本研究應用微分轉換混合有限差分法分析生物非傅立葉熱傳問題。有別其它積分轉換法，微分轉換法是依據泰勒展開式為基礎的函數轉換方法，能以系統化的處理程序，將線性及非線性微分方程式轉換為代數方程進行迭代求解，具有廣泛的應用及快速收斂的特性。
在文中首先介紹微分轉換理論的基本定義、性質及演算方法，接著探討此法混合有限差分法在各種生物非傅立葉熱傳問題上的應用。研究包含單層及雙層生物組織非傅立葉熱傳問題，考慮在定熱通量、定溫及溫度隨時間遞減等邊界條件，與熱源為高斯函數分佈及二次函數分佈情況時，討論並比較熱波模型生物熱傳方程式和Pennes熱傳方程式之熱響應，研究其中鬆弛時間、熱傳導係數、熱波傳遞速度、血液流動率、熱量分佈最大強度、磁性微粒擴散參數與二次函數熱源項等，對溫度分佈影響。
由研究結果發現，傅立葉熱傳定律的熱波具有非常大的傳遞速度，其溫度分佈為平滑連續曲線。非傅立葉熱傳定律之熱波理論，由於鬆弛時間之效應，造成熱以類似波的形式傳遞，其傳遞速度為一有限值。熱傳導係數與熱波傳遞速度成正比，故當熱傳導係數值越大則熱波傳遞越快。血液流動率越大，溫度下降的幅度也就越大，但熱波傳遞速度不受影響。由數值結果發現在腫瘤組織與正常組織交界處之溫度分佈，沒有振盪的現象發生，內部熱源的加熱方式，不會影響熱波傳遞速度。

In this research, the hybrid method which combines differential transformation and finite difference approximation techniques was employed to analyze non-Fourier bioheat transfer problems. Unlike other integral transform methods, differential transformation method is a transfer function that is based on the Taylor expansion serious; it converts linear and non-linear differential equations into a form of algebraic equations by constructing systematic processing program and iterate to find the solutions. Therefore, differential transformation method has a wide range of allocations and rapid convergence characteristics.
The basic definitions and properties of the differential transformation method were introduced briefly and the applications of this method combined with finite difference method on the non-Fourier bioheat transfer conduction problems were displayed later. This paper use the hybrid method to investigate the non-Fourier bioheat transfer conduction problems on single and double layers of living tissues including the boundary condition of constant heat flux, constant temperature and temperature decay function. It also analyzes the heat source term by Gaussian function and quadric spatial variation distribution. The effects of thermal wave model and Pennes model are employed and compared. The influences on temperature distribution by relaxation time, thermal conductivity, thermal wave propagation speed, perfusion rate of blood, the maximum strength of the spatial heating source, the parameter of diffusion by magnetic particles and quadric spatial variation heat source are studied and analyzed. When the blood perfusion rate is lager then the temperature decreases, but the thermal wave propagation speed is not affected.
The study results show that the thermal wave propagation speed is infinite in Fourier conduction law and the tempertaure distribution is continuous. For the influence of relaxation time, the propagation speed of thermal wave is finite and has a behavior like wave in thermal wave model of bioheat transfer. Proportional to the thermal conductivity and thermal wave velocity, so when the heat conduction coefficient values larger heat wave passes the faster. The numerical results are found that the transient temperature will not oscillate in the interface of tumor tissue and normal tissue. The type of internal heat source will not affect the thermal wave propagation speed.

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