基于中医舌诊理论的人舌三维温度场数值模拟与实验研究
|
摘要
对蕴藏于交叉学科领域内基础问题的深入研究常常是促成边缘学科飞速发展的重要环节,本文用热科学方法对传统医学的舌诊机理进行了深入研究。
以真实人舌血管铸型和实际传热状况下获取的舌体三维温度场作为技术平台,对舌体表观状态与生物传热特性的关键问题做了深层次研究,包括影响舌体温度场变化的机制与中医舌象的关系。从研究生物体信息的多维获取和综合分析方法入手,探索从舌体信息反映证候状况活动规律的科学性。生物体的血管分布形态和传热特性对舌面温度场有显著影响。以血管铸型为基础建立真实的生物体组织模型,通过计算血液和组织的耦合传热,重构生物体三维温度场是一种新的计算方法。然而人体器官血管铸型的获取绝非易事,采用血管铸型进行生物体三维温度场重构计算的方法将受到制约。
围绕上述研究,本文工作重点主要包括:(1)提出适合人体动脉血管树模拟的分步方法,生成人舌三维动脉血管树;(2)分析分支结构对血液换热的影响,并拟合得到血液的Nu数函数;(3)用提出的血管树模拟方法建立人舌三维动脉血管树物理模型,使用拟合得到的血液Nu数公式,建立重构人舌温度场的数学模型,并据此计算得到人舌三维温度场;(4)以中医认定“血瘀证”、“血虚证”以及健康人的红外热像为模板,与用数值计算方法获取的三维温度场进行对比,通过多参数的变异,探索生物传热与中医舌诊理论的相关性。
研究结果表明:用本文提出的分步模拟血管树方法生成的血管树符合人舌血管树的实际结构,而且可以通过修改血管树分支指数的取值建立血虚、血瘀人舌的血管树模型;血管分支结构中血液速度、温度、Nu数与直管段明显不同,且半径比、分支角、分支血管半径、分支血液流速对速度、温度及Nu数分布有明显影响;蒸发散热是舌面主要散热方式;用本文建立的人舌传热数学模型,由数值计算得到的血瘀、健康、血虚人舌的温度场,其舌面温度分布规律与测量得到的人舌红外热像基本一致;根血管入口位置、舌体代谢热、舌面参考湿度的改变可能是导致不同证候舌面温度具有不同分布规律的主要原因。
论文的创新点在于:(1)提出了适合人舌动脉血管树的分步模拟方法,用此方法可替代血管铸型实验;(2)拟合得到了血管分支结构中血液的Nu数公式;(3)以分步模拟方法获得的人舌动脉血管树为物理模型,对中医血瘀、血虚证以及健康人舌的温度场进行了数值模拟,并与相应测量热像进行了对比,量化研究了生物传热与中医舌诊理论的相关性。
Research deeply in the basis problem of the interdisciplinary field can cause fast development of borderline subject. In this dissertation the mechanism of tongue inspection in Traditional Chinese Medicine (TCM) is explored from the point of view of thermal science.
Based on simulation the 3D temperature field method in real vessel shape and real heated state, the superficial state and sixty-four-dollar question about bio-heat transfer has been studied, including the relationship of tongue manifestation and the variation rule of the tongue temperature field. By acquiring the information about organism by many mediums and analyzing synthetically, whether or not the information of tongue can reflect TCM syndrome was discussed. The vascularity and heat transfer of vessel tree has marked influence on the temperature field. Simulation the 3D temperature field of organisms is a new mathematic method as the conjugated transfer of heat is taken into account and the model of real tongue is constructed on the basis of vessel cast. However the vessel cast of human organ can not obtain easily, so this simulation method is limited which based on the vessel cast.
The emphases of this paper include: i) the stepwise method was proposed which was fitted for the generation the lingual arterial trees of human, and a 3D arterial trees model of human tongue was constructed. ii) The influence of the furcated configuration on the heat transfer of blood was analysed, and the Nusselt number function was obtained by fitting. iii) A mathematic model of lingual temperature field of human was proposed in which the arterial tree of human tongue formed by the stepwise method was set as physical model and the Nusselt number function was used. The 3D temperature field of human tongue was obtained by this model. iv) The temperature distribution of the surface of tongue of different people was measured by infrared thermal imager, including healthy people, people with blood stasis syndrome and people with blood deficiency syndrome. And these infrared thermal images were compared with the 3D temperature field of human tongue obtained by numerical simulation in order to quest for the pertinence between the mechanism of tongue inspection in TCM and bio-heat transfer.
Research results indicate that: i) the 3D arterial tree of human tongue formed by the stepwise method was in accord with the real configuration of lingual arterial trees of human. The arterial model of blood deficiency human tongue and blood stasis human tongue could be constructed by modifying the bifurcation exponent of vessel trees. ii) The distribution of velocity, temperature and the Nusselt number of blood in the furcated configuration was different with that in a straight tube. And the bifurcation ratio, the furcated angel, the radius and velocity of branching vessel had a marked influence on the distribution of velocity, temperature and the Nusselt number. iii) The export heat by vaporizing was the primary export heat. iv) By using the mathematic model of lingual temperature field of human propsed by this paper, the lingual temperature field of healthy people, blood stasis syndrome people and blood deficiency syndrome people were obtained. The rule of temperature distribution of the tongue surface gained by simulation was same with that of infrared thermal images. v) The mainly reason why the lingual temperature field of different TCM syndromes has different rules was the change of the position of root segment entrance, metabolic heat of tongue tissue, and the reference humidity of tongue surface.
The innovations of this paper lie in the following. i) The stepwise method was proposed which was fitted for the generation the lingual arterial trees of human. This method can substitute the vessel cast experiment. ii) The Nusselt number function of the blood in the furcated configuration was obtained by fitting. iii) Using the arterial tree of human tongue formed by the stepwise method as physical model, the lingual temperature field of healthy people, blood stasis syndrome people and blood deficiency syndrome people were simulated. And these results were compared with the infrared thermal images in order to research the pertinence between the mechanism of tongue inspection in TCM and bio-heat transfer.
以真实人舌血管铸型和实际传热状况下获取的舌体三维温度场作为技术平台,对舌体表观状态与生物传热特性的关键问题做了深层次研究,包括影响舌体温度场变化的机制与中医舌象的关系。从研究生物体信息的多维获取和综合分析方法入手,探索从舌体信息反映证候状况活动规律的科学性。生物体的血管分布形态和传热特性对舌面温度场有显著影响。以血管铸型为基础建立真实的生物体组织模型,通过计算血液和组织的耦合传热,重构生物体三维温度场是一种新的计算方法。然而人体器官血管铸型的获取绝非易事,采用血管铸型进行生物体三维温度场重构计算的方法将受到制约。
围绕上述研究,本文工作重点主要包括:(1)提出适合人体动脉血管树模拟的分步方法,生成人舌三维动脉血管树;(2)分析分支结构对血液换热的影响,并拟合得到血液的Nu数函数;(3)用提出的血管树模拟方法建立人舌三维动脉血管树物理模型,使用拟合得到的血液Nu数公式,建立重构人舌温度场的数学模型,并据此计算得到人舌三维温度场;(4)以中医认定“血瘀证”、“血虚证”以及健康人的红外热像为模板,与用数值计算方法获取的三维温度场进行对比,通过多参数的变异,探索生物传热与中医舌诊理论的相关性。
研究结果表明:用本文提出的分步模拟血管树方法生成的血管树符合人舌血管树的实际结构,而且可以通过修改血管树分支指数的取值建立血虚、血瘀人舌的血管树模型;血管分支结构中血液速度、温度、Nu数与直管段明显不同,且半径比、分支角、分支血管半径、分支血液流速对速度、温度及Nu数分布有明显影响;蒸发散热是舌面主要散热方式;用本文建立的人舌传热数学模型,由数值计算得到的血瘀、健康、血虚人舌的温度场,其舌面温度分布规律与测量得到的人舌红外热像基本一致;根血管入口位置、舌体代谢热、舌面参考湿度的改变可能是导致不同证候舌面温度具有不同分布规律的主要原因。
论文的创新点在于:(1)提出了适合人舌动脉血管树的分步模拟方法,用此方法可替代血管铸型实验;(2)拟合得到了血管分支结构中血液的Nu数公式;(3)以分步模拟方法获得的人舌动脉血管树为物理模型,对中医血瘀、血虚证以及健康人舌的温度场进行了数值模拟,并与相应测量热像进行了对比,量化研究了生物传热与中医舌诊理论的相关性。
Research deeply in the basis problem of the interdisciplinary field can cause fast development of borderline subject. In this dissertation the mechanism of tongue inspection in Traditional Chinese Medicine (TCM) is explored from the point of view of thermal science.
Based on simulation the 3D temperature field method in real vessel shape and real heated state, the superficial state and sixty-four-dollar question about bio-heat transfer has been studied, including the relationship of tongue manifestation and the variation rule of the tongue temperature field. By acquiring the information about organism by many mediums and analyzing synthetically, whether or not the information of tongue can reflect TCM syndrome was discussed. The vascularity and heat transfer of vessel tree has marked influence on the temperature field. Simulation the 3D temperature field of organisms is a new mathematic method as the conjugated transfer of heat is taken into account and the model of real tongue is constructed on the basis of vessel cast. However the vessel cast of human organ can not obtain easily, so this simulation method is limited which based on the vessel cast.
The emphases of this paper include: i) the stepwise method was proposed which was fitted for the generation the lingual arterial trees of human, and a 3D arterial trees model of human tongue was constructed. ii) The influence of the furcated configuration on the heat transfer of blood was analysed, and the Nusselt number function was obtained by fitting. iii) A mathematic model of lingual temperature field of human was proposed in which the arterial tree of human tongue formed by the stepwise method was set as physical model and the Nusselt number function was used. The 3D temperature field of human tongue was obtained by this model. iv) The temperature distribution of the surface of tongue of different people was measured by infrared thermal imager, including healthy people, people with blood stasis syndrome and people with blood deficiency syndrome. And these infrared thermal images were compared with the 3D temperature field of human tongue obtained by numerical simulation in order to quest for the pertinence between the mechanism of tongue inspection in TCM and bio-heat transfer.
Research results indicate that: i) the 3D arterial tree of human tongue formed by the stepwise method was in accord with the real configuration of lingual arterial trees of human. The arterial model of blood deficiency human tongue and blood stasis human tongue could be constructed by modifying the bifurcation exponent of vessel trees. ii) The distribution of velocity, temperature and the Nusselt number of blood in the furcated configuration was different with that in a straight tube. And the bifurcation ratio, the furcated angel, the radius and velocity of branching vessel had a marked influence on the distribution of velocity, temperature and the Nusselt number. iii) The export heat by vaporizing was the primary export heat. iv) By using the mathematic model of lingual temperature field of human propsed by this paper, the lingual temperature field of healthy people, blood stasis syndrome people and blood deficiency syndrome people were obtained. The rule of temperature distribution of the tongue surface gained by simulation was same with that of infrared thermal images. v) The mainly reason why the lingual temperature field of different TCM syndromes has different rules was the change of the position of root segment entrance, metabolic heat of tongue tissue, and the reference humidity of tongue surface.
The innovations of this paper lie in the following. i) The stepwise method was proposed which was fitted for the generation the lingual arterial trees of human. This method can substitute the vessel cast experiment. ii) The Nusselt number function of the blood in the furcated configuration was obtained by fitting. iii) Using the arterial tree of human tongue formed by the stepwise method as physical model, the lingual temperature field of healthy people, blood stasis syndrome people and blood deficiency syndrome people were simulated. And these results were compared with the infrared thermal images in order to research the pertinence between the mechanism of tongue inspection in TCM and bio-heat transfer.
引文
[1]刘静,任泽霈,王存诚.生物医学传热学的研究进展.力学进展, 1996, 26(2): 198~213
[2]王辉,吴建国.生物传热学及其医学应用.同济大学学报(医学版), 2004, 25(2): 159~162
[3]北京中医学院中医基础理论教研室.中医舌诊.北京:人民卫生出版社, 1977, 7~10
[4] Pennes H H. Analysis of tissue and arterial temperatures in the resting human forearm. Journal of Applied Physiology, 1948, 1: 93~122
[5] Jain R K. Analysis of heat transfer and temperature distributions in tissue during local and whole-body hyperthermia. In: Shitzer A, Eberthart R C, eds. Heat Transfer in Medicine and Biology: Analysis and Application. New York: Plenum Press, 1985, 3~54
[6] Chen M M, Holmes K K. Microvascular contributions to tissue heat transfer. Annals of the New York Academy of Sciences, 1980, 335: 137~150
[7] Liu J, Zhu L, Xu L. Studies on the three-dimensional temperature transients in the canine prostate during transurethral microwave thermal therapy. Journal of Biomechanical Engineering, 2000, 122(8): 372~379
[8] Deng Z S, Liu J. Mathematical modeling of temperature mapping over skin surface and its implementation in thermal disease diagnostics. Computers in Biology and Medicine, 2004, 34: 495~521
[9] Wullf W. The energy conservation equation for living tissue. IEEE Transactions on Biomedical Engineering, 1974, 21: 494~495
[10]王补宣,王艳民.生物传热基本方程的研究.工程热物理学报, 1993, 14(2): 166~170
[11]王补宣,王艳民,蔡伟明.直角坐标系中第二类边界条件下一维生物组织温度场的稳态分析解及实验研究.工程热物理学报, 1995, 16(1): 65~69
[12]蔡睿贤.一维不定常生物传热方程的解析解.科学通报, 1995, 40(15): 1361~1362
[13] Mudit K J, Patrick D W. A three-dimensional finite element model of radiofrequency ablation with blood flow and its experimental validation. Annals of Biomedical Engineering, 2000, 28(9): 1075~1084
[14] Ying He, Hao Liu, Ryutaro Himeno. A one-dimensional thermo-fluid model of blood circulation in the human upper limb. International Journal of Heat and Mass Transfer, 2004, 47(10): 2735~2745
[15] White J A, Dutton A W, Schmidt J A, et al. An accurate, convective energy equation based automated meshing technique for analysis of blood vessels and tissues. International Journal of Hyperthermia, 2000, 16(2): 145~158
[16] Deng Z Sh, Liu J. Effect of configuration between cryoprobe and large blood vessels on the tissue freezing during cryosurgery. Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China, 2005, 1~4
[17] Haemmerich D, Wright A W, Mahvi D M, et al. Hepatic bipolar radiofrequency ablation creates coagulation zones close to blood vessels: a finite element study. Medical & Biological Engineering and Computing, 2003, 41(3): 317~323
[18] Chato J C. Heat transfer to blood vessels. Journal of Biomechanical Engineering, 1980, 102(5): 110~118
[19]章琛曦,张素,张熘.聚焦超声消融肝癌时大血管位置对热场分布的影响.应用基础与工程科学学报, 2006, 14(3): 362~367
[20] Oana I C, Thaddeus V S, James R M, et al. Perturbations in hyperthermia temperature distributions associated with counter-current flow: numerical simulations and empirical verification. IEEE Transactions on Biomedical Engineering, 2000, 47(4): 435~443
[21] Chen Z K, Molloi S. Automatic 3D vascular tree construction in CT angiography. Computerized Medical Imaging and Graphics, 2003, 27: 469~479.
[22] Cemil K, Francis Q. A review of vessel extraction techniques and algorithms. ACM Computing Surveys, 2004, 36(2): 81~121
[23] Christos V B, Iraklis C K, Marina E P, et al. A method for 3D reconstruction of coronary arteries using biplane angiography and intravascular ultrasound images. Computerized Medical Imaging and Graphics, 2005, 29(8): 597~606
[24] Anil Martin S M, Andreas H M, Anja B, et al. Multidetector-row computed tomography vs. angiography and intravascular ultrasound for the evaluation of the diameter of proximal coronary arteries. International Journal of Cardiology, 2006, 110(1): 40~45
[25] Crezee J, Lagendijk J W. Temperature uniformity during hyperthermia: the impact of large vessels. Physics in Medicine and Biology, 1992, 37(1): 1321~1337
[26]程明亮,袁耀华,侯皓天.人体全身血管铸型标本的研制.解剖学研究, 2004, 26(3): 239~240
[27]涂晓斌,蒋先刚,刘二根,等.由平行切片图象重建血管的三维模型.华东交通大学学报, 2002, 19(4): 73~75
[28]王朝露.舌体三维温度场的数值模拟及不确定分析: [硕士学位论文].天津:天津大学, 2006
[29] Raaymakers B W, Crezee J, Lagendijk J W. Modeling individual temperature profiles from an isolated perfused bovine tongue. Physics in Medicine and Biology, 2000, 45(5): 765~780
[30] Mandelbrot B B. Fractals: form, chance, and dimensions. San Francisco, USA: W.H. Freeman and Company, 1977, 173~185
[31] Zamir M, Brown N. Arterial branching in various parts of the cardiovascular system. American Journal of Anatomy, 1982, 163: 295~307
[32] Zamir M, Wrigley S M, Langille B L. Arterial bifurcations in the ardiovascular system of a rat. Journal of General Physiology, 1983, 81: 325~335
[33]张志远.人体自相似及其容错原则.国外医学生物医学工程分册, 1996, 19(6): 311~317
[34] Zamir M. On fractal properties of arterial trees. Journal Of Theoretical Biology, 1999, 197: 517~526
[35] Zamir M. Fractal Dimensions and Multifractility in Vascular Branching. Journal Of Theoretical Biology, 2001, 212: 183~190
[36] Naomi T, Guy T, Tim D. A three-dimensional fractal model of tumour vasculature. Proceedings of the 26th Annual International Conference of the IEEE EMBS. San Francisco, USA, 2004, 9: 1~5
[37] El?bieta G, Marek R, Alicja K. Fractal models of circulatory system. Symmetrical and asymmetrical approach comparison. Chaos, Solitons & Fractals, 2005, 24(3): 707~715
[38] El?bieta G, Marek R, Alicja K. Blood flow simulation through fractal models of circulatory system. Chaos, Solitons and Fractals, 2006, 27(1): 1~7
[39] Meier J, Kleen M, Messmer K. A computer model of fractal myocardial perfusion heterogeneity to elucidate mechanisms of changes in critical coronary stenosis and hypotension. Bulletin of Mathematical Biology, 2004, 66(9): 1155~1171
[40] Johannes H G M V B, Stephen A R. Regional myocardial flow heterogeneity explained with fractal networks. The American journal of physiology, 1989, 257(8): 1670~1680
[41] Cohn, D L. Optimal systems: The vascular system. Bulletin of Mathematical Biology, 1954, 16(2): 59~74
[42] Kamiya A, Togawa T. Optimal branching structure of the vascular tree. Bulletin of Mathematical Biology, 1972, 34(6): 431~438
[43] Labarbera M. Principles of design of fluid transport systems in zoology. Science, 1990, 249(8): 992~999
[44] Schreiner W, Peter F B. Computer-optimization of vascular trees. IEEE Transactions on Biomedical Engineering, 1993, 40(5): 482~490
[45] Neumann F, Schreiner W, Neumann M. Computer simulation of coronary arterial trees. Advances in Engineering Software, 1997, 28(4): 353~357
[46] Van Leeuwen G M J, Kotte A N T J, Jan J W Lagendijk. A Flexible Algorithm for Construction of 3-D Vessel Networks for Use in Thermal Modeling. Transactions on Biomedical Engineering, 1998, 45(5): 596~604
[47] Karch R, Neumann F, Neumann M, et al. A Three-dimensional model for arterial tree representation, generated by constrained constructive optimization. Computers in Biology and Medicine, 1999, 29(1): 19~38
[48] Bezy W J, Bruno A. A 3D dynamic model of vascular trees. Journal of Biological Systems, 1999, 7(1): 11~31
[49] Schreiner W, Karch R, Neumann M, et al. Optimized arterial trees supplying hollow organs. Medical Engineering & Physics, 2006, 28(4): 416~429
[50] Kretowski M, Rolland Y, Johanne B W, et al. Fast algorithm for 3-D vascular tree modeling. Computer Methods and Programs in Biomedicine, 2003, 70(2): 129~136
[51]张燕.基于血管树结构的生物传热模型及其数值模拟: [硕士学位论文].北京:北京科技大学, 2006
[52] Van Leeuwen G M J, Kotte A N T J, Raaymakers B W. Temperature simulations in tissue with a realitic computer generated vessel network. Physics in Medicine and Biology, 2000, 45(1): 1035~1049
[53] Kotte A N T J, van Leeuwen G M J, Lagendijk J J W. Modelling the thermal impact of a discrete vessel tree. Physics in Medicine and Biology, 1999, 44(1): 57~74
[54] Raaymakers B W, Crezee J, Lagendijk J J W. Comparison of temperature distributions in interstitial hyperthermia: experiments in bovine tongues versus generic simulations. Physics in Medicine and Biology, 1998, 43(11): 1199~1214
[55] Charm S, Paltiel B, Kurland G S. Heat transfer coefficients in blood flow. Biorheology, 1968, 5(1): 133~145
[56] Shah J, Dos S I, Haemmerich D, et al. Instrument to measure the heat convection coefficient on the endothelial surface of arteries and veins. Medical & Biological Engineering and Computing, 2005, 43(4): 522~527
[57] Victor S A, Shah V L. Heat transfer to blood flowing in a tube. Biorheology, 1975, 123(3): 361~368
[58] Victor S A, Shah V L. Steady state heat transfer to blood flowing in the entrance region of a tube. International Journal of Heat and Mass Transfer, 1976, 19(6): 777~783
[59] Barozzi G S, Dumas A. Convective heat transfer coefficients in the circulation. Journal Biomechanical Engineering, 1991, 113(3): 308~313
[60] Shrivastava D, Roemer R. Theoretical evaluation of convective heat transfer coefficients in conjugated problems using the second law of thermodynamics. American Society of Mechanical Engineers, Bioengineering Division, New Orleans, 2002, 227~228
[61] Luisa C, Dos S I, Haemmerich D. Theoretical analysis of the heat convection coefficient in large vessels and the significance for thermal ablative therapies. Physics in Medicine and Biology, 2003, 48(12): 4125~4134
[62]刘静,王存诚.生物传热学.北京:科学出版社, 1997, 1~46
[63]魏润柏.热环境.上海:同济大学出版社, 1994, 108~132
[64]李伟.空气流动与人体对流换热: [硕士学位论文].上海:同济大学, 1996
[65] Nielsen M, Pedersen L. Studies on the heat loss by radiation and convection from the clothed human body. Acta Physiol., 1952, 27(3): 272~294
[66] Iberall A S, Schindler A M. On the physical basis of a theory of human thermoregulation. Journal of Dynamic Systems, Measurement, and Control, 1973, 95(3): 68~75
[67] J C切托.生物传热学基础.北京:科学出版社, 1991, 42~49
[68]诸凯,马一太,张伯礼.中医舌诊中的生物传热问题研究概况.上海中医药杂志, 2003, 37(2): 58~61
[69]魏璠,诸凯,何坚.生物传热学在中医舌诊定量化中的应用研究.中西医结合学报, 2003, 1(2): 135~137
[70]张伯礼,高秀梅,李艳.犬舌体传热与中医舌诊机制的实验研究.天津中医学院学报, 2002, 21(4): 35~36。
[71]章熙民,诸凯.应用红外热象技术测试舌面温度的研究.天津大学学报, 1991, 21(3): 21~24
[72]张沁芳.现代红外热图技术在中医舌诊中应用的研究: [硕士学位论文].天津:天津大学, 1988
[73]邹瑾.舌体横断面温度场的理论计算及血液灌注率特性研究: [硕士学位论文].天津:天津大学, 2002.
[74]李艳.舌体纵剖面温度场数值计算及传热模型研究: [硕士学位论文].天津:天津大学, 2003
[75]魏璠.舌体三维温度场的数值计算及传热特性研究: [硕士学位论文].天津:天津大学, 2004
[76]何坚.基于组织光学方法的生物体导热系数研究: [硕士学位论文].天津:天津大学, 2006
[77]王朝露.舌体三维温度场的数值模拟及不确定分析: [硕士学位论文].天津:天津大学, 2006
[78]姜智浩.不同病证舌红外热图像特征研究及影响因素分析: [博士学位论文].天津:天津中医药大学, 2007
[79] Braka A. The blood supply of dorsal tongue flaps. British Journal of Plastic Surgery, 1981, 32(4): 341~369
[80]吴海燕,何光褫.舌动脉的巨微解剖.第三军医大学学报, 1990, 12(2): 120~124
[81]王启华,伍思琪,靳士英.舌血管构筑及计量学研究.中国临床解剖学杂志, 1997, l5(2): 122~125
[82]周星,张天艳.正常人舌动脉经体表彩色超声多普勒检测.中国医学影像技术, 1999, l5(4): 277~278
[83] Lubashevsky I A, Gafiychuk V V. Analysis of the optimality principles responsible for vascular network architectonics. http://arxiv.org/abs/adap-org /9909003, 122~138
[84] Murray C D. The physiological principle of minimum work: the vascular system and the cost of the blood volume. Proc Natl Acad Sci U S A, 1926, 12(3): 207~214
[85] Cohn D. Optimal systems: the vascular system. Bulletin of Mathematical Biology, 1954, 16, 59~74
[86] Larry A T, Stella N, Alicia M Q, et al. Investigating Murray’s law in the chick embryo. Journal of Biomechanics, 2001, 34(1): 121~124
[87] Zamir M. Distributing and delivering vessels of the human heart. Journal of General Physiology, 1988, 91: 725~735
[88] Zamir M. Optimality principles in arterial branching. Journal of Theoretical Biology, 1976, 62, 227~251
[89] Suwa N, Fukasawa H, Sasaki Y. Estimation of intravascular blood pressure gradient by mathematical analysis of arterial casts. Tohoku Journal of Experimental Medicine, 1963, 79: 168~198
[90] Kurz H, Sandau K S. Modeling of blood vessel development-bifurcation pattern and hemodynamics, optimality and allometry. Journal of Theoretical Biology, 1997, 4: 261~281
[91] Uylings H. Optimization of diameters and bifurcation angles in lung and vascular tree structures. Bulletin of Mathematical Biology, 1977, 39: 509~520
[92] Changizi M A, Cherniak C. Modeling the large-scale geometry of human coronary arteries. Canadian Journal of Physiology and Pharmacology, 2000, 78: 603~611
[93] Arts T, Kruger R T I, Van Gerven W, et al. Propagation velocity and reflection of pressure waves in the canine coronary artery. American Journal of Physiology, 1979, 237: 469~474
[94] Van Bavel, Spaan E. Branching patterns in the porcine coronary arterial tree: estimation of flow heterogeneity. Circulation Research, 1992, 71(5): 1200~1212
[95] Zamir M, Sinclair P, Wonnacott T H. Relation between diameter and flow in major branches of the arch of the aorta. Journal of biomechanics, 1992, 25(11): 1303~1310
[96]张云杰. Pro/Enginner wildfire 2.0机械设计.北京:中国林业出版社, 2006, 5
[97] Schreiner W, Neumann F, Neumann M, et al. Structural quantification and bifurcation symmetry in arterial tree models generated by constrained constructive optimization. Journal of Theoretical Biology, 1996, 180(2): 161~174
[98] Anil K, Varshney C L, Sharma G C. Computational technique for flow in blood vessels with porous effects. Applied Mathematics and Mechanics, 2005, 26(1): 63~72
[99] Shrivastava D, Roemer R. Readdressing the issue of thermally significant blood vessels using a countercurrent vessel network. Journal of Biomechanical Engineering, 2006, 128(4): 210~216
[100] Cousins A K. On the Nusselt Number in Heat Transfer between Multiple Parallel Blood Vessels. Journal of Biomechanical Engineering, 1997, 119(1): 127~129
[101]王涛.高等传递过程原理.北京:化学工业出版社, 2005, 26~26
[102] Walburn F J, Schneck D J. A constitutive equation for whole human blood. Biorheology, 1976, 13(1): 201~214
[103]陶文铨.数值传热学.西安:西安交通大学出版社, 2001, 5~16
[104]陈琦,白景峰,陈亚珠.伴行血管在高强度聚焦超声下对温度场的影响.上海交通大学学报, 2004, 38(1): 130~134
[105]姜礼尚,庞之垣.有限元方法及其理论基础.北京:人民教育出版社, 1979, 178, 1~6
[106]龚曙光,谢桂兰. ANSYS操作命令与参数化编程.北京:机械工业出版社, 2004, 3~10
[107]王国强.实用工程数值模拟技术及其在ANSYS上的实践.西安:西北工业大学出版社, 2001, 273~310
[108]赵镇南.传热学.北京:高等教育出版社, 2002, 238~246
[109] W. M.罗森诺.传热学基础手册.北京:科学出版社, 1992, 496~497
[110]梁文懂,肖时钧.传递现象基础.北京:冶金工业出版社, 2000, 202~205
[111]李汝辉.传质学基础.北京:北京航空学院出版社, 1987, 111~112
[112]康英鹏.舌体湿分含量测量仪的研究与设计: [硕士学位论文].天津:天津大学, 2006
[113]叶真,曲延征,林礼务.正常人舌超声解剖及彩色多普勒血流图研究.中华超声影像学杂志, 1999, 8(3): 54~57
[114]赵莉莉,史庆辉,张明.超声测量240条舌动脉和颌外动脉内径及血流参数正常值.中国临床医学影像杂志, 2004, 15(7): 375~377
[115]白景峰,李国伟,陈亚珠.超声治疗热场有限元分析.中国生物医学工程学报, 23(4): 377~381
[2]王辉,吴建国.生物传热学及其医学应用.同济大学学报(医学版), 2004, 25(2): 159~162
[3]北京中医学院中医基础理论教研室.中医舌诊.北京:人民卫生出版社, 1977, 7~10
[4] Pennes H H. Analysis of tissue and arterial temperatures in the resting human forearm. Journal of Applied Physiology, 1948, 1: 93~122
[5] Jain R K. Analysis of heat transfer and temperature distributions in tissue during local and whole-body hyperthermia. In: Shitzer A, Eberthart R C, eds. Heat Transfer in Medicine and Biology: Analysis and Application. New York: Plenum Press, 1985, 3~54
[6] Chen M M, Holmes K K. Microvascular contributions to tissue heat transfer. Annals of the New York Academy of Sciences, 1980, 335: 137~150
[7] Liu J, Zhu L, Xu L. Studies on the three-dimensional temperature transients in the canine prostate during transurethral microwave thermal therapy. Journal of Biomechanical Engineering, 2000, 122(8): 372~379
[8] Deng Z S, Liu J. Mathematical modeling of temperature mapping over skin surface and its implementation in thermal disease diagnostics. Computers in Biology and Medicine, 2004, 34: 495~521
[9] Wullf W. The energy conservation equation for living tissue. IEEE Transactions on Biomedical Engineering, 1974, 21: 494~495
[10]王补宣,王艳民.生物传热基本方程的研究.工程热物理学报, 1993, 14(2): 166~170
[11]王补宣,王艳民,蔡伟明.直角坐标系中第二类边界条件下一维生物组织温度场的稳态分析解及实验研究.工程热物理学报, 1995, 16(1): 65~69
[12]蔡睿贤.一维不定常生物传热方程的解析解.科学通报, 1995, 40(15): 1361~1362
[13] Mudit K J, Patrick D W. A three-dimensional finite element model of radiofrequency ablation with blood flow and its experimental validation. Annals of Biomedical Engineering, 2000, 28(9): 1075~1084
[14] Ying He, Hao Liu, Ryutaro Himeno. A one-dimensional thermo-fluid model of blood circulation in the human upper limb. International Journal of Heat and Mass Transfer, 2004, 47(10): 2735~2745
[15] White J A, Dutton A W, Schmidt J A, et al. An accurate, convective energy equation based automated meshing technique for analysis of blood vessels and tissues. International Journal of Hyperthermia, 2000, 16(2): 145~158
[16] Deng Z Sh, Liu J. Effect of configuration between cryoprobe and large blood vessels on the tissue freezing during cryosurgery. Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China, 2005, 1~4
[17] Haemmerich D, Wright A W, Mahvi D M, et al. Hepatic bipolar radiofrequency ablation creates coagulation zones close to blood vessels: a finite element study. Medical & Biological Engineering and Computing, 2003, 41(3): 317~323
[18] Chato J C. Heat transfer to blood vessels. Journal of Biomechanical Engineering, 1980, 102(5): 110~118
[19]章琛曦,张素,张熘.聚焦超声消融肝癌时大血管位置对热场分布的影响.应用基础与工程科学学报, 2006, 14(3): 362~367
[20] Oana I C, Thaddeus V S, James R M, et al. Perturbations in hyperthermia temperature distributions associated with counter-current flow: numerical simulations and empirical verification. IEEE Transactions on Biomedical Engineering, 2000, 47(4): 435~443
[21] Chen Z K, Molloi S. Automatic 3D vascular tree construction in CT angiography. Computerized Medical Imaging and Graphics, 2003, 27: 469~479.
[22] Cemil K, Francis Q. A review of vessel extraction techniques and algorithms. ACM Computing Surveys, 2004, 36(2): 81~121
[23] Christos V B, Iraklis C K, Marina E P, et al. A method for 3D reconstruction of coronary arteries using biplane angiography and intravascular ultrasound images. Computerized Medical Imaging and Graphics, 2005, 29(8): 597~606
[24] Anil Martin S M, Andreas H M, Anja B, et al. Multidetector-row computed tomography vs. angiography and intravascular ultrasound for the evaluation of the diameter of proximal coronary arteries. International Journal of Cardiology, 2006, 110(1): 40~45
[25] Crezee J, Lagendijk J W. Temperature uniformity during hyperthermia: the impact of large vessels. Physics in Medicine and Biology, 1992, 37(1): 1321~1337
[26]程明亮,袁耀华,侯皓天.人体全身血管铸型标本的研制.解剖学研究, 2004, 26(3): 239~240
[27]涂晓斌,蒋先刚,刘二根,等.由平行切片图象重建血管的三维模型.华东交通大学学报, 2002, 19(4): 73~75
[28]王朝露.舌体三维温度场的数值模拟及不确定分析: [硕士学位论文].天津:天津大学, 2006
[29] Raaymakers B W, Crezee J, Lagendijk J W. Modeling individual temperature profiles from an isolated perfused bovine tongue. Physics in Medicine and Biology, 2000, 45(5): 765~780
[30] Mandelbrot B B. Fractals: form, chance, and dimensions. San Francisco, USA: W.H. Freeman and Company, 1977, 173~185
[31] Zamir M, Brown N. Arterial branching in various parts of the cardiovascular system. American Journal of Anatomy, 1982, 163: 295~307
[32] Zamir M, Wrigley S M, Langille B L. Arterial bifurcations in the ardiovascular system of a rat. Journal of General Physiology, 1983, 81: 325~335
[33]张志远.人体自相似及其容错原则.国外医学生物医学工程分册, 1996, 19(6): 311~317
[34] Zamir M. On fractal properties of arterial trees. Journal Of Theoretical Biology, 1999, 197: 517~526
[35] Zamir M. Fractal Dimensions and Multifractility in Vascular Branching. Journal Of Theoretical Biology, 2001, 212: 183~190
[36] Naomi T, Guy T, Tim D. A three-dimensional fractal model of tumour vasculature. Proceedings of the 26th Annual International Conference of the IEEE EMBS. San Francisco, USA, 2004, 9: 1~5
[37] El?bieta G, Marek R, Alicja K. Fractal models of circulatory system. Symmetrical and asymmetrical approach comparison. Chaos, Solitons & Fractals, 2005, 24(3): 707~715
[38] El?bieta G, Marek R, Alicja K. Blood flow simulation through fractal models of circulatory system. Chaos, Solitons and Fractals, 2006, 27(1): 1~7
[39] Meier J, Kleen M, Messmer K. A computer model of fractal myocardial perfusion heterogeneity to elucidate mechanisms of changes in critical coronary stenosis and hypotension. Bulletin of Mathematical Biology, 2004, 66(9): 1155~1171
[40] Johannes H G M V B, Stephen A R. Regional myocardial flow heterogeneity explained with fractal networks. The American journal of physiology, 1989, 257(8): 1670~1680
[41] Cohn, D L. Optimal systems: The vascular system. Bulletin of Mathematical Biology, 1954, 16(2): 59~74
[42] Kamiya A, Togawa T. Optimal branching structure of the vascular tree. Bulletin of Mathematical Biology, 1972, 34(6): 431~438
[43] Labarbera M. Principles of design of fluid transport systems in zoology. Science, 1990, 249(8): 992~999
[44] Schreiner W, Peter F B. Computer-optimization of vascular trees. IEEE Transactions on Biomedical Engineering, 1993, 40(5): 482~490
[45] Neumann F, Schreiner W, Neumann M. Computer simulation of coronary arterial trees. Advances in Engineering Software, 1997, 28(4): 353~357
[46] Van Leeuwen G M J, Kotte A N T J, Jan J W Lagendijk. A Flexible Algorithm for Construction of 3-D Vessel Networks for Use in Thermal Modeling. Transactions on Biomedical Engineering, 1998, 45(5): 596~604
[47] Karch R, Neumann F, Neumann M, et al. A Three-dimensional model for arterial tree representation, generated by constrained constructive optimization. Computers in Biology and Medicine, 1999, 29(1): 19~38
[48] Bezy W J, Bruno A. A 3D dynamic model of vascular trees. Journal of Biological Systems, 1999, 7(1): 11~31
[49] Schreiner W, Karch R, Neumann M, et al. Optimized arterial trees supplying hollow organs. Medical Engineering & Physics, 2006, 28(4): 416~429
[50] Kretowski M, Rolland Y, Johanne B W, et al. Fast algorithm for 3-D vascular tree modeling. Computer Methods and Programs in Biomedicine, 2003, 70(2): 129~136
[51]张燕.基于血管树结构的生物传热模型及其数值模拟: [硕士学位论文].北京:北京科技大学, 2006
[52] Van Leeuwen G M J, Kotte A N T J, Raaymakers B W. Temperature simulations in tissue with a realitic computer generated vessel network. Physics in Medicine and Biology, 2000, 45(1): 1035~1049
[53] Kotte A N T J, van Leeuwen G M J, Lagendijk J J W. Modelling the thermal impact of a discrete vessel tree. Physics in Medicine and Biology, 1999, 44(1): 57~74
[54] Raaymakers B W, Crezee J, Lagendijk J J W. Comparison of temperature distributions in interstitial hyperthermia: experiments in bovine tongues versus generic simulations. Physics in Medicine and Biology, 1998, 43(11): 1199~1214
[55] Charm S, Paltiel B, Kurland G S. Heat transfer coefficients in blood flow. Biorheology, 1968, 5(1): 133~145
[56] Shah J, Dos S I, Haemmerich D, et al. Instrument to measure the heat convection coefficient on the endothelial surface of arteries and veins. Medical & Biological Engineering and Computing, 2005, 43(4): 522~527
[57] Victor S A, Shah V L. Heat transfer to blood flowing in a tube. Biorheology, 1975, 123(3): 361~368
[58] Victor S A, Shah V L. Steady state heat transfer to blood flowing in the entrance region of a tube. International Journal of Heat and Mass Transfer, 1976, 19(6): 777~783
[59] Barozzi G S, Dumas A. Convective heat transfer coefficients in the circulation. Journal Biomechanical Engineering, 1991, 113(3): 308~313
[60] Shrivastava D, Roemer R. Theoretical evaluation of convective heat transfer coefficients in conjugated problems using the second law of thermodynamics. American Society of Mechanical Engineers, Bioengineering Division, New Orleans, 2002, 227~228
[61] Luisa C, Dos S I, Haemmerich D. Theoretical analysis of the heat convection coefficient in large vessels and the significance for thermal ablative therapies. Physics in Medicine and Biology, 2003, 48(12): 4125~4134
[62]刘静,王存诚.生物传热学.北京:科学出版社, 1997, 1~46
[63]魏润柏.热环境.上海:同济大学出版社, 1994, 108~132
[64]李伟.空气流动与人体对流换热: [硕士学位论文].上海:同济大学, 1996
[65] Nielsen M, Pedersen L. Studies on the heat loss by radiation and convection from the clothed human body. Acta Physiol., 1952, 27(3): 272~294
[66] Iberall A S, Schindler A M. On the physical basis of a theory of human thermoregulation. Journal of Dynamic Systems, Measurement, and Control, 1973, 95(3): 68~75
[67] J C切托.生物传热学基础.北京:科学出版社, 1991, 42~49
[68]诸凯,马一太,张伯礼.中医舌诊中的生物传热问题研究概况.上海中医药杂志, 2003, 37(2): 58~61
[69]魏璠,诸凯,何坚.生物传热学在中医舌诊定量化中的应用研究.中西医结合学报, 2003, 1(2): 135~137
[70]张伯礼,高秀梅,李艳.犬舌体传热与中医舌诊机制的实验研究.天津中医学院学报, 2002, 21(4): 35~36。
[71]章熙民,诸凯.应用红外热象技术测试舌面温度的研究.天津大学学报, 1991, 21(3): 21~24
[72]张沁芳.现代红外热图技术在中医舌诊中应用的研究: [硕士学位论文].天津:天津大学, 1988
[73]邹瑾.舌体横断面温度场的理论计算及血液灌注率特性研究: [硕士学位论文].天津:天津大学, 2002.
[74]李艳.舌体纵剖面温度场数值计算及传热模型研究: [硕士学位论文].天津:天津大学, 2003
[75]魏璠.舌体三维温度场的数值计算及传热特性研究: [硕士学位论文].天津:天津大学, 2004
[76]何坚.基于组织光学方法的生物体导热系数研究: [硕士学位论文].天津:天津大学, 2006
[77]王朝露.舌体三维温度场的数值模拟及不确定分析: [硕士学位论文].天津:天津大学, 2006
[78]姜智浩.不同病证舌红外热图像特征研究及影响因素分析: [博士学位论文].天津:天津中医药大学, 2007
[79] Braka A. The blood supply of dorsal tongue flaps. British Journal of Plastic Surgery, 1981, 32(4): 341~369
[80]吴海燕,何光褫.舌动脉的巨微解剖.第三军医大学学报, 1990, 12(2): 120~124
[81]王启华,伍思琪,靳士英.舌血管构筑及计量学研究.中国临床解剖学杂志, 1997, l5(2): 122~125
[82]周星,张天艳.正常人舌动脉经体表彩色超声多普勒检测.中国医学影像技术, 1999, l5(4): 277~278
[83] Lubashevsky I A, Gafiychuk V V. Analysis of the optimality principles responsible for vascular network architectonics. http://arxiv.org/abs/adap-org /9909003, 122~138
[84] Murray C D. The physiological principle of minimum work: the vascular system and the cost of the blood volume. Proc Natl Acad Sci U S A, 1926, 12(3): 207~214
[85] Cohn D. Optimal systems: the vascular system. Bulletin of Mathematical Biology, 1954, 16, 59~74
[86] Larry A T, Stella N, Alicia M Q, et al. Investigating Murray’s law in the chick embryo. Journal of Biomechanics, 2001, 34(1): 121~124
[87] Zamir M. Distributing and delivering vessels of the human heart. Journal of General Physiology, 1988, 91: 725~735
[88] Zamir M. Optimality principles in arterial branching. Journal of Theoretical Biology, 1976, 62, 227~251
[89] Suwa N, Fukasawa H, Sasaki Y. Estimation of intravascular blood pressure gradient by mathematical analysis of arterial casts. Tohoku Journal of Experimental Medicine, 1963, 79: 168~198
[90] Kurz H, Sandau K S. Modeling of blood vessel development-bifurcation pattern and hemodynamics, optimality and allometry. Journal of Theoretical Biology, 1997, 4: 261~281
[91] Uylings H. Optimization of diameters and bifurcation angles in lung and vascular tree structures. Bulletin of Mathematical Biology, 1977, 39: 509~520
[92] Changizi M A, Cherniak C. Modeling the large-scale geometry of human coronary arteries. Canadian Journal of Physiology and Pharmacology, 2000, 78: 603~611
[93] Arts T, Kruger R T I, Van Gerven W, et al. Propagation velocity and reflection of pressure waves in the canine coronary artery. American Journal of Physiology, 1979, 237: 469~474
[94] Van Bavel, Spaan E. Branching patterns in the porcine coronary arterial tree: estimation of flow heterogeneity. Circulation Research, 1992, 71(5): 1200~1212
[95] Zamir M, Sinclair P, Wonnacott T H. Relation between diameter and flow in major branches of the arch of the aorta. Journal of biomechanics, 1992, 25(11): 1303~1310
[96]张云杰. Pro/Enginner wildfire 2.0机械设计.北京:中国林业出版社, 2006, 5
[97] Schreiner W, Neumann F, Neumann M, et al. Structural quantification and bifurcation symmetry in arterial tree models generated by constrained constructive optimization. Journal of Theoretical Biology, 1996, 180(2): 161~174
[98] Anil K, Varshney C L, Sharma G C. Computational technique for flow in blood vessels with porous effects. Applied Mathematics and Mechanics, 2005, 26(1): 63~72
[99] Shrivastava D, Roemer R. Readdressing the issue of thermally significant blood vessels using a countercurrent vessel network. Journal of Biomechanical Engineering, 2006, 128(4): 210~216
[100] Cousins A K. On the Nusselt Number in Heat Transfer between Multiple Parallel Blood Vessels. Journal of Biomechanical Engineering, 1997, 119(1): 127~129
[101]王涛.高等传递过程原理.北京:化学工业出版社, 2005, 26~26
[102] Walburn F J, Schneck D J. A constitutive equation for whole human blood. Biorheology, 1976, 13(1): 201~214
[103]陶文铨.数值传热学.西安:西安交通大学出版社, 2001, 5~16
[104]陈琦,白景峰,陈亚珠.伴行血管在高强度聚焦超声下对温度场的影响.上海交通大学学报, 2004, 38(1): 130~134
[105]姜礼尚,庞之垣.有限元方法及其理论基础.北京:人民教育出版社, 1979, 178, 1~6
[106]龚曙光,谢桂兰. ANSYS操作命令与参数化编程.北京:机械工业出版社, 2004, 3~10
[107]王国强.实用工程数值模拟技术及其在ANSYS上的实践.西安:西北工业大学出版社, 2001, 273~310
[108]赵镇南.传热学.北京:高等教育出版社, 2002, 238~246
[109] W. M.罗森诺.传热学基础手册.北京:科学出版社, 1992, 496~497
[110]梁文懂,肖时钧.传递现象基础.北京:冶金工业出版社, 2000, 202~205
[111]李汝辉.传质学基础.北京:北京航空学院出版社, 1987, 111~112
[112]康英鹏.舌体湿分含量测量仪的研究与设计: [硕士学位论文].天津:天津大学, 2006
[113]叶真,曲延征,林礼务.正常人舌超声解剖及彩色多普勒血流图研究.中华超声影像学杂志, 1999, 8(3): 54~57
[114]赵莉莉,史庆辉,张明.超声测量240条舌动脉和颌外动脉内径及血流参数正常值.中国临床医学影像杂志, 2004, 15(7): 375~377
[115]白景峰,李国伟,陈亚珠.超声治疗热场有限元分析.中国生物医学工程学报, 23(4): 377~381
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |