近年來，隨著生物醫學工程的發展如低溫外科手術、腫瘤加熱療法、移植器官冷凍儲存、臨床醫學和疾病熱診斷技術等均有長足的進步。因此人體生物熱傳現象的研究逐漸從過去的定性問題發展到定量問題，生物熱傳學已成為一橫跨諸多領域與學科的新興科學，亦為學術界討論的焦點。本文將混合拉氏轉換法(Laplace transform technique)和中央差分法(Central difference method)並配合最小平方法(Least-squares method)和前人所量得生物組織(Biotissue)之溫度來預測其熱傳導係數，血流灌注率(Blood perfusion rate)以及血流速度(Blood flow velocity)等熱物理性質。首先利用中央差分法來分割空間域，並利用一階泰勒級數近似法(1st order Taylor’s series approximation)將非線性項予以線性化，而後以拉氏轉換法處理系統之時間域，最後再以高斯消去法(Gauss elimination method)和數值逆拉氏轉換法(Numerical inversion scheme of Laplace transform)解析轉換後之差分方程式以求取生物組織內之溫度分佈以便預測其熱物理性質。拉氏轉換法的優點是可以求得在某一特定時間的溫度值，而不需要由初始時間慢慢地求解。最小平方法的應用在於使數值結果能較快地收斂。本文將分兩種不同的理論模式分析討論，即Pennes[8]及Wang和Wang[10]兩種模式來分析。雖然至今有關預測金屬材料之熱物理性質的文獻很多，但利用實驗所量得之材料溫度來預測其熱物理性質和溫度之關係的文獻並不多相對地，有關實際預測生物組織之熱物理性質和溫度變化的文獻就更少了。再說，生物組織之熱物理性質的預測技巧對生物醫學熱傳(Biomedical heat transfer)的發展相當重要，所以本文頗具有實際應用的價值。

With the recent of advance in the biomedical engineering, the research of the bio-heat transfer for human body is increasingly from qualitative analysis to quantitative analysis. Therefore people have to know thoroughly the characteristic and theory of heat transfer for human body. The task of the present project is to perform a numerical simulation for estimating the thermal conductivity, blood perfusion rate and blood velocity of biotissue in vivo using given temperature measurements obtained by Pennes[8] , Trezek and Tewett[24]. The hybrid scheme of the Laplace transform technique and the central difference method in conjunction with the least-squares scheme and temperature measurements inside biotissue is applied to estimate the thermophysical properties of biotissue. Time-dependent terms in the governing differential equation and boundary conditions are removed by using the Laplace transform technique, and then the resulting differential equations are solved by using the central difference technique. Due to the application of Laplace transform technique, the temperature at a specific time can be calculated without step by step computation in the time domain. To date, many numerical methods have been proposed for measuring thermophysical properties of the metal material. However, a few numerical methods were proposed for estimating the functional forms of the thermal conductivity and heat capacity per unit volume with temperature measurements, especially for biotissue in vivo. Moreover, the thermophysical properties of biotissue are of increasingly importance for studying biomedical heat transfer. Thus, the present project is valuable for the development on biomedical heat transfer.

1.A. Shitzer and R. C. Eberhart(ed.), “Heat transfer in medicine & biology”, Analysis and Applications, Vol. 1,2, Plenum Press, 1985.
2.劉靜和王存誠編著，生物傳熱學，科學出版社，1997.
3.楊景山和何鍾琪，低溫生物學的現狀與展望，生理科學進展，Vol. 16, No. 4, pp. 296-301, 1985.
4.F. Montechia, “Microstrip-Antenna design for hyperthermia treatment of superficial tumors”, IEEE Trans. on Biomed. Eng., Vol. 39, No. 6, pp.580-588, 1992.
5.孫興國，低溫腦復甦，生物醫學中的熱物理探索，王存誠與陳槐卿主編，科學出版社，1994.
6.Y. V. Gulyaev, A. G. Markov, L. G. Koreneva and P. V. Zakharov, “Dynamical infrared hermography in humans”, IEEE Eng. in Medicine and Biology, Vol. 14, pp. 766-770, 1995.
7.W. J. Yang, Z. Z. Lin, Nengli Zhang and P. T. Yang, “Determination of uterine activity during labor by means of infrared thermography”, ASME J. Biomech. Eng., Vol. 115, pp. 254-256, 1993.
8.H. H. Pennes, “Analysis of tissue and arterial temperatures in the resting human forearm”, J. Appl. Physic., Vol. 1, pp.93-122, 1948.
9.W. Wulff, “The energy conservation equation for living tissue ”, IEEE Trans. On Biomed. Eng., BEM-21, pp.494-495, 1974.
10.B. X. Wang and Y. M. Wang, “Study on the basic equations of biomedical heat transfer”, Transport Phenomena Science and Technology, pp. 273-276, Beijing, China : Higher Education Press, 1992.
11.E. H. Wissler, Mathematical simulation of human thermal behavior by using whole-body models, pp. 325-373, (Chapter 13 E121), Plenum Press, 1985.
12.J. C. Chato, “Thermal problems in biotechnology”, ASME Symp. Ser., pp. 16-25, 1968(B).
13.T. A. Balasubramaniam and H. F. Bowman, “Thermal conductivity and thermal diffusivity of biomaterials: A simultaneous measurement technique”, ASME J. Biomech. Eng., Vol. 99, pp. 148-154, 1978.
14.M. M. Chen, K. R. Holmes and V. Rupinskas, “Pulse-decay method for measuring the thermal conductivity of tissue”, ASME J. Biomech. Eng., Vol. 103, pp. 253-260,1981.
15.J. W. Valvano, J. T. Allen and H. F. Bowman, “The simultaneous measurement of thermal conductivity, thermal diffusivity and perfusion in small volumes of tissue”, ASME J. Biomech. Eng., Vol. 106, pp. 192-197, 1984.
16.H. Arkin, K. R. Holmes, M. M. Chen and W. G. Bottje, “Thermal pulse-decay method for simultaneous of local thermal conductivity and blood perfusion: a theoretical analysis”, ASME J. Biomech. Eng., Vol. 108, pp. 208-214, 1986.
17.Z. Ren, J. Liu, C. Wang and X. Sun, “Boundary element method (BEM) for solving normal or inverse bioheat transfer problem of biological bodies with complex shape”, J. Thermal Science, Vol. 4, pp. 117-124, 1995.
18.G. Honing, and U. Hirdes, “A method for the numerical inversion of Laplace transforms”, J. Comp. Appl. Math., Vol. 9, pp. 113-132,1984.
19.H. T. Chen and J. Y. Lin, “Application of the Laplace transform to nonlinear transient problems”, Appl. Math. Modelling, Vol. 15, pp. 144-151, 1991.
20.彭見曙、夏雅琴和王蘊華，在受熱情況下局部組織溫度的預測，工程熱物理學報，Vol. 16, No. 2, pp. 225-229, 1995.
21.A. Shitzer and M. K. Kleiner, “On the relationship between blood perfusion, metabolism and temperature in biological tissue heat balance”, ASME J. Biomech. Eng., Vol. 102, pp. 162-169, 1980.
22.R. Kress and R. B. Roemer, “A comparative analysis of thermal blood perfusion measurement techniques”, ASME J. Biomech. Eng., Vol. 109, pp. 54-58, 1987.
23.J. Liu, Z. Ren, C. Wang and X. Sun, “Qualtiative experimental evidences for the thermal wave mechanisms of temperature oscillations in living tissue”, J. Thermal Science, Vol. 5, pp. 264-270, 1996.
24.G. J. Trezek and D. L. Tewett, “Nodal network simulation of transient temperature fields from cooling sources in anesthetized brain”, IEEE Biomed. Eng., Vol. BME-17, pp. 281-286, 1970.
25.J. Liu, Z. Ren and C. Wang, “A technique for identifying the total space or temperature dependent thermal parameters of biological materials in Vivo”, IEEE Biomed. Eng., Vol. 43(8), pp. 847-850, 1996.
26.G. Tr. Stolz, “Numerical solution to an inverse problem of heat condition for simple shapes,” ASME J. Heat Transfer, Vol. 82, pp. 20-26, Feb. 1960.
27.J. V. Beck, B. Litkouhi, and St. C. R. Clair, “Efficient sequential solution of nonlinear inverse heat conduction problem,” Numer. Heat Transfer, Vol. 5, pp. 275-286, 1982.
28.O. M. Alifanov, “Solution of an inverse problem of heat conduction by iteration method,” J. Eng. Phys., Vol. 26, No. 4, pp. 471-476, 1974.
29.N. M. Alnajem and M. N. Özisik, “A direct analytical approach for solving linear inverse heat conduction problems,” ASME J. Heat Transfer, Vol. 107, pp. 700-703, 1985.