Frederick J. Vetter

Three-dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy

The three-dimensional geometry and anisotropic properties of the heart give rise to nonhomogeneous distributions of stress, strain, electrical activation and repolarization. In this article we review the ventricular geometry and myofiber architecture of the heart, and the experimental and modeling studies of three-dimensional cardiac mechanics and electrophysiology. The development of a three-dimensional finite element model of the rabbit ventricular geometry and fiber architecture is described in detail. Finally, we review the experimental results, from the level of the cell to the intact organ, which motivate the development of coupled three-dimensional models of cardiac electromechanics and mechanoelectric feedback.

Three-Dimensional Stress and Strain in Passive Rabbit Left Ventricle: A Model Study

AbstractTo determine regional stress and strain distributions in rabbit ventricular myocardium, an anatomically detailed finite element model was used to solve the equations of stress equilibrium during passive filling of the left ventricle. Computations were conducted on a scalable parallel processing computer and performance was found to scale well with the number of processors used, so that stimulations previously requiring approximately 60 min were completed in just over 5 min. Epicardial strains from the model analysis showed good agreement (RMSE=0.007332) with experimental measurements when material properties were chosen such that cross fiber strain was more heterogeneous than fiber strain, which is also consistent with experimental observations in other species.

Optical Action Potential Upstroke Morphology Reveals Near-Surface Transmural Propagation Direction

The analysis of surface-activation patterns and measurements of conduction velocity in ventricular myocardium is complicated by the fact that the electrical wavefront has a complex 3D shape and can approach the heart surface at various angles. Recent theoretical studies suggest that the optical upstroke is sensitive to the subsurface orientation of the wavefront. Our goal here was to (1) establish the quantitative relationship between optical upstroke morphology and subsurface wavefront orientation using computer modeling and (2) test theoretical predictions experimentally in isolated coronary-perfused swine right ventricular preparations. We show in numerical simulations that by suitable placement of linear epicardial stimulating electrodes, the angle &phgr; of wavefronts with respect to the heart surface can be controlled. Using this method, we developed theoretical predictions of the optical upstroke shape dependence on &phgr;. We determined that the level VF* at which the rate of rise of the optical upstroke reaches the maximum linearly depends on &phgr;. A similar relationship was found in simulations with epicardial point stimulation. The optical mapping data were in good agreement with theory. Plane waves propagating parallel to myocardial fibers produced upstrokes with VF*<0.5, consistent with theoretical predictions for &phgr;>0. Similarly, we obtained good agreement with theory for plane waves propagating in a direction perpendicular to fibers (VF*>0.5 when &phgr;<0). Finally, during epicardial point stimulation, we discovered characteristic saddle-shaped VF* maps that were in excellent agreement with theoretically predicted changes in &phgr; during wavefront expansion. Our findings should allow for improved interpretation of the results of optical mapping of intact heart preparations.

Mechanoelectric Feedback in a Model of the Passively Inflated Left Ventricle

AbstractMechanoelectric feedback has been described in isolated cells and intact ventricular myocardium, but the mechanical stimulus that governs mechanosensitive channel activity in intact tissue is unknown. To study the interaction of myocardial mechanics and electrophysiology in multiple dimensions, we used a finite element model of the rabbit ventricles to simulate electrical propagation through passively loaded myocardium. Electrical propagation was simulated using the collocation-Galerkin finite element method. A stretch-dependent current was added in parallel to the ionic currents in the Beeler–Reuter ventricular action potential model. We investigated different mechanical coupling parameters to simulate stretch-dependent conductance modulated by either fiber strain, cross-fiber strain, or a combination of the two. In response to pressure loading, the conductance model governed by fiber strain alone reproduced the epicardial decrease in action potential amplitude as observed in experimental preparations of the passively loaded rabbit heart. The model governed by only cross-fiber strain reproduced the transmural gradient in action potential amplitude as observed in working canine heart experiments, but failed to predict a sufficient decrease in amplitude at the epicardium. Only the model governed by both fiber and cross-fiber strain reproduced the epicardial and transmural changes in action potential amplitude similar to experimental observations. In addition, dispersion of action potential duration nearly doubled with the same model. These results suggest that changes in action potential characteristics may be due not only to length changes along the long axis direction of the myofiber, but also due to deformation in the plane transverse to the fiber axis. The model provides a framework for investigating how cellular biophysics affect the function of the intact ventricles.

Epicardial Fiber Organization in Swine Right Ventricle and Its Impact on Propagation

Fiber organization is important for myocardial excitation and contraction. It can be a major factor in arrhythmogenesis and current distribution during defibrillation shocks. In this study, we report the discovery of a previously undetected thin epicardial layer in swine right ventricle (RV) with distinctly different fiber orientation, which significantly affects epicardial propagation. Experiments were conducted in isolated coronary-perfused right ventricular free wall preparations (n=8) stained with the voltage-sensitive dye di-4-ANEPPS. Optical signals were recorded from the epicardium with a CCD video camera at 800 fps. Preparations were sectioned parallel to the epicardial surface with a resolution of 50 &mgr;m or better. To link the histological data with the observed activation patterns, resulting fiber angles were introduced into a 3D computer model to simulate the electrical activation and voltage-dependent optical signals. In all preparations, we detected a thin epicardial layer with almost no depth-dependent fiber rotation. The thickness of this layer (z0) varied from 110 to 930 &mgr;m. At the boundary of this layer, we observed an abrupt change in fiber angle by 64±13° followed by a gradual fiber rotation in the underlying layers. In preparations with z0 <700 &mgr;m, optical mapping during epicardial stimulation revealed unusual diamond- and rectangular-shaped activation fronts with two axes of fast conduction. Computer simulations accurately predicted the features of the experimentally recorded activation fronts. The free wall of swine RV has a thin epicardial layer with distinctly different fiber orientation, which can significantly affect propagation and give rise to unusually shaped activation fronts. This is important for understanding electrical propagation in the heart, and further refines the existing knowledge of myocardial fiber architecture.

A finite element model of passive mechanics and electrical propagation in the rabbit ventricles

To study the interaction of electrical and mechanical processes in the three-dimensional heart, the authors have developed a high-order finite element model of the rabbit ventricles and used it to simulate electrical propagation and the passive mechanical response to ventricular filling in transversely isotropic myocardium. Simulations of passive mechanics showed good agreement with experimental epicardial strains. These simulations were conducted on a multiprocessor parallel platform and performance was shown to scale well with the number of processors used. Electrical propagation was simulated using the collocation-Galerkin method on portions of the anatomical model in both unloaded and deformed states. These models provide a framework for investigating how cellular biophysics integrates into the function of the intact ventricles.

On the performance and energy-efficiency of multi-core SIMD CPUs and CUDA-enabled GPUs

This paper explores the performance and energy efficiency of CUDA-enabled GPUs and multi-core SIMD CPUs using a set of kernels and full applications. Our implementations efficiently exploit both SIMD and thread-level parallelism on multi-core CPUs and the computational capabilities of CUDA-enabled GPUs. We discuss general optimization techniques for our CPU-only and CPU-GPU platforms. To fairly study performance and energy-efficiency, we also used two applications which utilize several kernels. Finally, we present an evaluation of the implementation effort required to efficiently utilize multi-core SIMD CPUs and CUDA-enabled GPUs for the benchmarks studied. Our results show that kernel-only performance and energy-efficiency could be misleading when evaluating parallel hardware; therefore, true results must be obtained using full applications. We show that, after all respective optimizations have been made, the best performing and energy-efficient platform varies for different benchmarks. Finally, our results show that PPEH (Performance gain Per Effort Hours), our newly introduced metric, can affectively be used to quantify efficiency of implementation effort across different benchmarks and platforms.

Time-varying left ventricular elastance determined by a finite element model

A finite element model of the left ventricle (LV) with an axisymmetric geometry has been developed to determine LV pressures and volumes. Regional myocardial contractions defined by the finite elements are then related to the time-varying LV elastance (instantaneous pressure over volume ratio). LV geometry is modeled as a truncated ellipsoid with user-defined parameters such as wall thickness, short axis length, and long axis length. The stress-strain relationship for each element is assumed to be linear but with a time-varying Youngs modulus. Empirical values of the Youngs modulus are assigned to finite elements for simulating normal and ischemic myocardium. The mesh generation is implemented in C++ and the stress-strain computation in Matlab. The finite element model produces reasonable geometry for normal and ischemic LV walls. More importantly, the LV ejection fraction and pressure and volume curves are consistent with typical clinical observations. The simplified model developed in this study is an effective and computationally efficient way to relate regional myocardial impairments to global LV functions and to generate LV elastance curves over an entire cardiac cycle.

Serum Natriuretic Peptides as Differential Biomarkers Allowing for the Distinction between Physiologic and Pathologic Left Ventricular Hypertrophy

Given the proven utility of natriuretic peptides as serum biomarkers of cardiovascular maladaptation and dysfunction in humans and the high cross-species sequence conservation of atrial natriuretic peptides, natriuretic peptides have the potential to serve as translational biomarkers for the identification of cardiotoxic compounds during multiple phases of drug development. This work evaluated and compared the response of N-terminal proatrial natriuretic peptide (NT-proANP) and N-terminal probrain natriuretic peptide (NT-proBNP) in rats during exercise-induced and drug-induced increases in cardiac mass after chronic swimming or daily oral dosing with a peroxisome proliferator-activated receptor γ agonist. Male Sprague-Dawley rats aged 8 to 10 weeks were assigned to control, active control, swimming, or drug-induced cardiac hypertrophy groups. While the relative heart weights from both the swimming and drug-induced cardiac hypertrophy groups were increased 15% after 28 days of dosing, the serum NT-proANP and NT-proBNP values were only increased in association with cardiac hypertrophy caused by compound administration. Serum natriuretic peptide concentrations did not change in response to adaptive physiologic cardiac hypertrophy induced by a 28-day swimming protocol. These data support the use of natriuretic peptides as fluid biomarkers for the distinction between physiological and drug-induced cardiac hypertrophy.

Mechanical function, glycolysis, and ultrastructure of perfused working mouse hearts following thoracic aortic constriction.

BACKGROUND Glycolytic flux in the mouse heart during the progression of left ventricular hypertrophy (LVH) and mechanical dysfunction has not been described. METHODS The main objectives of this study were to characterize the effects of thoracic aortic banding, of 3- and 6-week duration, on: (1) left ventricular (LV) systolic and diastolic function of perfused working hearts quantified by analysis of pressure-volume loops; (2) glycolytic flux in working hearts expressed as the rate of conversion of (3)H-glucose to (3)H(2)O, and (3) ultrastructure of LV biopsies assessed by quantitative and qualitative analysis of light and electron micrographs. RESULTS Results revealed that (1) indexes of systolic function, including LV end-systolic pressure, cardiac output, and rate of LV pressure development and decline, were depressed to similar degrees at 3 and 6 weeks post-banding; (2) diastolic dysfunction, represented by elevated LV end-diastolic pressure and volume, was more severe at 6 than at 3 weeks, consistent with a transition to failure; (3) a progressive decline in glycolytic flux that was roughly half the control rate by 6 weeks post-banding; and (4) structural derangements, manifested by increases in interstitial collagen content and myocyte Z-band disruption, that were more marked at 3 weeks than at 6 weeks. CONCLUSION The results are consistent with the view that myocyte damage, fibrosis, and suppressed glycolytic flux represent maladaptive structural and metabolic remodeling that contribute to the development of failure in high pressure load-induced LVH in the mouse.