Henggui Zhang

Models of cardiac tissue electrophysiology: Progress, challenges and open questions

Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.

Heterogeneous three-dimensional anatomical and electrophysiological model of human atria

Investigating the mechanisms underlying the genesis and conduction of electrical excitation in the atria at physiological and pathological states is of great importance. To provide knowledge concerning the mechanisms of excitation, we constructed a biophysical detailed and anatomically accurate computer model of human atria that incorporates both structural and electrophysiological heterogeneities. The three-dimensional geometry was extracted from the visible female dataset. The sinoatrial node (SAN) and atrium, including crista terminalis (CT), pectinate muscles (PM), appendages (APG) and Bachmanns bundle (BB) were segmented in this work. Fibre orientation in CT, PM and BB was set to local longitudinal direction. Descriptions for all used cell types were based on modifications of the Courtemanche et al. model of a human atrial cell. Maximum conductances of , and were modified for PM, CT, APG and atrioventricular ring to reproduce measured action potentials (AP). Pacemaker activity in the human SAN was reproduced by removing , but including , , and gradients of channel conductances as described in previous studies for heterogeneous rabbit SAN. Anisotropic conduction was computed with a monodomain model using the finite element method. The transversal to longitudinal ratio of conductivity for PM, CT and BB was 1 : 9. Atrial working myocardium (AWM) was set to be isotropic. Simulation of atrial electrophysiology showed initiation of APs in the SAN centre. The excitation spread afterwards to the periphery near to the region of the CT and preferentially towards the atrioventricular region. The excitation extends over the right atrium along PM. Both CT and PM activated the right AWM. Earliest activation of the left atrium was through BB and excitation spread over to the APG. The conduction velocities were 0.6 m s−1 for AWM, 1.2 m s−1 for CT, 1.6 m s−1 for PM and 1.1 m s−1 for BB at a rate of 63 bpm. The simulations revealed that bundles form dominant pathways for atrial conduction. The preferential conduction towards CT and along PM is comparable with clinical mapping. Repolarization is more homogeneous than excitation due to the heterogeneous distribution of electrophysiological properties and hence the action potential duration.

Tension of organizing filaments of scroll waves

We consider the asymptotic theory for the dynamics of organizing filaments of three-dimensional scroll waves. For a generic autowave medium where two dimensional vortices do not meander, we show that some of the coefficients of the evolution equation are always zero. This simpler evolution equation predicts a monotonic change of the total filament length with time, independently of initial conditions. Whether the filament will shrink or expand is determined by a single coefficient, the filament tension, that depends on the medium parameters. We illustrate the behaviour of scroll wave filaments with positive and negative tension by numerical experiments. In particular, we show that in the case of negative filament tension, the straight filament is unstable, and its evolution may lead to a multiplication of vortices.

3D virtual human atria: A computational platform for studying clinical atrial fibrillation

Despite a vast amount of experimental and clinical data on the underlying ionic, cellular and tissue substrates, the mechanisms of common atrial arrhythmias (such as atrial fibrillation, AF) arising from the functional interactions at the whole atria level remain unclear. Computational modelling provides a quantitative framework for integrating such multi-scale data and understanding the arrhythmogenic behaviour that emerges from the collective spatio-temporal dynamics in all parts of the heart. In this study, we have developed a multi-scale hierarchy of biophysically detailed computational models for the human atria--the 3D virtual human atria. Primarily, diffusion tensor MRI reconstruction of the tissue geometry and fibre orientation in the human sinoatrial node (SAN) and surrounding atrial muscle was integrated into the 3D model of the whole atria dissected from the Visible Human dataset. The anatomical models were combined with the heterogeneous atrial action potential (AP) models, and used to simulate the AP conduction in the human atria under various conditions: SAN pacemaking and atrial activation in the normal rhythm, break-down of regular AP wave-fronts during rapid atrial pacing, and the genesis of multiple re-entrant wavelets characteristic of AF. Contributions of different properties of the tissue to mechanisms of the normal rhythm and arrhythmogenesis were investigated. Primarily, the simulations showed that tissue heterogeneity caused the break-down of the normal AP wave-fronts at rapid pacing rates, which initiated a pair of re-entrant spiral waves; and tissue anisotropy resulted in a further break-down of the spiral waves into multiple meandering wavelets characteristic of AF. The 3D virtual atria model itself was incorporated into the torso model to simulate the body surface ECG patterns in the normal and arrhythmic conditions. Therefore, a state-of-the-art computational platform has been developed, which can be used for studying multi-scale electrical phenomena during atrial conduction and AF arrhythmogenesis. Results of such simulations can be directly compared with electrophysiological and endocardial mapping data, as well as clinical ECG recordings. The virtual human atria can provide in-depth insights into 3D excitation propagation processes within atrial walls of a whole heart in vivo, which is beyond the current technical capabilities of experimental or clinical set-ups.

Cardiac cell modelling: observations from the heart of the cardiac physiome project.

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field.

Sinus node dysfunction following targeted disruption of the murine cardiac sodium channel gene Scn5a

We have examined sino‐atrial node (SAN) function in hearts from adult mice with heterozygous targeted disruption of the Scn5a gene to clarify the role of Scn5a‐encoded cardiac Na+ channels in normal SAN function and the mechanism(s) by which reduced Na+ channel function might cause sinus node dysfunction. Scn5a+/− mice showed depressed heart rates and occasional sino‐atrial (SA) block. Their isolated peripheral SAN pacemaker cells showed a reduced Na+ channel expression and slowed intrinsic pacemaker rates. Wild‐type (WT) and Scn5a+/− SAN preparations exhibited similar activation patterns but with significantly slower SA conduction and frequent sino‐atrial conduction block in Scn5a+/− SAN preparations. Furthermore, isolated WT and Scn5a+/− SAN cells demonstrated differing correlations between cycle length, maximum upstroke velocity and action potential amplitude, and cell size. Small myocytes showed similar, but large myocytes reduced pacemaker rates, implicating the larger peripheral SAN cells in the reduced pacemaker rate that was observed in Scn5a+/− myocytes. These findings were successfully reproduced in a model that implicated iNa directly in action potential propagation through the SAN and from SAN to atria, and in modifying heart rate through a coupling of SAN and atrial cells. Functional alterations in the SAN following heterozygous‐targeted disruption of Scn5a thus closely resemble those observed in clinical sinus node dysfunction. The findings accordingly provide a basis for understanding of the role of cardiac‐type Na+ channels in normal SAN function and the pathophysiology of sinus node dysfunction and suggest new potential targets for its clinical management.

Biophysical Characterization of the Underappreciated and Important Relationship Between Heart Rate Variability and Heart Rate

Heart rate (HR) variability (HRV; beat-to-beat changes in the R-wave to R-wave interval) has attracted considerable attention during the past 30+ years (PubMed currently lists >17 000 publications). Clinically, a decrease in HRV is correlated to higher morbidity and mortality in diverse conditions, from heart disease to fetal distress. It is usually attributed to fluctuation in cardiac autonomic nerve activity. We calculated HRV parameters from a variety of cardiac preparations (including humans, living animals, Langendorff-perfused heart, and single sinoatrial nodal cell) in diverse species, combining this with data from previously published articles. We show that regardless of conditions, there is a universal exponential decay-like relationship between HRV and HR. Using 2 biophysical models, we develop a theory for this and confirm that HRV is primarily dependent on HR and cannot be used in any simple way to assess autonomic nerve activity to the heart. We suggest that the correlation between a change in HRV and altered morbidity and mortality is substantially attributable to the concurrent change in HR. This calls for re-evaluation of the findings from many articles that have not adjusted properly or at all for HR differences when comparing HRV in multiple circumstances.

Computer Three-Dimensional Reconstruction of the Atrioventricular Node

Because of its complexity, the atrioventricular node (AVN), remains 1 of the least understood regions of the heart. The aim of the study was to construct a detailed anatomic model of the AVN and relate it to AVN function. The electric activity of a rabbit AVN preparation was imaged using voltage-dependent dye. The preparation was then fixed and sectioned. Sixty-five sections at 60- to 340-&mgr;m intervals were stained for histology and immunolabeled for neurofilament (marker of nodal tissue) and connexin43 (gap junction protein). This revealed multiple structures within and around the AVN, including transitional tissue, inferior nodal extension, penetrating bundle, His bundle, atrial and ventricular muscle, central fibrous body, tendon of Todaro, and valves. A 3D anatomically detailed mathematical model (≈13 million element array) of the AVN and surrounding atrium and ventricle, incorporating all cell types, was constructed. Comparison of the model with electric activity recorded in experiments suggests that the inferior nodal extension forms the slow pathway, whereas the transitional tissue forms the fast pathway into the AVN. In addition, it suggests the pacemaker activity of the atrioventricular junction originates in the inferior nodal extension. Computer simulation of the propagation of the action potential through the anatomic model shows how, because of the complex structure of the AVN, reentry (slow–fast and fast–slow) can occur. In summary, a mathematical model of the anatomy of the AVN has been generated that allows AVN conduction to be explored.

Mathematical models of the electrical action potential of Purkinje fibre cells

Early development of ionic models for cardiac myocytes, from the pioneering modification of the Hodgkin–Huxley giant squid axon model by Noble to the iconic DiFrancesco–Noble model integrating voltage-gated ionic currents, ion pumps and exchangers, Ca2+ sequestration and Ca2+-induced Ca2+ release, provided a general description for a mammalian Purkinje fibre (PF) and the framework for modern cardiac models. In the past two decades, development has focused on tissue-specific models with an emphasis on the sino-atrial (SA) node, atria and ventricles, while the PFs have largely been neglected. However, achieving the ultimate goal of creating a virtual human heart will require detailed models of all distinctive regions of the cardiac conduction system, including the PFs, which play an important role in conducting cardiac excitation and ensuring the synchronized timing and sequencing of ventricular contraction. In this paper, we present details of our newly developed model for the human PF cell including validation against experimental data. Ionic mechanisms underlying the heterogeneity between the PF and ventricular action potentials in humans and other species are analysed. The newly developed PF cell model adds a new member to the family of human cardiac cell models developed previously for the SA node, atrial and ventricular cells, which can be incorporated into an anatomical model of the human heart with details of its electrophysiological heterogeneity and anatomical complexity.

Connexins in the Sinoatrial and Atrioventricular Nodes

The sinoatrial node (SAN) and the atrioventricular node (AVN) are specialized tissues in the heart: the SAN is specialized for pacemaking (it is the pacemaker of the heart), whereas the AVN is specialized for slow conduction of the action potential (to introduce a delay between atrial and ventricular activation during the cardiac cycle). These functions have special requirements regarding electrical coupling and, therefore, expression of connexin isoforms. Electrical coupling in the center of the SAN should be weak to protect it from the inhibitory electrotonic influence of the more hyperpolarized non-pacemaking atrial muscle surrounding the SAN. However, for the SAN to be able to drive the atrial muscle, electrical coupling should be strong in the periphery of the SAN. Consistent with this, in the center of the SAN there is no expression of Cx43 (the principal connexin of the working myocardium) and little expression of Cx40, but there is expression of Cx45 and Cx30.2, whereas in the periphery of the SAN Cx43 as well Cx45 is expressed. In the AVN, there is a similar pattern of expression of connexins as in the center of the SAN and this is likely to be in large part responsible for the slow conduction of the action potential.