Ventricular mechanics in diastole: material parameter sensitivity

Models of ventricular mechanics have been developed over the last 20 years to include finite deformation theory, anisotropic and inhomogeneous material properties and an accurate representation of ventricular geometry. As computer performance and the computational efficiency of the models improve, clinical application of these heart mechanics models is becoming feasible. One such application is to estimate myocardial material properties by adjusting the constitutive parameters to match wall deformation from MRI or ultrasound measurements, together with a measurement (or estimate) of ventricular pressure. Pigs are now the principal large animal model for these studies and in this paper we present the development of a new three-dimensional finite element model of the heart based on measurements of the geometry and the fibre and sheet orientations of pig hearts. The end-diastolic deformation of the model is computed using the "pole-zero" constitutive law which we have previously used to model the mechanics of passive myocardial tissue specimens. The sensitivities of end-diastolic fibre-sheet material strains and heart shape to changes in the material parameters are computed for the parameters of the pole-zero law in order to assess the utility of the models for inverse material property determination.     

Transplantation of elastin-secreting myoblast sheets improves cardiac function in infarcted rat heart

Myoblast sheet transplantation for cardiac failure is a promising therapy to enhance cardiac function via paracrine mechanism. However, their efficacies of treatment showed a gradual decline. The gene modification of the implanted myoblast is important in improving the long-term results of the treatment. Elastin fiber enhances the extensibility of the infarcted wall and can prevent left ventricular dilation. We therefore hypothesized that the elastin gene modification of the implanted myoblast could strengthen and maintain the long-term improvement effects of cardiac function. In this study, we evaluated long-term follow-up benefits of functional myoblast sheets that secrete elastin in an infarcted model. The animal models were divided into three groups: a group transplanted with nontransfected, wild-type, skeletal myoblast-type sheets (WT-rSkM); group transplanted with myoblast sheets that secreted elastin fragments (ELN-rSkM); and a control group (ligation only). Cardiac function was examined by echocardiography, and cardiac remodeling after infarction was evaluated by histological examination. The cardiac function was significantly improved and the left ventricle end-diastolic dimensions were significantly reduced in the ELN-rSkM group. Histological analysis showed that left ventricular remodeling was attenuated in the ELN-rSkM group and that elastic fiber was formed in the epicardial area of ELN-rSkM group. The functionalization of myoblast sheet by elastin gene transfer showed the long-term improvement of cardiac function. Expressed recombinant elastin fiber prevented the dilation of the left ventricular chamber after myocardial infarction. The functional myoblast sheet transplantation maintained the treatment effect by the paracrine effect of myoblast and the formed recombinant elastin.     

Epicardial suction: a new approach to mechanical testing of the passive ventricular wall

The lack of an appropriate three-dimensional constitutive relation for stress in passive ventricular myocardium currently limits the utility of existing mathematical models for experimental and clinical applications. Previous experiments used to estimate parameters in three-dimensional constitutive relations, such as biaxial testing of excised myocardial sheets or passive inflation of the isolated arrested heart, have not included significant transverse shear deformation or in-plane compression. Therefore, a new approach has been developed in which suction is applied locally to the ventricular epicardium to introduce a complex deformation in the region of interest, with transmural variations in the magnitude and sign of nearly all six strain components. The resulting deformation is measured throughout the region of interest using magnetic resonance tagging. A nonlinear, three-dimensional, finite element model is used to predict these measurements at several suction pressures. Parameters defining the material properties of this model are optimized by comparing the measured and predicted myocardial deformations. We used this technique to estimate material parameters of the intact passive canine left ventricular free wall using an exponential, transversely isotropic constitutive relation. We tested two possible models of the heart wall: first, that it was homogeneous myocardium, and second, that the myocardium was covered with a thin epicardium with different material properties. For both models, in agreement with previous studies, we found that myocardium was nonlinear and anisotropic with greater stiffness in the fiber direction. We obtained closer agreement to previously published strain data from passive filling when the ventricular wall was modeled as having a separate, isotropic epicardium. These results suggest that epicardium may play a significant role in passive ventricular mechanics.     

The importance of nonlinear tissue modelling in finite element simulations of infant head impacts

Despite recent efforts on the development of finite element (FE) head models of infants, a model capable of capturing head responses under various impact scenarios has not been reported. This is hypothesized partially attributed to the use of simplified linear elastic models for soft tissues of suture, scalp and dura. Orthotropic elastic constants are yet to be determined to incorporate the direction-specific material properties of infant cranial bone due to grain fibres radiating from the ossification centres. We report here on our efforts in advancing the above-mentioned aspects in material modelling in infant head and further incorporate them into subject-specific FE head models of a newborn, 5- and 9-month-old infant. Each model is subjected to five impact tests (forehead, occiput, vertex, right and left parietal impacts) and two compression tests. The predicted global head impact responses of the acceleration–time impact curves and the force–deflection compression curves for different age groups agree well with the experimental data reported in the literature. In particular, the newly developed Ogden hyperelastic model for suture, together with the nonlinear modelling of scalp and dura mater, enables the models to achieve more realistic impact performance compared with linear elastic models. The proposed approach for obtaining age-dependent skull bone orthotropic material constants counts both an increase in stiffness and decrease in anisotropy in the skull bone—two essential biological growth parameters during early infancy. The profound deformation of infant head causes a large stretch at the interfaces between the skull bones and the suture, suggesting that infant skull fractures are likely to initiate from the interfaces; the impact angle has a profound influence on global head impact responses and the skull injury metrics for certain impact locations, especially true for a parietal impact.     

Towards a biomechanics-based technique for assessing myocardial contractility: an inverse problem approach

This work presents the initial development and implementation of a novel 3D biomechanics-based approach to measure the mechanical activity of myocardial tissue, as a potential non-invasive tool to assess myocardial function. This technique quantifies the myocardial contraction forces developed within the ventricular myofibers in response to electro-physiological stimuli. We provide a 3D finite element formulation of a contraction force reconstruction algorithm, along with its implementation using magnetic resonance (MR) data. Our algorithm is based on an inverse problem solution governed by the fundamental continuum mechanics principle of conservation of linear momentum, under a first-order approximation of elastic and isotropic material conditions. We implemented our technique using a subject-specific ventricle model obtained by extracting the left ventricular anatomical features from a set of high-resolution cardiac MR images acquired throughout the cardiac cycle using prospective electrocardiographic gating. Cardiac motion information was extracted by non-rigid registration of the mid-diastole reference image to the remaining images of a 4D dataset. Using our technique, we reconstructed dynamic maps that show the contraction force distribution superimposed onto the deformed ventricle model at each acquired frame in the cardiac cycle. Our next objective will consist of validating this technique by showing the correlation between the presence of low contraction force patterns and poor myocardial functionality.     

Spiral waves in two-dimensional models of ventricular muscle: formation of a stationary core.

Previous experimental studies have clearly demonstrated the existence of drifting and stationary electrical spiral waves in cardiac muscle and their involvement in cardiac arrhythmias. Here we present results of a study of reentrant excitation in computer simulations based on a membrane model of the ventricular cell. We have explored in detail the parameter space of the model, using tools derived from previous numerical studies in excitation-dynamics models. We have found appropriate parametric conditions for sustained stable spiral wave dynamics (1 s of activity or approximately 10 rotations) in simulations of an anisotropic (ratio in velocity 4:1) cardiac sheet of 2 cm x 2 cm. Initially, we used a model that reproduced well the characteristics of planar electrical waves exhibited by thin sheets of sheep ventricular epicardial muscle during rapid pacing at a cycle length of 300 ms. Under these conditions, the refractory period was 147 ms; the action potential duration (APD) was 120 ms; the propagation velocity along fibers was 33 cm/s; and the wavelength along fibers was 4.85 cm. Using cross-field stimulation in this model, we obtained a stable self-sustaining spiral wave rotating around an unexcited core of 1.75 mm x 7 mm at a period of 115 ms, which reproduced well the experimental results. Thus the data demonstrate that stable spiral wave activity can occur in small cardiac sheets whose wavelength during planar wave excitation in the longitudinal direction is larger than the size of the sheet. Analysis of the mechanism of this observation demonstrates that, during rotating activity, the core exerts a strong electrotonic influence that effectively abbreviates APD (and thus wavelength) in its immediate surroundings and is responsible for the stabilization and perpetuation of the activity. We conclude that appropriate adjustments in the kinetics of the activation front (i.e., threshold for activation and upstroke velocity of the initiating beat) of currently available models of the cardiac cell allow accurate reproduction of experimentally observed self-sustaining spiral wave activity. As such, the results set the stage for an understanding of functional reentry in terms of ionic mechanisms.     

Strain-based estimation of time-dependent transmural myocardial architecture in the ovine heart

Left ventricular myofibers are connected by an extensive extracellular collagen matrix to form myolaminar sheets. Histological cardiac tissue studies have previously observed a pleated transmural distribution of sheets in the ovine heart, alternating sign of the sheet angle from epicardium to endocardium. The present study investigated temporal variations in myocardial fiber and sheet architecture during the cardiac cycle. End-diastolic histological measurements made at subepicardium, midwall, and subendocardium at an anterior-basal and a lateral-equatorial region of the ovine heart, combined with transmural myocardial Lagrangian strains, showed that the sheet angle but not the fiber angle varied temporally throughout the cardiac cycle. The magnitude of the sheet angle decreased during systole at all transmural depths at the anterior-basal site and at midwall and subendocardium depths at the lateral-equatorial site, making the sheets more parallel to the radial axis. These results support a previously suggested accordion-like wall-thickening mechanism of the myocardial sheets.     

Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip

Computational models may have the ability to quantify the relationship between hip morphology, cartilage mechanics and osteoarthritis. Most models have assumed the hip joint to be a perfect ball and socket joint and have neglected deformation at the bone-cartilage interface. The objective of this study was to analyze finite element (FE) models of hip cartilage mechanics with varying degrees of simplified geometry and a model with a rigid bone material assumption to elucidate the effects on predictions of cartilage stress. A previously validated subject-specific FE model of a cadaveric hip joint was used as the basis for the models. Geometry for the bone-cartilage interface was either: (1) subject-specific (i.e. irregular), (2) spherical, or (3) a rotational conchoid. Cartilage was assigned either a varying (irregular) or constant thickness (smoothed). Loading conditions simulated walking, stair-climbing and descending stairs. FE predictions of contact stress for the simplified models were compared with predictions from the subject-specific model. Both spheres and conchoids provided a good approximation of native hip joint geometry (average fitting error ～0.5 mm). However, models with spherical/conchoid bone geometry and smoothed articulating cartilage surfaces grossly underestimated peak and average contact pressures (50% and 25% lower, respectively) and overestimated contact area when compared to the subject-specific FE model. Models incorporating subject-specific bone geometry with smoothed articulating cartilage also underestimated pressures and predicted evenly distributed patterns of contact. The model with rigid bones predicted much higher pressures than the subject-specific model with deformable bones. The results demonstrate that simplifications to the geometry of the bone-cartilage interface, cartilage surface and bone material properties can have a dramatic effect on the predicted magnitude and distribution of cartilage contact pressures in the hip joint.     

Sarcomere length changes in a 3D mathematical model of the pig ventricles

Measurements of the geometry and fibrous-sheet structure of the left and right ventricles of the pig heart are fitted with a finite element model. Mechanical changes during the heart cycle are computed by solving the equations of motion under specified ventricular boundary conditions and using experimentally defined constitutive laws for the active and passive material properties of myocardial tissue. The resulting patterns of deformation, such as axial torsion and changes in wall thickness and base-apex length, are consistent with experimental observations. The model can therefore be used to predict sarcomere length changes and other strain patterns throughout the myocardium and throughout the cardiac cycle. Here we present sarcomere length changes at a limited number of material points within the wall. Sarcomere length typically varies by 10% above and below the unloaded length; although under the boundary conditions imposed in the current model the midwall circumferentially oriented sarcomere lengths increased by up to 20% at end diastole. We provide web-access details for a downloadable software program designed to provide more extensive information on mechanical deformation, such as the principal strains and muscle fibre cross-sectional area changes during the cardiac cycle.     

Contribution of laminar myofiber architecture to load-dependent changes in mechanics of LV myocardium

The ventricular myocardium consists of a syncytium of myocytes organized into branching, transmurally oriented laminar sheets approximately four cells thick. When systolic deformation is expressed in an axis system determined by the anatomy of the laminar architecture, laminar sheets of myocytes shear and laterally extend in an approximately radial direction. These deformations account for ~90% of normal systolic wall thickening in the left ventricular free wall. In the present study, we investigated whether the changes in systolic and diastolic function of the sheets were sensitive to alterations in systolic and diastolic load. Our results indicate that there is substantial reorientation of the laminar architecture during systole and diastole. Moreover, this reorientation is both site and load dependent. Thus as end-diastolic pressure is increased and the left ventricular wall thins, sheets shorten and rotate away from the radial direction due to transverse shearing, opposite of what occurs in systole. Both mechanisms of thickening contribute substantially to normal left ventricular wall function. Whereas the relative contributions of shear and extension are comparable at the base, sheet shear is the predominant factor at the apex. The magnitude of shortening/extension and shear increases with preload and decreases with afterload. These findings underscore the essential contribution of the laminar myocardial architecture for normal ventricular function throughout the cardiac cycle.     

Characterization of natural rubber as a bolus material for electron beam radiotherapy

BackgroundBolus is an accessory that is directly placed on the surface region to shift the radiation dose up to the skin during high energy photon and electron beam irradiations. The aim of this study was to mold the bolus using natural rubber material and assess both the physical and dosimetric characteristics.Materials and methodsA natural rubber with additional plasticizer material was fabricated as a bolus sheet. The physical properties of natural rubber bolus sheets have been investigated using computed tomography (CT) images. Gafchromic EBT3 films were used to acquire the dose at depth of 0, 2, 3, and 3.5 cm for the 9-MeV therapeutic electron beam. A comparison of our natural rubber bolus sheets to the commercial bolus sheets was studied.ResultsThe in-house natural rubber bolus sheets with the thickness of 0.32 and 0.52 cm were successfully made. Relative electron density of the two sheets was consistent with each other. However, similar to the commercial boluses, the natural rubber boluses were not provided with the same CT number over the whole sheet. Different bolus material gave different dose at the surface. Both material and thickness of the bolus showed a stronger impact on the dose beyond the depth of maximum dose.ConclusionBecause of the density, simple fabrication, and vast availability, natural rubber material has an effective potential to be used as a bolus sheet in radiotherapy     

hHGF overexpression in myoblast sheets enhances their angiogenic potential in rat chronic heart failure

After severe myocardial infarction (MI), heart failure results from ischemia, fibrosis, and remodeling. A promising therapy to enhance cardiac function and induce therapeutic angiogenesis via a paracrine mechanism in MI is myoblast sheet transplantation. We hypothesized that in a rat model of MI-induced chronic heart failure, this therapy could be further improved by overexpression of the antiapoptotic, antifibrotic, and proangiogenic hepatocyte growth factor (HGF) in the myoblast sheets. We studied the ability of wild type (L6-WT) and human HGF-expressing (L6-HGF) L6 myoblast sheet-derived paracrine factors to stimulate cardiomyocyte, endothelial cell, or smooth muscle cell migration in culture. Further, we studied the autocrine effect of hHGF-expression on myoblast gene expression profiles by use of microarray analysis. We induced MI in Wistar rats by left anterior descending coronary artery (LAD) ligation and allowed heart failure to develop for 4 weeks. Thereafter, we administered L6-WT (n = 15) or L6-HGF (n = 16) myoblast sheet therapy. Control rats (n = 13) underwent LAD ligation and rethoracotomy without therapy, and five rats underwent a sham operation in both surgeries. We evaluated cardiac function with echocardiography at 2 and 4 weeks after therapy, and analyzed cardiac angiogenesis and left ventricular architecture from histological sections at 4 weeks. Paracrine mediators from L6-HGF myoblast sheets effectively induced migration of cardiac endothelial and smooth muscle cells but not cardiomyocytes. Microarray data revealed that hHGF-expression modulated myoblast gene expression. In vivo, L6-HGF sheet therapy effectively stimulated angiogenesis in the infarcted and non-infarcted areas. Both L6-WT and L6-HGF therapies enhanced cardiac function and inhibited remodeling in a similar fashion. In conclusion, L6-HGF therapy effectively induced angiogenesis in the chronically failing heart. Cardiac function, however, was not further enhanced by hHGF expression.     

Fast Simulation of Mechanical Heterogeneity in the Electrically Asynchronous Heart Using the MultiPatch Module

Cardiac electrical asynchrony occurs as a result of cardiac pacing or conduction disorders such as left bundle-branch block (LBBB). Electrically asynchronous activation causes myocardial contraction heterogeneity that can be detrimental for cardiac function. Computational models provide a tool for understanding pathological consequences of dyssynchronous contraction. Simulations of mechanical dyssynchrony within the heart are typically performed using the finite element method, whose computational intensity may present an obstacle to clinical deployment of patient-specific models. We present an alternative based on the CircAdapt lumped-parameter model of the heart and circulatory system, called the MultiPatch module. Cardiac walls are subdivided into an arbitrary number of patches of homogeneous tissue. Tissue properties and activation time can differ between patches. All patches within a wall share a common wall tension and curvature. Consequently, spatial location within the wall is not required to calculate deformation in a patch. We test the hypothesis that activation time is more important than tissue location for determining mechanical deformation in asynchronous hearts. We perform simulations representing an experimental study of myocardial deformation induced by ventricular pacing, and a patient with LBBB and heart failure using endocardial recordings of electrical activation, wall volumes, and end-diastolic volumes. Direct comparison between simulated and experimental strain patterns shows both qualitative and quantitative agreement between model fibre strain and experimental circumferential strain in terms of shortening and rebound stretch during ejection. Local myofibre strain in the patient simulation shows qualitative agreement with circumferential strain patterns observed in the patient using tagged MRI. We conclude that the MultiPatch module produces realistic regional deformation patterns in the asynchronous heart and that activation time is more important than tissue location within a wall for determining myocardial deformation. The CircAdapt model is therefore capable of fast and realistic simulations of dyssynchronous myocardial deformation embedded within the closed-loop cardiovascular system.     

The influence of inflow boundary conditions on intra left ventricle flow predictions

The combination of computational fluid dynamics (CFD) and magnetic resonance imaging (MRI) offers a promising tool that enables the prediction of blood flow patterns in subject-specific cardiovascular models. The influence of the model geometry on the accuracy of the simulation is well recognized. This paper addresses the impact of different boundary conditions on subject-specific simulations of left ventricular (LV) flow. A novel hybrid method for prescribing effective inflow boundary conditions in the mitral valve plane has been developed. The detailed quantitative results highlight the strengths as well as the potential pitfalls of the approach.     

Fabrication of functional three-dimensional tissues by stacking cell sheets in vitro

The fabrication of 3D tissues retaining the original functions of tissues/organs in vitro is crucial for optimal tissue engineering and regenerative medicine. The fabrication of 3D tissues also contributes to the establishment of in vitro tissue/organ models for drug screening. Our laboratory has developed a fabrication system for functional 3D tissues by stacking cell sheets of confluent cultured cells detached from a temperature-responsive culture dish. Here we describe the protocols for the fabrication of 3D tissues by cell sheet engineering. Three-dimensional cardiac tissues fabricated by stacking cardiac cell sheets pulsate spontaneously, synchronously and macroscopically. Via this protocol, it is also possible to fabricate other tissues, such as 3D tissue including capillary-like prevascular networks, from endothelial cells sandwiched between layered cell sheets. Cell sheet stacking technology promises to provide in vitro tissue/organ models and more effective therapies for curing tissue/organ failures.     

Subject-specific tendon-aponeurosis definition in hill-type model predicts higher muscle forces in dynamic tasks

Neuromusculoskeletal models are a common method to estimate muscle forces. Developing accurate neuromusculoskeletal models is a challenging task due to the complexity of the system and large inter-subject variability. The estimation of muscles force is based on the mechanical properties of tendon-aponeurosis complex. Most neuromusculoskeletal models use a generic definition of the tendon-aponeurosis complex based on in vitro test, perhaps limiting their validity. Ultrasonography allows subject-specific estimates of the tendon-aponeurosis complex's mechanical properties. The aim of this study was to investigate the influence of subject-specific mechanical properties of the tendon-aponeurosis complex on a neuromusculoskeletal model of the ankle joint. Seven subjects performed isometric contractions from which the tendon-aponeurosis force-strain relationship was estimated. Hopping and running tasks were performed and muscle forces were estimated using subject-specific tendon-aponeurosis and generic tendon properties. Two ultrasound probes positioned over the muscle-tendon junction and the mid-belly were combined with motion capture to estimate the in vivo tendon and aponeurosis strain of the medial head of gastrocnemius muscle. The tendon-aponeurosis force-strain relationship was scaled for the other ankle muscles based on tendon and aponeurosis length of each muscle measured by ultrasonography. The EMG-driven model was calibrated twice - using the generic tendon definition and a subject-specific tendon-aponeurosis force-strain definition. The use of subject-specific tendon-aponeurosis definition leads to a higher muscle force estimate for the soleus muscle and the plantar-flexor group, and to a better model prediction of the ankle joint moment compared to the model estimate which used a generic definition. Furthermore, the subject-specific tendon-aponeurosis definition leads to a decoupling behaviour between the muscle fibre and muscle-tendon unit in agreement with previous experiments using ultrasonography. These results indicate the use of subject-specific tendon-aponeurosis definitions in a neuromusculoskeletal model produce better agreement with measured external loads and more physiological model behaviour.     

Subject-specific finite element model of the pelvis: development, validation and sensitivity studies

A better understanding of the three-dimensional mechanics of the pelvis, at the patient-specific level, may lead to improved treatment modalities. Although finite element (FE) models of the pelvis have been developed, validation by direct comparison with subject-specific strains has not been performed, and previous models used simplifying assumptions regarding geometry and material properties. The objectives of this study were to develop and validate a realistic FE model of the pelvis using subject-specific estimates of bone geometry, location-dependent cortical thickness and trabecular bone elastic modulus, and to assess the sensitivity of FE strain predictions to assumptions regarding cortical bone thickness as well as bone and cartilage material properties. A FE model of a cadaveric pelvis was created using subject-specific computed tomography image data. Acetabular loading was applied to the same pelvis using a prosthetic femoral stem in a fashion that could be easily duplicated in the computational model. Cortical bone strains were monitored with rosette strain gauges in ten locations on the left hemipelvis. FE strain predictions were compared directly with experimental results for validation. Overall, baseline FE predictions were strongly correlated with experimental results (r2=0.824), with a best-fit line that was not statistically different than the line y=x (experimental strains = FE predicted strains). Changes to cortical bone thickness and elastic modulus had the largest effect on cortical bone strains. The FE model was less sensitive to changes in all other parameters. The methods developed and validated in this study will be useful for creating and analyzing patient-specific FE models to better understand the biomechanics of the pelvis.     

The use of adipose-derived stem cells as sheets for wound healing

Cellular therapies have shown immense promise in the treatment of nonhealing wounds. Cell sheets are an emerging strategy in tissue engineering, and these cell sheets are promising as a delivery method of mesenchymal stem cells to the wound bed. Cell sheet technology utilizes temperature dependent polymers to allow for lifting of cultured cells and extracellular matrix without the use of digestive enzymes. While mesenchymal stem cells (MSCs) have shown success in cell sheets for myocardial repair, examination of cell sheets in the field of wound healing has been limited. We previously developed a novel cell sheet composed of human adipose-derived stem cells (ASCs). Both single and triple layer cell sheets were examined in a full-thickness murine wound model. The treatment cell sheets were compared with untreated controls and analyzed at timepoints of 7, 14, 18 and 21 d. The ASC cell sheets showed increased healing at 7, 14 and 18 d, and this effect was increased in the triple layer cell sheet group. Future development of these cell sheets will focus on increasing angiogenesis in the wound bed, utilizing multiple cell types, and examining allogeneic cell sheets. Here we review our experiment, expand upon our future directions and discuss the potential of an off-the-shelf cell sheet. In the field of wound healing, such a cell sheet is both clinically and scientifically exciting.     

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.