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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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:
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.
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.
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.
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.