Optimal Control Problem for Bio-Heat Equation Due to Induced Microwave
-
摘要: 用一组方程式描述均匀平板状生物组织的热传导,分析其分布式的最优控制问题,研究该生物组织在肿瘤局部特殊点上达到所必需的温度,通过控制微波,使微波辐射的诱导作用,在手术进程的总时间内,该肿瘤点达到过高热.研究在手术过程不同时间点上生物组织温度与其长度间的依赖关系,使肿瘤达到期望的温度值.Abstract: A distributed optimal control problem for a system described by bio-heat equation for a homogeneous plane slab of tissue was analytically investigated so that a required temperature of the tissue at a particular point of location of tumor in hyperthermia could be attained with in a total time of operation of the process due to induced microwave radiation which was taken as control. Here the temperature of the tissue against the length of the tissue at different tmies of operation of the process was considered for investigation to atta in the desired temperature of the tumor.
-
Key words:
- bio-heat equation /
- hyperthermia /
- optimization /
- microwave /
- tumor
-
[1] Deng Z S, Liu J. Analytical study of bioheat transfer problems with spatial or transient heating on skin surface or inside biological bodies[J]. Trans ASME J Biomech Eng, 2002, 124(6): 638-649. doi: 10.1115/1.1516810 [2] Dhar P K, Sinha D K. Optimal temperature control in hyperthermia by artificial surface cooling[J].Int J Systems Sci, 1989, 20(11): 2275-2282. doi: 10.1080/00207728908910303 [3] Wagter C D. Optimization of simulated two-dimensional temperature distributions induced by multiple electromagnetic applicators[J]. IEEE Trans, Micro Theory Techni MTT, 1986, 34(5): 589-596. doi: 10.1109/TMTT.1986.1133397 [4] Butkovsky A G. Distributed Control System[M]. New York: American Elsevier Publishing Company, 1969: 334-335. [5] Dhar P K, Sinha D K. Temperature control of tissue by transient-induced microwave[J]. Int J Systems Sci, 1988, 19(10): 2051-2055. doi: 10.1080/00207728808964097 [6] Das S K, Clegg T S, Samulski T V. Computational techniques for fast hyperthermia temperature optimization[J]. Am Assoc Phy Med, 1999, 26(2): 319-328. [7] Kowalski M E, Behnia B, Webh A G, et al. Optimization of electro-magnetic phased arrays for hyperthermia via magnetic resonance temperature estimation[J]. IEEE Trans Biomed Eng, 2002, 49(11): 1229-1241. doi: 10.1109/TBME.2002.804602 [8] Loulou T, Scott E P. Thermal dose optimization in hyperthermia treatments by using the conjugate gradient method[J]. Numerical Heat Transfer, Part A, 2002, 42(7): 661-683. doi: 10.1080/10407780290059756 [9] Kowalski M E, Jin J M. A temperature-based feedback control system for electromagnetic phased arrays hyperthermia: theory and simulation[J]. Phys Med Biol, 2003, 48(5): 633-651. doi: 10.1088/0031-9155/48/5/306 [10] Bagaria H G, Johnson D T. Transient solution to the bioheat equation and optimization for magnetic fluid hyperthermia treatment[J]. Int J of Hyperthermia, 2005, 21(1): 57-75. doi: 10.1080/02656730410001726956 [11] Cheng K S, Stakhursky V, Craciunescu O I, et al. Fast temperature optimization of multi-source hyperthermia applicators with reduced order modelling of ‘virtual sources’[J]. Phys Med Biol, 2008, 53(6): 1619-1635. doi: 10.1088/0031-9155/53/6/008 [12] Kuznetsov A V. Optimization problems for bio-heat equation[J]. International Communications in Heat and Mass Transfer, 2006, 33(5): 537-543. doi: 10.1016/j.icheatmasstransfer.2006.01.012 [13] Lee E B, Markus L. Foundations of Optimal Control Theory[M]. The SIAM Series in Applied Mathematics, New York: John Wiley and Sons, 1967: 20. [14] Arora D, Minor M A, Mikhail S, et al. Control of thermal therapies with moving power deposition field[J]. Phys Med Biol, 2006, 51(5): 1201-1219. doi: 10.1088/0031-9155/51/5/011
点击查看大图
计量
- 文章访问数: 1266
- HTML全文浏览量: 43
- PDF下载量: 809
- 被引次数: 0