Workshop 1: Cardiac Electrophysiology and Arrhythmia

(September 25,2006 - September 29,2006 )

Organizers


James Keener
Mathematics & Bioengineering, University of Utah
Rai Winslow
School of Medicine & Whiting School of Engineering, Johns Hopkins University

The workshop will concentrate on atrial and ventricular electrophysiology from models of the biophysics of single ion channels to predicting the electrocardiogram recorded at the body's surface. An overarching theme will be how mathematical models can elucidate mechanisms, improve diagnoses, and identify therapeutic targets for cardiac arrhythmias.

Topics will include:

  • Molecular Biology of Cardiac Ion Channels and Transporters
  • Formulation and Application of Integrative Models of the Cardiac Myoycte
  • Tissue and Organ Models
  • Arrhythmia Mechanisms
  • Excitation-Contraction Coupling

Accepted Speakers

Don Bers
Physiology , Loyola University
Candido Cabo
Pharmacology, Columbia University
Carlos Castillo-Chavez
Department of Mathematics and Statistics, Arizona State University
Colleen Clancy
Physiology and Biophysics, Cornell University
Mario Delmar
Pharmacology, SUNY Upstate Medical University
Igor Efimov
Biomedical Engineering, Washington University
Martin Falcke
Hahn Meitner Institut, Dept. SF5
Clara Franzini-Armstrong
Cell and Developmental Biology, University of Pennsylvania
Michael Guevara
Physiology, McGill University, Macdonald Campus
Sandor Gyorke
Physiology and Cell Biology, The Ohio State University
Craig Henriquez
Biomedical Engineering & Computer Science, Duke University
Peter Hunter
Bioengineering Institute, University of Auckland
Saleet Jafri
Computational Sciences, George Mason University
Kenneth Laurita
Heart and Vascular Research Center, Case Western Reserve University
Jonathan Lederer
Biotechnology Inst. & Dept. of Physiology, University of Maryland at Baltimore
Michael Miller
Biomedical Engineering, Johns Hopkins University
Sasha Panfilov
Theoretical Biology , Rijksuniversiteit te Utrecht
Randall Rasmusson
Physiology and Biophysics , University at Buffalo (SUNY)
David Rosenbaum
Medicine & Biomedical Engineering, Case Western Reserve University
Yoram Rudy
Cardiac Bioelectricity Center, Washington University
Greg Smith
Applied Science, College of William and Mary
Natalia Trayanova
Department of Biomedical Engineering , Johns Hopkins University
Rai Winslow
School of Medicine & Whiting School of Engineering, Johns Hopkins University
Monday, September 25, 2006
Time Session
09:10 AM
10:00 AM
Colleen Clancy - Subtleties of Na+ Channel Gating Revealed by Theoretical Modeling: Understanding genetic perturbations and disease

Naturally occurring mutations in cardiac Na+ channels can disrupt channel gating and cause electrical abnormalities that increase susceptibility to cardiac arrhythmia. We have used a theoretical approach to simulate the effects of perturbations in discrete kinetics processes on channel gating and cellular electrical activity. Many mutations in cardiac INa linked to the Long-QT Syndrome (LQTs) result in a gain of function due to a fraction of channels that fail to inactivate (burst) leading to persistent current during depolarization. However, electrophysiological characterization of some Na+ channel linked Long-QT mutants has revealed that some do not. Interestingly, a number of these mutants share a common abnormality, namely increased rates of channel recovery from inactivation. We use experimental and theoretical approaches to reveal that mutation induced faster recovery from inactivation results can allow channel reopening during repolarization and cause severe prolongation of the action potential. We have also investigated the increased susceptibility to drug induced arrhythmia in African American carriers (4.6 millions) of a common polymorphism (S1102 to Y1102) in cardiac INa The study used a combined experimental and theoretical investigation. Although the experimental data suggested that the polymorphism Y1102 had subtle effects on Na+ channel function, the integrative model simulations revealed an increased susceptibility to arrhythmogenic-triggered activity in the presence of drug block (Splawski et al., 2002).

10:15 AM
11:05 AM
Randall Rasmusson - Biology and Modeling of Cardiac K Channels

Cardiac potassium channels control the process of repolarization. During repolarization several potassium channels are active and a precise timing of interaction during repolarization is required for proper action potential behavior. On a molecular level, mutations in key potassium channels have been closely linked to arrhythmias, in spite of mutations causing seemingly minor changes in action potential shape and/or channel kinetics. This sensitivity to the exact kinetic behavior of ion channels emphasizes the importance of precise modeling of potassium channel function. We model potassium channel function beginning at the level of molecular structure. Various elements of physical structure constrain the possible kinetic models for description of channel kinetics. In the example of the Kv1.4 and Kv4.3 channels which mediate various components of the cardiac transient outward current, activation occurs with a sigmoid delay. Inactivation has at least two components, often termed N-type and C-type inactivation. Both are functionally coupled to the process of activation. N-type inactivation occurs via a "ball and chain" mechanism. C-type inactivation is less well defined but involves residues at the outer mouth of the pore which are coupled to large scale movements of the intracellular pore mouth, S6 and other domains of the channel. These large scale changes mediate strong interactions between C-type and N-type inactivation which cause the rate limiting step for recovery to be determined by the properties of C-type inactivation. These kinetic properties are essential for determining the restitution and recovery processes of the cardiac action potential.

11:20 AM
12:10 PM
Jonathan Lederer - Cardiac Ca Dynamics

Cardiac Ca Dynamics

02:30 PM
03:20 PM
Don Bers - Cardiac L-type Ca Channels, RyR2s and SERCA2a

Cardiac L-type Ca Channels, RyR2s and SERCA2a

03:35 PM
04:25 PM
Don Bers - Cardiac L-type Ca Channels, RyR2s and SERCA2a

Cardiac L-type Ca Channels, RyR2s and SERCA2a

Tuesday, September 26, 2006
Time Session
08:35 AM
09:25 AM
Yoram Rudy - Relating Ion-Channel Kinetic Properties to Cardiac Repolarization and Repolarization Abnormalities using Computational Biology

Cardiac excitation and arrhythmogenesis involve intimate interactions between processes at different scales of the cardiac system from ion channel, to the whole cell, to the multicellular tissue. Mathematical models of cellular electrophysiology have been very helpful in identifying and characterizing such interactions and in elucidating mechanisms. In my presentation, I will provide examples of interactions between ion channel kinetics and the cellular environment in the context of mutations and action potential repolarization. In the first example (Clancy and Rudy, Cardiovascular Research 2001; 50: 301-313), the long QT cellular phenotype of HERG mutation is shown to result from the specific kinetic changes to IKr (the rapid delayed rectifier) and their effect during the action potential. Early afterdepolarizations are generated through an interaction between the mutant IKr channels and the L-type Ca2+ channels. In a second example (Silva and Rudy, Circulation 2005; 112: 1384-1391), I will use computational biology to explain how the kinetic properties of IKs (the slow delayed rectifier) that are conferred by molecular subunit interactions, determine its participation in rate-dependent repolarization and facilitate its role as "repolarization reserve."


Supported by NIH Merit Award R37-HL33343 and Grant RO1-HL49054 from the National Heart, Lung and Blood Institute.

09:40 AM
10:30 AM
Rai Winslow - Calcium-Induced Calcium-Release: Insights From Studies of Heart Failure

Heart failure is a disease with high mortality and a distinctive organ and cellular phenotype. The cellular phenotype is distinguished by both action potential prolongation and reduction of both amplitude and rate of decline of the intracellular calcium transient. Our early studies of this disease were focused on measuring ion channels, membrane transporters and Ca cycling proteins with altered expression in end-stage heart failure and using models to interpret the functional significance of these changes. These studies revealed that while voltage-gated K channels were down-regulated in end-stage heart failure, this down-regulation could not explain AP prolongation of altered Ca transients. Rather, altered expression of the proteins involved in Ca cycling seemed to play the dominant role. In thistalk, we will review these early findings, and discuss how they have informed the design of new models of the calcium-induced calcium-release process in the cardiac myocyte.

10:45 AM
11:35 AM
Martin Falcke - Stochastic Models of Complex Molecules

Cells exhibit complex nonlinear dynamics which may appear as oscillations, excitability or even subcellulr structure formation. The elemental building blocks of that dynamics are complex molecules which often have several internal degrees of freedom. Typically, these molecules have active and inactive states. The dynamics of these molecules relevant for the global process can be described in terms of a distribution of hitting time to the active state (renewal process). The presentation introduces a method to calculate that distribution exactly. The method is suitable in particular for very small molecule numbers, i.e. in the range where other methods to calculate first passage probability densities (e.g. linear Fokker-Planck-Eq.) fail.

01:50 PM
02:40 PM
Peter Hunter - Tissue and Organ Level Cardiac Electrophysiological Modelling

To incorporate cell-based ion channel electrophysiology models into tissue and organ level simulations of myocardial activation, it is important to understand how current flows through and between cells in the three dimensional fibrous-sheet architecture of ventricular myocardium. The cardiac group in the Auckland Bioengineering Institute has developed an instrument for imaging the 3D structure of myocardial tissue and has developed bidomain reaction-diffusion models that incorporate the measured structure at length scales of 0.2m -1.0mm. By comparing the propagation of activation wavefronts using these detailed structural models with coarser grained continuum models that approximate the fibrous-sheet structure on a larger length scale, it is possible to derive a conductivity tensor for the tissue that can be used in the intact organ level simulations. Other issues that will be discussed are: (i) the use of the CellML model repository (www.cellml.org/models) for defining the cell equations and tissue constitutive laws, and (ii) the coupling of electrical activation based on reaction-diffusion equations to large deformation mechanics in the beating heart.


This work was done in collaboration with: Travis M. Austin, Darren A. Hooks, David P. Nickerson, Andrew J. Pullan, Gregory B. Sands, Bruce H. Smaill, and Mark L. Trew1.

02:55 PM
03:45 PM
Michael Miller - Computational Anatomy and the Infinite Dimensional Diffeomorphisms

Over the past 10 years computational anatomy has emerged as a quantitative subfield of Medical Image Analysis. Computational anatomy is the study of biological shape via the infinite dimensional diffeomorphisms. This talk will review progress on the (i) the construction of the group of diffeomorphisms via flows, (ii) the model of anatomical orbit as a group action of diffeomorphisms on exemplars (deformable template) with associated metric structure, and (iii) the variational problems associated with inference of the hidden flows connecting configurations in the anatomical orbit. Applications will be described in metric comparison of shapes in human anatomy and in growth and development sequences.

Wednesday, September 27, 2006
Time Session
08:30 AM
09:20 AM
Sasha Panfilov - Modeling Electrical Conduction in the Cardiac Ventricles

Cardiac arrhythmias and sudden cardiac death is the leading cause of death accounting for about 1 death in 10 in industrialized countries. Although cardiac arrhythmias has been studied for well over a century, their underlying mechanisms remain largely unknown. One of the main problems in studies of cardiac arrhythmias is that they occur at the level of the whole organ only, while in most of the cases only single cell experiments can be performed. Due to these limitations alternative approaches such as mathematical modeling are of great interest. From mathematical point of view excitation of the heart is described by a system of non-linear parabolic PDEs of the reaction diffusion type with anisotropic diffusion operator. Cardiac arrhythmias correspond to the solutions of these equations in form of 2D or 3D vortices characterized by their filaments. In my talk I will present a short overview of two directions of our research:



  1. Filament dynamics in anisotropic cardiac tissue. I will present a method that can be used to predict filament shapes in anisotropic tissue based on data on the arrival times of the excitation in given slab of cardiac tissue. The method is extension of the 'minimal principle for rotor filaments' proposed by Wellner et al., (PNAS,v.99:8015-8018,2002). We demonstrate that this principle can be reformulated using the eikonal equation for wave propagation in the same medium in which the scroll wave rotates.

  2. Development of virtual human heart model. Here I will report on development of an anatomically accurate model for the human heart. The model integrates our knowledge about electrophysiology of the human heart from a single cell to the whole organ and allows us to study mechanisms of cardiac arrhythmias in the human heart, where experimental interventions are very limited. I will present results of our studies of 3D organization of ventricular fibrillation in human heart and compare our conclusions to the available experimental and clinical data. In general, we find that ventricular fibrillation in the human heart may be organized by a small number of vortex filaments (around 10) and should have much simpler structure than thought before. I will also present our recent results on implementation of clinically measured heterogeneity of human ventricles and on modelling of effects of these heterogeneities on ventricular fibrillation.

09:35 AM
10:25 AM
Natalia Trayanova - Bidomain Models: Inducing and Terminating VF

Bidomain Models: Inducing and Terminating VF

10:40 AM
11:30 AM
Candido Cabo - Cellular Mechanisms of Stability of Reentrant Tachycardias in Infarcted Hearts: A Computational Approach

Reentrant circuits causing sustained ventricular tachycardia (i.e. lasting more than 30 sec) in the canine infarcted heart have a figure-8 activation pattern with a central (CCP) and an outer pathway (OP). Infarction causes extensive remodeling of ion channel function and gap junction conductance in the border zone of the infarct. The pattern of remodeling in the CCP and OP is heterogeneous. In the OP, Cx43 is located at the intercalated disks but side-to-side gap junction conductance (Gj) is reduced by 90% (end-to-end Gj is normal). End-to-end and side-to-side Gj in the CCP are both normal but Cx43 redistributes along the lateral membrane. Remodeling of the sodium and L-type calcium channel causes a loss of function in INa and ICa, T which is more marked in the CCP than in the OP. Even though, in general, heterogeneous myocardium is associated with unstable reentrant circuits, reentrant circuits in canine infarcted hearts are stable. Here, we use computer models of the infarcted canine heart to understand how the heterogeneities in ion channel function and gap junction conductance described experimentally lead to stable reentrant tachycardias.

11:45 AM
12:35 PM
Craig Henriquez - Modeling the Arrhythmogenic Substrate: Incorporating Heterogeneity at the Microscale in Cardiac Tissue Models

Some arrhythmias are the result of certain channelopathies caused by a mutation or mutations in genes coding for ion channel subunits or the proteins that regulate them and can occur in the absence of any structural changes to the heart muscle. Other arrhythmias, however, are only manifested when there are significant structural changes in the tissue, such as modulation of cell size and morphology, infiltration of fibroblasts, increased non-uniformity in the interstitial space and changes in the number and distribution of gap junction connexons. While there has been rapid growth in the use of computer models to study the mechanisms of normal and abnormal cardiac conduction, the bulk of the models represent the tissue as structurally uniform and continuous, often without consideration of the effects of the extracellular space. In this talk, I present a brief overview of the evolution of cardiac tissue models and introduce a novel computational approach for studying propagation in three-dimensions at the microscale. In this model, individual myoctyes are represented as discrete units comprising an intracellular space, bounded by a membrane and embedded in an interstitium. The model builds off the work of Spach Heidlage (Circ. Res, 1995) and differs from the classical monodomain or bidomain models in that it can incorporate realistic cell morphologies, channel distributions and cell-to-cell connectivities that are associated with an arrhythmogenic substrate. Simulations results are presented that demonstrate how the framework can be used to study the effects of structural changes, such as those arising from disease and aging of the myocardium, on impulse propagation and signal waveshape that cannot be easily captured in traditional tissue models.

02:35 PM
03:25 PM
Michael Guevara - Synchronization Rhythms in the Heart

During normal activity in the heart, in any given excitable cell there is one action potential for each action potential of the sinoatrial node, with a time delay that is more or less fixed from beat to beat. This 1:1 synchronization can break down in several ways: e.g., there can be Wenckebach rhythms, alternans (2:2 rhythm), or a direct transition to 2:1 rhythm. We provide experimental evidence for these transitions in experimental work on single ventricular cells, as well as in ionic models and in the much simpler piecewise-linear FitzHugh-Nagumo equations. We describe how the dynamics can, on occasion, be reduced to the analysis of one-dimensional maps, wherein multistability (the simultaneous presence of two or more periodic rhythms, depending on initial conditions) arises. Extensions of this work to multicellular systems and its relevance to the understanding of the generation of certain cardiac arrhythmias will also be presented.

03:40 PM
04:30 PM
Guy Salama - Wavelets, Wavebreaks and Ventricular Fibrillation

We present a probability density approach to modeling heterogeneous calcium (Ca) release from stochastic functional units (SFUs) or "couplons" of cardiac myocytes. Coupled advection-reaction equations are derived relating the time-dependent probability density of subsarcolemmal subspace and junctional sarcoplasmic reticulum [Ca] conditioned on the state of each SFU. When these equations are coupled to ODEs for the bulk myoplasmic and SR [Ca], a realistic but minimal model of cardiac Ca-induced Ca release via local triggering of Ca sparks is produced. This modeling approach avoids the computationally demanding task of resolving spatial aspects of global Ca signaling, while accurately representing heterogeneous local Ca signals in a population of diadic subspaces and junctional SR depletion domains. The equations are solved numerically using a high-resolution finite difference scheme. The approach is validated for a physiologically realistic number of SFUs and benchmarked for computational efficiency by comparison to traditional Monte Carlo simulations. The probability density approach produces Ca release that is graded with changes in membrane potential and depolarization duration and represents a new class of deterministic whole cell models that efficiently represent important aspects of stochastic Ca channel gating and localized Ca dynamics. This project is joint work with G. S. Blair Williams, Marco A. Huertas, Eric A. Sobie, and M. Saleet Jafri.

Thursday, September 28, 2006
Time Session
09:00 AM
09:50 AM
Mario Delmar - Arrhythmogenic Right Ventricular Cardiomyopathy (ARVC): A disease of the intercalated disc

ARVC is an inherited cardiac disease characterized by ventricular fibrofatty infiltration, predominantly in the right ventricle, and a high incidence of arrhythmias and sudden death. ARVC is responsible for a number of cases of exercise - related sudden cardiac death in the youth. In this presentation, I will review the clinical, anatomo-pathological and genetic characteristics of ARVC and describe new data indicating that, at least in some cases, ARVC may be accompanied by loss of the structural and molecular integrity of the cardiac intercalated disc. The clinical features of ARVC may be related to significant remodeling of the intercalated disc structures, including gap junctions.

09:00 AM
09:50 AM
Saleet Jafri - The Spatial Spread of Calcium Sparks in the Sarcomere

Cardiac excitation-contraction coupling describes the chain of events from the initiation of depolarization of the sarcolemma of the cardiac myocyte through contraction. We investigate how microstructural and physiological features affect the spatial spread of calcium sparks which are considered to be the elementary events of excitation-contraction coupling through a computational study. The basic model consists of two dyads positions on opposite sides of a T-tubule and the adjacent half sarcomeres. The model suggests that in order to simulate the spatial spread of calcium i.e. a full-width at half maximum (FWHM) of 2.0 microns seen in experiments, calcium release from both dyads must occur. The model also simulates the local depletion of the sarcoplasmic reticulum seen in experiments and suggests that this observed depletion is composed of large depletion of the junctional sarcoplasmic reticulum and small depletion of the network sarcoplasmic reticulum which appear as a small over all depletion due to the effects of the dyes used and confocal imaging techniques. The model then is expanded to include multiple release sites and is used to account for spontaneous calcium waves seen in calcium overload conditions. Such conditions might occur in heart failure and lead to cardiac arrhythmias.


This project is joint work with Hena R. Ramay, W. Jonathan Lederer, and Eric A. Sobie and was supported by the NSF.

10:05 AM
10:55 AM
David Rosenbaum - Alternans

Alternans

10:05 AM
10:55 AM
Greg Smith - A Probability Density Approach to Modeling Local Calcium Signaling and Stochastic Functional Unit Activity in Cardiac Myocytes

A Probability Density Approach to Modeling Local Calcium Signaling and Stochastic Functional Unit Activity in Cardiac Myocytes

11:10 AM
12:00 PM
Igor Efimov - Reentrant Arrhythmias

Reentrant Arrhythmias

01:30 PM
02:20 PM
Kenneth Laurita - Arrhythmia Mechanisms: Myocardial Infarction

Ventricular remodeling associated with myocardial infarction (MI) promotes a substrate that is the leading cause of ventricular arrhythmias, frequently presenting as sudden cardiac death. The usual cause of ventricular arrhythmias associated with late MI is, in part, reentrant excitation resulting from electrophysiological heterogeneity due to coexistence of infarcted, border zone and viable myocardial tissue. To better understand the mechanisms of arrhythmogenesis associated with MI, studies have meticulously focused on altered ionic currents, action potentials, and cell-to-cell coupling associated with viable cells in the border zone. Likewise, abnormal conduction, such as wave break, impulse block, and slow conduction, have been well documented in late MI. However, the exact causal relationship between abnormal cellular electrophysiology, conduction abnormalities, and arrhythmogenesis associated with late MI is not completely understood. Novel experimental techniques can be used to illuminate the mechanistic relationship between abnormal cellular electrophysiology and arrhythmogenesis associated with late MI and, possibly, lead to new therapeutic approaches.

03:10 PM
04:00 PM
Sandor Gyorke - Regulation of Intracellular Calcium Release in Normal and Diseased Heart

Davis Heart & Lung Research Institute, Ohio State University, Columbus, OH In cardiac muscle, calcium release from the sarcoplasmic reticulum (SR) is central to the process of excitation-contraction coupling. Calcium is released through specialized calcium-permeable channels called ryanodine receptors (RyR2s) and causes shortening of the contractile filaments. The RyR2 channel interacts with a number of SR proteins including triadin, junctin and calsequestrin that work in synchrony to control SR calcium release during the cardiac cycle. In my presentation I will discuss the mechanisms of RyR2 regulation by these auxiliary proteins and how genetic and acquired defects in these mechanisms can lead to cardiac diseases such as arrhythmia and heart failure.

04:15 PM
05:05 PM
Clara Franzini-Armstrong - Calcium Release Units, the Macromolecular Complexes Responsible for Calcium Release in Cardiac Myocytes

Cardiac excitation at the cellular level is initiated by release of Ca2+ from the junctional cisternae of the sarcoplasmic reticulum (jSR). The jSR is closely associated with and controlled by surface membrane/T tubules within units called Calcium Release Units (CRUs). The jSR membrane and lumen are occupied by a number of proteins that are linked to each other both structurally and functionally. The ryanodine receptor (RyR) or SR Ca2+ release channel is the focus of interactions involving the luminal Ca2+ binding protein calsequestrin and the two jSR membrane proteins junctin and triadin. Overexpression of all CSQ, Jn and Tr (in collaboration with L.R. Jones) and a null mutation of CSQ (in collaboration with B.C. Knollman, L.R. Jones and K. Pfeifer) have structural effects which serve to illustrate the roles of the three CRU components in the architecture and function of CRUs. L type calcium channels in T tubules (the DHPRs) act as voltage sensor initiating the signal for jSR Ca2+ release via RyRs. Differences in the relative positioning of DHPRs and RyRs between cardiac and skeletal muscles are at the basis of the known differences in e-c coupling between the two striated muscles.


Supported by NIH Merit Award HL48093 from the National Heart, Lung and Blood Institute.

Friday, September 29, 2006
Time Session
Name Email Affiliation
Aguda, Baltazar bdaguda@gmail.com MBI - Long Term Visitor, Bioinformatics Institute, Singapore
Andrabi, Sumaira Unknown, Unknown
Bazil, Jason jbazil@purdue.edu Biomedical Engineering, Purdue University
Bers, Don dbers@lumc.edu Physiology , Loyola University
Besse, Ian ibesse@math.uiowa.edu Applied Mathematical & Computational Sciences, University of Iowa
Best, Janet jbest@mbi.osu.edu
Billman, George billman.1@osu.edu Physiology and Cell Biology, The Ohio State University
Buzzard, Greg buzzard@math.purdue.edu Dept. of Mathematics, Purdue University
Cabo , Candido ccabo.citytech.cuny.edu Pharmacology, Columbia University
Carnes, Cynthia carnes.4@osu.edu College of Pharmacy, The Ohio State University
Castillo-Chavez, Carlos ccchavez@asu.edu Department of Mathematics and Statistics, Arizona State University
Clancy, Colleen clc7003@med.cornell.edu Physiology and Biophysics, Cornell University
Coombes, Stephen stephen.coombes@nottingham.ac.uk School of Mathematical Sciences, University of Nottingham
Cutler, Michael mcutler@metrohealth.org Heart and Vascular Research, Case Western Reserve University
Davis, Jonathan davis.812@osu.edu Physiology and Cell Biology, The Ohio State University
Del Rio, Carlos del-rio.4@osu.edu Electrical & Computer Eng./Physiology and Cell Bio., The Ohio State University
Delmar, Mario delmarm@upstate.edu Pharmacology, SUNY Upstate Medical University
Djordjevic, Marko mdjordjevic@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Efimov, Igor igor@wustl.edu Biomedical Engineering, Washington University
Enciso, German German_Enciso@hms.harvard.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Enyeart, Michael mwe8@cornell.edu Biomedical Sciences, Cornell University
Falcke, Martin falcke@hmi.de Hahn Meitner Institut, Dept. SF5
Fink, Martin martin.fink@physiol.ox.ac.uk Physiology, Anatomy and Genetics, University of Oxford
Franzini-Armstrong, Clara armstroc@mail.med.upenn.edu Cell and Developmental Biology, University of Pennsylvania
Goel, Pranay goelpra@helix.nih.gov Mathematical Biosciences Institute (MBI), The Ohio State University
Gong, Yunfan yug2002@med.cornell.edu Medicine (Cardiology), Cornell University
Grajdeanu, Paula pgrajdeanu@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Griffith, Boyce griffith@cims.nyu.edu Courant Institute, New York University
Guevara , Michael Physiology, McGill University, Macdonald Campus
Gyorke, Sandor Sandor.Gyorke@osumc.edu Physiology and Cell Biology, The Ohio State University
Hake, Johan hake@simula.no Scientific Computing, Simula Research Laboratory
Hanslien, Monica monicaha@simula.no Scientific Computing, Simula Research Laboratory
Henriquez , Craig ch@duke.edu Biomedical Engineering & Computer Science, Duke University
Hunter, Peter p.hunter@auckland.ac.nz Bioengineering Institute, University of Auckland
Iacombe, Veronique Iacombe.2@osu.edu College of Pharmacy, The Ohio State University
Isaacson, Samuel isaacson@math.utah.edu Department of Mathematics, University of Utah
Jafri, Saleet sjafri@gmu.edu Computational Sciences, George Mason University
Kanu, Uche uche.kanu@gmail.l.google.com Biomedical Engineering, Cornell University
Keener, James keener@math.utah.edu Mathematics & Bioengineering, University of Utah
Kerckhoffs, Roy roy@bioeng.ucsd.edu Bioengineering 0412, University of California, San Diego
Kim, Yangjin ykim@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Kohr, Mark Kohr.6@osu.edu Physiology and Cell Biology, The Ohio State University
Laurita, Kenneth klaurita@metrohealth.org Heart and Vascular Research Center, Case Western Reserve University
Lederer, Jonathan lederer@umbi.umd.edu Biotechnology Inst. & Dept. of Physiology, University of Maryland at Baltimore
Lee, Pilhwa leep@cims.nyu.edu Mathematics, Courant Institute of Mathematical Sciences
Linge, Svein s-ohm@online.no Scientific Computing, Simula Research Lab
Lou, Yuan lou@math.ohio-state.edu MBI - Long Term Visitor, The Ohio State University
Maoz, Anat maoz@cs.cornell.edu Computational Biology and Medicine, Cornell University
Martone, Maryann mmartone@ucsd.edu NCMIR & Neurosciences, University of California, San Diego
Michailova, Anushka amihaylo@bioeng.ucsd.edu Bioengineering, University of California, San Diego
Miller, Michael mim@cis.jhu.edu Biomedical Engineering, Johns Hopkins University
Nevai, Andrew anevai@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Ng, Bart bng@math.iupui.edu MBI - Long Term Visitor, Indiana University--Purdue University
Oster, Andrew aoester@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Palmer, Brian Brian.Palmer@osumc.edu Heart and Lung Institute, The Ohio State University
Panfilov , Sasha A.V.Panfilov@bio.uu.nl Theoretical Biology , Rijksuniversiteit te Utrecht
Poornima, Bhupathy bhupathy.1@osu.edu Physiology and Cell Biology, The Ohio State University
Puglisi, Jose (Pepe) jpuglis@lumc.edu Physiology, Loyola University
Rasmusson , Randall rr32@buffalo.edu Physiology and Biophysics , University at Buffalo (SUNY)
Rempe, Michael mrempe@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Roberts, Byron byr2001@med.cornell.edu Division of Cardiology, Cornell University
Rosenbaum, David dar12@psu.edu Medicine & Biomedical Engineering, Case Western Reserve University
Rudy, Yoram rudy@wustl.edu Cardiac Bioelectricity Center, Washington University
Rundell, Ann rundell@ecn.purdue.edu Purdue University, Purdue University
Salama, Guy gsalama@pitt.edu Cell Biology and Physiology , University of Pittsburgh
Schugart, Richard richard.schugart@wku.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Sher, Anna anna.sher@comlab.ox.ac.uk Computational Biology Group, University of Oxford
Smith, Greg greg@as.wm.edu Applied Science, College of William and Mary
Srinivasan, Partha p.srinivasan35@csuohio.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Stigler, Brandy bstigler@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Szomolay, Barbara b.szomolay@imperial.ac.uk Mathematical Biosciences Institute (MBI), The Ohio State University
Terje Lines, Glenn glennli@simula.no Scientific Computing, Simula Research Laboratory
Thul, Ruediger ruediger.thul@nottingham.ac.uk School of Mathematical Sciences, University of Nottingham
Tian, Paul tianjj@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Trayanova, Natalia ntrayanova@jhu.edu Department of Biomedical Engineering , Johns Hopkins University
Tveito, Aslak aslak@simula.no Simula Research Lab
Wang, Honglan wang.1002@osu.edu Physiology and Cell Biology, The Ohio State University
Wheeler, Debra wheeler.28@osu.edu Physiology and Cell Biology, The Ohio State University
Winslow, Rai School of Medicine & Whiting School of Engineering, Johns Hopkins University
Zemlin, Christian zemlinc@upstate.edu Pharmacology, University at Buffalo (SUNY)
Zhang, Linghai liz5@lehigh.edu MBI - Long Term Visitor, Lehigh University
Ziolo, Mark ziolo.1@osu.edu Dept. of Physiology and Cell Biology, The Ohio State University
Cardiac L-type Ca Channels, RyR2s and SERCA2a

Cardiac L-type Ca Channels, RyR2s and SERCA2a

Na-Ca Exchange in Cardiac Myocytes

Na-Ca Exchange in Cardiac Myocytes

Cellular Mechanisms of Stability of Reentrant Tachycardias in Infarcted Hearts: A Computational Approach

Reentrant circuits causing sustained ventricular tachycardia (i.e. lasting more than 30 sec) in the canine infarcted heart have a figure-8 activation pattern with a central (CCP) and an outer pathway (OP). Infarction causes extensive remodeling of ion channel function and gap junction conductance in the border zone of the infarct. The pattern of remodeling in the CCP and OP is heterogeneous. In the OP, Cx43 is located at the intercalated disks but side-to-side gap junction conductance (Gj) is reduced by 90% (end-to-end Gj is normal). End-to-end and side-to-side Gj in the CCP are both normal but Cx43 redistributes along the lateral membrane. Remodeling of the sodium and L-type calcium channel causes a loss of function in INa and ICa, T which is more marked in the CCP than in the OP. Even though, in general, heterogeneous myocardium is associated with unstable reentrant circuits, reentrant circuits in canine infarcted hearts are stable. Here, we use computer models of the infarcted canine heart to understand how the heterogeneities in ion channel function and gap junction conductance described experimentally lead to stable reentrant tachycardias.

Subtleties of Na+ Channel Gating Revealed by Theoretical Modeling: Understanding genetic perturbations and disease

Naturally occurring mutations in cardiac Na+ channels can disrupt channel gating and cause electrical abnormalities that increase susceptibility to cardiac arrhythmia. We have used a theoretical approach to simulate the effects of perturbations in discrete kinetics processes on channel gating and cellular electrical activity. Many mutations in cardiac INa linked to the Long-QT Syndrome (LQTs) result in a gain of function due to a fraction of channels that fail to inactivate (burst) leading to persistent current during depolarization. However, electrophysiological characterization of some Na+ channel linked Long-QT mutants has revealed that some do not. Interestingly, a number of these mutants share a common abnormality, namely increased rates of channel recovery from inactivation. We use experimental and theoretical approaches to reveal that mutation induced faster recovery from inactivation results can allow channel reopening during repolarization and cause severe prolongation of the action potential. We have also investigated the increased susceptibility to drug induced arrhythmia in African American carriers (4.6 millions) of a common polymorphism (S1102 to Y1102) in cardiac INa The study used a combined experimental and theoretical investigation. Although the experimental data suggested that the polymorphism Y1102 had subtle effects on Na+ channel function, the integrative model simulations revealed an increased susceptibility to arrhythmogenic-triggered activity in the presence of drug block (Splawski et al., 2002).

Arrhythmogenic Right Ventricular Cardiomyopathy (ARVC): A disease of the intercalated disc

ARVC is an inherited cardiac disease characterized by ventricular fibrofatty infiltration, predominantly in the right ventricle, and a high incidence of arrhythmias and sudden death. ARVC is responsible for a number of cases of exercise - related sudden cardiac death in the youth. In this presentation, I will review the clinical, anatomo-pathological and genetic characteristics of ARVC and describe new data indicating that, at least in some cases, ARVC may be accompanied by loss of the structural and molecular integrity of the cardiac intercalated disc. The clinical features of ARVC may be related to significant remodeling of the intercalated disc structures, including gap junctions.

Reentrant Arrhythmias

Reentrant Arrhythmias

Stochastic Models of Complex Molecules

Cells exhibit complex nonlinear dynamics which may appear as oscillations, excitability or even subcellulr structure formation. The elemental building blocks of that dynamics are complex molecules which often have several internal degrees of freedom. Typically, these molecules have active and inactive states. The dynamics of these molecules relevant for the global process can be described in terms of a distribution of hitting time to the active state (renewal process). The presentation introduces a method to calculate that distribution exactly. The method is suitable in particular for very small molecule numbers, i.e. in the range where other methods to calculate first passage probability densities (e.g. linear Fokker-Planck-Eq.) fail.

Calcium Release Units, the Macromolecular Complexes Responsible for Calcium Release in Cardiac Myocytes

Cardiac excitation at the cellular level is initiated by release of Ca2+ from the junctional cisternae of the sarcoplasmic reticulum (jSR). The jSR is closely associated with and controlled by surface membrane/T tubules within units called Calcium Release Units (CRUs). The jSR membrane and lumen are occupied by a number of proteins that are linked to each other both structurally and functionally. The ryanodine receptor (RyR) or SR Ca2+ release channel is the focus of interactions involving the luminal Ca2+ binding protein calsequestrin and the two jSR membrane proteins junctin and triadin. Overexpression of all CSQ, Jn and Tr (in collaboration with L.R. Jones) and a null mutation of CSQ (in collaboration with B.C. Knollman, L.R. Jones and K. Pfeifer) have structural effects which serve to illustrate the roles of the three CRU components in the architecture and function of CRUs. L type calcium channels in T tubules (the DHPRs) act as voltage sensor initiating the signal for jSR Ca2+ release via RyRs. Differences in the relative positioning of DHPRs and RyRs between cardiac and skeletal muscles are at the basis of the known differences in e-c coupling between the two striated muscles.


Supported by NIH Merit Award HL48093 from the National Heart, Lung and Blood Institute.

Synchronization Rhythms in the Heart

During normal activity in the heart, in any given excitable cell there is one action potential for each action potential of the sinoatrial node, with a time delay that is more or less fixed from beat to beat. This 1:1 synchronization can break down in several ways: e.g., there can be Wenckebach rhythms, alternans (2:2 rhythm), or a direct transition to 2:1 rhythm. We provide experimental evidence for these transitions in experimental work on single ventricular cells, as well as in ionic models and in the much simpler piecewise-linear FitzHugh-Nagumo equations. We describe how the dynamics can, on occasion, be reduced to the analysis of one-dimensional maps, wherein multistability (the simultaneous presence of two or more periodic rhythms, depending on initial conditions) arises. Extensions of this work to multicellular systems and its relevance to the understanding of the generation of certain cardiac arrhythmias will also be presented.

Regulation of Intracellular Calcium Release in Normal and Diseased Heart

Davis Heart & Lung Research Institute, Ohio State University, Columbus, OH In cardiac muscle, calcium release from the sarcoplasmic reticulum (SR) is central to the process of excitation-contraction coupling. Calcium is released through specialized calcium-permeable channels called ryanodine receptors (RyR2s) and causes shortening of the contractile filaments. The RyR2 channel interacts with a number of SR proteins including triadin, junctin and calsequestrin that work in synchrony to control SR calcium release during the cardiac cycle. In my presentation I will discuss the mechanisms of RyR2 regulation by these auxiliary proteins and how genetic and acquired defects in these mechanisms can lead to cardiac diseases such as arrhythmia and heart failure.

Modeling the Arrhythmogenic Substrate: Incorporating Heterogeneity at the Microscale in Cardiac Tissue Models

Some arrhythmias are the result of certain channelopathies caused by a mutation or mutations in genes coding for ion channel subunits or the proteins that regulate them and can occur in the absence of any structural changes to the heart muscle. Other arrhythmias, however, are only manifested when there are significant structural changes in the tissue, such as modulation of cell size and morphology, infiltration of fibroblasts, increased non-uniformity in the interstitial space and changes in the number and distribution of gap junction connexons. While there has been rapid growth in the use of computer models to study the mechanisms of normal and abnormal cardiac conduction, the bulk of the models represent the tissue as structurally uniform and continuous, often without consideration of the effects of the extracellular space. In this talk, I present a brief overview of the evolution of cardiac tissue models and introduce a novel computational approach for studying propagation in three-dimensions at the microscale. In this model, individual myoctyes are represented as discrete units comprising an intracellular space, bounded by a membrane and embedded in an interstitium. The model builds off the work of Spach Heidlage (Circ. Res, 1995) and differs from the classical monodomain or bidomain models in that it can incorporate realistic cell morphologies, channel distributions and cell-to-cell connectivities that are associated with an arrhythmogenic substrate. Simulations results are presented that demonstrate how the framework can be used to study the effects of structural changes, such as those arising from disease and aging of the myocardium, on impulse propagation and signal waveshape that cannot be easily captured in traditional tissue models.

Tissue and Organ Level Cardiac Electrophysiological Modelling

To incorporate cell-based ion channel electrophysiology models into tissue and organ level simulations of myocardial activation, it is important to understand how current flows through and between cells in the three dimensional fibrous-sheet architecture of ventricular myocardium. The cardiac group in the Auckland Bioengineering Institute has developed an instrument for imaging the 3D structure of myocardial tissue and has developed bidomain reaction-diffusion models that incorporate the measured structure at length scales of 0.2m -1.0mm. By comparing the propagation of activation wavefronts using these detailed structural models with coarser grained continuum models that approximate the fibrous-sheet structure on a larger length scale, it is possible to derive a conductivity tensor for the tissue that can be used in the intact organ level simulations. Other issues that will be discussed are: (i) the use of the CellML model repository (www.cellml.org/models) for defining the cell equations and tissue constitutive laws, and (ii) the coupling of electrical activation based on reaction-diffusion equations to large deformation mechanics in the beating heart.


This work was done in collaboration with: Travis M. Austin, Darren A. Hooks, David P. Nickerson, Andrew J. Pullan, Gregory B. Sands, Bruce H. Smaill, and Mark L. Trew1.

The Spatial Spread of Calcium Sparks in the Sarcomere

Cardiac excitation-contraction coupling describes the chain of events from the initiation of depolarization of the sarcolemma of the cardiac myocyte through contraction. We investigate how microstructural and physiological features affect the spatial spread of calcium sparks which are considered to be the elementary events of excitation-contraction coupling through a computational study. The basic model consists of two dyads positions on opposite sides of a T-tubule and the adjacent half sarcomeres. The model suggests that in order to simulate the spatial spread of calcium i.e. a full-width at half maximum (FWHM) of 2.0 microns seen in experiments, calcium release from both dyads must occur. The model also simulates the local depletion of the sarcoplasmic reticulum seen in experiments and suggests that this observed depletion is composed of large depletion of the junctional sarcoplasmic reticulum and small depletion of the network sarcoplasmic reticulum which appear as a small over all depletion due to the effects of the dyes used and confocal imaging techniques. The model then is expanded to include multiple release sites and is used to account for spontaneous calcium waves seen in calcium overload conditions. Such conditions might occur in heart failure and lead to cardiac arrhythmias.


This project is joint work with Hena R. Ramay, W. Jonathan Lederer, and Eric A. Sobie and was supported by the NSF.

Arrhythmia Mechanisms: Myocardial Infarction

Ventricular remodeling associated with myocardial infarction (MI) promotes a substrate that is the leading cause of ventricular arrhythmias, frequently presenting as sudden cardiac death. The usual cause of ventricular arrhythmias associated with late MI is, in part, reentrant excitation resulting from electrophysiological heterogeneity due to coexistence of infarcted, border zone and viable myocardial tissue. To better understand the mechanisms of arrhythmogenesis associated with MI, studies have meticulously focused on altered ionic currents, action potentials, and cell-to-cell coupling associated with viable cells in the border zone. Likewise, abnormal conduction, such as wave break, impulse block, and slow conduction, have been well documented in late MI. However, the exact causal relationship between abnormal cellular electrophysiology, conduction abnormalities, and arrhythmogenesis associated with late MI is not completely understood. Novel experimental techniques can be used to illuminate the mechanistic relationship between abnormal cellular electrophysiology and arrhythmogenesis associated with late MI and, possibly, lead to new therapeutic approaches.

Cardiac Ca Dynamics

Cardiac Ca Dynamics

Computational Anatomy and the Infinite Dimensional Diffeomorphisms

Over the past 10 years computational anatomy has emerged as a quantitative subfield of Medical Image Analysis. Computational anatomy is the study of biological shape via the infinite dimensional diffeomorphisms. This talk will review progress on the (i) the construction of the group of diffeomorphisms via flows, (ii) the model of anatomical orbit as a group action of diffeomorphisms on exemplars (deformable template) with associated metric structure, and (iii) the variational problems associated with inference of the hidden flows connecting configurations in the anatomical orbit. Applications will be described in metric comparison of shapes in human anatomy and in growth and development sequences.

Modeling Electrical Conduction in the Cardiac Ventricles

Cardiac arrhythmias and sudden cardiac death is the leading cause of death accounting for about 1 death in 10 in industrialized countries. Although cardiac arrhythmias has been studied for well over a century, their underlying mechanisms remain largely unknown. One of the main problems in studies of cardiac arrhythmias is that they occur at the level of the whole organ only, while in most of the cases only single cell experiments can be performed. Due to these limitations alternative approaches such as mathematical modeling are of great interest. From mathematical point of view excitation of the heart is described by a system of non-linear parabolic PDEs of the reaction diffusion type with anisotropic diffusion operator. Cardiac arrhythmias correspond to the solutions of these equations in form of 2D or 3D vortices characterized by their filaments. In my talk I will present a short overview of two directions of our research:



  1. Filament dynamics in anisotropic cardiac tissue. I will present a method that can be used to predict filament shapes in anisotropic tissue based on data on the arrival times of the excitation in given slab of cardiac tissue. The method is extension of the 'minimal principle for rotor filaments' proposed by Wellner et al., (PNAS,v.99:8015-8018,2002). We demonstrate that this principle can be reformulated using the eikonal equation for wave propagation in the same medium in which the scroll wave rotates.

  2. Development of virtual human heart model. Here I will report on development of an anatomically accurate model for the human heart. The model integrates our knowledge about electrophysiology of the human heart from a single cell to the whole organ and allows us to study mechanisms of cardiac arrhythmias in the human heart, where experimental interventions are very limited. I will present results of our studies of 3D organization of ventricular fibrillation in human heart and compare our conclusions to the available experimental and clinical data. In general, we find that ventricular fibrillation in the human heart may be organized by a small number of vortex filaments (around 10) and should have much simpler structure than thought before. I will also present our recent results on implementation of clinically measured heterogeneity of human ventricles and on modelling of effects of these heterogeneities on ventricular fibrillation.

Biology and Modeling of Cardiac K Channels

Cardiac potassium channels control the process of repolarization. During repolarization several potassium channels are active and a precise timing of interaction during repolarization is required for proper action potential behavior. On a molecular level, mutations in key potassium channels have been closely linked to arrhythmias, in spite of mutations causing seemingly minor changes in action potential shape and/or channel kinetics. This sensitivity to the exact kinetic behavior of ion channels emphasizes the importance of precise modeling of potassium channel function. We model potassium channel function beginning at the level of molecular structure. Various elements of physical structure constrain the possible kinetic models for description of channel kinetics. In the example of the Kv1.4 and Kv4.3 channels which mediate various components of the cardiac transient outward current, activation occurs with a sigmoid delay. Inactivation has at least two components, often termed N-type and C-type inactivation. Both are functionally coupled to the process of activation. N-type inactivation occurs via a "ball and chain" mechanism. C-type inactivation is less well defined but involves residues at the outer mouth of the pore which are coupled to large scale movements of the intracellular pore mouth, S6 and other domains of the channel. These large scale changes mediate strong interactions between C-type and N-type inactivation which cause the rate limiting step for recovery to be determined by the properties of C-type inactivation. These kinetic properties are essential for determining the restitution and recovery processes of the cardiac action potential.

Alternans

Alternans

Relating Ion-Channel Kinetic Properties to Cardiac Repolarization and Repolarization Abnormalities using Computational Biology

Cardiac excitation and arrhythmogenesis involve intimate interactions between processes at different scales of the cardiac system from ion channel, to the whole cell, to the multicellular tissue. Mathematical models of cellular electrophysiology have been very helpful in identifying and characterizing such interactions and in elucidating mechanisms. In my presentation, I will provide examples of interactions between ion channel kinetics and the cellular environment in the context of mutations and action potential repolarization. In the first example (Clancy and Rudy, Cardiovascular Research 2001; 50: 301-313), the long QT cellular phenotype of HERG mutation is shown to result from the specific kinetic changes to IKr (the rapid delayed rectifier) and their effect during the action potential. Early afterdepolarizations are generated through an interaction between the mutant IKr channels and the L-type Ca2+ channels. In a second example (Silva and Rudy, Circulation 2005; 112: 1384-1391), I will use computational biology to explain how the kinetic properties of IKs (the slow delayed rectifier) that are conferred by molecular subunit interactions, determine its participation in rate-dependent repolarization and facilitate its role as "repolarization reserve."


Supported by NIH Merit Award R37-HL33343 and Grant RO1-HL49054 from the National Heart, Lung and Blood Institute.

Wavelets, Wavebreaks and Ventricular Fibrillation

We present a probability density approach to modeling heterogeneous calcium (Ca) release from stochastic functional units (SFUs) or "couplons" of cardiac myocytes. Coupled advection-reaction equations are derived relating the time-dependent probability density of subsarcolemmal subspace and junctional sarcoplasmic reticulum [Ca] conditioned on the state of each SFU. When these equations are coupled to ODEs for the bulk myoplasmic and SR [Ca], a realistic but minimal model of cardiac Ca-induced Ca release via local triggering of Ca sparks is produced. This modeling approach avoids the computationally demanding task of resolving spatial aspects of global Ca signaling, while accurately representing heterogeneous local Ca signals in a population of diadic subspaces and junctional SR depletion domains. The equations are solved numerically using a high-resolution finite difference scheme. The approach is validated for a physiologically realistic number of SFUs and benchmarked for computational efficiency by comparison to traditional Monte Carlo simulations. The probability density approach produces Ca release that is graded with changes in membrane potential and depolarization duration and represents a new class of deterministic whole cell models that efficiently represent important aspects of stochastic Ca channel gating and localized Ca dynamics. This project is joint work with G. S. Blair Williams, Marco A. Huertas, Eric A. Sobie, and M. Saleet Jafri.

A Probability Density Approach to Modeling Local Calcium Signaling and Stochastic Functional Unit Activity in Cardiac Myocytes

A Probability Density Approach to Modeling Local Calcium Signaling and Stochastic Functional Unit Activity in Cardiac Myocytes

Bidomain Models: Inducing and Terminating VF

Bidomain Models: Inducing and Terminating VF

Calcium-Induced Calcium-Release: Insights From Studies of Heart Failure

Heart failure is a disease with high mortality and a distinctive organ and cellular phenotype. The cellular phenotype is distinguished by both action potential prolongation and reduction of both amplitude and rate of decline of the intracellular calcium transient. Our early studies of this disease were focused on measuring ion channels, membrane transporters and Ca cycling proteins with altered expression in end-stage heart failure and using models to interpret the functional significance of these changes. These studies revealed that while voltage-gated K channels were down-regulated in end-stage heart failure, this down-regulation could not explain AP prolongation of altered Ca transients. Rather, altered expression of the proteins involved in Ca cycling seemed to play the dominant role. In thistalk, we will review these early findings, and discuss how they have informed the design of new models of the calcium-induced calcium-release process in the cardiac myocyte.