跳动心脏的计算机仿真及其分布式软件架构的设计
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
  • 英文题名:COMPUTER SIMULATION ON PULSATILE HEART AND ITS CONSTRUCTION USING THE DISTRIBUTED SOFTWARE ARCHITECTURE
  • 作者:张力锋
  • 论文级别:博士
  • 学科专业名称:生物医学工程与仪器
  • 学位年度:2001
  • 导师:吕维雪
  • 学科代码:0831
  • 学位授予单位:浙江大学
  • 论文提交日期:2001-05-01
摘要
在心电正问题和逆问题的研究中,心电仿真模型扮演了一个关键角色。一方面,
    心电正问题研究者不断将新的心脏生理物理知识用于建立心脏模型,以求获得理
    想的输出结果;另一方面,心电逆问题工作者希望能获得最大程度接近真实的心
    脏电模型,以便于他们用于获得各种病理心脏输出的特征知识。正因为心电仿真
    起了这么一个特殊重要的作用,建立一个精确的、尽可能与真实情况相符合的心
    电模型成了许多心电工作者孜孜以求的目标。以往的心电研究者为了提高心电模
    型的仿真精度,要么采用更加精细的心肌单元划分、更加复杂精确的兴奋仿真算
    法和兴奋步长;要么考虑电兴奋传播和人体躯干的各向异性、考虑肺等人体器官
    存在造成的影响等。这些工作的确都有效提高了心电仿真的精度,但是,最终心
    脏模型本身仍然存在着不可避免的误差。
     应该看到,心脏是个集电生理学、动力学、血液流体力学以及神经、生化控
    制等于一身的极其复杂的综合系统,为了得到尽可能精确的心电模型,就不能把
    眼光局限于单纯狭义的心电领域内,尽管它仿真的只是心电现象。由于心脏电生
    理、动力学等各相关学科具有的固有的复杂性,再加上受到计算机内存和运算速
    度的制约,使得构造复合型心脏模型的研究长期停滞不前。近来随着计算机技术
    的迅猛发展以及心脏动力学研究的日趋成熟,再加上Tagged MRJ等先进标测技
    术的出现,使得电学-动力学复合心脏的建模仿真成为可能。本文在浙江大学生
    物医学工程研究所十多年心电建模仿真研究的基础上,开展了这方面的研究。针
    对传统心电模型由于没有考虑心脏在一个心动周期内的收缩舒张运动从而给其
    输出造成误差的这一难以克服的弊端,本文尝试建立起能反映心脏真实运动的跳
    动心脏模型。首先重构了传统静态电学心脏的结构使之能反应动力学特色,在动
    力学成像和仿真研究的基础上,用力学形变数据去修正电学心脏模型中心室收缩
    期每时刻心偶极子坐标位置的变化,从而首次在国际上构造了初步的电学-动力
    学复合心脏模型——跳动心脏模型。在新的电学-动力学心脏模型基础上,展开
    了正常心脏和心肌缺血等心脏疾病的对比仿真研究,验证了动力学因素对于构建
    精确心电模型的重要性。此外,针对现代心电仿真软件的日益大型化和复杂化的
    趋势,本文利用最新的分布式软件技术,重新设计了心电模型使之具有了能适应
    这一趋势的关键特征,为今后国际范围内心电软件构造的标准化以及分工合作奠
    定了基础。
     本文的研究工作主要包括:
     ●分析总结了电学心脏的研究进展和方法论,讨论了这些研究工作的意义
     和存在的局限性,指出了所有的这些研究方法,都没有脱离出“静态”
     心脏模型的范畴,在本质上始终存在着不可避免的误差。
     ●分析总结了心脏力学的研究进展和方法论,讨论了几种力学成像技术的
     优点和不足;在用有限元(FEM)方法构建的左心室(LV)力学心脏模型的
     基础上,研究了电学心脏的输出兴奋时序作为力学心脏的输入,对于力
     学心脏模型的重要意义,运用该兴奋时序数据作为力学仿真的兴奋力载
     荷,得到了心脏的力学形变数据。
     ●在对电学心脏模型和动力学心脏模型分析的基础上,首先重构了传统的
    
    
     浙江大学博士学位论文
     电学心脏模型,使之在结构上能体现出动力学特征。利用力学成像数据
     建立了跳动心脏的初步模型:然后使用了电学心脏模型产生的兴奋时序
     作为力学心脏模型的载荷输入,通过FEM力学心脏模型仿真运算得到的
     输出形变数据,来修正电学心脏模型的等效偶极子在心动周期每一时刻
     的坐标位置的变化。这样,首次成功将动力学因素引入了电学心脏模型,
     创建了真正意义上的电学-动力学复合心脏模型——跳动心脏模型;最
     后,通过将成像法和力学仿真结合的思路,进一步完善了该模型。
     .在得到跳动心脏模型之后,进一步研究了各个力学形变因素对于心电模
    _型输出的影响。通过对比仿真试验结果,表明长轴收缩是作用最显著的
    叼 一’“”—””一’”’—”一”””-’-””—-””一’”一—一’.”二”——一厂二
     形变因素,决定了跳动心脏输出的基本框架;心尖扭曲具有修正T波形
     状的功效。这两者共同决定了跳动心脏的输出特征,是力学形变中最起
     作用的因素。
     .在新的跳动心脏模型的基础上,作者进行了常规心脏和病态心脏的心电
     仿真试验,试验结果表明了新的模型对于常规心脏的心电图(ECGX 体
     表电位图①SPM贿比原有的电学心脏模型更能体现出完整的心电信
     息,尤其在体现常规12导联心电图中的T波和BSPM图的ST段时刻上;
The electrical heart model plays a key role in the research work of forward problem and inverse problem in electrocardiograph (ECG). At one hand, new physical and physiological knowledge of human heart keep being used to construct the heart model, and at the other hand, the scholar of inverse problem eager to obtain a heart model as precise as possible which can be employed to study the characteristic symptom of pathological heart. As a result of all these, to build an ideal heart model become many scholars' research emphases. To improve the precision of electrical heart model, cardiac researchers have investigated many methods: they divide heart model into much tinier myocardial units, employ much more complicate excitation propagation simulation algorithm and assume much shorter excitation step than ever. Or, they consider the inhomogeneous torso and the myocardial anisotropy and the existence of the human lung and then introduce these factors into their electrical heart models. Those methods do take effect more or less, but at last the heart model itself still has unavoidable errors.
    Human heart, which is known as the center of the cardiovascular system, should be understood as a complex synthesis that is integrated with electrical, mechanical, neural, and biochemical properties. So, if we want to build an ideal heart model, we shouldn't limit our viewpoint within the separate electrical or mechanical area although its function is simulating the electrical or mechanical activity of human heart. For a long time, the effort to construct a composite heart model hasn't resulted any significant achievement because of the inherent complexity of many related areas of heart research and the limitation of the computer capability. Recent study at the cardiomechanic area reveals many important mechanisms of human heart and constant innovation in computer hardware and software nowadays brings us the unprecedented computational capability. And more, some advanced iatrical-imaging technologies such as tagged MRI etc. have appeared at recent days. All these progresses made it possible to build an electrical-mechanical composite heart model. Based on the research work of Biomedical Institute of Zhejiang University in the past decade, this article launch on this project. The traditional electrical heart model has been reconstructed to reflect the mechanical property firstly, and then we introduce the mechanical deformation data, which is produced by the tagged MRI and the mechanical heart model, into the electrical heart model to adjust the displacement of the equivalent dipole during one cardiac cycle. Therefore, an elementary electrical-mechanical composite heart model- pulsatile heart model is built at the first time in the world. After that, we use the new model to simulate the ECG and BSPM of the normal heart and the pathological heart and then compare its output with the original heart model's. The result substantiates the importance of the mechanical factor in the construction process of heart modeling. Moreover, this article proposes new software technology-distributed software architecture to redesign the heart model at last.
    
    
    
    In this article, the author has done the following research work:
    ? The methodologies and developments of the previous electrical heart modeling are reviewed and the meaning and limitation existing in them are analyzed in detail. Based on these discussions, the author point out that all these methods belong to the "static" heart modeling and thus have the unavoidable output errors.
    ? The methodologies and developments of the previous cardiomechanics are reviewed and the meaning and limitation existing in mechanical imaging methods and mechanical heart modeling are analyzed in detail.
    ? The traditional electrical heart model has been reconstructed to reflect the mechanical property firstly, and then we introduce the mechanical deformation data, which is produced by the tagged MRI and the mechanical heart model, into the electrical heart model to adjust the displacement of the equ
引文
AAbe H, NakamuraT, Motomiya, M, et al. Stresses in left ventricular wall and biaxial stress-strain relation of the cardiac muscle fiber for the potassium arrested heart Trans ASME, J Biomech Eng 1978, 100: 116-121
    Abildskov J.A, et al," The primary T wave-a new ECG waveform", Am. Heart J.,Vol.91, pp.242,1971
    Akaishi M, Weintraub WS, Schnieder RM, et al. Analysis of systolic bulging: mechanical characteristics of acutely ischemic myocardium in the conscious dog. Circ Res. 1986, 58:209-217.
    Alpert, NR. Cardiac hypertrophy. Academic Press, 1971, New York.
    Amini A, Duncan J. Pointwise tracking of left-ventricular motion in 3D. Proc IEEE Workshop on Visual Motion. 1991, (Princeton,NJ): 294-298.
    Aoki M. et al, "3D propagation medal for simulation of the ventricular depolarization and repolarization processes and induced body surface potentials, ECG body surface Mapping", van Dam R. et al, The Netherlands, 1986, Chap.36
    Aoki M, et al. Three dimensional simulation of the ventricular depolarization and repolarization processes and body surface potentials: normal heart and bundle branch block. IEEE Trans.On BME. 1987, 34:454-469
    Arenal A, Villemaire C, Nattel S. Mechanism of selective epicardial activation delay during acute myocardial ischaemia in dogs. Circ. 1993,88:2381-2388.
    Armour JA, Randall WC. Structure basis for cardiac function. Am J Physiol. 1970,218:1517-1523.
    Arts T, Reneman RS, Veenstra. A model of the mechanics of the left ventricle. Ann Biomed Eng 1979, 7: 299-318.
    Arts, T, Veenstra, PC Reneman, RS Epicardial deformation and left ventricular wall mechanics during ejection in the dog. Am J Physiol. 1982,243: H379-H390
    Avis MA, Sipkema P, Westerhof N. Modeling pressure-area relations of coronary blood vessels embedded in cardiac muscle in diastole and systole. Am J Physiol. 1995,268: H2531-H2543.
    Axel L, Dougherty L, Heartwall motion, improved method of spatial modulation of magnetization for MR imaging, Radiology. 1989,172:349-350.
    Azhari H, Grenadier H, Dinnar U, et al. Quantitative characterization and sorting of three dimensional geometries: application to left ventricles in-vivo. IEEE Trans Biomed Eng. 1989, 36: 322-332.
    Azhari H, Sideman S, Weiss JL, et al. Three-dimensional mapping of acute ischemia regions using MRI: wall thickening versus motion analysis. Am J physiol. 1990,259: H1492-H1503.
    Azhari H, Buchalter MB, Sideman S, et al. A conical model to describe the nonuniformity of the left ventricular twisting motion. Ann Biomed Engng. 1992,20:149-165.
    Barr R.C.,et al. Relating epicardial to body surface potential distributions by means of transfer coefficients based on geometry measurements. IEEE Trans. On BME. 1977;24:1-11
    Barta E, Adam D, Salant F et al 3-D ventricular myocardial electrical excitation: a minimal orthogonal pathways model. Ann Biomed Engng 1987,15:443-456.
    Bethe et al,"Die biologischen Rhythmus-phanomene als selbstandige bzwerzwun Kippvorgange be tractet", Pfluegers Arch, Phsiol., 1, 1940
    Beyar R, Sideman S. The dynamic twisting of the left ventricle: a computer study. Ann Biomed Engng. 1984,15: 443-456.
    Beyar R., Sideman S. A computer study of the left ventricular performance based on fiber structure, sarcomere dynamics, and transmural electrical propagation velocity. Circ Res, 1984,55: 358-375
    
    
    
    Beyar R, Sideman S. Effect of the twisting motion on the nonunifornuties of transmyocardial fiber mechanics and energy demand-A theoretical study. IEEE Trans Biomed Engng. 1985, BME-32(10) : 764-769.
    Beyar R, Sideman S. The dynamic twisting of the left ventricle. Ann Biomed Eng. 1986,14: 547-562.
    Beyar R, Yin F, Hausknecht M, et al Dependency of left ventricular twist shortening relationship on cardiac cycle phase. Am J Physiol. 1989,257: HI 119-H1128.
    Beyar R, Sideman S. A model of left ventricular contraction and transmural ventricular deformation. IEEE Computers in Cardiology. 1990,15-17.
    Beyar R, Sideman S. Mechanical pathophysiology of some heart disease: a therotical model. Med Biol Eng Comput. 1990,29 237-248.
    Birkelland S, Westby J, Matre K, et al Myocardial contraction patterns in nonischaemic and ischaemic regions during acute coronary insufficiency. Eur Heart J. 1991,19:651-667.
    Bogen DK, Rabinwitz SA, Neeleman A, et al. An analysis of the mechanical disadvantage of myocardial infarction in the canine left ventricles. Circ Res. 1980,47:728-741.
    Bogen DK, Needleman A, McMahon TA, et al. An analysis of myocardial infarction: the effect of regional shanges in contractility. Circ Res. 1984, 55: 805-815.
    Borow KM, Green LH, Grossman W, et al. Left ventricular end-systolic stress-shorting and stress-length relations in humans. Am J Cardiol. 1982, 50:1301-1308.
    Bovendeerd, PHM, Arts, T, Huyghe, JM, et al. Dependence of local left ventricular wall mechanics on myocardial fiber orientation :a model study. J Biomechanics. 1992,25:1129-1140
    Bovendeerd PHM, Hughe JM, Arts T, et al. Influence of endocardial-epicardial crossover muscle fibers on left ventricular wall mechanics.J Biomechanics. 1994,27(7) : 941-951.
    Brady AJ. Fed Proc.1965,24,1410-1420
    Buchalter MB, Weiss JL, Rogers WJ, et al. Non-invasive quantification of left ventricular rotational deformation in normal humans using magnetic resonance imaging myocardial tagging. Circulation. 1990,81:1236-1244.
    Budgett D.M.,et al. Comparison of measured and computed epicardial potentials from a patient-specific inverse model. J.Electrocardial. 1993;26(suppl.):165-173
    Chadwick RS. Mechanics of the left ventricle. Biophys J. 1982, 39:279-288.
    Chang F., Jose LR, Chang K. Analysis of thick laminated composites. J Compos Mater, 1990, 24: 801-822
    Chen CJ, Kwak BM, Rim K, et al. A model for an active left ventricle deformation-formulation of a nonlinear quasi-steady finite element analysis for orthotropic, three-dimensional myocardium. Int Conf Finite Element Biomech. 1980,2:640-655.
    Clancy EA, Smith JM,Cohen RJ. A simple electrical-mechanical model of the heart, applied to the study of electrical-mechanical altemans. IEEE Trans Biomed Engng. 1991, 38(6) : 551-560.
    Clark NR, Reichek N, Bergey P, et al. Circumferential myocardial shortening in the normal human left ventricle. Assessment by magnetic resonance imaging using spatial modulation of magnetization. Circulation. 1991, 84: 67-74.
    Cohen LD, Cohen I. A finite element method applied to new active contour models and 3D reconstruction from cross sections. Proc 3~(rd) International Conference on Computer Vision. (ICCV90) , 1990, (Osaka, Japan): 587-591.
    Craib W.H,, "A study of the electrical field surrounding active heart muscle". Heart, Vol. 14, pp.71-, 1927
    Gul'ko et al, "Mechanism of the formation of closed pathways of conduction in excitable media", Biophysics, 17,
    
    
     1972
    Daming Wei et al, "Computer simulation of superventricular tachcardia with the WPW syndrome using 3D heart models", J. of ECG, Vol.23, No.3,1990
    Dassen et al, "A mathematical model of conduction system to study the mechanism of cardiac arrhythmias" , Computers in Cardiology, 1982, IEEE, Computer Society Press
    Dassen et al, "A mathematical model to study reentrant cardiac arrhythmias" , PhD thesis , Univ. of Limburg Maastricht, The Netherlands, 1993
    D'Alche P. et al, "A mechanoelectrical model reproducing ECG.VCG and electrical cardiac field from mono-phasicaction potentials", J.Eleccardiol, Vol.4, pp!87,1971
    Demer, LL, Yin, FCP. Passive biaxial mechanical properties of isolated canine myocardium. J Physiol (Lond.) 1983,339:615-630.
    Deswysen BA. Parameter estimation of a simple model of the left ventricle and of the systemic vascular bed with particular attention to the physical meaning of the left ventricular parameters. IEEE Trans Biomed Eng. 1977, BME-24,29-38.
    Durrer D. et al, "Total excitation of the isolated human heart", Circ. ,Vol.41,1970
    Einthoven W. et al, "liber die richtung und die manifesto grosse der potentials chwankungen im menschlichen herzen und uber den einfluss der herzlage auf die form des elektrokardograms", Pfluegers Arch. Physiol.,Vol. 150, pp.275-,1913( Am. Heart J., Vol.40, pp.163-, 1950 )
    Edman KAP, Nilsson E. Relationship between force and velocity of shortening in rabbit papillary muscle. Acta Physiol Scand 1972: 85:488-500.
    Edwards CH, Rankin JS, Mchale PA, et al. effects of ischemia on left ventricular regional function in the conscious dog. Am J Physiol 1981,240: H413-H420.
    Eiichi TANAKA, Osamu TANAKA. Constitutive modeling of cardiac muscle taking account of contraction mechanism. 日本机械学会论文集(C编), 1997, 63: 803-309
    Falsetti HL, Mates RE, Grant C, et al. Left ventricular wall stress calculated from one-plane cineaogiography. Circ Res. 1970,26:71-83.
    Feint TS. Diastolic pressure-volume relations and distribution of pressure and fiber extension across the wall of a model left ventricle. Biophys J 1979,28:143-166.
    Fox CC Hutchins GM. The architecture of the human ventricular myocardium. Johns Hopkins Med J 1972 ,130: 289-299.
    Fung YC. Biomechanics: mechanical properties of living tissues. Springer-Vertag New York, 1981.
    Fung YC. Biomechanics: Circulation. 1984, Springer, New York.
    Fung YC. Biomechanics: motion, flow, stress and growth. 1990,Springer, New York.
    Fung YC. Keynote on physiology and function from multidimensional images: motion and mechanics. SPIE, 1995.
    Gabor D. & Nelson C. V. Determination of the resultant dipole of the heart from measurements on the body surface. J.Appl.Phys. 1954:25:413-416allagher KP, Gerren RA, Stiring MC, et al. The distribution Gof functional impairment across the lateral border of acutely ischemia myocardium. Circ Res. 1986, 58: 570-583.
    Garrido N, Wedeen VJ, Kwong KK, et al. Anisotrophy of water diffusion in myocardium of the rat Circ Res. 1994, 74:789-793.
    Gelemter KL.,et al. A mathematical-physical model of the genesis of the electrocardiogram. J.Biophys.
    
    
     1964;4:285-301
    Gescslowitz D.B. The concept of an equivalent cardiac generator. In Biom. Scien. Instrum. 1963;1:325-336 Ghista DN, Sandier H An analytic elastic-viscoelastic model for the shape and forces in the left ventricle. J Biomech. 1969,2: 35-47.
    Ghista DN, Hamid MS. Finite element stress analysis of the human left ventricle where irregular shape is developed from single plane cineangiogram. Comput Programs Biomed. 1977,7:219-231.
    Ghista DN, Ray G. Cardiac assessment mechanics: 1 left ventricular mechanomyocardiography, a new approach to the detection of diseased myocardial elements and states. Med Biol Engng Camp, 1980,18:271-280.
    Glantz SA. A three-element model describes excised cat papillary muscle elasticity. Am Physiol, 1975, 228: 284-294.
    Goto Y, Igarashi Y, Yamada O, et al. Hyperkinesis without the frank-starling mechanism in a nonischemic region of acutely ischemic excised canine heart. Circulation 1988,77(2) : 468-477.
    Gould P, Ghista DN, Brombolich L, et al. In vivo stresses in the human left ventricular wall: analysis accounting for the irregular 3-dimensional geometry and comparison with idealized geometry analysis. J Biomech, 1972, 5: 521-539.
    Grant et al, "The mechanism of A-V arrhythmias: with an electronic analogue of the human A-V node" , Am. J. Med., 20,1956
    Greenbaum RA, Ho SY, Gibson DG, et al. Left ventricular fiber architecture in man. Br Heart J. 1981, 45: 248-263.
    Grossman W, McLaurin LP. diastolic properties of the left ventricule. Ann Intern Med. 1976,84: 316-326
    Guccione JM, McCulloch AD, Waldman LK. Passive material properties of intact ventricular myocardium determined from a cylindrical model. ASME, J Biomech Engng. 1991,113:42-55.
    Guccione, JM, Costa, KD, McCulloch AD. Finite element stress analysis of left ventricular mechanics in the beating dog heart. J Biomechanics. 1995,28(10) : 1167-1177
    Gullberg GT, Sitek A, Bella ER, et al. Imaging the mechanical, electrical, and physiological properties of the heart. Proc 20th Ann Int Conf IEEE Eng Med Bio Soc. 1998,20(1) : 496-501
    Han GJ, Chandran KB, Gotteiner ML, et al. Application of finite-element analysis with optimization to assess the in vivo non-linear myocardial material properties using ecbocardiographic imaging. Med. Biol. Eng. Comput., 1993,31: 459-467
    Han J., Hoa SV A three-dimensional multi-layer composite finite element for stress analysis of composite laminates, Int J Nura Meth Eng, 1993,36, 3903-3914
    Hanna WT. A simulation of human heart function. BiophysJ. 1973,13:603-621.
    Harumi K. et al, "A theoretic model of the T wave", Circ. ,Vol.34, pp.657-, 1966
    Hawkes RC, Holland GN, Moore WS, et al. Nuclear magnetic resonance (NMR) tomography of the normal heart J Comput Assist Tomogr. 1981, 5: 605-612
    He B.,et al. An equivalent body surface charge model representing three-dimensional bioelectrical activity. IEEE Trans. On BME. 1995;42(7) :637-646
    Hess OM, Osakada G, Lavelle KP, et al. Diastolic myocardial wall stiffness and ventricular relaxation during partial and complete coronary occlusions in the conscious dog. Circ Res J. 1983,52: 387-400.
    Hill AV. Time heart of shorting and the dynamic constants of muscle. Proc R Soc, 1938, B126:136-195.
    Hirota Y. A clinical study of left ventricular relaxation. Circulation. 1980,62:756-763.
    Hoffman JIE Determinants and prediction of transmural myocardial perfusion. Circulation. 1987,58: 381-391.
    Hood WP, Thomson WJ, Rackley CE, et al. Comparison of calculation of left ventricular wall stress in man from thin-walled and thick walled ellipsoidal models. Circ Res. 1969,24: 575-582.
    
    
    
    Horan L.G. et al, "A theoretical examination of ventricular repolarization and the secondary T-wave", Circ.Res., Vol.42 , pp.750,1978
    Horowitz A, Perl M, Siderunan S, et al. Comprehensive model for simulation of left ventricle mechanics: Part 2. Implementation and results analysis. Med BioLEngng Comput. 1986, 24, 150-156. Fung YC. Biorheology of soft tissues. Biorheology. 1973,10: 139-155
    Horowitz A, Sheinman I, Lanir Y, et al. Nonlinear incompressible finite element for simulating loading of cardiac tissue-part 1: two dimensional formulation for thin myocardial strips. ASME J Biomech engng. 1988, 110: 57-61.
    Horowitz A, Sheinman I, Lanir Y. Nonlinear incompressible finite element for simulating loading of cardiac tissue-part 2: three dimensional formulation for thick ventricular wall segments. ASME J Biomech engng. 1988,110: 62-68.
    Huisman RM, Sipkema P, Westerhof N, et al. Comparison of models used to calculated left ventricular wall force. Med Biol Comput. 1980,18:133-144.
    Humphrey JD, Yin FCP. A new constitutive formulation for characterizing the mechanical behavior of soft tissues. Biophy J. 1987,52:563-570.
    Humphrey JD, Yin FCP. Constitutive relations and finite deformation of passive cardiac tissue: stress analysis in the left ventricle. Circ Res. 1989,65: 805-817.
    Hung WC, Goldof D. Adaptive-size meshes for rigid and nonrigid shape analysis and synthesis, IEEE Trans Pattern Analysis and Machine Intelligence. (PAMI).1993,15(6) : 611-616.
    Hunter PJ, Smaill BH. The analysis of cardiac function: a continuum approach. Prog Biophys molec Biol. 1988, 52:101-164.
    Huyghe JM, Blankevoort L, Grootenboer HJ, et al. A non-linear, viscoelastic, axisymmetric, two-phase finite element model of the passive left ventricle. Proc 4th Meeting Europ. Soc Biomechanics, Davos, Switzerland, Sept. 1984, Martinus Nijhoff Publ., Dorecht, 1985, The Nethelands, 257-262.
    Huyghe JM, Oomens CWJ, Van Campen DH, et al. Low Reynolds number steady state flow through a branching network of rigid vessels, I: mixture theory. Biorheology, 1989(a), 26: 55-71.
    Huyghe JM, Oomens CWJ, Van Campen DH, et al. Low Reynolds number steady state flow through a branching network of rigid vessels, II: a finite element model. Biorheology, 1989(b), 26:73-84.
    Huyghe JM, Van Campen DH, Arts T, et al. A two-phase finite element model of the diastole left ventricle. J Biomch. 1991-a,24(7) : 527-538.
    Huyghe JM, Van Campen DH, Arts T, et al. The constitutive behavior of passive heart muscletissue: A quasi-linear viscoelastic formulation. J Biomcb. 1991-b, 24(9) : 841-849.
    Huyghe JM, Arts T, Van camoen DH, et al. Porous medium finite element model of the beating left ventricle. Am J Physiol. 1992,31: H1256-H1267
    Ikeda K, et al. Use of body surface electrocardiographic mapping to localize the asynergic site in previous myocardial infarction. J Electrocardiol, 1990,23(1) : 13-21. Ishikawa T. et al, "The body surface isopotential maps of the nontransmural infarctions", Jpn. Circ. J. ,Vol.44, pp.128,1980
    Jack et al, "Electric current flow in excitable cells", Clarendon Press, Oxford, 1975
    Jan KM Distribution of myocardial stress and its influence on coronary blood flow. J Biomechanics. 1985,18:815-820.
    Janz RF, Grimm AF. Deformation of the diastolic left ventricle. I. Nonlinear elastic effects. Biophys J, 1973,13: 689-704.
    Janz RF, Inbert BR, Moritary TF Deformation of the diastolic left ventricle. II. Nonlinear geometric effects. J
    
    
     Biomech,1974,7 509-516
    Jantz RF, Waldron RJ. Predicted effect of chronic apical aneurysms on the passive stiffness of human left ventricle. Circ Res 1978,42(2) : 255-263
    Katho et al, "A mathematical model of automaticity in the sinus node and AV juncton based on weakly copaled relaxation oscillators", Comput. Res., 10,1977
    Koiwa Y, Hashiguchi R, Ohyama T, et al. Measurement of instantaneous viscoelastic properties by impledance-frequency curve of the ventricle. Am J Physiol. 1986,250,H672-H684.
    Koiwa Y, Ohyama T, Takagi T ,et al. The left ventricular vibration mode in the transfer function method and at the moent of the first heart sound. Front Med Biol. Eng 1988,1,59-70.
    Laskey WK, Reichek N, Sutton MSJ. Matching of myocardial oxygen consumption to mechanical load in human left ventricular hypertrophy and dysfunction. JACC. 1984, 3:291-300.
    Lessick J, Sideman S, Azhari H, et al. Regional three-dimensional geometry and function of left ventricles with fibrous aneurysms, a cine-computered tomography study. Circulation 1991, 84: 1072-1086.
    Lessick J, Sideman S, Azhari H, et al. Evalution of regional load in acute ischemia by three-dimensional curvatures analysis of the left ventricle. Ann Biomed Engng, 1993,21:147-161.
    L.J.Leon et al, "Computer model of excitation and recovery in the anisotropic myocardium," J.Electrocardil., vol.24, pp.1-41, 1991.
    Lew WYW, Ban-Hayashi E. Mechanisms of improving regional and global ventricular function by pre-load alterations during acute ischaemia in the canine left ventricle. Circ. 1985,72:1125-1134.
    Licko et al, "Analog simulation of A-V conduction block and Wenckebach phenomena", Computer Biol. Med. 1, 1971
    Lima JAC, Becker LC, Jacques MD, et al. Impaired thickening of nonischemic myocardium during acute regional ischemia in the dog. Circulation. 1985,71(5) -1048-1059.
    Little WC, Downes TR Clinical evaluation of left ventricular diastolic performance. Prog in Cardiovasc. Dis. 1990, 32,: 273-290.
    Loeffle L, Sagawa K. A one-dimensional viscoelastic model of cat heart muscle studies by small length perturbations during isometric contraction. Circ Res., 1975,36:498-512.
    Lower R. Tractus de corde. In: Early science in Oxford, UK: RT Gunther, 1932. London: Swansons, Pall Mall Reprint; 1968.
    Lu Weixue , Xu zhenyao, Fu yingjie. Microcomputer-based cardiac field simulation model. Med Biol Eng Comput, 1993, 31: 384-387
    Lue weixue, Xia Ling. Three-dimensional simulation of epicardial potentials using a microcomputer-based heart-torso model. Med Eng Phy, 1995,17:625-632
    Lu Weixue, Xia Ling. Computer simulation of epicardial potentials using a heart-torso model with realistic geometry. IEEE Trans Biomed Eng, 1996,43:211-217
    Maier SE, Fisher SE, McKinnon GC, et al. Acquisition and evaluation of tagged magnetic resonance images of the human left ventricle. Computerized Medical Imaging and Graphics. 1992,16(2) : 73-80
    Malik et al, "Computer simulation of cardiac conduction system", Compt. Biomed. Res., 16,1983
    Mann T, Goldberg S, Mudge GH, et al. Factors contributing to altered left ventricular diastolic properties during angina pectoris. Circulation. 1979,59:14-20.
    Marcus ML, Stanford W, Hajducao ZD, et al. Ultrafast computed-tomography in the diagnosis of cardiac disease. Am J Cardiol. 1989,64: E54-E59.
    Maroko PR, Braunwald. Modification of myocardial infarction size after coronary occlusion. Ann Int Med 1973, 79: 720-733.
    
    
    
    Masata TOKUDA, Kiyotsugu SEKIOKA, Takahiro UENO, et al. Nuerical simulator for estination of mechanical function of human left ventriclc(Study of basic system). JSME, 1994,37(A1) : 64-70.
    McCulloch AD, Guccione JM, Waldman LK, et al. Large-scale finite element analysis of the beating heart. Crit Rev Biomed Eng, 1992,20:427-449.
    McCulloch AD, Costa KD. Three-dimensional finite element models from magnetic resonance images as a structural framework for continuum analysis of the heart. SPIE, 199S, 2433: 309-317.
    Mchale PA, Greenfield JC. Evaluation of several geometric models for estimation of left ventricular circumferential wall stress. Circ Res. 1973, 33: 303-312.
    Mclnemey T, Terzopoulos D. A finite element based deformable model for 3D biomedical image segmentation. SPIE, 1993, 1905:254-259.
    Mclnemey T, Terzopoulos D. A finite element model for 3D shape reconstruction and nonrigid motion tracking. Proc. 4~(th) International Conference on Computer Vision. (ICCV93) , 1993, (Berlin, Germany): 518-523.
    Mcpherson DD, Skorton DJ, Kodiyalam S, et al. Finite element analysis of myocardial diastolic function using three-dimensional echocardiographyic resconstructions: application of a new method for study of acute ischemia in dogs. Circ. Res., 1987,60: 674-682.
    McVeigh ER, Zerhouni EA. Noninvasive measurement of transmural gridents in myocardial strain with magnetic resonce imaging. Radiology. 1991,180:677-683
    Messinger-Rapport B.J.,et al. The inverse problem in electrocardiography: a model study of the effects of geometry and conductivity parameters on the reconstruction of epicardial potentials. IEEE Trans. On BME. 1986;7:667-676
    Millane et al, "A computer model of cardiac conduction", Aust. Phys. Eng. Sci. Med. ,3,1980
    Miller W.T. et al, "Simulation studies of the ECG: I. the normal heart", Cirs. Res., Vol.43. pp.301,1978
    Miller W.T. et al, "Simulation studies of the ECG: II. the ischemic heart", Cirs. Res., Vol.43, pp.315,1978
    Mirsky I Left ventricular stresses in the intact human heart. Biophys J. 1969,9:189-208.
    Mirsky I, Parmley WW. Assessment of passive elastic stiffness for isolated heart muscle and the intact heart. Circ Res. 1973, 33: 233-243.
    Mirsky I. Ventricular and arterial wall stresses based on large deformation analysis. Biophys J. 1973, 13:1141-1159.
    Mirsky I Effects of anisotropy and nonhomogenity on left ventricular stresses in the intact heart. Bull Math Biophys. 1973,32: 197-213.
    Mirsky I, Pasipolarides A. Clinical assessment of diastolic function. Prog Cardiovasc. Dis. 1990, 32:291-318.
    Mirsky I, Ghista DN, Sandier H. Cardiac mechanics physiological clinical and mathematical considerations. New York, John Wiley &Sons, 1974:45
    Moe et al, "A computer model of artial fibrillation" , Am. Heart J., 67,1964
    Moriarity TF. The law of laplace, its limitations as a relation for diastolic pressure, volume, or wall stress of the left ventricle. Circ Res. 1980,46: 321-331.
    Moskowitz SW. On the mechanics of left ventricular diastole. J Biomech 1979,13: 301-311.
    Moskowtz, SE. Effects of inertia and viscoelasticity in late rapid filling of the left ventricle. J Biomech 1981,14: 443-445.
    Moulton MJ, Creswell LL, Hu N., et al. Applications of 3_D finite element modeling to the study of ventricular physiology. SPIE, 1995,2433: 318-328.
    Moulton M.J., Creswell LL, Actis RL, et al. An inverse approach to determining myocardial material properties. J Biomech 1995; 28(8) : 935-948.
    Murti V, Valliappan S. Numerical inverse isoparametric mapping in the remeshing and nodal quantity contouring.
    
     Computer & Structures, 1986,22: 1011-1021.
    Murti V, Wliappan S. Numerical inverse isoparametric mapping in 3DFEM. Computer & Structures, 1988, 29: 611-622.
    Nakanno K, Sugawara M Jamiya K, et al. A new approach to defining regional work of ventricle and evaluating regional cardiac function: means wall stress-natural logarithm of reciprocal of wall thickness relationship. Heart and Vessels. 1986,2: 74-80.
    Nevo E, Lanir Y. Structural finite deformation model of the left ventricle during diastole and systole.Trans ASME. J Biomech Engng. 1989, 111: 342-349.
    Nevo E, Lanir Y. Parameter estimation of left ventricular performance. IEEE Computers in Cardiology. 1990, 251-254.
    Nielsen P.M.F, dice IJ, Smaill BH, et al. Mathematical model of geometry and fibrous structure of the heart. Am J Physiol 1991; 260: H1365-H1378
    Noble MIM, Bowen TE, Hefner LL. Circ Res. 1969,24: 821-834.
    Novak, VP, Yin, FCP, Humphrey, JD. Regional mechanical properties of passive of passive myocardium, J. Biomechanics 1994,27(4) : 403-412
    Okajima M, et al. Computer simulation of the propagation process in excitation of the ventricles. Circ.Res. 1968,23:203-211
    Omens JH, Fung YC. Residual strain in rat left ventricle. Circ Res. 1990,66: 37-45.
    Omens JH, May KD, McCulloch AD. Transmural distribution of three-dimensional strain in the isolated arrested canine left ventricle. Am J Physiol 1991,261:H918-928.
    Okajima M. et al, "Computer simulation of the propagation process in excitation of the ventricles", Cirs. Res., Vol.23, pp.203,1968
    Osakada G, Sasayama S, Kawai C, et al. The analysis of left ventricular wall thickness and shear by an ultrasonic triangulation technique in the dog. Circ Res. 1980,47:173-181.
    Panda SC, Natarajan R, Finite element method of stress analysis in the human left ventricular layered wall structure. Med Biol Engng Comp, 1977,15:67-71.
    Panda SC., Natarajan R. Finite element analysis of laminated composite plates. Int J Num Meth Eng, 1979, 14: 69-79
    Panfilov AV, Holden AV eds., Computational biology of the heart, John Wily & Sons. Chichester, England, 1997.
    Pao YC, Ritman EL, Woods EH. Finite element analysis of left ventricular myocardial stress. J Biomech. 1974,7: 469-477.
    Pao YC, Robb RA, Ritman EL.,et al. Plain-strain finite-element analysis of reconstructed diastolic left ventricular cross-section. Ann Biomed Eng. 1976,4:232-249.
    Pao YC, Ritman EL. Viscoelastic fibrous finite element, dynamic analysis of the beating heart. Proc Symp Appl Comput Methods. 1977,477-486.
    Pao YC, Ritman EL. Comparative characterization of the infarcted and reperfused ventricular wall muscle by finite element analysis and a myocardial muscle-blood composite model. Comput Biomed Res. 1998,31:18-31.
    Park J, Metaxas D, Axel L. Analysis of left ventricular wall motion based on volumetric deformable models and MRI_SPAMM. Medical Imaging Analysis. 1996,1(1) : 53-71.
    Park J, Metaxas D, Young AA, et al. Deformation model s with parameter functions for cardiac motion analysis from tagged MRI data. IEEE Med Imag. 1996,15(3) : 278-289.
    Park J., Metaxas DN., Axel L. Quantification and visualization of the 3D nonrigid motion of the left ventricle. SPIE, 1997, 3033: 298-308.
    Parmley WW, Sonnenblick EH. Series elasticity of heart muscle: Its relations to contractile element velocity and
    
    
     proposed muscle models. Circ Res. 1967,20: 112-123.
    Parmley WW, Chuck L,Kivowitz C, et al. In vivo length-tension relations of human ventricular aneurysms. Am J Cardiol 1973, 32: 889-894.
    Patterson RE, Kirk ES. Coronary steal mechanisms in dogs with one-vessel occlusion and other arteries normal. Circ. 1983, 67: 1009-1015.
    Pentland A, Sclaroff S,. Closed-form solutions for physically based shape modeling and recognition. IEEE Trans Pattern Analysis and Machine Intelligence. (PAMI). 1991,13(7) : 715-729.
    Perl, M.,Horowitz,A.and Sideman.S. Comprehensive model for the description of left ventricle mechanics: Part 1. model description and simulation procedure. Med. Biol.Engng Comput. 1986,24,145-149.
    Pfeffer MA, Braunwald E. Ventricular remodeling after myocardial infarction. Experimental observations and clinical implications. Circulation. 1990, 81: 1161-1172.
    Pierce WH. Body forces and pressures in elastic models of the myocardium. Biophys J. 1981, 34: 35-59.
    Pilkington T.C.,et al. A comparison of finite element and integral formulations for the calculation of electrocardiographic potentials. IEEE Tans. On BME. 1985;32:166-177
    Pinto JG, Fung YC. Mechanical properties of the heart muscle in the passive state. J Biomechanics. 1973a, 6: 597-616.
    Pinto JG, Fung YC. Mechanical properties of stimulated papillary muscle in quick-release experiment. J Biomechanics. 1973b, 6: 617-630.
    Pinto JG. Some mechanical consideration in the selection and testing of papillary muscle. ASME J Biomech Engng. 1980,102(1) : 61-66.
    Pinto JG. A constitutive description of contracting papillary muscle and its implications to the dynamics of the intact heart. ASME J Biomech. 1987,109:181-191
    Plonsey R, Barr RC. Mathematical modeling of electrical activity of the heart. J Electrocardiol. 1987, 20: 219-226.
    Pollack GH, Huntsman LL, Verdugo P. Circ Res. 1972, 31: 569-579.
    Pollard AE, et al. Computer simulation of activation in an anatomically based model of the human ventricular conduction system. IEEE Trans.On BME. 1991,38:982-996
    Purcell C.,et al. Moving dipole inverse solutions using realistic torso models. IEEE Trans. On BME. 1991;38:82-93
    Reichek N, Wilson J, Sutton MSJ, et al. Noninvasive determination of left ventricular end-systolic stress: validation of the method and initial application. Circulation. 1982:65: 99-108.
    Reichek N. Magnetic resonance imaging for assessment of myocardial function. Magnetic Resonance Quarterly. 1991,7:255-274.
    Rosenberg et al, "A new mathematical model of electrical cardiac activity", Math. Biosic., 14,1972
    Ross MA, Streeter DD Nonuniform subendocardial fiber orientation in the normal macaque left ventricule. Eur J Cardiol. 1975, 3: 229-247.
    Rudy Y. & Plonsey R. The eccentric spheres models as the basis for a study of the geometry and inhomogeneities in electrocardiography. IEEE Trans. On BME. 1979;7:392-399
    Sagawa K. The ventricular pressure-volume diagram revisited. Circ Res. 1978,43:677-687.
    Sandier H, Alderman E Left ventriclar tension and stress in man. Circ Res. 1963,13:91-104.
    Sarnoff SJ,Braunwald E, Welch JR, et al. Hemodynamic determinants of oxygen consumption of the heart with specical reference to the tension time index. Am J physiol. 1958,192:148-156.
    
    
    
    Scott CH, Sutton MS, Gusani FN, et al. Effect of dobutamine on regional left ventricular function measured by tagged magnetic resonance imaging in normal subjects. Am J cardiol. 1999, S3:412-417.
    Selvester R.H et al, "Digital computer model of a total body ECG surface map",Circ.,Vol.38,1968
    Selvester R.H. et al, "Computer simulation of the ECG" , Computer Tech. in Cardiolog, Cady, L.D., Ed., Marcel Dekker, New York, 1979, Chap.9
    Shahidi A.V.,et al. Forward and inverse problem of electrocardigraphy:modeling and recovery of epicardial potentials in human. IEEE Trans. On BME. 1994;41-249-256
    Shi P, Amini A, Robinson G, et al. Shape-based 4D left ventricular myocardial function analysis. Proc IEEE Workshop on Biomedical Image Analysis. 1994, (Seattle, WA): 88-97.
    Sonnen blick EH. Force-velocity relations in mammalian heart muscle. Am J Physiol. 1962,202:931-939.
    Sonnenblick, EH. Series elastic and contractile elements in heart muscle: change in muscle length Am J Physiol. 1964,207: 1330-1338
    Spurgeon HA,Thome PR, Yin FCP, et al Increased dynamic stiffness of trabeculae cameae from senescent rats. Am J physiol. 1977,232-H373-H380.
    Stanley P.C.,et al. The combination method . a numerical technique for electrocardiographic calculations. IEEE Trans.On BME. 1989;36:456-461
    Streeter DD, Bassett DL. An engineering analysis of myocardial fiber orientation in pig's left ventricle in systole. Aaat. Rec. 1966,155: 503-511.
    Streeter, DD., Spotnitz HM, Patel DP, et al. Fiber orientation in the canine left ventricle during diastole and systole Circ Res. 1969,24:339-347.
    Streeter DD, Vaisnav RN, Patel DJ, et al. Stress Distribution in the canine left ventricle during diastole and systole. Biophys J 1970,10: 345-363.
    Streeter, DD. , Powers WE, Ross MA. ,et al. Three-dimensional fiber orientation in mammalian left ventricular wall,In Cardiovascular System Dynamics(Edited by Baan, J., et al.). 1978,73-84. MIT Press.Cambridge
    Streeter, DD. Gross morphology and fiber geometry of the heart In Handbook of physiology-The Cardiovascular system I, "Vol 1. The Heart, Ch 4, 61-112. Am Physiol Soc. Bethesda, MD., 1979.
    Suga H, Sagawa K Instantaneous pressure-volume relationships and their ratio in the excised, supported canine left ventricle. Circ Res. 1974, 35:117-126.
    Suga H. Total mechanical energy of a ventricle model and cardiac oxygen consumption. Am J Physiol. 1979,236: H498-H505.
    Sunagawa K, Maughan WL, Sagawa ES. Effect of regional ischaemia on the left ventricular end-systolic pressure-volume relationship of isolated canine hearts Circ Res. 1983,52:170-178.
    Suzuki K, et al. Revalution of the vectorcardiographic criteria in case of myocardial infarction: a comparative study of the vectorcardiogram, the left ventriculogram and the scitigram. J Electrocardiol, 1980,13:253-259
    Swan HJC. Left ventricular systolic and diastolic dysfunction in the acute phase of myocardial ischemia and infarction, and in the later phases of recovery, function follows morphology. Eur Heart J. 1993,14(suppl. A ): 48-56.
    Taber LA. On a nonlinear theory for muscle shells part 1-theoretical development Trans ASME J Biomech Engng. 1991, 113 56-62.
    Taber LA. On a nonlinear theory for muscle shells: part 2-application to the beating left ventricle. Trans ASME J Biomech Engng. 1991,113:63-71.
    Tani J.Yamamoto H, Honda H, et al. Estimation of left ventricular myocardial elasticity and viscosity by a thick-walled spherical model. Med. Biol. Eng. Comput., 1993 ,31: 325-332.
    Taratorin AM, Sideman S, Beyar R. 3D dynamic functional mapping of cardiac mechanics. SPIE. 1993, 1905:
    
     294-306.
    Templeton GH, Donald TC, Mitchell JH, et al. Dynamic stiffness of papillary muscle during contraction and relaxation. Am J Physiol. 1973,224:693-698.
    Tennant R, Wiggers CJ.The effect of coronary occlusion on myocardial contraction. Am J Physol. 1935, 112: 351-3561.
    Terzopoulos D, Metaxas D. Dynamic 3D models with local and global deformations: Deformation superquadrics. IEEE Trans on Pattern Analysis and Machine Intelligence. 1991,13(7) : 703-729.
    Theroux P, Ross J, Frankin D, et al. Regional myocardial function in the conscious dog during acute coronary occlusion and responses to morphine, propranolol, Nitroglycerin, and lidocaine. Circ. 1976, 53: 302-314.
    Theroux P, Ross JJ, Frankin D, et al. Regional myocardial function and dimensions early and late after myocardial infarction in the unanesthetized dog. Cir Res. 1977,40: 158-165.
    Torrent-Guasp F. The cardiac muscle. Fundacin Juan, Madrid. 1973.
    Tozeren A. Static analysis of the left ventricle. Trans ASME, J Biomech Engng. 1983,105: 39-46.
    Throne RD.,et al. A generalized eigensystem approach to the inverse problem of electrocardiography. IEEE Trans. On BME. 1994;41:592-600
    Thiry P.s. et al, "On electrophysiological activity of the normal heart" , J Franklin Inst., Vol.297, pp.377,1974
    Van Campen DH, Huyghe JM, Bovendeerd PHM, et al. : Biomechanics of the heart muscle. Eur J Mech A/Solids, 1994,13(4-suppl): 19-41.
    Van Capelle et al, "Computer simulation of arrhythmias in network of coupled excitable element", Circ. Res., 47, 1980
    Von dec Pol et al, "The heart beat considered as a relaxation oscillation and an electrical model of the heart" , Philos. Mag., 6,1928
    Van der Broek JHJM, Vab der Brok MHLM. Application of an ellipsoidal heart model in studying left ventricular contractions. J Biomech 1979,13:493-503.
    Van Dijk, P. Direct cardiac NMR imaging of heart wall and blood flow velocity. J Comput Assist Tomogr. 1984,8: 429-436.
    Wagner, GS, et al. Evaluation of a QRS scoring system for estimating myocardial infact size. Circulation. 1982,65(2) : 342-347
    Waller A.D., "On the electromotive changes connected with the beat of the mammalian heart and of the human heart in particular", Philos. Trans.R.Soc.London Ser.B.Vol. 180, pp. 169-, 1889
    Waldman LK, Fung YC, Covell JW, et al. Transmural myocardial deformation in the canine left ventricle: normal in vivo three-dimensional finite strain. Circ Res. 1985, 57:152-163.
    Waldman LK, Nosan D, Villarreal F J, et al. Relation between transmural deformation and local myodiber direction in canine left ventricle. Cir Res. 1988,63:550-562.
    Wang JJ, Li JKL, Drzewiecki G Analysis of effect of two concurrent ischaemic zones on left ventricular function . Med Biol Eng Comput., 1996, 34,477-480.
    Weber KT, Janicki JS. The heart as a muscle pump system and the concept of heart failure. Am Heart J, 1979, 98: 371-384.
    Weisman HF, Bush DE, Mannisi JA, et al. Global cardiac remodeling after acute myocardial infarction: a study in the rat model. JACC. 1985, 5: 1355-1362.
    Weiss M, Forrester W. A model for the assessment of left ventricular compliance: the effects of hypertrophy and infarction. Cardvasc Res. 1975, 9: 544-553.
    
    
    
    Willson et al, "The distribution of the currents of action and of injury displayed by heart muscle and other excitable tissues", Univ. of Michigan Press, Ann Arbor, 1933
    Wong AYK, Rautaharju PM. Stress distribution within the left ventricular wall approximated as a thick ellipsoidel shell. Am Heart J. 1968, 75: 649~662.
    Woods RH. A few application of physical theorem to membranes in the human body in a state of tension. J Anat Physiol. 1892, 26: 362~370.
    Yettram AL, Vinson Ca, Glibson GD. Computer modeling of the human left ventricle. Trans ASME,1982, 104:148~152.
    Yettram AL.,Vinson CA, Gibson DG. Effect of myocardial fiber architecture on the behavior of the human left ventricle in diastole. J Biomed Engng. 1983, 5: 321~328.
    Yettram AL., Beecham MC. An analytical method for determination of along-fiber to cross-fiber elastic modulus ration in ventricular myocardium—a feasibility study. Med Eng phys, 1998, 20:103~108 Yin FCP. Circulation Research. 1981,49(4): 829~842.
    Yin FCP Application of the finite element method to ventricular mechanics. CRC Critical Review in Biomed Engng. 1985,4:311~342
    Young AA, Axel L. Three-dimensional motion and deforamtion of the heart wall: estimation with spatial modulation of magnetization—a model-based approach. Radiology. 1992, 185: 241~247.
    Young AA, Imai H, Chang CN, et al. Two-dimensional left ventricular deformation during systole using magnetic resonance imaging with spatial modulation of magnetization. Circulation. 1994, 89: 740~752.
    Young AA, Kraitvhman DL, Dougherty L, et al. Tracking and finite element analysis of stripe deformation in magnetic resonance tagging. IEEE Med Imag. 1995 14(3): 413~421.
    Zerhouni EA, Parish DM, Rogers WJ, et al. Human heart tagging with MRI imagins-a method for noninvasive assessment of myocardial motion. Radiology. 1988, 169: 59~63.
    吕维雪,符影杰,徐振耀.心电图QRST波仿真模型的构造与实现.中国科学(B集),1991,11:1201~1208.
    段云所.室性心律仿真建模与算法研究及心律失常机理探讨.浙江大学博士学位论文.1995,6.
    段云所,夏灵,吕维雪.心肌电特性参数对心律影响的定量仿真研究.中国生物医学工程学报.1998,17(4):310~319.
    符影杰.心电场仿真研究.浙江大学博士学位论文.1990,6.
    徐振耀.心脏电活动的计算机仿真研究.浙江大学博士学位论文.1991,1.
    夏灵.基于心电仿真模型参数解的心电逆向问题研究.浙江大学博士学位论文.1995,12.
    夏灵,吕维雪.基于虚拟心脏的心电逆向题求解.中国生物医学工程学报.1998,17(1):302~309.
    肖国臻.基于不均匀性和各相异性的计算机虚拟心脏模型.浙江大学博士学位论文.1997,4.
    李光林.基于虚拟心脏仿真模型的心电场逆问题的研究.浙江大学博士学位论文.1997,4.
    刘锋.左心室三维有限元力学心脏模型的建立及其应用.浙江大学博士学位论文 1999,12.
    李光林,吕维雪.从体表电位分布图提取陈旧性心肌梗塞诊断信息的研究.生物物理学报,1998,14(2):289~295.
    冯元桢.生物力学.科学出版社,1983.
    刁颖敏.生物力学的原理与应用.同济大学出版社,1991.
    丁光宏 张心忠 李惜惜 柳兆荣.心脏与血管相互耦合的动力原理—分布参数模型.水动
    
    
    陈灏珠,李宗明.内科学(第三版).人民卫生出版社,1990.
    李广生,王凡.心肌病理学.上海科学技术出版社,1983.
    戴瑞鸿.心肌梗塞.上海科技出版社,1987:37~47.
    山东医学院附属医院 实用心电图学 山东科学技术出版社,1979
    德田正孝.心脏左心室力学的机能评伵数值构造 日本机械学会论文集(A编),1994,60:2478~2483.
    R.M.琼斯 复合材料力学.上海科学技术出版社,1981.
    王成勖,邵敏.有限单元法基本原理和数值方法.清华大学出版社,1997.
    K.J巴特.有限元分析中的数值方法.科学出版社,1985.
    黄光远,刘维倩,刘小军.反问题与计算力学.计算结构力学及其应用.1993,10(3):302~306.
    曾建超,俞志和.虚拟现实的技术与应用.清华大学出版社,1996.
    汪成为,高文,王行仁.灵境技术的理论、实践和应用.清华大学出版社,1996.
    潘爱民.COM原理与应用 清华大学出版社,2000.

© 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