Arrhythmogenic Current Generation by Myofilament-Triggered Ca2+ Release and Sarcomere Heterogeneity.

Heterogeneous mechanical dyskinesis has been implicated in many arrhythmogenic phenotypes. Strain-dependent perturbations to cardiomyocyte electrophysiology may contribute to this arrhythmogenesis through processes referred to as mechanoelectric feedback. Although the role of stretch-activated ion currents has been investigated using computational models, experimental studies suggest that mechanical strain may also promote arrhythmia by facilitating calcium wave propagation. To investigate whether strain-dependent changes in calcium affinity to the myofilament may promote arrhythmogenic intracellular calcium waves, we modified a mathematical model of rabbit excitation-contraction coupling coupled to a model of myofilament activation and force development. In a one-dimensional compartmental analysis, we bidirectionally coupled 50 sarcomere models in series to model calcium diffusion and stress transfer between adjacent sarcomeres. These considerations enabled the model to capture 1) the effects of mechanical feedback on calcium homeostasis at the sarcomeric level and 2) the combined effects of mechanical and calcium heterogeneities at the cellular level. The results suggest that in conditions of calcium overload, the vulnerable window of stretch-release to trigger suprathreshold delayed afterdepolarizations can be affected by heterogeneity in sarcomere length. Furthermore, stretch and sarcomere heterogeneity may modulate the susceptibility threshold for delayed afterdepolarizations and the aftercontraction wave propagation velocity.

Computational quantification of patient-specific changes in ventricular dynamics associated with pulmonary hypertension.

Pulmonary arterial hypertension (PAH) causes an increase in the mechanical loading imposed on the right ventricle (RV) that results in progressive changes to its mechanics and function. Here, we quantify the mechanical changes associated with PAH by assimilating clinical data consisting of reconstructed three-dimensional geometry, pressure, and volume waveforms, as well as regional strains measured in patients with PAH (n = 12) and controls (n = 6) within a computational modeling framework of the ventricles. Modeling parameters reflecting regional passive stiffness and load-independent contractility as indexed by the tissue active tension were optimized so that simulation results matched the measurements. The optimized parameters were compared with clinical metrics to find usable indicators associated with the underlying mechanical changes. Peak contractility of the RV free wall (RVFW) γRVFW,max was found to be strongly correlated and had an inverse relationship with the RV and left ventricle (LV) end-diastolic volume ratio (i.e., RVEDV/LVEDV) (RVEDV/LVEDV)+ 0.44, R2 = 0.77). Correlation with RV ejection fraction (R2 = 0.50) and end-diastolic volume index (R2 = 0.40) were comparatively weaker. Patients with with RVEDV/LVEDV > 1.5 had 25% lower γRVFW,max (P < 0.05) than that of the control. On average, RVFW passive stiffness progressively increased with the degree of remodeling as indexed by RVEDV/LVEDV. These results suggest a mechanical basis of using RVEDV/LVEDV as a clinical index for delineating disease severity and estimating RVFW contractility in patients with PAH.NEW & NOTEWORTHY This article presents patient-specific data assimilation of a patient cohort and physical description of clinical observations.

Patient-Specific Computational Analysis of Ventricular Mechanics in Pulmonary Arterial Hypertension.

Patient-specific biventricular computational models associated with a normal subject and a pulmonary arterial hypertension (PAH) patient were developed to investigate the disease effects on ventricular mechanics. These models were developed using geometry reconstructed from magnetic resonance (MR) images, and constitutive descriptors of passive and active mechanics in cardiac tissues. Model parameter values associated with ventricular mechanical properties and myofiber architecture were obtained by fitting the models with measured pressure-volume loops and circumferential strain calculated from MR images using a hyperelastic warping method. Results show that the peak right ventricle (RV) pressure was substantially higher in the PAH patient (65 mmHg versus 20 mmHg), who also has a significantly reduced ejection fraction (EF) in both ventricles (left ventricle (LV): 39% versus 66% and RV: 18% versus 64%). Peak systolic circumferential strain was comparatively lower in both the left ventricle (LV) and RV free wall (RVFW) of the PAH patient (LV: -6.8% versus -13.2% and RVFW: -2.1% versus -9.4%). Passive stiffness, contractility, and myofiber stress in the PAH patient were all found to be substantially increased in both ventricles, whereas septum wall in the PAH patient possessed a smaller curvature than that in the LV free wall. Simulations using the PAH model revealed an approximately linear relationship between the septum curvature and the transseptal pressure gradient at both early-diastole and end-systole. These findings suggest that PAH can induce LV remodeling, and septum curvature measurements may be useful in quantifying transseptal pressure gradient in PAH patients.

A cell-based framework for modeling cardiac mechanics.

Cardiomyocytes are the functional building blocks of the heart-yet most models developed to simulate cardiac mechanics do not represent the individual cells and their surrounding matrix. Instead, they work on a homogenized tissue level, assuming that cellular and subcellular structures and processes scale uniformly. Here we present a mathematical and numerical framework for exploring tissue-level cardiac mechanics on a microscale given an explicit three-dimensional geometrical representation of cells embedded in a matrix. We defined a mathematical model over such a geometry and parametrized our model using publicly available data from tissue stretching and shearing experiments. We then used the model to explore mechanical differences between the extracellular and the intracellular space. Through sensitivity analysis, we found the stiffness in the extracellular matrix to be most important for the intracellular stress values under contraction. Strain and stress values were observed to follow a normal-tangential pattern concentrated along the membrane, with substantial spatial variations both under contraction and stretching. We also examined how it scales to larger size simulations, considering multicellular domains. Our work extends existing continuum models, providing a new geometrical-based framework for exploring complex cell-cell and cell-matrix interactions.

Electromechanical feedback with reduced cellular connectivity alters electrical activity in an infarct injured left ventricle: a finite element model study.

Myocardial infarction (MI) significantly alters the structure and function of the heart. As abnormal strain may drive heart failure and the generation of arrhythmias, we used computational methods to simulate a left ventricle with an MI over the course of a heartbeat to investigate strains and their potential implications to electrophysiology. We created a fully coupled finite element model of myocardial electromechanics consisting of a cellular physiological model, a bidomain electrical diffusion solver, and a nonlinear mechanics solver. A geometric mesh built from magnetic resonance imaging (MRI) measurements of an ovine left ventricle suffering from a surgically induced anteroapical infarct was used in the model, cycled through the cardiac loop of inflation, isovolumic contraction, ejection, and isovolumic relaxation. Stretch-activated currents were added as a mechanism of mechanoelectric feedback. Elevated fiber and cross fiber strains were observed in the area immediately adjacent to the aneurysm throughout the cardiac cycle, with a more dramatic increase in cross fiber strain than fiber strain. Stretch-activated channels decreased action potential (AP) dispersion in the remote myocardium while increasing it in the border zone. Decreases in electrical connectivity dramatically increased the changes in AP dispersion. The role of cross fiber strain in MI-injured hearts should be investigated more closely, since results indicate that these are more highly elevated than fiber strain in the border of the infarct. Decreases in connectivity may play an important role in the development of altered electrophysiology in the high-stretch regions of the heart.

Computational models of ventricular mechanics and adaptation in response to right-ventricular pressure overload.

Pulmonary arterial hypertension (PAH) is associated with substantial remodeling of the right ventricle (RV), which may at first be compensatory but at a later stage becomes detrimental to RV function and patient survival. Unlike the left ventricle (LV), the RV remains understudied, and with its thin-walled crescent shape, it is often modeled simply as an appendage of the LV. Furthermore, PAH diagnosis is challenging because it often leaves the LV and systemic circulation largely unaffected. Several treatment strategies such as atrial septostomy, right ventricular assist devices (RVADs) or RV resynchronization therapy have been shown to improve RV function and the quality of life in patients with PAH. However, evidence of their long-term efficacy is limited and lung transplantation is still the most effective and curative treatment option. As such, the clinical need for improved diagnosis and treatment of PAH drives a strong need for increased understanding of drivers and mechanisms of RV growth and remodeling (G&R), and more generally for targeted research into RV mechanics pathology. Computational models stand out as a valuable supplement to experimental research, offering detailed analysis of the drivers and consequences of G&R, as well as a virtual test bench for exploring and refining hypotheses of growth mechanisms. In this review we summarize the current efforts towards understanding RV G&R processes using computational approaches such as reduced-order models, three dimensional (3D) finite element (FE) models, and G&R models. In addition to an overview of the relevant literature of RV computational models, we discuss how the models have contributed to increased scientific understanding and to potential clinical treatment of PAH patients.

A method for automatically optimizing medical devices for treating heart failure: designing polymeric injection patterns.

Heart failure continues to present a significant medical and economic burden throughout the developed world. Novel treatments involving the injection of polymeric materials into the myocardium of the failing left ventricle (LV) are currently being developed, which may reduce elevated myofiber stresses during the cardiac cycle and act to retard the progression of heart failure. A finite element (FE) simulation-based method was developed in this study that can automatically optimize the injection pattern of the polymeric "inclusions" according to a specific objective function, using commercially available software tools. The FE preprocessor TRUEGRID((R)) was used to create a parametric axisymmetric LV mesh matched to experimentally measured end-diastole and end-systole metrics from dogs with coronary microembolization-induced heart failure. Passive and active myocardial material properties were defined by a pseudo-elastic-strain energy function and a time-varying elastance model of active contraction, respectively, that were implemented in the FE software LS-DYNA. The companion optimization software LS-OPT was used to communicate directly with TRUEGRID((R)) to determine FE model parameters, such as defining the injection pattern and inclusion characteristics. The optimization resulted in an intuitive optimal injection pattern (i.e., the one with the greatest number of inclusions) when the objective function was weighted to minimize mean end-diastolic and end-systolic myofiber stress and ignore LV stroke volume. In contrast, the optimization resulted in a nonintuitive optimal pattern (i.e., 3 inclusions longitudinallyx6 inclusions circumferentially) when both myofiber stress and stroke volume were incorporated into the objective function with different weights.

Multivalency of Sonic hedgehog conjugated to linear polymer chains modulates protein potency.

A potently active multivalent form of the protein Sonic hedgehog (Shh) was produced by bioconjugation of a modified recombinant form of Shh to the linear polymers poly(acrylic acid) (pAAc) and hyaluronic acid (HyA) via a two-step reaction exploiting carboimiide and maleimide chemistry. Efficiency of the conjugation was approximately 75% even at stoichiometric ratios of 30 Shh molecules per linear HyA chain (i.e., 30:1 Shh/HyA). Bioactivity of the conjugates was tested via a cellular assay across a range of stoichiometric ratios of Shh molecules to HyA linear chains, which was varied from 0.6:1 Shh/HyA to 22:1 Shh/HyA. Results indicate that low conjugation ratios decrease Shh bioactivity and high ratios increase this activity beyond the potency of monomeric Shh, with approximately equal activity between monomeric soluble Shh and conjugated Shh at 7:1 Shh/HyA. In addition, high-ratio constructs increased angiogenesis determined by the in vivo chick chorioallantoic membrane (CAM) assay. These results are captured by a kinetic model of multiple interactions between the Shh/HyA conjugates and cell surface receptors resulting in higher cell signaling at lower bulk Shh concentrations.

Efficient estimation of personalized biventricular mechanical function employing gradient-based optimization.

Individually personalized computational models of heart mechanics can be used to estimate important physiological and clinically-relevant quantities that are difficult, if not impossible, to directly measure in the beating heart. Here, we present a novel and efficient framework for creating patient-specific biventricular models using a gradient-based data assimilation method for evaluating regional myocardial contractility and estimating myofiber stress. These simulations can be performed on a regular laptop in less than 2 h and produce excellent fit between measured and simulated volume and strain data through the entire cardiac cycle. By applying the framework using data obtained from 3 healthy human biventricles, we extracted clinically important quantities as well as explored the role of fiber angles on heart function. Our results show that steep fiber angles at the endocardium and epicardium are required to produce simulated motion compatible with measured strain and volume data. We also find that the contraction and subsequent systolic stresses in the right ventricle are significantly lower than that in the left ventricle. Variability of the estimated quantities with respect to both patient data and modeling choices are also found to be low. Because of its high efficiency, this framework may be applicable to modeling of patient specific cardiac mechanics for diagnostic purposes.

Theoretical impact of the injection of material into the myocardium: a finite element model simulation.

BACKGROUND: To treat cardiac injuries created by myocardial infarcts, current approaches seek to add cells and/or synthetic extracellular matrices to the damaged ventricle to restore function. Because definitive myocardial regeneration remains undemonstrated, we propose that cardiac changes observed from implanted materials may result from altered mechanisms of the ventricle. METHODS AND RESULTS: We exploited a validated finite element model of an ovine left ventricle with an anteroapical infarct to examine the short-term effect of injecting material to the left ventricular wall. The model's mesh and regional material properties were modified to simulate expected changes. Three sets of simulations were run: (1) single injection to the anterior border zone; (2) therapeutic multiple border zone injections; and (3) injection of material to the infarct region. Results indicate that additions to the border zone decrease end-systolic fiber stress proportionally to the fractional volume added, with stiffer materials improving this attenuation. As a potential therapy, small changes in wall volume (approximately 4.5%) reduce elevated border zone fiber stresses from mean end-systole levels of 28.2 kPa (control) to 23.3 kPa (treatment), similar to levels of 22.5 kPA computed in remote regions. In the infarct, injection improves ejection fraction and the stroke volume/end-diastolic volume relationship but has no effect on the stroke volume/end-diastolic pressure relationship. CONCLUSIONS: Simulations indicate that the addition of noncontractile material to a damaged left ventricular wall has important effects on cardiac mechanics, with potentially beneficial reduction of elevated myofiber stresses, as well as confounding changes to clinical left ventricular metrics.

Organ-level validation of a cross-bridge cycling descriptor in a left ventricular finite element model: effects of ventricular loading on myocardial strains.

Although detailed cell-based descriptors of cross-bridge cycling have been applied in finite element (FE) heart models to describe ventricular mechanics, these multiscale models have never been tested rigorously to determine if these descriptors, when scaled up to the organ-level, are able to reproduce well-established organ-level physiological behaviors. To address this void, we here validate a left ventricular (LV) FE model that is driven by a cell-based cross-bridge cycling descriptor against key organ-level heart physiology. The LV FE model was coupled to a closed-loop lumped parameter circulatory model to simulate different ventricular loading conditions (preload and afterload) and contractilities. We show that our model is able to reproduce a linear end-systolic pressure volume relationship, a curvilinear end-diastolic pressure volume relationship and a linear relationship between myocardial oxygen consumption and pressure-volume area. We also show that the validated model can predict realistic LV strain-time profiles in the longitudinal, circumferential, and radial directions. The predicted strain-time profiles display key features that are consistent with those measured in humans, such as having similar peak strains, time-to-peak-strain, and a rapid change in strain during atrial contraction at late-diastole. Our model shows that the myocardial strains are sensitive to not only LV contractility, but also to the LV loading conditions, especially to a change in afterload. This result suggests that caution must be exercised when associating changes in myocardial strain with changes in LV contractility. The methodically validated multiscale model will be used in future studies to understand human heart diseases.

An integrative appraisal of mechano-electric feedback mechanisms in the heart.

Mechanically-induced alterations in cardiac electrophysiology are referred to as mechano-electric feedback (MEF), and play an important role in electrical regulation of cardiac performance. The influence of mechanical stress and strain on electrophysiology has been investigated at all levels, however the role of MEF in arrhythmia remains poorly understood. During the normal contraction of the heart, mechano-sensitive processes are an implicit component of cardiac activity. Under abnormal mechanical events, stretch-activated mechanisms may contribute to local or global changes in electrophysiology (EP). While such mechanisms have been hypothesised to be involved in mechanically-initiated arrhythmias, the details of these mechanisms and their importance remain elusive. We assess the theoretical role of stretch mechanisms using coupled models of cellular electrophysiology and sarcomere contraction dynamics. Using models of single ventricular myocytes, we first investigated the potential MEF contributions of stretch-activated currents (SAC), and stretch-induced myofilament calcium release, to test how strain and fibrosis may alter cellular electrophysiology. For all models investigated, SACs were alone not sufficient to create a pro-arrhythmic perturbation of the action potential with stretch. However, when combined with stretch-induced myofilament calcium release, the action potential could be shortened depending on the timing of the strain. This effect was highly model dependent, with a canine epicardial EP model being the most sensitive. These model results suggest that known mechanisms of mechano-electric coupling in cardiac myocyte may be sufficient to be pro-arrhythmic, but only in combination and under specific strain patterns.

An integrated electromechanical-growth heart model for simulating cardiac therapies.

An emerging class of models has been developed in recent years to predict cardiac growth and remodeling (G&R). We recently developed a cardiac G&R constitutive model that predicts remodeling in response to elevated hemodynamics loading, and a subsequent reversal of the remodeling process when the loading is reduced. Here, we describe the integration of this G&R model to an existing strongly coupled electromechanical model of the heart. A separation of timescale between growth deformation and elastic deformation was invoked in this integrated electromechanical-growth heart model. To test our model, we applied the G&R scheme to simulate the effects of myocardial infarction in a realistic left ventricular (LV) geometry using the finite element method. We also simulate the effects of a novel therapy that is based on alteration of the infarct mechanical properties. We show that our proposed model is able to predict key features that are consistent with experiments. Specifically, we show that the presence of a non-contractile infarct leads to a dilation of the left ventricle that results in a rightward shift of the pressure volume loop. Our model also predicts that G&R is attenuated by a reduction in LV dilation when the infarct stiffness is increased.

Increased cell membrane capacitance is the dominant mechanism of stretch-dependent conduction slowing in the rabbit heart: a computational study.

Volume loading of the cardiac ventricles is known to slow electrical conduction in the rabbit heart, but the mechanisms remain unclear. Previous experimental and modeling studies have investigated some of these mechanisms, including stretch-activated membrane currents, reduced gap junctional conductance, and altered cell membrane capacitance. In order to quantify the relative contributions of these mechanisms, we combined a monomain model of rabbit ventricular electrophysiology with a hyperelastic model of passive ventricular mechanics. First, a simplified geometric model with prescribed homogeneous deformation was used to fit model parameters and characterize individual MEF mechanisms, and showed good qualitative agreement with experimentally measured strain-CV relations. A 3D model of the rabbit left and right ventricles was then compared with experimental measurements from optical electrical mapping studies in the isolated rabbit heart. The model was inflated to an end-diastolic pressure of 30 mmHg, resulting in epicardial strains comparable to those measured in the anterior left ventricular free wall. While the effects of stretch activated channels did alter epicardial conduction velocity, an increase in cellular capacitance was required to explain previously reported experimental results. The new results suggest that for large strains, various mechanisms can combine and produce a biphasic relationship between strain and conduction velocity. However, at the moderate strains generated by high end-diastolic pressure, a stretch-induced increase in myocyte membrane capacitance is the dominant driver of conduction slowing during ventricular volume loading.

Bioinjection treatment: effects of post-injection residual stress on left ventricular wall stress.

Injection of biomaterials into diseased myocardium has been associated with decreased myofiber stress, restored left ventricular (LV) geometry and improved LV function. However, its exact mechanism(s) of action remained unclear. In this work, we present the first patient-specific computational model of biomaterial injection that accounts for the possibility of residual strain and stress introduced by this treatment. We show that the presence of residual stress can create more heterogeneous regional myofiber stress and strain fields. Our simulation results show that the treatment generates low stress and stretch areas between injection sites, and high stress and stretch areas between the injections and both the endocardium and epicardium. Globally, these local changes are translated into an increase in average myofiber stress and its standard deviation (from 6.9 ± 4.6 to 11.2 ± 48.8 kPa and 30 ± 15 to 35.1 ± 50.9 kPa at end-diastole and end-systole, respectively). We also show that the myofiber stress field is sensitive to the void-to-size ratio. For a constant void size, the myofiber stress field became less heterogeneous with decreasing injection volume. These results suggest that the residual stress and strain possibly generated by biomaterial injection treatment can have large effects on the regional myocardial stress and strain fields, which may be important in the remodeling process.

Algisyl-LVR™ with coronary artery bypass grafting reduces left ventricular wall stress and improves function in the failing human heart.

BACKGROUND: Left ventricular (LV) wall stress reduction is a cornerstone in treating heart failure. Large animal models and computer simulations indicate that adding non-contractile material to the damaged LV wall can potentially reduce myofiber stress. We sought to quantify the effects of a novel implantable hydrogel (Algisyl-LVR™) treatment in combination with coronary artery bypass grafting (i.e. Algisyl-LVR™+CABG) on both LV function and wall stress in heart failure patients. METHODS AND RESULTS: Magnetic resonance images obtained before treatment (n=3), and at 3 months (n=3) and 6 months (n=2) afterwards were used to reconstruct the LV geometry. Cardiac function was quantified using end-diastolic volume (EDV), end-systolic volume (ESV), regional wall thickness, sphericity index and regional myofiber stress computed using validated mathematical modeling. The LV became more ellipsoidal after treatment, and both EDV and ESV decreased substantially 3 months after treatment in all patients; EDV decreased from 264 ± 91 ml to 146 ± 86 ml and ESV decreased from 184 ± 85 ml to 86 ± 76 ml. Ejection fraction increased from 32 ± 8% to 47 ± 18% during that period. Volumetric-averaged wall thickness increased in all patients, from 1.06 ± 0.21 cm (baseline) to 1.3 ± 0.26 cm (3 months). These changes were accompanied by about a 35% decrease in myofiber stress at end-of-diastole and at end-of-systole. Post-treatment myofiber stress became more uniform in the LV. CONCLUSIONS: These results support the novel concept that Algisyl-LVR™+CABG treatment leads to decreased myofiber stress, restored LV geometry and improved function.

Scleral reinforcement through host tissue integration with biomimetic enzymatically degradable semi-interpenetrating polymer network.

Enzymatically degradable semi-interpenetrating polymer networks (edsIPNs) were explored for their biocompatibility and ability to promote new scleral tissue growth, as a means of reinforcing the posterior wall of the eye. The edsIPNs comprised thermoresponsive poly(N-isopropylacrylamide-co-acrylic acid), customizable peptide crosslinkers cleavable by matrix metalloproteinases, and interpenetrating linear poly(acrylic acid)-graft-peptide chains to engage with cell surface receptors. Rheological studies revealed an increase in stiffness at body temperature; the complex shear modulus |G*| was 14.13 +/- 6.13 Pa at 22 degrees C and 63.18 +/- 12.24 Pa at 37 degrees C, compatible with injection at room temperature. Primary chick scleral fibroblasts and chondrocytes cultured on edsIPN increased by 15.1- and 11.1-fold, respectively, over 11 days; both exhibited delayed onset of exponential growth compared with the cells plated on tissue culture polystyrene. The edsIPN was delivered by retrobulbar injection (100 microL) to nine 2-week-old chicks to assess biocompatibility in vivo. Ocular axial dimensions were assessed using A-scan ultrasonography over 28 days, after which eyes were processed for histological analysis. Although edsIPN injections did not affect the rate of ocular elongation, the outer fibrous sclera showed significant thickening. The demonstration that injectable biomimetic edsIPNs stimulate scleral fibrous tissue growth represents proof-of-principle for a novel approach for scleral reinforcement and a potential therapy for high myopia.

Biomimetic matrices for myocardial stabilization and stem cell transplantation.

Although natural biological matrices have demonstrated modest improvement in the survival of cells transplanted into the infarcted myocardium, these materials have not been amenable to systematic optimization and therefore have limited potential to treat postinfarct cardiac injuries. Here we have developed tunable bioactive semi-interpenetrating polymer network (sIPN) hydrogels with matrix metalloproteinase (MMP) labile crosslinkers to be used as an assistive microenvironment for transplantation of bone marrow-derived mesenchymal stem cells (BMSCs) into the infarcted myocardium. Injectable sIPN hydrogels were designed with a range of mechanical and biological properties that yielded material-dependent BMSC proliferation in vitro. Five groups were evaluated to treat myocardial infarction (MI) in adult mice: saline injection; green fluorescent protein (GFP)(+)-BMSCs delivered in saline; a sIPN matrix; a sIPN + GFP(+)-BMSCs; and Matrigel™ + GFP(+)-BMSCs. Injection of cells alone created a transient improvement in LV function that declined over time, and the synthetic hydrogel without cells resulted in the highest LV function at 6 weeks. Donor GFP-positive cells were detected after matrix-enhanced transplantation, but not without matrix support. Biomimetic sIPN hydrogel matrices succeeded both in mechanically supporting the injured myocardium and modestly enhancing donor cell survival. These matrices provide a foundation for systematic development of "pro-survival" microenvironments, and improvement in the long-term results of cardiac stem cell transplantation therapies.

Effect of adjustable passive constraint on the failing left ventricle: a finite-element model study.

BACKGROUND: Passive constraint is used to prevent left ventricular dilation and subsequent remodeling. However, there has been concern about the effect of passive constraint on diastolic left ventricular chamber stiffness and pump function. This study determined the relationship between constraint, diastolic wall stress, chamber stiffness, and pump function. We tested the hypothesis that passive constraint at 3 mm Hg reduces wall stress with minimal change in pump function. METHODS: A three-dimensional finite-element model of the globally dilated left ventricle based on left ventricular dimensions obtained in dogs that had undergone serial intracoronary microsphere injection was created. The model was adjusted to match experimentally observed end-diastolic left ventricular volume and midventricular wall thickness. The experimental results used to create the model were previously reported. A pressure of 3, 5, 7, and 9 mm Hg was applied to the epicardium. Fiber stress, end-diastolic pressure-volume relationship, end-systolic pressure-volume relationship, and the stroke volume-end-diastolic pressure (Starling) relationship were calculated. RESULTS: As epicardial constraint pressure increased, fiber stress decreased, the end-diastolic pressure-volume relationship shifted to the left, and the Starling relationship shifted down and to the right. The end-systolic pressure-volume relationship did not change. A constraining pressure of 2.3 mm Hg was associated with a 10% reduction in stroke volume, and mean end-diastolic fiber stress was reduced by 18.3% (inner wall), 15.3% (mid wall), and 14.2% (outer wall). CONCLUSIONS: Both stress and cardiac output decrease in a linear fashion as the amount of passive constraint is increased. If the reduction in cardiac output is to be less than 10%, passive constraint should not exceed 2.3 mm Hg. On the other hand, this amount of constraint may be sufficient to reverse eccentric hypertrophy after myocardial infarction.