fibrosis stage. The optimal value of porosity may be a useful index for early detection and obtained approximately 90% accuracy.

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