Computational modelling of biological systems: tools and visions

We are currently witnessing the advent of a revolutionary new tool for biomedical research. Complex biochemically, biophysically and pharmacologically detailed mathematical models of ‘living cells’ are being arranged in morphologically representative tissue assemblies, and, using large–scale supercomputers, utilized to produce anatomically structured models of integrated tissue and organ function. This provides biomedical sciences with a radical new tool: ‘in silico’ organs, organ systems and, ultimately, organisms. In silico models will be a crucial tool for biomedical research and development in the new millennium, extracting knowledge from the vast amount of increasingly detailed data, and integrating this into a comprehensive analytical description of biological function with predictive power: the Physiome. Our review will illustrate this approach using the example of the cardiovascular system, which, along with neurophysiology, has been at the forefront of analytical bio–mathematical modelling for many years, and which is about to deliver the first anatomico–physiological model of a whole organ. Already, electrophysiologically detailed cardiac cell models have been incorporated into mathematical descriptions of representative ventricular tissue architecture and anatomy, including the coronary vasculature, and assimilated to realistic representation of ventricular active and passive mechanical properties. This is being extended by matching atrial models and linked to an artificial torso to compute the body surface electrocardiogram as a function of sub–cellular activity during various (patho–)physiological conditions. We will illustrate the utility of in silico biological research in the context of refinement and partial replacement of in vivo and in vitro experimental work, show the potential of this approach for devising patient–specific treatment strategies, and try to forecast the impact of this new technology on biomedical research, health–care, and related industries.

[1]  D. Noble.  A modification of the Hodgkin—Huxley equations applicable to Purkinje fibre action and pacemaker potentials , 1962, The Journal of physiology.

[2]  A V Holden,et al.  Re-entrant activity and its control in a model of mammalian ventricular tissue , 1996, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[3]  D. Noble.  Cardiac Action and Pacemaker Potentials based on the Hodgkin-Huxley Equations , 1960, Nature.

[4]  R. Winslow,et al.  Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. , 1998, Biophysical journal.

[5]  F. P. Mall,et al.  On the muscular architecture of the ventricles of the human heart , 1911 .

[6]  J. Cohn,et al.  The effect of carvedilol on morbidity and mortality in patients with chronic heart failure. U.S. Carvedilol Heart Failure Study Group. , 1996, The New England journal of medicine.

[7]  P. Hunter,et al.  Modelling the mechanical properties of cardiac muscle. , 1998, Progress in biophysics and molecular biology.

[8]  D DiFrancesco,et al.  Reciprocal role of the inward currents ib, Na and if in controlling and stabilizing pacemaker frequency of rabbit sino-atrial node cells , 1992, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[9]  Denis Noble,et al.  The development of mathematical models of the heart , 1995 .

[10]  Peter Grindrod,et al.  One-way blocks in excitable media , 1995 .

[11]  P Kohl,et al.  Mechanosensitive connective tissue: potential influence on heart rhythm. , 1996, Cardiovascular research.

[12]  A. George,et al.  Molecular mechanism for an inherited cardiac arrhythmia , 1995, Nature.

[13]  M. Janse,et al.  Electrophysiological mechanisms of ventricular arrhythmias resulting from myocardial ischemia and infarction. , 1989, Physiological reviews.

[14]  José Jalife,et al.  Measurements of curvature in an ionic model of cardiac tissu , 1995 .

[15]  D. Noble,et al.  Improved guinea-pig ventricular cell model incorporating a diadic space, IKr and IKs, and length- and tension-dependent processes. , 1998, The Canadian journal of cardiology.

[16]  J Malmivuo,et al.  Detailed model of the thorax as a volume conductor based on the visible human man data. , 1998, Journal of medical engineering & technology.

[17]  J. Clark,et al.  A model of the action potential and underlying membrane currents in a rabbit atrial cell. , 1996, The American journal of physiology.

[18]  Nicolas Peter Smith.  Coronary flow mechanics: an anatomically based mathematical model of coronary blood flow coupled to cardiac contraction , 1999 .

[19]  A V Holden,et al.  Qualitative modeling of mechanoelectrical feedback in a ventricular cell. , 1997, Bulletin of mathematical biology.

[20]  Q Gan,et al.  Neural modeling with dynamically adjustable threshold and refractory period. , 1992, Bio Systems.

[21]  D P Corey,et al.  Theoretical reconstruction of myotonia and paralysis caused by incomplete inactivation of sodium channels. , 1993, Biophysical journal.

[22]  P J Hunter,et al.  A three-dimensional finite element method for large elastic deformations of ventricular myocardium: II--Prolate spheroidal coordinates. , 1996, Journal of biomechanical engineering.

[23]  Y. Lai,et al.  Generation and propagation of normal and abnormal pacemaker activity in network models of cardiac sinus node and atrium , 1995 .

[24]  P Kohl,et al.  Mechanosensitive fibroblasts in the sino‐atrial node region of rat heart: interaction with cardiomyocytes and possible role , 1994, Experimental physiology.

[25]  J C Hancox,et al.  Alteration of HERG current profile during the cardiac ventricular action potential, following a pore mutation. , 1998, Biochemical and biophysical research communications.

[26]  R L Winslow,et al.  Modeling the cellular basis of altered excitation-contraction coupling in heart failure. , 1998, Progress in biophysics and molecular biology.

[27]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[28]  T. Chay,et al.  Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic beta-cells. , 1997, Biophysical journal.

[29]  M J Janse,et al.  Morphology and electrophysiology of the mammalian atrioventricular node. , 1988, Physiological reviews.

[30]  E. Zerhouni,et al.  Human heart: tagging with MR imaging--a method for noninvasive assessment of myocardial motion. , 1988, Radiology.

[31]  P Kohl,et al.  Cellular mechanisms of cardiac mechano-electric feedback in a mathematical model. , 1998, The Canadian journal of cardiology.

[32]  C. Luo,et al.  A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. , 1994, Circulation research.

[33]  Arun V. Holden,et al.  Mathematics: The restless heart of a spiral , 1997, Nature.

[34]  J. Clark,et al.  Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization. , 1998, Circulation research.

[35]  D. Noble,et al.  Effects of gap junction conductance on dynamics of sinoatrial node cells: two-cell and large-scale network models , 1994, IEEE Transactions on Biomedical Engineering.

[36]  P. Hunter,et al.  Stretch-induced changes in heart rate and rhythm: clinical observations, experiments and mathematical models. , 1999, Progress in biophysics and molecular biology.

[37]  Howard A. Frank,et al.  EXTERNAL MECHANICAL CARDIAC STIMULATION , 1976 .

[38]  D. L. Bassett,et al.  An engineering analysis of myocardial fiber orientation in pig's left ventricle in systole , 1966 .

[39]  D Noble,et al.  Modelling of sodium-overload arrhythmias and their suppression. , 1998, The Canadian journal of cardiology.

[40]  K. Clarke,et al.  Energy metabolism and contractile function in rat heart during graded, isovolumic perfusion using 31P nuclear magnetic resonance spectroscopy. , 1987, Journal of molecular and cellular cardiology.

[41]  W H Lamers,et al.  Immunohistochemical delineation of the conduction system. I: The sinoatrial node. , 1993, Circulation research.

[42]  Denis Noble,et al.  The Logic of life : the challenge of integrative physiology , 1993 .

[43]  Gul'ko Fb,et al.  Mechanism of formation of closed propagation pathways in excitable media , 1972 .

[44]  D Durrer,et al.  Computer Simulation of Arrhythmias in a Network of Coupled Excitable Elements , 1980, Circulation research.

[45]  D Ghista,et al.  In vivo stresses in the human left ventricular wall: analysis accounting for the irregular 3-dimensional geometry and comparison with idealised geometry analyses. , 1972, Journal of biomechanics.

[46]  G. Bock,et al.  The Limits of Reductionism in Biology , 1998 .

[47]  N. Maglaveras,et al.  Unidirectional block in cardiac fibers: effects of discontinuities in coupling resistance and spatial changes in resting membrane potential in a computer simulation study , 1992, IEEE Transactions on Biomedical Engineering.

[48]  G. Tomaselli,et al.  Structure and function of voltage‐gated sodium channels , 1998, The Journal of physiology.

[49]  M J Janse,et al.  Why does atrial fibrillation occur? , 1997, European heart journal.

[50]  P. Hunter,et al.  Laminar structure of the heart: a mathematical model. , 1997, The American journal of physiology.

[51]  R L Winslow,et al.  Comparison of putative cooperative mechanisms in cardiac muscle : length dependence and dynamic responses , 1999 .

[52]  Teresa Ree Chay,et al.  Modeling Slowly Bursting Neurons via Calcium Store and Voltage-Independent Calcium Current , 1996, Neural Computation.

[53]  A. Varghese,et al.  Modeling the functional role of SA node-atrial interdigitation , 1994, Computers in Cardiology 1994.

[54]  D. Noble,et al.  The ionic currents underlying pacemaker activity in rabbit sino-atrial node: experimental results and computer simulations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[55]  M Delmar,et al.  Immunohistochemical Localization of Gap Junction Protein Channels in Hamster Sinoatrial Node in Correlation with Electrophysiologic Mapping of the Pacemaker Region , 1994, Journal of cardiovascular electrophysiology.

[56]  J. Onuchic,et al.  Theory of protein folding: the energy landscape perspective. , 1997, Annual review of physical chemistry.

[57]  Balth van der Pol Jun Docts. Sc.,et al.  LXXII. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart , 1928 .

[58]  F B Gul'ko,et al.  [Mechanism of formation of closed propagation pathways in excitable media]. , 1972, Biofizika.

[59]  F. M.,et al.  The Concise Oxford Dictionary of Current English , 1929, Nature.

[60]  T Opthof,et al.  Functional morphology of the mammalian sinuatrial node. , 1987, European heart journal.

[61]  A V Holden,et al.  Computer simulation of re-entry sources in myocardium in two and three dimensions. , 1993, Journal of theoretical biology.

[62]  Jamie Goode,et al.  Novartis Foundation Symposium 213 - The Limits of Reductionism in Biology , 1998 .

[63]  J M Dieudonné.  The left ventricle as confocal prolate spheroids. , 1969, The Bulletin of mathematical biophysics.

[64]  Henggui Zhang,et al.  Spiral wave breakdown in an excitable medium model of cardiac tissue , 1995 .

[65]  V. Fast,et al.  Cardiac tissue geometry as a determinant of unidirectional conduction block: assessment of microscopic excitation spread by optical mapping in patterned cell cultures and in a computer model. , 1995, Cardiovascular research.

[66]  M Lei,et al.  Swelling-induced decrease in spontaneous pacemaker activity of rabbit isolated sino-atrial node cells. , 1998, Acta physiologica Scandinavica.

[67]  D. Noble,et al.  Modelling myocardial ischaemia and reperfusion. , 1998, Progress in biophysics and molecular biology.

[68]  R L Winslow,et al.  Dynamics of abnormal pacemaking activity in cardiac Purkinje fibers. , 1994, Journal of theoretical biology.

[69]  土肥 一夫,et al.  The Concise Oxford Dictionary of Current Englishと英和辞典 , 2001 .

[70]  Arthur J Moss,et al.  SCN5A mutations associated with an inherited cardiac arrhythmia, long QT syndrome , 1995, Cell.

[71]  A. Winfree,et al.  Electrical turbulence in three-dimensional heart muscle. , 1994, Science.

[72]  T. Chay,et al.  Modelling receptor-controlled intracellular calcium oscillators. , 1991, Cell calcium.

[73]  A. Grimm,et al.  Deformation of the diastolic left ventricle. Nonlinear elastic effects. , 1973, Biophysical journal.

[74]  G S Kassab,et al.  Morphometry of pig coronary arterial trees. , 1993, The American journal of physiology.

[75]  M J Lab,et al.  Contraction-excitation feedback in myocardium. Physiological basis and clinical relevance. , 1982, Circulation research.

[76]  Denis Noble,et al.  Simulating cardiac sinus and atrial network dynamics on the Connection Machine , 1993 .

[77]  R. Winslow,et al.  Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, II: model studies. , 1999, Circulation research.

[78]  J B Bassingthwaighte,et al.  Blood flows and metabolic components of the cardiome. , 1998, Progress in biophysics and molecular biology.

[79]  D. Noble,et al.  A model of the single atrial cell: relation between calcium current and calcium release , 1990, Proceedings of the Royal Society of London. B. Biological Sciences.

[80]  A. Young,et al.  Right ventricular midwall surface motion and deformation using magnetic resonance tagging. , 1996, The American journal of physiology.

[81]  P. Hunter,et al.  The analysis of cardiac function: a continuum approach. , 1988, Progress in biophysics and molecular biology.

[82]  J. Clark,et al.  A mathematical model of a rabbit sinoatrial node cell. , 1994, The American journal of physiology.

[83]  E McVeigh,et al.  Model studies of the role of mechano-sensitive currents in the generation of cardiac arrhythmias. , 1998, Journal of theoretical biology.

[84]  W. Rogers,et al.  Preliminary report: effect of encainide and flecainide on mortality in a randomized trial of arrhythmia suppression after myocardial infarction. , 1989, The New England journal of medicine.

[85]  Rolf Kötter,et al.  Striatal mechanisms in Parkinson's disease: new insights from computer modeling , 1998, Artif. Intell. Medicine.

[86]  R Wilders,et al.  Action potential conduction between a ventricular cell model and an isolated ventricular cell. , 1996, Biophysical journal.

[87]  P. Hunter,et al.  Myocardial constitutive laws for continuum mechanics models of the heart. , 1995, Advances in experimental medicine and biology.

[88]  D. Noble,et al.  Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of basic cellular mechanisms , 1987, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[89]  J B Bassingthwaighte,et al.  Toward modeling the human physionome. , 1995, Advances in experimental medicine and biology.

[90]  D DiFrancesco,et al.  A model of cardiac electrical activity incorporating ionic pumps and concentration changes. , 1985, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[91]  G. W. Beeler,et al.  Reconstruction of the action potential of ventricular myocardial fibres , 1977, The Journal of physiology.

[92]  R. FitzHugh.  Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations , 1960, The Journal of general physiology.

[93]  P. Ursell,et al.  Structural and Electrophysiological Changes in the Epicardial Border Zone of Canine Myocardial Infarcts during Infarct Healing , 1985, Circulation research.

[94]  G. Breithardt,et al.  Genetic basis and molecular mechanism for idiopathic ventricular fibrillation , 1998, Nature.

[95]  Frederick Sachs,et al.  Modeling Mechanical-Electrical Transduction in the Heart , 1994 .

[96]  H. Jongsma,et al.  Sudden cardiac death: A matter of faulty ion channels? , 1998, Current Biology.