在體外組織內圓柱型發熱源附近
非穩態溫度分佈之研究

熱療法治療腫瘤，熱源附近的溫度分佈為影響熱療成效最重要之因素之一。本研究探討在熱療進行中，組織內圓柱型發熱源附近之暫態溫度分佈，已進行之研究工作包括：建立暫態能量平衡數學模式、利用數值方法解出發熱源附近暫態溫度分佈、進行體外組織實驗、利用實驗數據迴歸數學模式中之參數以及比較實驗數據與數學模式等。體外組織實驗乃將鎳鉻絲插入豬肝中，並通電加熱，以探討鎳鉻絲附近豬肝溫度隨時間變化之情形。通電加熱之程序為：先通電加熱300秒，其後斷電50秒，再通電50秒，如此斷電、通電連續三次，至600秒時結束實驗。本研究共進行兩組實驗，第一組實驗鎳鉻絲長度(豬肝厚度)為24 mm，通電之功率為1.530 W，第二組實驗鎳鉻絲長度(豬肝厚度)為25 mm，通電之功率為2.892 W。在假設熱傳導係數( k )為常數之前提下，本研究比較在體外組織(豬肝)內圓柱型熱源附近暫態溫度分佈之實驗數據與數學模式，結果顯示如果將數學模式中兩個參數( k及hm )同時做雙變數最佳搜尋，則針對第一組實驗數據可得k* = 0.7222 W/m-K， hm* = 132.5 W/m2-K，實驗數據與數學模式之平均誤差 Err = 2.388 ℃；針對第二組實驗可得k* = 0.7010 W/m-K，hm* = 171.4 W/m2-K，平均誤差Err = 3.720 ℃。本研究亦利用前人在文獻中發表之公式來計算豬肝之熱傳導係數( k )與溫度( T )之關係，再利用實驗數據與非線性迴歸技術算出數學模式中之最佳熱傳係數( hm*)。如此，雖然可將必須利用實驗數據迴歸之參數減為一個，但是實驗與模式之平均誤差則比將熱傳導係數(k)固定在0.5080 W/m-K者略高。

關鍵字

熱療；組織；溫度分佈

並列摘要

In treatment of tumor by hyperthermia, the temperature profile around the heat source is the major factor influencing the effect of hyperthermia. In this study, the transient temperature profile around a cylindrical heat source in the tissue is studied during hyperthermia treatment. The research work includes developing a mathematical model for transient energy balance, solving the transient temperature profile around the heat source by numerical method, conducting experiment in a dead tissue, obtaining parameters in the mathematical model by data regression, and comparison between experimental data and model calculations. The experiment in dead tissue was conducted by first inserting a nickel-chromium wire into pork liver, and then heating the wire with direct current, in order to study the change of liver temperature with time around the Ni-Cr wire. The heating process by direct current includes: closing the circuit for 300 s, opening it for 50 s, closing it again for 50 s, repeating to open and close the circuit for two more times, and stopping the experiment at 600 s from the beginning. Two experiments have been run in this study. The first run has the length of Ni-Cr wire, the thickness of pork liver, of 24 mm and DC power of 1.530 W, while the second run has the length of 25 mm and DC power of 2.892 W. Assuming the heat conductivity, k, is a constant, the results of two-parameter data regression show that heat conductivity, k*, is 0.7222 W/m-K, heat transfer coefficient, hm*, is 132.5 W/m2-K, and average error, Err, is 2.388℃ for the first run. Similarly, k*=0.7010 W/m-K, hm*=171.4 W/m2-K and Err=3.720℃ for the second run. On the other hand, the temperature dependence of heat conductivity reported in the literature was used in this study to calculate k as function of temperature, and single-parameter data regression was used to obtain the heat transfer coefficient. The results show that the average error for k being a function of temperature is slightly higher than for k being a constant of 0.5080W/m-K.

並列關鍵字

hyperthermia ； tissue ； temperature profiles

參考文獻

[1]Diederich CJ. Thermal ablation and high-temperature thermal therapy: overview of technology and clinical implementation. Int J Hyperthermia. 2005;21:745-53.

[2]Dewey WC. Arrhenius relationship from the molecule and cell to the clinic. Int J Hyperthermia. 1994;10:457-83.

[3]Welch AJ, Motamedi M, Rastergar S, Le Carpentier GL, Jansen D. Laser thermal ablation. Photochem Photobiol. 1991;53:815-23.

[4]Stauffer PR. Evolving technology for thermal therapy of cancer. Int J Hyperthermia. 2005;21:731-44.

[5]Lepock JR. How do cells respond to their thermal environment? Int J Hyperthermia. 2005;21:681-7.

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在體外組織內圓柱型發熱源附近非穩態溫度分佈之研究

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