SIAM News Blog

Cardiac Modeling

The Road from Equations to the Clinic

By Natalia A. Trayanova

Advances in computer modeling, as they transform many traditional areas of physics and engineering, are also transforming our understanding of the function of the heart in health and disease. Modern cardiac researchers are increasingly aware that appropriate models and simulation can help interpret an array of experimental data and dissect important physiological mechanisms and interrelationships. Decades of developments in cardiac simulation have rendered the heart the most highly integrated example of a “virtual organ.” These developments are firmly anchored in the long history of cardiac cell modeling, which dates back more than 50 years, to publication of the first model of the cardiac cell action potential, and are rooted in iterative interactions between modeling and experimentation.

Cardiac cell (myocyte) action potential models often take the form of coupled systems of nonlinear ordinary differential equations describing current flow through ion channels, pumps, and exchangers, as well as subcellular calcium cycling; model equations are solved to observe how states (concentrations of molecules) evolve in time as they interact with one another and respond to inputs. Over the years, models of myocyte action potential have improved rapidly, with the incorporation of validated biophysical relations and descriptions of many subcellular processes and pathways regulating the electrical function of the cell. The result has been dramatic enhancement of the physiological relevance of heart cell models.

Over the last two decades, cardiac modeling has also progressed to the level of the tissue and the whole heart, where the propagation of a wave of action potential is simulated by a reaction–diffusion partial differential equation. The reaction–diffusion PDE describes current flow through tissue composed of myocytes that are electrically connected via low-resistance gap junctions. Cardiac tissue has orthotropic electrical conductivities that arise from the cellular organization of the myocardium (cardiac muscle) into fibers and laminar sheets. Global conductivity values are obtained by combining the fiber-and-sheet organization with myocyte-specific local conductivity values. Current flow in the tissue is driven by ionic exchanges across cell membranes during the myocyte action potential. Simulation of electrical wave propagation in the myocardium entails simultaneous solution of the PDE and the set of action potential ODEs over the tissue volume. In certain cases, such as simulation of the delivery of an external current to the myocardium, use of a system of coupled PDEs rather than a single PDE allows for an explicit representation of current flow in the extracellular space.

Simulated arrhythmia in a model of a patient heart with myocardial infarction. White arrows indicate direction of propagation of the re-entrant wave sustaining the arrhythmia. The dashed red circle encloses the predicted optimal target of catheter ablation. Reprinted from H. Ashikaga, H. Arevalo, F. Vadakkumpadan, R.C. Blake 3rd, J.D. Bayer, S. Nazarian, M. Muz Zviman, H. Tandri, R.D. Berger, H. Calkins, D.A. Herzka, N.A. Trayanova, and H.R. Halperin, “Feasibility of Image-Based Simulation to Estimate Ablation Target in Human Ventricular Arrhythmia,” Heart Rhythm, April 19, 2013, Epub ahead of print; doi:10.1016/j.hrthm.2013.04.015; pii:S1547-5271(13)00437-2;
The progress made in simulating cardiac electrical behavior at the organ level is the most exciting, and it is there that the author’s laboratory has made its most significant contributions. In general, many of the emergent, integrative behaviors in the heart result not only from complex interactions within a specific level but also from feed-forward and feedback interactions connecting a broad range of levels in the biological hierarchy. The ability to construct multiscale models of the electrical functioning of the heart, representing integrative behavior from the molecule to the entire organ, is of particular significance, as it paves the way for clinical applications of cardiac organ modeling. In the clinic, as in labs in which electrophysiological measurements are made in intact animals, assessment of function is conducted at the level of the entire organ. Validating the whole-heart simulations at that level ensures their predictive capabilities and the possibility of their entry into the realm of healthcare.

The key to attaining predictive capabilities for multiscale cardiac models at the organ level has been the use of individual models, either MRI- or CT-based, of the geometry of the heart, and the application of diffusion tensor MR imaging (DTMRI) to measure the anatomy, fiber, and sheet structure of the heart in cases of ex vivo studies. This has led to a new generation of whole-heart image-based models with unprecedented structural and biophysical detail. Clearly, modeling the function of the heart has benefitted significantly from the revolution in medical imaging.

Cardiac models have been used to gain insight into mechanisms of arrhythmia in many disease settings. In addition, a major thrust in computational cardiac electrophysiology is to use models as a testbed for the evaluation of new antiarrhythmic drug therapies. It is now possible to test hypotheses regarding mechanisms of drug action on the scale of the whole heart. Multiscale heart models of antiarrhythmic drug interactions with ion channels have provided insight into why certain pharmacological interventions result in drug-induced arrhythmia, whereas others do not. This work has the potential to help guide the drug development pipeline—a process well known for both high failure rate and high cost.

The use of heart models in personalized diagnosis, treatment planning, and prevention of sudden cardiac death is also slowly becoming a reality. The feasibility of subject-specific modeling has been demonstrated through the use of heart models reconstructed from clinical MRI scans to evaluate infarct-related ventricular tachycardia (fast and often lethal arrhythmia). Such applications of whole-heart modeling are expected to help predict optimal locations for the procedure known as catheter ablation in the hearts of individual patients, as well as to stratify patients for arrhythmic risk.

Nowadays, whole-heart image-based multiscale models of cardiac electrical behavior are not the whole story. Combined with models of cardiac mechanics, these models are being integrated into increasingly “multi-physics” whole-heart models of cardiac electromechanical behavior. Such multiscale whole-heart electromechanics models are being applied in a patient-specific manner to investigate improved methods for cardiac resynchronization therapy in dyssynchronous heart failure. Recently, in a step toward comprehensive modeling of cardiac function, efforts have been made to link electromechanical models of the heart with fluid dynamics models.

Computer simulations of the function of the diseased heart represent an important research avenue in the new discipline of computational medicine. Biophysically detailed models of the heart assembled with data from clinical imaging modalities that incorporate electromechanical and structural remodeling in cardiac disease could become a first line of screening for new therapies and approaches, new diagnostic developments, and new methods of disease prevention. Bedside implementation of patient-specific cardiac simulations could become one of the most thrilling examples of CSE-based approaches in translational medicine.

This article is based on the author’s invited lecture at the SIAM CSE meeting in Boston, in February 2013. A recording of the talk has been posted at

Natalia A. Trayanova is the Murray B. Sachs Professor in the Department of Biomedical Engineering and the Institute of Computational Medicine at Johns Hopkins University.

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