Chris P. Bradley

Whole heart action potential duration restitution properties in cardiac patients: a combined clinical and modelling study

Steep action potential duration (APD) restitution has been shown to facilitate wavebreak and ventricular fibrillation. The global APD restitution properties in cardiac patients are unknown. We report a combined clinical electrophysiology and computer modelling study to: (1) determine global APD restitution properties in cardiac patients; and (2) examine the interaction of the observed APD restitution with known arrhythmia mechanisms. In 14 patients aged 52–85 years undergoing routine cardiac surgery, 256 electrode epicardial mapping was performed. Activation–recovery intervals (ARI; a surrogate for APD) were recorded over the entire ventricular surface. Mono‐exponential restitution curves were constructed for each electrode site using a standard S1–S2 pacing protocol. The median maximum restitution slope was 0.91, with 27% of all electrode sites with slopes < 0.5, 29% between 0.5 and 1.0, and 20% between 1.0 and 1.5. Eleven per cent of restitution curves maintained slope > 1 over a range of diastolic intervals of at least 30 ms; and 0.3% for at least 50 ms. Activation–recovery interval restitution was spatially heterogeneous, showing regional organization with multiple discrete areas of steep and shallow slope. We used a simplified computer model of 2‐D cardiac tissue to investigate how heterogeneous APD restitution can influence vulnerability to, and stability of re‐entry. Our model showed that heterogeneity of restitution can act as a potent arrhythmogenic substrate, as well as influencing the stability of re‐entrant arrhythmias. Global epicardial mapping in humans showed that APD restitution slopes were organized into regions of shallow and steep slopes. This heterogeneous organization of restitution may provide a substrate for arrhythmia.

Noninvasive electrical imaging of the heart: theory and model development.

AbstractThe aim of this work is to begin quantifying the performance of a recently developed activation imaging algorithm of Huiskamp and Greensite [IEEE Trans. Biomed. Eng. 44:433–446]. We present here the modeling and computational issues associated with this process. First, we present a practical construction of the appropriate transfer matrix relating an activation sequence to body surface potentials from a general boundary value problem point of view. This approach makes explicit the role of different Greens functions and elucidates features (such as the anisotropic versus isotropic distinction) not readily apparent from alternative formulations. A new analytic solution is then developed to test the numerical implementation associated with the transfer matrix formulation presented here and convergence results for both potentials and normal currents are given. Next, details of the construction of a generic porcine model using a nontraditional data-fitting procedure are presented. The computational performance of this model is carefully examined to obtain a mesh of an appropriate resolution to use in inverse calculations. Finally, as a test of the entire approach, we illustrate the activation inverse procedure by reconstructing a known activation sequence from simulated data. For the example presented, which involved two ectopic focii with large amounts of Gaussian noise (100 μV rms) present in the torso signals, the reconstructed activation sequence had a similarity index of 0.880 when compared to the input source.

OpenCMISS: A multi-physics & multi-scale computational infrastructure for the VPH/Physiome project

The VPH/Physiome Project is developing the model encoding standards CellML (cellml.org) and FieldML (fieldml.org) as well as web-accessible model repositories based on these standards (models.physiome.org). Freely available open source computational modelling software is also being developed to solve the partial differential equations described by the models and to visualise results. The OpenCMISS code (opencmiss.org), described here, has been developed by the authors over the last six years to replace the CMISS code that has supported a number of organ system Physiome projects. OpenCMISS is designed to encompass multiple sets of physical equations and to link subcellular and tissue-level biophysical processes into organ-level processes. In the Heart Physiome project, for example, the large deformation mechanics of the myocardial wall need to be coupled to both ventricular flow and embedded coronary flow, and the reaction-diffusion equations that govern the propagation of electrical waves through myocardial tissue need to be coupled with equations that describe the ion channel currents that flow through the cardiac cell membranes. In this paper we discuss the design principles and distributed memory architecture behind the OpenCMISS code. We also discuss the design of the interfaces that link the sets of physical equations across common boundaries (such as fluid-structure coupling), or between spatial fields over the same domain (such as coupled electromechanics), and the concepts behind CellML and FieldML that are embodied in the OpenCMISS data structures. We show how all of these provide a flexible infrastructure for combining models developed across the VPH/Physiome community.

Organization of ventricular fibrillation in the human heart: experiments and models.

Sudden cardiac death is a major health problem in the industrialized world. The lethal event is typically ventricular fibrillation (VF), during which the co‐ordinated regular contraction of the heart is overthrown by a state of mechanical and electrical anarchy. Understanding the excitation patterns that sustain VF is important in order to identify potential therapeutic targets. In this paper, we studied the organization of human VF by combining clinical recordings of electrical excitation patterns on the epicardial surface during in vivo human VF with simulations of VF in an anatomically and electrophysiologically detailed computational model of the human ventricles. We find both in the computational studies and in the clinical recordings that epicardial surface excitation patterns during VF contain around six rotors. Based on results from the simulated three‐dimensional excitation patterns during VF, which show that the total number of electrical sources is 1.4 ± 0.12 times greater than the number of epicardial rotors, we estimate that the total number of sources present during clinically recorded VF is 9.0 ± 2.6. This number is approximately fivefold fewer compared with that observed during VF in dog and pig hearts, which are of comparable size to human hearts. We explain this difference by considering differences in action potential duration dynamics across these species. The simpler spatial organization of human VF has important implications for treatment and prevention of this dangerous arrhythmia. Moreover, our findings underline the need for integrated research, in which human‐based clinical and computational studies complement animal research.

Mathematical modelling of the heart: cell to organ

Abstract Single cell and whole organ mathematical models of cardiac electrophysiology, mechanics and metabolism are presented. The important elements of each model are outlined and, in particular, the methods, techniques and considerations for coupling each element together to create an integrated cardiac model are discussed. Results for both individual tissue and whole organ simulations are presented along with preliminary results from coupled models.

Imaging electrocardiographic dispersion of depolarization and repolarization during ischemia: Simultaneous body surface and epicardial mapping

Background—Myocardial ischemia creates abnormal electrophysiological substrates that result in life-threatening ventricular arrhythmias. Identifying patients at risk of such abnormalities by use of body surface electrical measures is controversial. We investigated the sensitivity of torso measures, recorded simultaneously with epicardial electrograms, to changes in dispersion of depolarization and repolarization during localized ventricular ischemia. Methods and Results—Ventricular epicardial electrograms were recorded from 5 anesthetized pigs with a 127-electrode sock. A controllable suture snare was used to ligate the left anterior descending coronary artery (LAD). The chest was reclosed, and a vest with 256 ECG electrodes was fitted to the torso. Simultaneous arrays of epicardial electrograms and torso ECGs were recorded during LAD occlusion and reperfusion. Activation-recovery intervals (ARIs), QTu and RTu dispersion (where u indicates upstroke), and QRST integrals were calculated, and these data were fitted to anatomically customized computational models of the swine ventricular epicardium and torso. LAD occlusion caused the epicardial ARI dispersion to steadily increase, whereas the location of shortest ARI shifted from the posterobasal ventricular tissue (control) to the anteroapical myocardium, distal to the suture snare. These changes were associated with a steady increase in the torso RTu dispersion as the shortest RTu interval moved from the right shoulder (control) to the sternum. QTu and RTu dispersion determined from the 12-lead ECG did not consistently reflect the myocardial changes. Conclusions—Although changes in myocardial repolarization dispersion resulting from localized ischemia are not reliably reflected in temporal indices derived from the 12-lead ECG, they can be readily identified with high-resolution torso ECG mapping.

Experiment-model interaction for analysis of epicardial activation during human ventricular fibrillation with global myocardial ischaemia

We describe a combined experiment-modelling framework to investigate the effects of ischaemia on the organisation of ventricular fibrillation in the human heart. In a series of experimental studies epicardial activity was recorded from 10 patients undergoing routine cardiac surgery. Ventricular fibrillation was induced by burst pacing, and recording continued during 2.5 min of global cardiac ischaemia followed by 30 s of coronary reflow. Modelling used a 2D description of human ventricular tissue. Global cardiac ischaemia was simulated by (i) decreased intracellular ATP concentration and subsequent activation of an ATP sensitive K⁺ current, (ii) elevated extracellular K⁺ concentration, and (iii) acidosis resulting in reduced magnitude of the L-type Ca²⁺ current I(Ca,L). Simulated ischaemia acted to shorten action potential duration, reduce conduction velocity, increase effective refractory period, and flatten restitution. In the model, these effects resulted in slower re-entrant activity that was qualitatively consistent with our observations in the human heart. However, the flattening of restitution also resulted in the collapse of many re-entrant waves to several stable re-entrant waves, which was different to the overall trend we observed in the experimental data. These findings highlight a potential role for other factors, such as structural or functional heterogeneity in sustaining wavebreak during human ventricular fibrillation with global myocardial ischaemia.

The computational performance of a high-order coupled FEM/BEM procedure in electropotential problems

Presents a thorough analysis of the computational performance of a coupled cubic Hermite boundary element/finite element procedure. This C/sup 1/ (i.e., value and derivative continuous) method has been developed specifically for electropotential problems, and has been previously applied to torso and skull problems. Here, the behavior of this new procedure is quantified by solving a number of dipole in spheres problems. A detailed set of results generated with a wide range of the various input parameters (such as dipole orientation, location, conductivity, and solution method used in each spherical shell [either finite element or boundary elements]) is presented. The new cubic Hermite boundary element procedure shows significantly better accuracy and convergence properties and a significant reduction in CPU time than a traditional boundary element procedure which uses linear or constant elements. Results using the high-order method are also compared with other computational methods which have had quantitative results published for electropotential problems. In all eases, the high-order method offered a significant improvement in computational efficiency by increasing the solution accuracy for the same, or fewer, solution degrees of freedom.

An experimental model to correlate simultaneous body surface and epicardial electropotential recordings in vivo

Our aim was to simultaneously record dense arrays of electropotential signals from the heart and body surface of a closed-chest anaesthetised pig during an acute period of regional ventricular ischaemia. After fitting a suture snare to the equatorial region of the left anterior descending (LAD) coronary artery, an electrode sock containing 127 stainless steel contact electrodes (spaced approximately 7 mm apart) was positioned over the ventricular epicardium. The chest was re-closed and fitted an elasticated vest containing 256 ECG electrodes (spaced approximately 15 mm apart). Electrode locations were measured using a mechanical digitising arm and projected onto a customised 3D mathematical model of the porcine torso and heart. Finite element fitted body surface potential maps (BSPMs) and epicardial activation sequences were used to interpret the electropotential signals. Data were sampled at 2 kHz and recorded at 20 s intervals during a four minute period of LAD occlusion, followed by a period of reperfusion and recovery. During occlusion, propagation of epicardial activation slowed monotonically across the ischaemic region and this was clearly associated with a zone of ST segment elevation in the BSPM and Lead V1 ECG, whilst the Lead II ECG remained relatively unchanged. The epicardial activation sequence had largely recovered after 60 s of reperfusion, although there was still evidence of slowed activation across the ischaemic region compared to the control. Electrocardiac activity had fully restored to its control state after six minutes of reperfusion. Simultaneous recordings of this type will provide an experimental model to be used together with our integrated computational framework to assess the accuracy and sensitivity of activation inverse ECG algorithms during normal and patho-physiological states. 2002 Elsevier

Application of the BEM in biopotential problems

Abstract We describe how the boundary element method (BEM) can be used in the general field of biopotential problems. We present here a cubic Hermite boundary element procedure for this purpose and show how this approach is computationally more efficient than traditional BEM procedures for solving potential-related problems. We also show how these C 1 interpolation functions can be used to model the complex domains that are present in many biopotential problems. Illustrative biopotentials results for two different clinically important areas are given. The first area deals with potentials generated by the heart (electrocardiography) while the second field is related to potentials arising from brain activity (electroencephalography).