1. Optimization of Applied Thermal Power on Tumor Regions with Thermally Significant Blood Vessels to Reach Therapeutic Tissue Temperatures
Huang-Wen Huang1*, Tzu-Ching Shih2, Chihng-Tsung Liauh3, Tzyy-Leng Horng4 1 Department of Software Engineering, Tamkang University, I-lan County, Taiwan
2 Department of Medical Radiology Technology, China Medical University, Taichung, Taiwan
3 Department of Mechanical Engineering, Kun-shan University of Science and Technology, Tainan, Taiwan
4 Department of Applied Mathematics, Feng Chia University, Taichung ,Taiwan
Abstract
Materials and Methods
The objective of this paper is to investigate the optimization of applied thermal power in a tumorous region which consists of thermally significant blood vessel(s) during hyperthermia. Pennes’ bio-heat transfer equation (BHTE) was developed to model temperatures in the living tissues, and other developed alternative equations having the same goal with attempting to formulate a single, general field equation that could predict the overall characteristics of the temperature distribution in tissues.
The present paper used a tissue heat transfer model which was not a general field equation approximation, but which instead retained both the presence of the blood vessels and the major, basic physics of the blood vessel/tissue heat transfer processes. It was called a fully conjugated blood vessel network model (FCBVNM) or countercurrent blood vessel network (CBVN) model which was published in Therefore, a tumor region situated in cases of many thermally significant blood vessels nearby (or embedded) with attempts to find therapeutic heating temperatures in tumor would be discussed. Optimization scheme of applied thermal power on tissue and tumor regions in order to reach therapeutic tissue temperatures was also studied and presented.
Results
Materials and Methods
Figures 3(a-e) (top row from left to right) are temperature distributions at x = 38 mm (4 mm away from the front boundary), x = 42 mm (the front boundary), x = 52 mm (middle of the treated region), x = 62 mm (the back boundary) and x = 66 mm (4 mm away from the back boundary) planes respectively with a perfusion rate of 0.5 kg·m-3s-1 after power optimization scheme. The blood flow rate is about 320 mm/sec in level 1 branch vessel. Figures 3(a‘-e‘) (bottom row from left to right) are thermal absorbed power distributions at the corresponding planes respectively. No power presents on the planes at x=38 mm and 66 mm.
Methods and Materials
Materials and Methods
Figure 1(a) is a transparent view of parallelepiped showing internal heated tumor region with 20 x 20 x 20 mm3. The level 1 largest blood vessel is running through the volume’s edge from (42, 40, 40) mm to (62, 40, 40) mm. Figure 1(b) shows the location of the cubic volume in a parallelepiped by indicating its 8 corners’ coordinates, and Figure 1(c) is a dissecting transparent view of all associated arterial blood vessel paths in the cubic volume. Veinous vessels do not appear in the figure, and within the volume, there are 2 branches of level blood vessels as expanded dissecting view indicates.
Figures 4 shows comparison of power absorption in treated tumor region for different thermal models after optimization. BHTE is the case when no blood vessel presents. BHTE+CBVN+W=0.123 means that BHTE is having a countercurrent blood vessel network present with blood flow rate at main artery (level 1 vessel) about 80 mm/sec and perfusion in the tissue is kg/(m3s). And BHTE+CBVN+W=0.5 is the same as previous case but with blood flow rate about 320 mm/sec and the perfusion is 0.5 kg/(m3s) in tissues.
Conclusion
Materials and Methods
At present results, cold spots and significant cooling effects of blood flow rate by vessels in the treated region present vital characteristics in the CBVN model. These phenomena reveal same critical situations during treatments. Unsuccessful hyperthermia treatments lead to survival of cancerous tissues. Thus, insufficient net absorbed thermal energy in local tissue region is one of the major problems.
Figure 2 shows the flow chart of optimization scheme. The optimized thermal power distribution in the treated cubic volume is computed in order to reach ideal therapeutic tissue temperature distribution.