- Email: [email protected]
Modeling the human cardiome in silico
EDITORIAL Modeling the human cardiome in silico Andrew D. McCulloch, PhD
The past two decades have seen impressive success for reductionist biologic science, generating new experimental data at an unprecedented rate. The list of organisms with completely sequenced genomes is growing each month. In June, the completion of a draft sequence of the entire human genome was announced amid much fanfare. Molecular mechanisms for fundamental processes such as ligand-receptor interactions and signal transduction are being elucidated in exquisite structural detail. However, as attention turns to the next phases, such as cataloging protein structures (proteomics), it is clear to biologists that the challenge is much greater than assigning functions to individual genes. Most cell functions require the coordinated interaction of numerous gene products. Metabolic or signaling pathways, for example, can be considered the expression of a “genetic circuit,” a wiring diagram for cellular function.1 And the layers of complexity do not end at the plasma membrane. Tissue and organ functions require the interactions of large ensembles of cells in functional units and networks.2 No amount of biochemical or cellular detail is sufficient to completely describe a ventricular arrhythmia, for example. Ventricular anatomic properties are equally important. To identify the comprehensive approach that will be needed to reintegrate molecular and genetic data into a quantitative understanding of physiology and pathophysiology in the whole organism, Bassingthwaighte3 coined the term “physiome.” Literally, the term reflects an integrative approach to physiology, meaning life (“physio”) as a whole (“ome”). The Physiome Project (http://www.physiome.org/) was conceived as a multicenter, international collaboration to coordinate integrative studies of quantitative physiologic function. The project was endorsed in 1997 by the International Union of Physiological Sciences at a conFrom the Department of Bioengineering, the Whitaker Institute of Biomedical Engineering, La Jolla, Calif. Reprint requests: Andrew D. McCulloch, Department of Bioengineering, the Whitaker Institute of Biomedical Engineering, University of California-San Diego, 9500 Gilman Dr, La Jolla, CA 92093-0412; [email protected]. J Nucl Cardiol 2000;7:496-9. Copyright © 2000 by the American Society of Nuclear Cardiology. 1071-3581/2000/$12.00 + 0 43/39/109682 doi:10.1067/mnc.2000.109682 496
ference in St. Petersburg, Russia, called “On Designing the Physiome Project.” In addition, the Physiome Project is recognized by organizations such as the American Institute of Medical and Biological Engineering. In April 1998, the first Microcirculation Physiome Project Working Group Meeting was held as a satellite to the “Experimental Biology ‘98” meeting, and more than 100 scientists attended. In September 1999, a similar number of participants attended the “Physiome Symposium: Integrated Biology of the Heart” in Seattle, Washington. The Physiome Project has two major goals: the cataloging of physiologic information into databases for online query and retrieval and the systematic organization of those data into quantitative models of integrated systems.3 The long-range goal is to improve the understanding of human physiology and pathophysiology by integrating quantitative information both vertically across scales of biologic organization from genome to organism and horizontally across interacting physiologic functions and processes. Projects such as the Human Genome Project and its spin-offs have generated hundreds of databases of molecular sequence and structure information such as GenBank (http://www.ncbi.nlm.nih.gov/Genbank/) and the Protein Data Bank (http://www.rcsb.org/pdb/). These databases in turn have generated demand for online tools for data-mining, homology searching, sequence alignment, and numerous other analyses. One of the best entry points for those interested in the burgeoning field of bioinformatics is the National Center for Biotechnology Information Web site (http://www.ncbi.nlm.nih.gov/). In contrast, a major obstacle to the progress of the Physiome Project is the lack of databases for the morphology and physiologic function of cells, tissues, and organs. Although there are, for example, some excellent databases of metabolic pathways such as the Metabolic Pathways Database (MPW) (http://wit.mcs.anl.gov/MPW/) and the Kyoto Encyclopedia of Genes and Genomes (KEGG) (http://www.genome.ad.jp/kegg/), there are not yet comprehensive public databases of myocyte ion channel kinetics or coronary vascular structure. This is one reason that the Physiome Project has focused on developing integrated theoretical and computational models. Models, even incomplete ones, can provide a formal framework for classifying and organizing data derived from experimental biology, particularly
Journal of Nuclear Cardiology Volume 7, Number 5;496-9
McCulloch Modeling the human cardiome in silico
497
Figure 1. Some major functional subsystems of the cardiome.
those data that serve as model parameters. With numeric models to simulate interacting processes, researchers can reveal emergent properties of the system, test prediction against experimental observation, and define the specific needs for new experimental studies. The integrated models have the potential to support and inform decisions about drug design, gene-targeting, biomedical engineering, and clinical diagnosis and management. Such integrative modeling will require a combination of analysis on the basis of physicochemical first principles and systems engineering approaches by which information can be communicated between different subsystems and across hierarchies of the integrated system. Systems models also provide a means to include necessary subsystems, which are not yet characterized in sufficient detail to be modeled from first principles, within the integrated system. This effort will in turn demand new software tools for model implementation, interoperation, and validation. It will also require a large and dedicated multidisciplinary community of scientists to accept the tedious chore of defining ontologies and standards for physiologic data representation and modeling. The Cardiome Project Within the Physiome Project, there will therefore be many subprojects concerning specific organ systems. The aims of the Cardiome Project should sound a familiar tone to the nuclear cardiologist: to integrate data and models on the anatomy and structure, hemodynamics and metabolism, mechanics and electrophysiology, and regulation and control of the normal and diseased heart. The whole Cardiome Project is envisaged as a largescale multidisciplinary, multicenter effort.4 Its beginnings were presented by Glass et al5 and Noble.6 The challenges of integrating models of many aspects of
such an organ system, including its structure, anatomy, biochemistry, control systems, hemodynamics, mechanics, and electrophysiology, have been the theme of recent workshops.7 Some of the major components of the cardiome for which computational models have been developed recently include ventricular anatomy and fiber structure,8 coronary network topology and hemodynamics,9,10 oxygen transport and substrate delivery,11 myocyte metabolism,12 ionic currents,6,13 impulse propagation,14 excitation-contraction coupling,15 neural control of heart rate and blood pressure,16 cross-bridge cycling,17 tissue mechanics,18 cardiac fluid dynamics and valve mechanics,19 and ventricular growth and remodeling.20 Of particular interest to the nuclear cardiologist are whole-organ, lumped-parameter models describing transport and exchange of substrates and accounting for the spatial distribution of the coronary arteries, regional myocardial blood flows, and uptake and metabolism of glucose, fatty acids, and oxygen used for the energy to form adenosine triphosphate, which is in turn used to fuel the work of contraction and ion pumping. Data from nuclear medicine have been essential in this area both for estimating the kinetic parameters of mass transport in the heart and for providing independent measurements with which to validate such models. A unique resource for nuclear cardiologists interested in numerical models and simulation for circulatory mass transport and exchange is the National Simulation Resource (http://nsr.bioeng.washington.edu). Indeed, cardiac imaging in general has a crucial role in the Cardiome Project. If models built from data on structural and functional building blocks are to be integrated into anatomically detailed 3-dimensional simulations, they must be validated independently, with functional data from the intact heart. If such models are to find clinical application, it will be necessary to build
498
McCulloch Modeling the human cardiome in silico
patient-specific simulations from clinically accessible data. For example, we have developed parametric computational techniques for modeling the mechanics, transport processes, and electrophysiology of the heart wall as a 3-dimensional anisotropic material continuum, while incorporating kinetic and structural information from the cellular level. These models rely on representations of 3dimensional ventricular geometry and fiber architecture, which are increasingly being derived from imaging modalities such as magnetic resonance imaging. To explore how these models can be extended and integrated with others, we have defined 6 major functional modules for initial attention in the Cardiome Project (Figure 1).4 They are: 1. Coronary artery anatomy and regional myocardial flows for substrate and oxygen delivery 2. Metabolism of the substrate for energy metabolism, fatty acid and glucose, the tricarboxylic acid cycle, and oxidative phosphorylation 3. Purine nucleoside and purine nucleotide metabolism, describing the formation of adenosine triphosphate and the regulation of its degradation to adenosine in endothelial cells and myocytes and its effects on coronary vascular resistance 4. Excitation-contraction coupling: calcium release and reuptake and the relations between these and the strength and extent of sarcomere shortening 5. The transmembrane ionic currents and their propagation across the myocardium 6. Sarcomere dynamics and the 3-dimensional mechanics of the ventricular myocardium during the cardiac cycle Naturally, the scheme in Figure 1 contains numerous omissions, such as the coronary venous system and its interactions with myocardial stresses, regulation of intracellular enzymes by secondary processes, vascular and tissue remodeling, protein metabolism, systemic influences on total body vascular resistance, changes in cardiac pool sizes of glycogen and diphosphoglycerides and triphosphoglycerides, neurohumoral regulation of contractility and coronary flow, and many other features. Nevertheless, it should provide a framework to incorporate these later. More importantly, despite these limitations, a model like this should provide an opportunity to answer important questions in integrative cardiac physiology that have eluded intuitive understanding. One excellent example is the physical and biologic basis of flow and contractile heterogeneity in the myocardium. Another is the role of intracellular inorganic phosphate accumulation on contractile dysfunction during acute myocardial ischemia.
Journal of Nuclear Cardiology September/October 2000
Opportunities Although the scientific aspects of the Cardiome Project are daunting and could occupy many lifetimes of research, it is important to recognize that the process itself is the essence of the project rather than an ultimate end point. In this respect, the Physiome Project differs fundamentally from the Human Genome project. What makes the Cardiome Project timely is the growing appreciation that it is scientifically necessary and technically feasible. However, progress at this stage has been inhibited by the lack of modeling tools, software, and databases for large-scale model integration and collaboration. Hopefully, the new tools and models being developed today will eventually find their way to the clinic. How quickly that happens will depend on the level of support from national agencies and industry and the interest of students and physicians. Early signs suggest strong interest from all quarters. I thank Professor James Bassingthwaighte, University of Washington, for introducing me to the physiome concept, shaping my ideas, and encouraging my participation in this project.
References 1. Palsson BO. What lies beyond bioinformatics? Nat Biotechnol 1997;15:3-4. 2. Boyd CAR, Noble D. The Logic of life: the challenge of integrative physiology. New York: Oxford University Press; 1993. 3. Bassingthwaighte JB. Toward modeling the human physionome. Adv Exp Med Biol 1995;382:331-9. 4. Bassingthwaighte JB. Design and strategy for the Cardionome Project. Adv Exp Med Biol 1997;430:325-39. 5. Glass L, Hunter P, McCulloch AD, editors. Theory of heart: biomechanics, biophysics and nonlinear dynamics of cardiac function. New York: Springer-Verlag; 1991. 6. Noble D. The development of mathematical models of the heart. Chaos Solitons Fractals 1995;5:321-33. 7. McCulloch A, Bassingthwaighte J, Hunter P, Noble D. Computational biology of the heart: from structure to function. Progr Biophys Mol Biol 1998;69:153-5. 8. Vetter FJ, McCulloch AD. Three-dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy. Progr Biophys Mol Biol 1998;69:157-83. 9. Kassab GS, Berkley J, Fung YC. Analysis of pig’s coronary arterial blood flow with detailed anatomical data. Ann Biomed Eng 1997;25:204-17. 10. Kroll K, Wilke N, Jerosch-Herold M, Wang Y, Zhang Y, Bache RJ, et al. Modeling regional myocardial flows from residue functions of an intravascular indicator. Am J Physiol 1996;271:H1643-55. 11. Li Z, Yipintsoi T, Bassingthwaighte JB. Nonlinear model for capillary-tissue oxygen transport and metabolism. Ann Biomed Eng 1997;25:604-19. 12. Gustafson LA, Kroll K. Downregulation of 5’-nucleotidase in rabbit heart during coronary underperfusion. Am J Physiol 1998;274:H529-38. 13. Luo CH, Rudy Y. A dynamic model of the cardiac ventricular action potential. I. Simulation of ionic currents and concentration changes. Circ Res 1994;74:1071-96. 14. Winslow R, Cai D, Varghese A, Lai Y-C. Generation and propagation of normal and abnormal pacemaker activity in network models of cardiac sinus node and atrium. Chaos Solitons Fractals 1995;5:491-512.
Journal of Nuclear Cardiology Volume 7, Number 5;496-9
15. Jafri MS, Rice JJ, Winslow RL. Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load [published erratum appears in Biophys 1998;74:3313]. Biophys J 1998;74:1149-68. 16. Rose WC, Schwaber JS. Analysis of heart rate-based control of arterial blood pressure. Am J Physiol 1996;271:H812-22. 17. Zahalak GI, de Laborderie V, Guccione JM. The effects of cross-fiber deformation on axial fiber stress in myocardium. J Biomech Eng 1999;121:376-85.
McCulloch Modeling the human cardiome in silico
499
18. Costa K, Hunter PJ, Rogers JM, Guccione JM, Waldman LK, McCulloch AD. A three-dimensional finite element method for large elastic deformations of ventricular myocardium: I—Cylindrical and spherical polar coordinates. J Biomech Eng 1996;118:452-63. 19. Peskin CS, McQueen DM. Cardiac fluid dynamics. Crit Rev Biomed Eng 1992;29:451-9. 20. Lin IE, Taber LA. A model for stress-induced growth in the developing heart. J Biomech Eng 1995;117:343-9.
The past two decades have seen impressive success for reductionist biologic science, generating new experimental data at an unprecedented rate. The list of organisms with completely sequenced genomes is growing each month. In June, the completion of a draft sequence of the entire human genome was announced amid much fanfare. Molecular mechanisms for fundamental processes such as ligand-receptor interactions and signal transduction are being elucidated in exquisite structural detail. However, as attention turns to the next phases, such as cataloging protein structures (proteomics), it is clear to biologists that the challenge is much greater than assigning functions to individual genes. Most cell functions require the coordinated interaction of numerous gene products. Metabolic or signaling pathways, for example, can be considered the expression of a “genetic circuit,” a wiring diagram for cellular function.1 And the layers of complexity do not end at the plasma membrane. Tissue and organ functions require the interactions of large ensembles of cells in functional units and networks.2 No amount of biochemical or cellular detail is sufficient to completely describe a ventricular arrhythmia, for example. Ventricular anatomic properties are equally important. To identify the comprehensive approach that will be needed to reintegrate molecular and genetic data into a quantitative understanding of physiology and pathophysiology in the whole organism, Bassingthwaighte3 coined the term “physiome.” Literally, the term reflects an integrative approach to physiology, meaning life (“physio”) as a whole (“ome”). The Physiome Project (http://www.physiome.org/) was conceived as a multicenter, international collaboration to coordinate integrative studies of quantitative physiologic function. The project was endorsed in 1997 by the International Union of Physiological Sciences at a conFrom the Department of Bioengineering, the Whitaker Institute of Biomedical Engineering, La Jolla, Calif. Reprint requests: Andrew D. McCulloch, Department of Bioengineering, the Whitaker Institute of Biomedical Engineering, University of California-San Diego, 9500 Gilman Dr, La Jolla, CA 92093-0412; [email protected]. J Nucl Cardiol 2000;7:496-9. Copyright © 2000 by the American Society of Nuclear Cardiology. 1071-3581/2000/$12.00 + 0 43/39/109682 doi:10.1067/mnc.2000.109682 496
ference in St. Petersburg, Russia, called “On Designing the Physiome Project.” In addition, the Physiome Project is recognized by organizations such as the American Institute of Medical and Biological Engineering. In April 1998, the first Microcirculation Physiome Project Working Group Meeting was held as a satellite to the “Experimental Biology ‘98” meeting, and more than 100 scientists attended. In September 1999, a similar number of participants attended the “Physiome Symposium: Integrated Biology of the Heart” in Seattle, Washington. The Physiome Project has two major goals: the cataloging of physiologic information into databases for online query and retrieval and the systematic organization of those data into quantitative models of integrated systems.3 The long-range goal is to improve the understanding of human physiology and pathophysiology by integrating quantitative information both vertically across scales of biologic organization from genome to organism and horizontally across interacting physiologic functions and processes. Projects such as the Human Genome Project and its spin-offs have generated hundreds of databases of molecular sequence and structure information such as GenBank (http://www.ncbi.nlm.nih.gov/Genbank/) and the Protein Data Bank (http://www.rcsb.org/pdb/). These databases in turn have generated demand for online tools for data-mining, homology searching, sequence alignment, and numerous other analyses. One of the best entry points for those interested in the burgeoning field of bioinformatics is the National Center for Biotechnology Information Web site (http://www.ncbi.nlm.nih.gov/). In contrast, a major obstacle to the progress of the Physiome Project is the lack of databases for the morphology and physiologic function of cells, tissues, and organs. Although there are, for example, some excellent databases of metabolic pathways such as the Metabolic Pathways Database (MPW) (http://wit.mcs.anl.gov/MPW/) and the Kyoto Encyclopedia of Genes and Genomes (KEGG) (http://www.genome.ad.jp/kegg/), there are not yet comprehensive public databases of myocyte ion channel kinetics or coronary vascular structure. This is one reason that the Physiome Project has focused on developing integrated theoretical and computational models. Models, even incomplete ones, can provide a formal framework for classifying and organizing data derived from experimental biology, particularly
Journal of Nuclear Cardiology Volume 7, Number 5;496-9
McCulloch Modeling the human cardiome in silico
497
Figure 1. Some major functional subsystems of the cardiome.
those data that serve as model parameters. With numeric models to simulate interacting processes, researchers can reveal emergent properties of the system, test prediction against experimental observation, and define the specific needs for new experimental studies. The integrated models have the potential to support and inform decisions about drug design, gene-targeting, biomedical engineering, and clinical diagnosis and management. Such integrative modeling will require a combination of analysis on the basis of physicochemical first principles and systems engineering approaches by which information can be communicated between different subsystems and across hierarchies of the integrated system. Systems models also provide a means to include necessary subsystems, which are not yet characterized in sufficient detail to be modeled from first principles, within the integrated system. This effort will in turn demand new software tools for model implementation, interoperation, and validation. It will also require a large and dedicated multidisciplinary community of scientists to accept the tedious chore of defining ontologies and standards for physiologic data representation and modeling. The Cardiome Project Within the Physiome Project, there will therefore be many subprojects concerning specific organ systems. The aims of the Cardiome Project should sound a familiar tone to the nuclear cardiologist: to integrate data and models on the anatomy and structure, hemodynamics and metabolism, mechanics and electrophysiology, and regulation and control of the normal and diseased heart. The whole Cardiome Project is envisaged as a largescale multidisciplinary, multicenter effort.4 Its beginnings were presented by Glass et al5 and Noble.6 The challenges of integrating models of many aspects of
such an organ system, including its structure, anatomy, biochemistry, control systems, hemodynamics, mechanics, and electrophysiology, have been the theme of recent workshops.7 Some of the major components of the cardiome for which computational models have been developed recently include ventricular anatomy and fiber structure,8 coronary network topology and hemodynamics,9,10 oxygen transport and substrate delivery,11 myocyte metabolism,12 ionic currents,6,13 impulse propagation,14 excitation-contraction coupling,15 neural control of heart rate and blood pressure,16 cross-bridge cycling,17 tissue mechanics,18 cardiac fluid dynamics and valve mechanics,19 and ventricular growth and remodeling.20 Of particular interest to the nuclear cardiologist are whole-organ, lumped-parameter models describing transport and exchange of substrates and accounting for the spatial distribution of the coronary arteries, regional myocardial blood flows, and uptake and metabolism of glucose, fatty acids, and oxygen used for the energy to form adenosine triphosphate, which is in turn used to fuel the work of contraction and ion pumping. Data from nuclear medicine have been essential in this area both for estimating the kinetic parameters of mass transport in the heart and for providing independent measurements with which to validate such models. A unique resource for nuclear cardiologists interested in numerical models and simulation for circulatory mass transport and exchange is the National Simulation Resource (http://nsr.bioeng.washington.edu). Indeed, cardiac imaging in general has a crucial role in the Cardiome Project. If models built from data on structural and functional building blocks are to be integrated into anatomically detailed 3-dimensional simulations, they must be validated independently, with functional data from the intact heart. If such models are to find clinical application, it will be necessary to build
498
McCulloch Modeling the human cardiome in silico
patient-specific simulations from clinically accessible data. For example, we have developed parametric computational techniques for modeling the mechanics, transport processes, and electrophysiology of the heart wall as a 3-dimensional anisotropic material continuum, while incorporating kinetic and structural information from the cellular level. These models rely on representations of 3dimensional ventricular geometry and fiber architecture, which are increasingly being derived from imaging modalities such as magnetic resonance imaging. To explore how these models can be extended and integrated with others, we have defined 6 major functional modules for initial attention in the Cardiome Project (Figure 1).4 They are: 1. Coronary artery anatomy and regional myocardial flows for substrate and oxygen delivery 2. Metabolism of the substrate for energy metabolism, fatty acid and glucose, the tricarboxylic acid cycle, and oxidative phosphorylation 3. Purine nucleoside and purine nucleotide metabolism, describing the formation of adenosine triphosphate and the regulation of its degradation to adenosine in endothelial cells and myocytes and its effects on coronary vascular resistance 4. Excitation-contraction coupling: calcium release and reuptake and the relations between these and the strength and extent of sarcomere shortening 5. The transmembrane ionic currents and their propagation across the myocardium 6. Sarcomere dynamics and the 3-dimensional mechanics of the ventricular myocardium during the cardiac cycle Naturally, the scheme in Figure 1 contains numerous omissions, such as the coronary venous system and its interactions with myocardial stresses, regulation of intracellular enzymes by secondary processes, vascular and tissue remodeling, protein metabolism, systemic influences on total body vascular resistance, changes in cardiac pool sizes of glycogen and diphosphoglycerides and triphosphoglycerides, neurohumoral regulation of contractility and coronary flow, and many other features. Nevertheless, it should provide a framework to incorporate these later. More importantly, despite these limitations, a model like this should provide an opportunity to answer important questions in integrative cardiac physiology that have eluded intuitive understanding. One excellent example is the physical and biologic basis of flow and contractile heterogeneity in the myocardium. Another is the role of intracellular inorganic phosphate accumulation on contractile dysfunction during acute myocardial ischemia.
Journal of Nuclear Cardiology September/October 2000
Opportunities Although the scientific aspects of the Cardiome Project are daunting and could occupy many lifetimes of research, it is important to recognize that the process itself is the essence of the project rather than an ultimate end point. In this respect, the Physiome Project differs fundamentally from the Human Genome project. What makes the Cardiome Project timely is the growing appreciation that it is scientifically necessary and technically feasible. However, progress at this stage has been inhibited by the lack of modeling tools, software, and databases for large-scale model integration and collaboration. Hopefully, the new tools and models being developed today will eventually find their way to the clinic. How quickly that happens will depend on the level of support from national agencies and industry and the interest of students and physicians. Early signs suggest strong interest from all quarters. I thank Professor James Bassingthwaighte, University of Washington, for introducing me to the physiome concept, shaping my ideas, and encouraging my participation in this project.
References 1. Palsson BO. What lies beyond bioinformatics? Nat Biotechnol 1997;15:3-4. 2. Boyd CAR, Noble D. The Logic of life: the challenge of integrative physiology. New York: Oxford University Press; 1993. 3. Bassingthwaighte JB. Toward modeling the human physionome. Adv Exp Med Biol 1995;382:331-9. 4. Bassingthwaighte JB. Design and strategy for the Cardionome Project. Adv Exp Med Biol 1997;430:325-39. 5. Glass L, Hunter P, McCulloch AD, editors. Theory of heart: biomechanics, biophysics and nonlinear dynamics of cardiac function. New York: Springer-Verlag; 1991. 6. Noble D. The development of mathematical models of the heart. Chaos Solitons Fractals 1995;5:321-33. 7. McCulloch A, Bassingthwaighte J, Hunter P, Noble D. Computational biology of the heart: from structure to function. Progr Biophys Mol Biol 1998;69:153-5. 8. Vetter FJ, McCulloch AD. Three-dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy. Progr Biophys Mol Biol 1998;69:157-83. 9. Kassab GS, Berkley J, Fung YC. Analysis of pig’s coronary arterial blood flow with detailed anatomical data. Ann Biomed Eng 1997;25:204-17. 10. Kroll K, Wilke N, Jerosch-Herold M, Wang Y, Zhang Y, Bache RJ, et al. Modeling regional myocardial flows from residue functions of an intravascular indicator. Am J Physiol 1996;271:H1643-55. 11. Li Z, Yipintsoi T, Bassingthwaighte JB. Nonlinear model for capillary-tissue oxygen transport and metabolism. Ann Biomed Eng 1997;25:604-19. 12. Gustafson LA, Kroll K. Downregulation of 5’-nucleotidase in rabbit heart during coronary underperfusion. Am J Physiol 1998;274:H529-38. 13. Luo CH, Rudy Y. A dynamic model of the cardiac ventricular action potential. I. Simulation of ionic currents and concentration changes. Circ Res 1994;74:1071-96. 14. Winslow R, Cai D, Varghese A, Lai Y-C. Generation and propagation of normal and abnormal pacemaker activity in network models of cardiac sinus node and atrium. Chaos Solitons Fractals 1995;5:491-512.
Journal of Nuclear Cardiology Volume 7, Number 5;496-9
15. Jafri MS, Rice JJ, Winslow RL. Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load [published erratum appears in Biophys 1998;74:3313]. Biophys J 1998;74:1149-68. 16. Rose WC, Schwaber JS. Analysis of heart rate-based control of arterial blood pressure. Am J Physiol 1996;271:H812-22. 17. Zahalak GI, de Laborderie V, Guccione JM. The effects of cross-fiber deformation on axial fiber stress in myocardium. J Biomech Eng 1999;121:376-85.
McCulloch Modeling the human cardiome in silico
499
18. Costa K, Hunter PJ, Rogers JM, Guccione JM, Waldman LK, McCulloch AD. A three-dimensional finite element method for large elastic deformations of ventricular myocardium: I—Cylindrical and spherical polar coordinates. J Biomech Eng 1996;118:452-63. 19. Peskin CS, McQueen DM. Cardiac fluid dynamics. Crit Rev Biomed Eng 1992;29:451-9. 20. Lin IE, Taber LA. A model for stress-induced growth in the developing heart. J Biomech Eng 1995;117:343-9.