Martyn P. Nash

Evidence for Multiple Mechanisms in Human Ventricular Fibrillation

Background— The mechanisms that sustain ventricular fibrillation (VF) in the human heart remain unclear. Experimental models have demonstrated either a periodic source (mother rotor) or multiple wavelets as the mechanism underlying VF. The aim of this study was to map electrical activity from the entire ventricular epicardium of human hearts to establish the relative roles of these mechanisms in sustaining early human VF. Methods and Results— In 10 patients undergoing cardiac surgery, VF was induced by burst pacing, and 20 to 40 seconds of epicardial activity was sampled (1 kHz) with a sock containing 256 unipolar contact electrodes connected to a UnEmap system. Signals were interpolated from the electrode sites to a fine regular grid (100×100 points), and dominant frequencies (DFs) were calculated with a fast Fourier transform with a moving 4096-ms window (10-ms increments). Epicardial phase was calculated at each grid point with the Hilbert transform, and phase singularities and activation wavefronts were identified at 10-ms intervals. Early human VF was sustained by large coherent wavefronts punctuated by periods of disorganized wavelet behavior. The initial fitted DF intercept was 5.11±0.25 (mean±SE) Hz (P<0.0001), and DF increased at a rate of 0.018±0.005 Hz/s (P<0.01) during VF, whereas combinations of homogeneous, heterogeneous, static, and mobile DF domains were observed for each of the patients. Epicardial reentry was present in all fibrillating hearts, typically with low numbers of phase singularities. In some cases, persistent phase singularities interacted with multiple complex wavelets; in other cases, VF was driven at times by a single reentrant wave that swept the entire epicardium for several cycles. Conclusions— Our data support both the mother rotor and multiple wavelet mechanisms of VF, which do not appear to be mutually exclusive in the human heart.

Modelling passive diastolic mechanics with quantitative MRI of cardiac structure and function

The majority of patients with clinically diagnosed heart failure have normal systolic pump function and are commonly categorized as suffering from diastolic heart failure. The left ventricle (LV) remodels its structure and function to adapt to pathophysiological changes in geometry and loading conditions, which in turn can alter the passive ventricular mechanics. In order to better understand passive ventricular mechanics, a LV finite element (FE) model was customized to geometric data segmented from in vivo tagged magnetic resonance images (MRI) data and myofibre orientation derived from ex vivo diffusion tensor MRI (DTMRI) of a canine heart using nonlinear finite element fitting techniques. MRI tissue tagging enables quantitative evaluation of cardiac mechanical function with high spatial and temporal resolution, whilst the direction of maximum water diffusion in each voxel of a DTMRI directly corresponds to the local myocardial fibre orientation. Due to differences in myocardial geometry between in vivo and ex vivo imaging, myofibre orientations were mapped into the geometric FE model using host mesh fitting (a free form deformation technique). Pressure recordings, temporally synchronized to the tagging data, were used as the loading constraints to simulate the LV deformation during diastole. Simulation of diastolic LV mechanics allowed us to estimate the stiffness of the passive LV myocardium based on kinematic data obtained from tagged MRI. Integrated physiological modelling of this kind will allow more insight into mechanics of the LV on an individualized basis, thereby improving our understanding of the underlying structural basis of mechanical dysfunction under pathological conditions.

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.

Coupling multi-physics models to cardiac mechanics

We outline and review the mathematical framework for representing mechanical deformation and contraction of the cardiac ventricles, and how this behaviour integrates with other processes crucial for understanding and modelling heart function. Building on general conservation principles of space, mass and momentum, we introduce an arbitrary Eulerian-Lagrangian framework governing the behaviour of both fluid and solid components. Exploiting the natural alignment of cardiac mechanical properties with the tissue microstructure, finite deformation measures and myocardial constitutive relations are referred to embedded structural axes. Coupling approaches for solving this large deformation mechanics framework with three dimensional fluid flow, coronary hemodynamics and electrical activation are described. We also discuss the potential of cardiac mechanics modelling for clinical applications.

Whole heart APD 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.

Phase Mapping of Cardiac Fibrillation

Received January 25, 2009; accepted October 6, 2009. Phase is a descriptor that tracks the progression of a defined region of myocardium through the action potential and has been demonstrated to be an effective parameter in analyzing spatiotemporal changes during fibrillation. In this review, the basic principles behind phase mapping are presented mainly in the context of ventricular fibrillation (VF), atrial fibrillation (AF), and fibrillation from experimental monolayer data. During fibrillation, the phase distribution changes over time, depending on activation patterns. Analyzing these phase patterns provides us insight into the fibrillatory dynamics and helps clarify the mechanisms of cardiac fibrillation and modulation by interventions. Winfree1 introduced the phase analysis to study cardiac fibrillation in the late eighties. This time-encoding technique deals with a scenario where the activation periods are the same over the surface being mapped. To deal with the scenario of varying activation period over the mapped surface (common in animal and human fibrillation models), Gray et al2,3⇓ introduced the state-space encoding concept from nonlinear dynamics. In analyzing spatiotemporal phase maps constructed from electric or optical mapping of the surface of heart during VF, points around which the phase progresses through a complete cycle from −π to +π are of great interest. At these points, the phase becomes indeterminate and the activation wave fronts hinge to these points and rotate around them in an organized fashion. These points in the phase map are called phase singularity (PS) points. Bray et al4 developed a procedure to locate PS points in a phase map. Nash et al5 used phase mapping to study the entire ventricular epicardium of human hearts with a sock containing 256 unipolar contact electrodes. The development of this phase mapping tool has led to better understanding of fibrillation dynamics as evidenced by the …

Electromechanical wavebreak in a model of the human left ventricle

In the present report, we introduce an integrative three-dimensional electromechanical model of the left ventricle of the human heart. Electrical activity is represented by the ionic TP06 model for human cardiac cells, and mechanical activity is represented by the Niederer-Hunter-Smith active contractile tension model and the exponential Guccione passive elasticity model. These models were embedded into an anatomic model of the left ventricle that contains a detailed description of cardiac geometry and the fiber orientation field. We demonstrated that fiber shortening and wall thickening during normal excitation were qualitatively similar to experimental recordings. We used this model to study the effect of mechanoelectrical feedback via stretch-activated channels on the stability of reentrant wave excitation. We found that mechanoelectrical feedback can induce the deterioration of an otherwise stable spiral wave into turbulent wave patterns similar to that of ventricular fibrillation. We identified the mechanisms of this transition and studied the three-dimensional organization of this mechanically induced ventricular fibrillation.

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.

Creating Individual-specific Biomechanical Models of the Breast for Medical Image Analysis

RATIONALE AND OBJECTIVES Anatomically realistic biomechanical models of the breast potentially provide a reliable way of mapping tissue locations across medical images, such as mammograms, magnetic resonance imaging (MRI), and ultrasound. This work presents a new modeling framework that enables us to create biomechanical models of the breast that are customized to the individual. We demonstrate the frameworks capabilities by creating models of the left breasts of two volunteers and tracking their deformations across MRIs. MATERIALS AND METHODS We generate customized finite element models by automatically fitting geometrical models to segmented data from breast MRIs, and characterizing the in vivo mechanical properties (assuming homogeneity) of the breast tissues. For each volunteer, we identified the unloaded configuration by acquiring MRIs of the breast under neutral buoyancy (immersed in water). Such imaging is clearly not practical in the clinical setting; however, these previously unavailable data provide us with important data with which to validate models of breast biomechanics. Internal tissue features were identified in the neutral buoyancy images and tracked to the prone gravity-loaded state using the modeling framework. RESULTS The models predicted deformations with root-mean-square errors of 4.2 and 3.6 mm in predicting the skin surface of the gravity-loaded state for each volunteer. Internal tissue features were tracked with a mean error of 3.7 and 4.7 mm for each volunteer. CONCLUSIONS The models capture breast shape and internal deformations across the images with clinically acceptable accuracy. Further refinement of the framework and incorporation of more anatomic detail will make these models useful for breast cancer diagnosis.