Mechanism underlying mechanical dysfunction in the border zone of left ventricular aneurysm: a finite element model study

Post-infarct evolution of ventricular and myocardial function

Adverse ventricular remodeling following acute myocardial infarction (MI) may induce ventricular dilation, fibrosis, and loss of global contractile function, possibly resulting in heart failure (HF). Understanding the relation between the time-dependent changes in material properties of the myocardium and the contractile function of the heart may further our understanding of the development of HF post-MI and guide the development of novel therapies. A finite element model of cardiac mechanics was used to model MI in a thick-walled truncated ellipsoidal geometry. Infarct core and border zone comprised 9.6 and 8.1% of the LV wall volume, respectively. Acute MI was modeled by inhibiting active stress generation. Chronic MI was modeled by the additional effect of infarct material stiffening, wall thinning and fiber reorientation. In acute MI, stroke work decreased by 25%. In the infarct core, fiber stress was reduced but fiber strain was increased, depending on the degree of infarct stiffening. Fiber work density was equal to zero. Healthy tissue adjacent to the infarct showed decreased work density depending on the degree of infarct stiffness and the orientation of the myofibers with respect to the infarct region. Thinning of the wall partially restored this loss in work density while the effects of fiber reorientation were minimal. We found that the relative loss in pump function in the infarcted heart exceeds the relative loss in healthy myocardial tissue due to impaired mechanical function in healthy tissue adjacent to the infarct. Infarct stiffening, wall thinning and fiber reorientation did not affect pump function but did affect the distribution of work density in tissue adjacent to the infarct.

Physical model of end-diastolic and end-systolic pressure-volume relationships of a heart

Left ventricular stiffness and contractility, characterized by the end-diastolic pressure-volume relationship (EDPVR) and the end-systolic pressure-volume relationship (ESPVR), are two important indicators of the performance of the human heart. Although much research has been conducted on EDPVR and ESPVR, no model with physically interpretable parameters combining both relationships has been presented, thereby impairing the understanding of cardiac physiology and pathology. Here, we present a model that evaluates both EDPVR and ESPVR with physical interpretations of the parameters in a unified framework. Our physics-based model fits the available experimental data and in silico results very well and outperforms existing models. With prescribed parameters, the new model is used to predict the pressure-volume relationships of the left ventricle. Our model provides a deeper understanding of cardiac mechanics and thus will have applications in cardiac research and clinical medicine.

Apical post-infarction ventricular septal defect blockage using the direct externalization and enmeshment to the right ventricular moderator band concept: case series

Background

Transcatheter treatment in post-infarction ventricular septal defects can be unique and complex; hence, the development of a new technique is needed to improve outcomes.

Summary

We describe two cases in which large and complex apical post-infarction ventricular septal defects were treated with a novel transcatheter approach as salvage and the other due to refusal for open surgical repair. By direct externalization and enmeshment of a device to the right ventricular moderator band, the defect was blocked and immediate improvement of haemodynamics was achieved.

Conclusion

In large, complex, apical post-infarction ventricular septal defects with no apical rims, the DEXTER technique allows for exclusion of the defect and vestigialization of the right ventricular apex. An immediate and dramatic haemodynamic improvement can therefore be achieved.

Cardiac hypertrophy simulations using parametric and echocardiography-based left ventricle model with shell finite elements

In our paper, we simulated cardiac hypertrophy with the use of shell elements in parametric and echocardiography-based left ventricle (LV) models. The hypertrophy has an impact on the change in the wall thickness, displacement field and the overall functioning of the heart. We computed both eccentric and concentric hypertrophy effects and tracked changes in the ventricle shape and wall thickness. Thickening of the wall was developed under the influence of concentric hypertrophy, while the eccentric hypertrophy produces wall thinning. To model passive stresses we used the recently developed material modal based on the Holzapfel experiments. Also, our specific shell composite finite element models for heart mechanics are much smaller and simpler to use with respect to conventional 3D models. Furthermore, the presented modeling approach of the echocardiography-based LV can serve as the basis for practical applications since it relies on the true patient-specific geometry and experimental constitutive relationships. Our model gives an insight into hypertrophy development in realistic heart geometries, and it has the potential to test medical hypotheses regarding hypertrophy evolution in a healthy and heart with a disease, under the influence of different conditions and parameters.

Material property alterations for phenotypes of heart failure with preserved ejection fraction: A numerical study of subject-specific porcine models

A substantial proportion of heart failure patients have a preserved left ventricular (LV) ejection fraction (HFpEF). This condition carries a high burden of morbidity and mortality and has limited therapeutic options. left ventricular pressure overload leads to an increase in myocardial collagen content, causing left ventricular stiffening that contributes to the development of heart failure patients have a preserved left ventricular ejection fraction. Although several heart failure patients have a preserved left ventricular ejection fraction models have been developed in recent years to aid the investigation of mechanical alterations, none has investigated different phenotypes of the disease and evaluated the alterations in material properties. In this study, two similar healthy swine were subjected to progressive and prolonged pressure overload to induce diastolic heart failure characteristics, providing a preclinical model of heart failure patients have a preserved left ventricular ejection fraction. Cardiac magnetic resonance imaging (cMRI) scans and intracardiac pressures were recorded before and after induction. In both healthy and disease states, a corresponding finite element (FE) cardiac model was developed via mesh morphing of the Living Heart Porcine model. The material properties were derived by calibrating to its passive and active behavior. The change in the passive behavior was predominantly isotropic when comparing the geometries before and after induction. Myocardial thickening allowed for a steady transition in the passive properties while maintaining tissue incompressibility. This study highlights the importance of hypertrophy as an initial compensatory response and might also pave the way for assessing disease severity.

How viscous is the beating heart?: Insights from a computational study

Understanding tissue rheology is critical to accurately model the human heart. While the elastic properties of cardiac tissue have been extensively studied, its viscous properties remain an issue of ongoing debate. Here we adopt a viscoelastic version of the classical Holzapfel Ogden model to study the viscous timescales of human cardiac tissue. We perform a series of simulations and explore stress-relaxation curves, pressure-volume loops, strain profiles, and ventricular wall strains for varying viscosity parameters. We show that the time window for model calibration strongly influences the parameter identification. Using a four-chamber human heart model, we observe that, during the physiologically relevant time scales of the cardiac cycle, viscous relaxation has a negligible effect on the overall behavior of the heart. While viscosity could have important consequences in pathological conditions with compromised contraction or relaxation properties, we conclude that, for simulations within the physiological range of a human heart beat, we can reasonably approximate the human heart as hyperelastic.

Cardiac mesh morphing method for finite element modeling of heart failure with preserved ejection fraction

Numerical modeling of heart biomechanics can realistically capture morphological variations in diseases and has been helpful in advancing our understanding of the physiology. Subject-specific models require anatomic representation of medical images, and it is desirable to have a consistently repeatable models for any given morphology. In this study, we propose a novel and easily adaptable cardiac reconstruction algorithm by morphing an existing discretized mesh of an advanced finite element (FE) model, to match anatomies acquired from porcine cardiac magnetic resonance imaging (cMRI) scans. The morphing algorithm involves iterative FE simulations with visco-hyperelastic material properties. The living heart porcine model (LHPM) was chosen as the input baseline FE mesh, in order to preserve detailed anatomical features that cannot be captured in routine scans such as myofiber orientations and conduction pathways. The algorithm was demonstrated for the recreation of porcine hearts of a healthy subject and of a subject induced with heart failure with preserved ejection fraction (HFpEF) conditions, where there were substantial hypertrophy and anatomical alterations. We further used the morphed meshes for FE modeling of cardiac contraction and relaxation, thus demonstrating the applicability of the proposed algorithm in producing viable meshes. The results show that our algorithm can recreate the characteristic anatomical changes of cardiac remodeling, including heart muscle thickening, as well as replicate the reduction in ventricular volume. This algorithm allows for the creation of subject-specific models with the same mesh connectivity, thus enabling spatial comparison and analysis of pathologic progress.

A finite element model of the cardiac ventricles with coupled circulation: Biventricular mesh generation with hexahedral elements, airbags and a functional mockup interface to the circulation

INTRODUCTION

Finite element (FE) mechanics models of the heart are becoming more sophisticated. However, there is lack of consensus about optimal element type and coupling of FE models to the circulation. We describe biventricular (left (LV) and right (RV) ventricles) FE mechanics model creation using hexahedral elements, airbags and a functional mockup interface (FMI) to lumped-parameter models of the circulation.

METHODS

Cardiac MRI (CMR) was performed in two healthy volunteers and a single patient with ischemic heart disease (IHD). CMR images were segmented and surfaced, meshing with hexahedral elements was performed with a "thin butterfly with septum" topology. LV and RV inflow and outflow airbags were coupled to lumped-parameter circulation models with an FMI interface. Pulmonary constriction (PAC) and vena cava occlusion (VCO) were simulated and end-systolic pressure-volume relations (ESPVR) were calculated.

RESULTS

Mesh construction was prompt with representative contouring and mesh adjustment requiring 32 and 26 min Respectively. The numbers of elements ranged from 4104 to 5184 with a representative Jacobian of 1.0026 ± 0.4531. Agreement between CMR-based surfaces and mesh was excellent with root-mean-squared error of 0.589 ± 0.321 mm. The LV ESPVR slope was 3.37 ± 0.09 in volunteers but 2.74 in the IHD patient. The effect of PAC and VCO on LV ESPVR was consistent with ventricular interaction (p = 0.0286).

CONCLUSION

Successful co-simulation using a biventricular FE mechanics model with hexahedral elements, airbags and an FMI interface to lumped-parameter model of the circulation was demonstrated. Future studies will include comparison of element type and study of cardiovascular pathologies and device therapies.

The role of regional myocardial topography post-myocardial infarction on infarct extension

Infarct extension involves necrosis of healthy myocardium in the border zone (BZ), progressively enlarging the infarct zone (IZ) and recruiting the remote zone (RZ) into the BZ, eventually leading to heart failure. The mechanisms underlying infarct extension remain unclear, but myocyte stretching has been suggested as the most likely cause. Using human patient-specific left-ventricular (LV) numerical simulations established from cardiac magnetic resonance imaging (MRI) of myocardial infarction (MI) patients, the correlation between infarct extension and regional mechanics abnormality was investigated by analysing the fibre stress-strain loops (FSSLs). FSSL abnormality was characterised using the directional regional external work (DREW) index, which measures FSSL area and loop direction. Sensitivity studies were also performed to investigate the effect of infarct stiffness on regional myocardial mechanics and potential for infarct extension. We found that infarct extension was correlated to severely abnormal FSSL in the form of counter-clockwise loop at the RZ close to the infarct, as indicated by negative DREW values. In regions demonstrating negative DREW values, we observed substantial fibre stretching in the isovolumic relaxation (IVR) phase accompanied by a reduced rate of systolic shortening. Such stretching in IVR phase in part of the RZ was due to its inability to withstand the high LV pressure that was still present and possibly caused by regional myocardial stiffness inhomogeneity. Further analysis revealed that the occurrence of severely abnormal FSSL due to IVR fibre stretching near the RZ-BZ boundary was due to a large amount of surrounding infarcted tissue, or an excessively stiff IZ.

A Comparison of Fiber Based Material Laws for Myocardial Scar

The mechanics of most soft tissues in the human body are determined by the organization of their collagen fibers. Predicting how mechanics will change during growth and remodeling of those tissues requires constitutive laws that account for the density and dispersion of collagen fibers. Post-infarction scar in the heart, a mechanically and structurally complex material, does not yet have a validated fiber-based constitutive model. In this study, we tested four different constitutive laws employing exponential or polynomial strain-energy functions and accounting for either mean fiber orientation alone or the details of the fiber distribution about that mean. We quantified the goodness of fit of each law to mechanical testing data from 6-week-old myocardial scar in the rat using both sum of squared error (SSE) and the Akaike Information Criterion (AIC) to account for differences in the number of material parameters within the constitutive laws. We then compared their ability to prospectively predict the mechanics of independent myocardial scar samples from other time points during healing. Our analysis suggests that a constitutive law with a polynomial form that incorporates detailed information about collagen fiber distribution using a structure tensor provides excellent fits with just two parameters and reasonable predictions of myocardial scar mechanics from measured structure alone in scars containing sufficiently high collagen content.

Effects of Left Ventricular Hypertrophy and Myocardial Stiffness on Myocardial Strain Under Preserved Ejection Fraction

Despite numerous experimental observations regarding heart failure with preserved ejection fraction (HFpEF), which is characterized mainly by left ventricular hypertrophy and a left ventricular ejection fraction over 50%, myocardial dynamics under HFpEF have not yet been fully clarified, particularly regarding the relationship between myocardial strain distribution and myocardial work. To address this issue, we numerically investigated radial distribution of myocardial strain during a cardiac cycle with fixed internal volume at the end of the systolic and diastolic phases under different mechanical conditions, such as those involving myocardial thickness and elasticity of myocardial fibers. The myocardium was a modeled as a visco-hyperelastic continuous material. This model was taken into account that active contractile stress along the myocardial fiber direction depends on membrane potential change. Our numerical results showed that both radial and circumferential strains decreased as wall thickness increased, which reflected cardiac hypertrophy, but that myocardial work became larger than that observed with thin ventricular walls. Further, the change in left ventricular diastolic internal pressure caused circumferential strain, while fiber stiffness contributed to radial strain. Since peak circumferential strain was well estimated by the maximum difference between total internal and myocardial volumes, measuring the epicardial contraction rate should be helpful in understanding patients with HFpEF.

Towards the simulation of active cardiac mechanics using a smoothed finite element method

In the last decades, various computational models have been developed to simulate cardiac electromechanics. The most common numerical tool is the finite element method (FEM). However, this method crucially depends on the mesh quality. For complex geometries such as cardiac structures, it is convenient to use tetrahedral discretisations which can be generated automatically. On the other hand, such automatic meshing with tetrahedrons together with large deformations often lead to elements distortion and volumetric locking. To overcome these difficulties, different smoothed finite element methods (S-FEMs) have been proposed in the recent years. They are known to be volumetric locking free, less sensitive to mesh distortion and so far have been used e.g. in simulation of passive cardiac mechanics. In this work, we extend for the first time node-based S-FEM (NS-FEM) towards active cardiac mechanics. Firstly, the sensitivity to mesh distortion is tested and compared to that of FEM. Secondly, an active contraction in circumferentially aligned fibre direction is modelled in the healthy and the infarcted case. We show, that the proposed method is more robust with respect to mesh distortion and computationally more efficient than standard FEM. Being furthermore free of volumetric locking problems makes S-FEM a promising alternative in modelling of active cardiac mechanics, respectively electromechanics.

Mechanical difference of left ventricle between rabbits of myocardial infarction and hypertrophy

The analysis of cardiac wall stress is of importance to understand the development of heart failure (HF). The aim of the study is to carry out the cardiac mechanics analysis to show the changes of left ventricular (LV) wall stresses after LV hypertrophy (LVH) and myocardial infarction (MI). Here, LVH and MI were generated in rabbit hearts through the transverse aortic constriction (TAC) and the distal left circumflex (LCx) artery ligation operations, respectively. Physiological and CT measurements were carried out at postoperative 2 and 4 weeks, based on which a finite element (FE) model was developed to perform the mechanics computation. We found a gradual increase of end-diastolic myofiber stress in free wall and interventricular septum of LVH and MI (higher stress in the free wall than the septum). In the interventricular septum, the 4-weeks LVH group has the highest ED myofiber stresses (11.378 ± 3.022 kPa), while the 4-weeks MI group has the highest ED myofiber stresses (13.494 ± 2.835 kPa) in the free wall. LVH increased myocardial volume (3.49 ± 0.07 and 4.52 ± 0.26 ml at postoperative 2 and 4 weeks) while MI increased LV volume (from 2.75 ± 0.29 to 4.19 ± 0.27 ml). LVH and MI had different distributions of local myofiber stress.

Biomechanics of infarcted left ventricle: a review of modelling

Mathematical modelling in biomechanics of infarcted left ventricle (LV) serves as an indispensable tool for remodelling mechanism exploration, LV biomechanical property estimation and therapy assessment after myocardial infarction (MI). However, a review of mathematical modelling after MI has not been seen in the literature so far. In the paper, a systematic review of mathematical models in biomechanics of infarcted LV was established. The models include comprehensive cardiovascular system model, essential LV pressure-volume and stress-stretch models, constitutive laws for passive myocardium and scars, tension models for active myocardium, collagen fibre orientation optimization models, fibroblast and collagen fibre growth/degradation models and integrated growth-electro-mechanical model after MI. The primary idea, unique characteristics and key equations of each model were identified and extracted. Discussions on the models were provided and followed research issues on them were addressed. Considerable improvements in the cardiovascular system model, LV aneurysm model, coupled agent-based models and integrated electro-mechanical-growth LV model are encouraged. Substantial attention should be paid to new constitutive laws with respect to stress-stretch curve and strain energy function for infarcted passive myocardium, collagen fibre orientation optimization in scar, cardiac rupture and tissue damage and viscoelastic effect post-MI in the future.

Myocardial injection of a thermoresponsive hydrogel with reactive oxygen species scavenger properties improves border zone contractility

The decrease in contractility in myocardium adjacent (border zone; BZ) to a myocardial infarction (MI) is correlated with an increase in reactive oxygen species (ROS). We hypothesized that injection of a thermoresponsive hydrogel, with ROS scavenging properties, into the MI would decrease ROS and improve BZ function. Fourteen sheep underwent antero-apical MI. Seven sheep had a comb-like copolymer synthesized from N-isopropyl acrylamide (NIPAAm) and 1500 MW methoxy poly(ethylene glycol) methacrylate, (NIPAAm-PEG1500), injected (20 × 0.5 mL) into the MI zone 40 min after MI (MI + NIPAAm-PEG1500) and seven sheep were MI controls. Cardiac MRI was performed 2 weeks before and 6 weeks after MI + NIPAAm-PEG1500. BZ wall thickness at end systole was significantly higher for MI + NIPAAm-PEG1500 (12.32 ± 0.51 mm/m² MI + NIPAAm-PEG1500 vs. 9.88 ± 0.30 MI; p = .023). Demembranated muscle force development for BZ myocardium 6 weeks after MI was significantly higher for MI + NIPAAm-PEG1500 (67.67 ± 2.61 mN/m² MI + NIPAAm-PEG1500 vs. 40.53 ± 1.04 MI; p < .0001) but not significantly different from remote myocardium or BZ or non-operated controls. Levels of ROS in BZ tissue were significantly lower in the MI + NIPAAm-PEG1500 treatment group (hydroxyl p = .0031; superoxide p = .0182). We conclude that infarct injection of the NIPAAm-PEG1500 hydrogel with ROS scavenging properties decreased ROS and improved contractile protein function in the border zone 6 weeks after MI.

Force-dependent recruitment from myosin OFF-state increases end-systolic pressure-volume relationship in left ventricle

Finite element (FE) modeling is becoming increasingly prevalent in the world of cardiac mechanics; however, many existing FE models are phenomenological and thus do not capture cellular-level mechanics. This work implements a cellular-level contraction scheme into an existing nonlinear FE code to model ventricular contraction. Specifically, this contraction model incorporates three myosin states: OFF-, ON-, and an attached force-generating state. It has been speculated that force-dependent transitions from the OFF- to ON-state may contribute to length-dependent activation at the cellular level. The current work investigates the contribution of force-dependent recruitment out of the OFF-state to ventricular-level function, specifically the Frank-Starling relationship, as seen through the end-systolic pressure-volume relationship (ESPVR). Five FE models were constructed using geometries of rat left ventricles obtained via cardiac magnetic resonance imaging. FE simulations were conducted to optimize parameters for the cellular contraction model such that the differences between FE predicted ventricular pressures for the models and experimentally measured pressures were minimized. The models were further validated by comparing FE predicted end-systolic strain to experimentally measured strain. Simulations mimicking vena cava occlusion generated descending pressure volume loops from which ESPVRs were calculated. In simulations with the inclusion of the OFF-state, using a force-dependent transition to the ON-state, the ESPVR calculated was steeper than in simulations excluding the OFF-state. Furthermore, the ESPVR was also steeper when compared to models that included the OFF-state without a force-dependent transition. This suggests that the force-dependent recruitment of thick filament heads from the OFF-state at the cellular level contributes to the Frank-Starling relationship observed at the organ level.

A Novel MRI-Based Finite Element Modeling Method for Calculation of Myocardial Ischemia Effect in Patients With Functional Mitral Regurgitation

BACKGROUND

Functional Mitral Regurgitation (FMR) associated with coronary artery disease affects nearly 3 million patients in the United States. Both myocardial infarction (MI) and ischemia contribute to FMR development but uncertainty as to which patients will respond to revascularization (REVASC) of ischemia alone prevents rational decision making about FMR therapy. The aim of this study was to create patient-specific cardiac MRI (CMR) informed finite element (FE) models of the left ventricle (LV), calculate regional LV systolic contractility and then use optimized systolic material properties to simulate the effect of revascularization (virtual REVASC).

METHODS

We describe a novel FE method able to predict the effect of myocardial ischemia on regional LV function. CMR was obtained in five patients with multi-vessel coronary disease and FMR before and 3 months after percutaneous REVASC and a single healthy volunteer. Patient-specific FE models were created and divided into 17 sectors where the systolic contractility parameter, T m a x of each sector was a function of regional stress perfusion (SP-CMR) and myocardial infarction (LGE-CMR) scores. Sector-specific circumferential and longitudinal end-systolic strain and LV volume from CSPAMM were used in a formal optimization to determine the sector based myocardial contractility, T m a x and ischemia effect, α. Virtual REVASC was simulated by setting α to zero.

RESULTS

The FE optimization successfully converged with good agreement between calculated and experimental end-systolic strain and LV volumes. Specifically, the optimized T max for the healthy myocardium for five patients and the volunteer was 495.1, 336.8, 173.5, 227.9, 401.4, and 218.9 kPa. The optimized α was found to be 1.0, 0.44, and 0.08 for Patients 1, 2, and 3, and 0 for Patients 4 and 5. The calculated average of radial strain for Patients 1, 2, and 3 at baseline and after virtual REVASC was 0.23 and 0.25, respectively.

CONCLUSION

We developed a novel computational method able to predict the effect of myocardial ischemia in patients with FMR. This method can be used to predict the effect of ischemia on the regional myocardium and promises to facilitate better understanding of FMR response to REVASC.

Open-Source Routines for Building Personalized Left Ventricular Models From Cardiac Magnetic Resonance Imaging Data

Creating patient-specific models of the heart is a promising approach for predicting outcomes in response to congenital malformations, injury, or disease, as well as an important tool for developing and customizing therapies. However, integrating multimodal imaging data to construct patient-specific models is a nontrivial task. Here, we propose an approach that employs a prolate spheroidal coordinate system to interpolate information from multiple imaging datasets and map those data onto a single geometric model of the left ventricle (LV). We demonstrate the mapping of the location and transmural extent of postinfarction scar segmented from late gadolinium enhancement (LGE) magnetic resonance imaging (MRI), as well as mechanical activation calculated from displacement encoding with stimulated echoes (DENSE) MRI. As a supplement to this paper, we provide MATLAB and Python versions of the routines employed here for download from SimTK.

The role of end-diastolic myocardial fibre stretch on infarct extension

Myocardial infarct extension, a process involving the enlargement of infarct and border zone, leads to progressive degeneration of left ventricular (LV) function and eventually gives rise to heart failure. Despite carrying a high risk, the causation of infarct extension is still a subject of much speculation. In this study, patient-specific LV models were developed to investigate the correlation between infarct extension and impaired regional mechanics. Subsequently, sensitivity analysis was performed to examine the causal factors responsible for the impaired regional mechanics observed in regions surrounding the infarct and border zone. From our simulations, fibre strain, fibre stress and fibre stress-strain loop (FSSL) were the key biomechanical variables affected in these regions. Among these variables, only FSSL was correlated with infarct extension, as reflected in its work density dissipation (WDD) index value, with high WDD indices recorded at regions with infarct extension. Impaired FSSL is caused by inadequate contraction force generation during the isovolumic contraction and ejection phases. Our further analysis revealed that the inadequacy in contraction force generation is not necessarily due to impaired myocardial intrinsic contractility, but at least in part, due to inadequate muscle fibre stretch at end-diastole, which depresses the ability of myocardium to generate adequate contraction force in the subsequent systole (according to the Frank-Starling law). Moreover, an excessively stiff infarct may cause its neighbouring myocardium to be understretched at end-diastole, subsequently depressing the systolic contractile force of the neighbouring myocardium, which was found to be correlated with infarct extension.

Biomechanical assessment of remote and postinfarction scar remodeling following myocardial infarction

The importance of collagen remodeling following myocardial infarction (MI) is extensively investigated, but little is known on the biomechanical impact of fibrillar collagen on left ventricle post-MI. We aim to identify the significant effects of the biomechanics of types I, III, and V collagen on physio-pathological changes of murine hearts leading to heart failure. Immediately post-MI, heart reduces its function (EF = 40.94 ± 2.12%) while sarcomeres' dimensions are unchanged. Strikingly, as determined by immunohistochemistry staining, type V collagen fraction significantly grows in remote and scar for sustaining de novo-types I and III collagen fibers' assembly while hindering their enzymatic degradation. Thereafter, the compensatory heart function (EF = 63.04 ± 3.16%) associates with steady development of types I and III collagen in a stiff remote (12.79 ± 1.09 MPa) and scar (22.40 ± 1.08 MPa). In remote, the soft de novo-type III collagen uncoils preventing further expansion of elongated sarcomeres (2.7 ± 0.3 mm). Once the compensatory mechanisms are surpassed, the increased turnover of stiff type I collagen (>50%) lead to a pseudo-stable biomechanical regime of the heart (≅9 MPa) with reduced EF (50.55 ± 3.25%). These end-characteristics represent the common scenario evidenced in patients suffering from heart failure after MI. Our pre-clinical data advances the understanding of the cause of heart failure induced in patients with extended MI.

Regional and temporal changes in left ventricular strain and stiffness in a porcine model of myocardial infarction

The aim of the present study was to serially track how myocardial infarction (MI) impacts regional myocardial strain and mechanical properties of the left ventricle (LV) in a large animal model. Post-MI remodeling has distinct regional effects throughout the LV myocardium. Regional quantification of LV biomechanical behavior could help explain changes in global function and thus advance clinical assessment of post-MI remodeling. The present study is based on a porcine MI model to characterize LV biomechanics over 28 days post-MI via speckle-tracking echocardiography (STE). Regional myocardial strain and strain rate were recorded in the circumferential, radial, and longitudinal directions at baseline and at 3, 14, and 28 days post-MI. Regional myocardial wall stress was calculated using standard echocardiographic metrics of geometry and Doppler-derived hemodynamic measurements. Regional diastolic myocardial stiffness was calculated from the resultant stress-strain relations. Peak strain and phasic strain rates were nonuniformly reduced throughout the myocardium post-MI, whereas time to peak strain was increased to a similar degree in the MI region and border zone by 28 days post-MI. Elevations in diastolic myocardial stiffness in the MI region plateaued at 14 days post-MI, after which a significant reduction in MI regional stiffness in the longitudinal direction occurred between 14 and 28 days post-MI. Post-MI biomechanical changes in the LV myocardium were initially limited to the MI region but nonuniformly extended into the neighboring border zone and remote myocardium over 28 days post-MI. STE enabled quantification of regional and temporal differences in myocardial strain and diastolic stiffness, underscoring the potential of this technique for clinical assessment of post-MI remodeling. NEW & NOTEWORTHY For the first time, speckle-tracking echocardiography was used to serially track regional biomechanical behavior and mechanical properties postmyocardial infarction (post-MI). We found that changes initially confined to the MI region extended throughout the myocardium in a nonuniform fashion over 28 days post-MI. Speckle-tracking echocardiography-based evaluation of regional changes in left ventricular biomechanics could advance both clinical assessment of left ventricular remodeling and therapeutic strategies that target aberrant biomechanical behavior post-MI.

Construction and Validation of Subject-Specific Biventricular Finite-Element Models of Healthy and Failing Swine Hearts From High-Resolution DT-MRI

Predictive computational modeling has revolutionized classical engineering disciplines and is in the process of transforming cardiovascular research. This is particularly relevant for investigating emergent therapies for heart failure, which remains a leading cause of death globally. The creation of subject-specific biventricular computational cardiac models has been a long-term endeavor within the biomedical engineering community. Using high resolution (0.3 × 0.3 × 0.8 mm) ex vivo data, we constructed a precise fully subject-specific biventricular finite-element model of healthy and failing swine hearts. Each model includes fully subject-specific geometries, myofiber architecture and, in the case of the failing heart, fibrotic tissue distribution. Passive and active material properties are prescribed using hyperelastic strain energy functions that define a nearly incompressible, orthotropic material capable of contractile function. These materials were calibrated using a sophisticated multistep approach to match orthotropic tri-axial shear data as well as subject-specific hemodynamic ventricular targets for pressure and volume to ensure realistic cardiac function. Each mechanically beating heart is coupled with a lumped-parameter representation of the circulatory system, allowing for a closed-loop definition of cardiovascular flow. The circulatory model incorporates unidirectional fluid exchanges driven by pressure gradients of the model, which in turn are driven by the mechanically beating heart. This creates a computationally meaningful representation of the dynamic beating of the heart coupled with the circulatory system. Each model was calibrated using subject-specific experimental data and compared with independent in vivo strain data obtained from echocardiography. Our methods produced highly detailed representations of swine hearts that function mechanically in a remarkably similar manner to the in vivo subject-specific strains on a global and regional comparison. The degree of subject-specificity included in the models represents a milestone for modeling efforts that captures realism of the whole heart. This study establishes a foundation for future computational studies that can apply these validated methods to advance cardiac mechanics research.

Evaluation of a Novel Finite Element Model of Active Contraction in the Heart

Finite element (FE) modeling is becoming a widely used approach for the investigation of global heart function. In the present study, a novel model of cellular-level systolic contraction, which includes both length- and velocity-dependence, was implemented into a 3D non-linear FE code. To validate this new FE implementation, an optimization procedure was used to determine the contractile parameters, associated with sarcomeric function, by comparing FE-predicted pressure and strain to experimental measures collected with magnetic resonance imaging and catheterization in the ventricles of five healthy rats. The pressure-volume relationship generated by the FE models matched well with the experimental data. Additionally, the regional distribution of end-systolic strains and circumferential-longitudinal shear angle exhibited good agreement with experimental results overall, with the main deviation occurring in the septal region. Moreover, the FE model predicted a heterogeneous distribution of sarcomere re-lengthening after ventricular ejection, which is consistent with previous in vivo studies. In conclusion, the new FE active contraction model was able to predict the global performance and regional mechanical behaviors of the LV during the entire cardiac cycle. By including more accurate cellular-level mechanisms, this model could provide a better representation of the LV and enhance cardiac research related to both systolic and diastolic dysfunction.

Changes and classification in myocardial contractile function in the left ventricle following acute myocardial infarction

In this research, we hypothesized that novel biomechanical parameters are discriminative in patients following acute ST-segment elevation myocardial infarction (STEMI). To identify these biomechanical biomarkers and bring computational biomechanics ‘closer to the clinic’, we applied state-of-the-art multiphysics cardiac modelling combined with advanced machine learning and multivariate statistical inference to a clinical database of myocardial infarction. We obtained data from 11 STEMI patients (ClinicalTrials.gov NCT01717573) and 27 healthy volunteers, and developed personalized mathematical models for the left ventricle (LV) using an immersed boundary method. Subject-specific constitutive parameters were achieved by matching to clinical measurements. We have shown, for the first time, that compared with healthy controls, patients with STEMI exhibited increased LV wall active tension when normalized by systolic blood pressure, which suggests an increased demand on the contractile reserve of remote functional myocardium. The statistical analysis reveals that the required patient-specific contractility, normalized active tension and the systolic myofilament kinematics have the strongest explanatory power for identifying the myocardial function changes post-MI. We further observed a strong correlation between two biomarkers and the changes in LV ejection fraction at six months from baseline (the required contractility (r = − 0.79, p < 0.01) and the systolic myofilament kinematics (r = 0.70, p = 0.02)). The clinical and prognostic significance of these biomechanical parameters merits further scrutinization.

Personalised computational cardiology: Patient-specific modelling in cardiac mechanics and biomaterial injection therapies for myocardial infarction

Predictive computational modelling in biomedical research offers the potential to integrate diverse data, uncover biological mechanisms that are not easily accessible through experimental methods and expose gaps in knowledge requiring further research. Recent developments in computing and diagnostic technologies have initiated the advancement of computational models in terms of complexity and specificity. Consequently, computational modelling can increasingly be utilised as enabling and complementing modality in the clinic—with medical decisions and interventions being personalised. Myocardial infarction and heart failure are amongst the leading causes of death globally despite optimal modern treatment. The development of novel MI therapies is challenging and may be greatly facilitated through predictive modelling. Here, we review the advances in patient-specific modelling of cardiac mechanics, distinguishing specificity in cardiac geometry, myofibre architecture and mechanical tissue properties. Thereafter, the focus narrows to the mechanics of the infarcted heart and treatment of myocardial infarction with particular attention on intramyocardial biomaterial delivery.

Short term doxycycline treatment induces sustained improvement in myocardial infarction border zone contractility

Decreased contractility in the non-ischemic border zone surrounding a MI is in part due to degradation of cardiomyocyte sarcomeric components by intracellular matrix metalloproteinase-2 (MMP-2). We recently reported that MMP-2 levels were increased in the border zone after a MI and that treatment with doxycycline for two weeks after MI was associated with normalization of MMP-2 levels and improvement in ex-vivo contractile protein developed force in the myocardial border zone. The purpose of the current study was to determine if there is a sustained effect of short term treatment with doxycycline (Dox) on border zone function in a large animal model of antero-apical myocardial infarction (MI). Antero-apical MI was created in 14 sheep. Seven sheep received doxycycline 0.8 mg/kg/hr IV for two weeks. Cardiac MRI was performed two weeks before, and then two and six weeks after MI. Two sheep died prior to MRI at six weeks from surgical/anesthesia-related causes. The remaining 12 sheep completed the protocol. Doxycycline induced a sustained reduction in intracellular MMP-2 by Western blot (3649±643 MI+Dox vs 9236±114 MI relative intensity; p = 0.0009), an improvement in ex-vivo contractility (65.3±2.0 MI+Dox vs 39.7±0.8 MI mN/mm²; p<0.0001) and an increase in ventricular wall thickness at end-systole 1.0 cm from the infarct edge (12.4±0.6 MI+Dox vs 10.0±0.5 MI mm; p = 0.0095). Administration of doxycycline for a limited two week period is associated with a sustained improvement in ex-vivo contractility and an increase in wall thickness at end-systole in the border zone six weeks after MI. These findings were associated with a reduction in intracellular MMP-2 activity.

Excessive volume of hydrogel injectates may compromise the efficacy for the treatment of acute myocardial infarction

Biomaterial injectates are promising as a therapy for myocardial infarction to inhibit the adverse ventricular remodeling. The current study explored interrelated effects of injectate volume and infarct size on treatment efficacy. A finite element model of a rat heart was utilized to represent ischemic infarcts of 10%, 20%, and 38% of left ventricular wall volume and polyethylene glycol hydrogel injectates of 25%, 50%, and 75% of the infarct volume. Ejection fraction was 49.7% in the healthy left ventricle and 44.9%, 46.4%, 47.4%, and 47.3% in the untreated 10% infarct and treated with 25%, 50%, and 75% injectate, respectively. Maximum end-systolic infarct fiber stress was 41.6, 53.4, 44.7, 44.0, and 45.3 kPa in the healthy heart, the untreated 10% infarct, and when treated with the three injectate volumes, respectively. Treating the 10% and 38% infarcts with the 25% injectate volume reduced the maximum end-systolic fiber stress by 16.3% and 34.7% and the associated strain by 30.2% and 9.8%, respectively. The results indicate the existence of a threshold for injectate volume above which efficacy does not further increase but may decrease. The efficacy of an injectate in reducing infarct stress and strain changes with infarct size. Copyright © 2016 John Wiley & Sons, Ltd.

Moderate Ischemic Mitral Regurgitation After Posterolateral Myocardial Infarction in Sheep Alters Left Ventricular Shear but Not Normal Strain in the Infarct and Infarct Borderzone

BACKGROUND

Chronic ischemic mitral regurgitation (CIMR) is associated with poor outcome. Left ventricular (LV) strain after posterolateral myocardial infarction (MI) may drive LV remodeling. Although moderate CIMR has been previously shown to affect LV remodeling, the effect of CIMR on LV strain after posterolateral MI remains unknown. We tested the hypothesis that moderate CIMR alters LV strain after posterolateral MI.

METHODS

Posterolateral MI was created in 10 sheep. Cardiac magnetic resonance imaging with tags was performed 2 weeks before and 2, 8, and 16 weeks after MI. The left and right ventricular volumes were measured, and regurgitant volume indexed to body surface area (regurgitant volume index) was calculated as the difference between left ventricle and right ventricle stroke volumes divided by body surface area. Three-dimensional strain was calculated.

RESULTS

Circumferential strain (Ecc) and longitudinal strain (Ell) were reduced in the infarct proper, MI borderzone, and remote myocardium 16 weeks after MI. In addition, radial circumferential (Erc) and radial longitudinal (Erl) shear strains were reduced in remote myocardium but increased in the infarct and borderzone 16 weeks after MI. Of all strain components, however, only Erc was affected by regurgitant volume index (p = 0.0005). There was no statistically significant effect of regurgitant volume index on Ecc, Ell, Erl, or circumferential longitudinal shear strain (Ecl).

CONCLUSIONS

Moderate CIMR alters radial circumferential shear strain after posterolateral MI in sheep. Further studies are needed to determine the effect of shear strain on myocyte hypertrophy and the effect of mitral repair on myocardial strain.

Biomechanics of Cardiac Function

The heart pumps blood to maintain circulation and ensure the delivery of oxygenated blood to all the organs of the body. Mechanics play a critical role in governing and regulating heart function under both normal and pathological conditions. Biological processes and mechanical stress are coupled together in regulating myocyte function and extracellular matrix structure thus controlling heart function. Here, we offer a brief introduction to the biomechanics of left ventricular function and then summarize recent progress in the study of the effects of mechanical stress on ventricular wall remodeling and cardiac function as well as the effects of wall mechanical properties on cardiac function in normal and dysfunctional hearts. Various mechanical models to determine wall stress and cardiac function in normal and diseased hearts with both systolic and diastolic dysfunction are discussed. The results of these studies have enhanced our understanding of the biomechanical mechanism in the development and remodeling of normal and dysfunctional hearts. Biomechanics provide a tool to understand the mechanism of left ventricular remodeling in diastolic and systolic dysfunction and guidance in designing and developing new treatments.

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.

Residual Stress Impairs Pump Function After Surgical Ventricular Remodeling: A Finite Element Analysis

BACKGROUND

Surgical ventricular restoration (Dor procedure) is generally thought to reduce left ventricular (LV) myofiber stress (FS) but to adversely affect pump function. However, the underlying mechanism is unclear. The goal of this study was to determine the effect of residual stress (RS) on LV FS and pump function after the Dor procedure.

METHODS

Previously described finite element models of the LV based on magnetic resonance imaging data obtained in 5 sheep 16 weeks after anteroapical myocardial infarction were used. Simulated polyethylene terephthalate fiber (Dacron) patches that were elliptical and 25% of the infarct opening area were implanted using a virtual suture technique (VIRTUAL-DOR). In each case, diastole and systole were simulated, and RS, FS, LV volumes, systolic and diastolic function, and pump (Starling) function were calculated.

RESULTS

VIRTUAL-DOR was associated with significant RS that was tensile (2.89 ± 1.31 kPa) in the remote myocardium and compressive (234.15 ± 65.53 kPa) in the border zone. VIRTUAL-DOR+RS (compared with VIRTUAL-DOR-NO-RS) was associated with further reduction in regional diastolic and systolic FS, with the greatest change in the border zone (43.5-fold and 7.1-fold, respectively; p < 0.0001). VIRTUAL-DOR+RS was also associated with further reduction in systolic and diastolic volumes (7.9%; p = 0.0606, and 10.6%; p = 0.0630, respectively). The resultant effect was a further reduction in pump function after VIRTUAL-DOR+RS.

CONCLUSIONS

Residual stress that occurs after the Dor procedure is positive (tensile) in the remote myocardium and negative (compressive) in the border zone and associated with reductions in FS and LV volumes. The resultant effect is a further reduction in LV pump (Starling) function.

A Novel Method for Quantifying Smooth Regional Variations in Myocardial Contractility Within an Infarcted Human Left Ventricle Based on Delay-Enhanced Magnetic Resonance Imaging

Heart failure is increasing at an alarming rate, making it a worldwide epidemic. As the population ages and life expectancy increases, this trend is not likely to change. Myocardial infarction (MI)-induced adverse left ventricular (LV) remodeling is responsible for nearly 70% of heart failure cases. The adverse remodeling process involves an extension of the border zone (BZ) adjacent to an MI, which is normally perfused but shows myofiber contractile dysfunction. To improve patient-specific modeling of cardiac mechanics, we sought to create a finite element model of the human LV with BZ and MI morphologies integrated directly from delayed-enhancement magnetic resonance (DE-MR) images. Instead of separating the LV into discrete regions (e.g., the MI, BZ, and remote regions) with each having a homogeneous myocardial material property, we assumed a functional relation between the DE-MR image pixel intensity and myocardial stiffness and contractility--we considered a linear variation of material properties as a function of DE-MR image pixel intensity, which is known to improve the accuracy of the model's response. The finite element model was then calibrated using measurements obtained from the same patient--namely, 3D strain measurements-using complementary spatial modulation of magnetization magnetic resonance (CSPAMM-MR) images. This led to an average circumferential strain error of 8.9% across all American Heart Association (AHA) segments. We demonstrate the utility of our method for quantifying smooth regional variations in myocardial contractility using cardiac DE-MR and CSPAMM-MR images acquired from a 78-yr-old woman who experienced an MI approximately 1 yr prior. We found a remote myocardial diastolic stiffness of C(0) = 0.102 kPa, and a remote myocardial contractility of T(max) = 146.9 kPa, which are both in the range of previously published normal human values. Moreover, we found a normalized pixel intensity range of 30% for the BZ, which is consistent with the literature. Based on these regional myocardial material properties, we used our finite element model to compute patient-specific diastolic and systolic LV myofiber stress distributions, which cannot be measured directly. One of the main driving forces for adverse LV remodeling is assumed to be an abnormally high level of ventricular wall stress, and many existing and new treatments for heart failure fundamentally attempt to normalize LV wall stress. Thus, our noninvasive method for estimating smooth regional variations in myocardial contractility should be valuable for optimizing new surgical or medical strategies to limit the chronic evolution from infarction to heart failure.

Mechanics of pericardial effusion: A simulation study

Pericardial effusion is a pathological accumulation of fluid within pericardial cavity, which may compress heart chambers with hemodynamic impairment. We sought to determine the mechanics underlying the physiology of the hemodynamic impairment due to pericardial effusion using patient-specific computational modeling. Computational models of left ventricle and right ventricle were based on magnetic resonance images obtained from patients with pericardial effusion and controls. Myocardial material parameters were adjusted, so that volumes of ventricular chambers and pericardial effusion agreed with magnetic resonance imaging data. End-diastolic and end-systolic pressure–volume relationships as well as stroke volume were determined to evaluate impaired cardiac function of biventricular model. Distributions of myocardial fiber stresses and their regional variation along left ventricular wall were compared between patient groups. Both end-diastolic and end-systolic pressure–volume relationships shifted to the left for patients with pericardial effusion, with right ventricle diastolic filling particularly restricted. Left ventricle function as estimated by Starling curve was reduced by pericardial effusion. End-systolic fiber stress of left ventricle was significantly reduced as compared to that found for healthy patients. Myocardial stress was found increased at interventricular septum when compared to that exerted at lateral wall of left ventricle. Right ventricular myocardial stress was reduced as a consequence of the pressure equalization between right ventricle and pericardial effusion. Diastolic right ventricle collapse in patients with pericardial effusion is related to higher myocardial fiber stress on interventricular septum and to an extensible pericardium reducing motion of ventricular chambers, with right ventricle particularly restrained. These findings likely portend progression of pericardial effusion to cardiac tamponade.

Numerical evaluation of myofiber orientation and transmural contractile strength on left ventricular function

The left ventricle (LV) of the heart is composed of a complex organization of cardiac muscle fibers, which contract to generate force and pump blood into the body. It has been shown that both the orientation and contractile strength of these myofibers vary across the ventricular wall. The hypothesis of the current study is that the transmural distributions of myofiber orientation and contractile strength interdependently impact LV pump function. In order to quantify these interactions a finite element (FE) model of the LV was generated, which incorporated transmural variations. The influences of myofiber orientation and contractile strength on the Starling relationship and the end-systolic (ES) apex twist of the LV were assessed. The results suggest that reductions in contractile strength within a specific transmural layer amplified the effects of altered myofiber orientation in the same layer, causing greater changes in stroke volume (SV). Furthermore, when the epicardial myofibers contracted the strongest, the twist of the LV apex was greatest, regardless of myofiber orientation. These results demonstrate the important role of transmural distribution of myocardial contractile strength and its interplay with myofiber orientation. The coupling between these two physiologic parameters could play a critical role in the progression of heart failure.

Regional myocardial three-dimensional principal strains during postinfarction remodeling

BACKGROUND

The purpose of this study was to quantify myocardial three-dimensional (3D) principal strains as the left ventricle (LV) remodels after myocardial infarction (MI). Serial quantification of myocardial strains is important for understanding the mechanical response of the LV to MI. Principal strains convert the 3D LV wall-based strain matrix with three normal and three shear elements, to a matrix with three nonzero normal elements, thereby eliminating the shear elements, which are difficult to physically interpret.

METHODS

The study was designed to measure principal strains of the remote, border zone, and infarct regions in a porcine model of post-MI LV remodeling. Magnetic resonance imaging was used to measure function and strain at baseline, 1 week, and 4 weeks after infarct. Principal strain was measured using 3D acquisition and the optical flow method for displacement tracking.

RESULTS

Principal strains were altered as the LV remodeled. Maximum principal strain magnitude decreased in all regions, including the noninfarcted remote, while maximum principal strain angles rotated away from the radial direction in the border zone and infarct. Minimum principal strain magnitude followed a similar pattern; however, strain angles were altered in all regions. Evolution of principal strains correlated with adverse LV remodeling.

CONCLUSIONS

Using a state-of-the-art imaging and optical flow method technique, 3D principal strains can be measured serially after MI in pigs. Results are consistent with progressive infarct stretching as well as with decreased contractile function in the border zone and remote myocardial regions.

Myofilament dysfunction contributes to impaired myocardial contraction in the infarct border zone

After myocardial infarction, a poorly contracting nonischemic border zone forms adjacent to the infarct. The cause of border zone dysfunction is unclear. The goal of this study was to determine the myofilament mechanisms involved in postinfarction border zone dysfunction. Two weeks after anteroapical infarction of sheep hearts, we studied in vitro isometric and isotonic contractions of demembranated myocardium from the infarct border zone and a zone remote from the infarct. Maximal force development (Fmax) of the border zone myocardium was reduced by 31 ± 2% versus the remote zone myocardium (n = 6/group, P < 0.0001). Decreased border zone Fmax was not due to a reduced content of contractile material, as assessed histologically, and from myosin content. Furthermore, decreased border zone Fmax did not involve altered cross-bridge kinetics, as assessed by muscle shortening velocity and force development kinetics. Decreased border zone Fmax was associated with decreased cross-bridge formation, as assessed from muscle stiffness in the absence of ATP where cross-bridge formation should be maximized (rigor stiffness was reduced 34 ± 6%, n = 5, P = 0.011 vs. the remote zone). Furthermore, the border zone myocardium had significantly reduced phosphorylation of myosin essential light chain (ELC; 41 ± 10%, n = 4, P < 0.05). However, for animals treated with doxycycline, an inhibitor of matrix metalloproteinases, rigor stiffness and ELC phosphorylation were not reduced in the border zone myocardium, suggesting that doxycycline had a protective effect. In conclusion, myofilament dysfunction contributes to postinfarction border zone dysfunction, myofilament dysfunction involves impaired cross-bridge formation and decreased ELC phosphorylation, and matrix metalloproteinase inhibition may be beneficial for limiting postinfarct border zone dysfunction.

Distribution of normal human left ventricular myofiber stress at end diastole and end systole: a target for in silico design of heart failure treatments

Ventricular wall stress is believed to be responsible for many physical mechanisms taking place in the human heart, including ventricular remodeling, which is frequently associated with heart failure. Therefore, normalization of ventricular wall stress is the cornerstone of many existing and new treatments for heart failure. In this paper, we sought to construct reference maps of normal ventricular wall stress in humans that could be used as a target for in silico optimization studies of existing and potential new treatments for heart failure. To do so, we constructed personalized computational models of the left ventricles of five normal human subjects using magnetic resonance images and the finite-element method. These models were calibrated using left ventricular volume data extracted from magnetic resonance imaging (MRI) and validated through comparison with strain measurements from tagged MRI (950 ± 170 strain comparisons/subject). The calibrated passive material parameter values were C0 = 0.115 ± 0.008 kPa and B0 = 14.4 ± 3.18; the active material parameter value was Tmax = 143 ± 11.1 kPa. These values could serve as a reference for future construction of normal human left ventricular computational models. The differences between the predicted and the measured circumferential and longitudinal strains in each subject were 3.4 ± 6.3 and 0.5 ± 5.9%, respectively. The predicted end-diastolic and end-systolic myofiber stress fields for the five subjects were 2.21 ± 0.58 and 16.54 ± 4.73 kPa, respectively. Thus these stresses could serve as targets for in silico design of heart failure treatments.

Estimating the Myocardium's Angle of Three-Dimensional Trajectory, Using the Tracking of Sequential Two-Dimensional Echocardiography Images

BACKGROUND

In this study, the angle of the myocardium's trajectory in three dimensions (ф) was estimated by simultaneous use of long-axis and short-axis views of left ventricle septum two-dimensional images. Then correlation of three-dimensional trajectory's angle with the rotation angle from the long (χ) and short (θ) axis views was estimated and compared at the three levels of base, mid and apex of the interventricular septum wall.

METHODS

Two-dimensional echocardiography images of long- and short-axis views of 19 healthy men were recorded and analyzed. Using an electrocardiogram of each individual, the images of the two views were synchronized. The interventricular septum wall motion at the three levels of base, mid and apex were estimated, using a block matching algorithm throughout three cardiac cycles. Considering the defined system of coordinates and the position vectors in long and short-axis views, the 3-dimensional angle of the trajectory was calculated.

RESULTS

Maxima of the ф, θ, and χ angles were extracted at 16.33 ± 3.01, 10.61 ± 3.38, and 15.11 ± 3.30 degrees at base level, 22.77 ± 4.95, 7.78 ± 2.96, and 16.72 ± 2.66 degrees at mid level and 14.60 ± 5.81, 10.37 ± 5.48, and 8.79 ± 3.32 degrees at apex level, respectively, of the septum wall, respectively. This study shows significant correlation between the angle of 3-dimensional trajectory (ф) with the angle in short axis view (θ) of the septum wall at the apex level; and also with the angle in long axis view (χ) of the septum wall at base and mid levels.

CONCLUSION

Due to the motion of the wall of the left ventricle in three dimensions, and the non-isotropic structure of myofibers, the angle of 3-dimensional trajectory was estimated using the speckle tracking method of 2-dimentional echocardiography images.

Applications of computational modeling in cardiac surgery

Although computational modeling is common in many areas of science and engineering, only recently have advances in experimental techniques and medical imaging allowed this tool to be applied in cardiac surgery. Despite its infancy in cardiac surgery, computational modeling has been useful in calculating the effects of clinical devices and surgical procedures. In this review, we present several examples that demonstrate the capabilities of computational cardiac modeling in cardiac surgery. Specifically, we demonstrate its ability to simulate surgery, predict myofiber stress and pump function, and quantify changes to regional myocardial material properties. In addition, issues that would need to be resolved in order for computational modeling to play a greater role in cardiac surgery are discussed.

Studying the influence of hydrogel injections into the infarcted left ventricle using the element-free Galerkin method

Myocardial infarction is an increasing health problem worldwide. Because of an under-supply of blood, the cardiomyocytes in the affected region permanently lose their ability to contract. This in turn gradually weakens the overall heart function. A new therapeutic approach based on the injection of a gel into the infarcted area aims to support the healing and to inhibit adverse remodelling that can lead to heart failure. A computational model is the basis for obtaining a better understanding of the heart mechanics, in particular, how myocardial infarction and gel injections affect its pumping performance. A strain invariant-based stored energy function is proposed to account for the passive mechanical behaviour of the model, which also makes provision for active contraction. To incorporate injections an additive homogenization approach is introduced. The numerical framework is developed using an in-house code based on the element-free Galerkin method. The main focus of this contribution is to investigate the influence of gel injections on the mechanics of the left ventricle during the diastolic filling and systolic isovolumetric (isochoric) contraction phases. It is found that gel injections are able to reduce the elevated fibre stresses caused by an infarct.

Simulation of left ventricular function during dyskinetic or akinetic aneurysm

The purpose of our study was to simulate the hemodynamics of left ventricular function after left ventricular aneurysm (LVA) of various sizes and to validate the results of this computer based simulation with patient data. We developed an equivalent electronic circuit (EEC) that reflects the hemodynamic conditions of LVA (after acute myocardial infraction) while taking into consideration the resetting of the sympathetic nervous tone in the heart and systemic circuit, the fluctuating intrathoracic pressure during respiration and passive relaxation of the ventricle during diastole. The key feature of the EEC was a subcircuit representing the LVA, with a subcircuit to measure ventricular blood volume (i.e. intraventricular "shunting" of blood flow during systole and diastole) between the unaffected section of the left ventricle and its aneurysm. This EEC model can simulate akinetic or dyskinetic LVAs of different sizes and provides realistic beat-to-beat ventricular blood flow and pressure tracings that were validated by pressure-volume loop diagrams and by published patient data. In agreement with published data, simulated dyskinetic LVAs have a considerably greater impact on ventricular function than akinetic LVAs. The hemodynamic effects of ventricular systolic dysfunction following LVA were also evaluated. We conclude that the EEC model qualitatively and to a significant degree quantitatively represents conditions in patients with a dyskinetic or an akinetic LVA and provides realistic beat-to-beat ventricular blood flow and pressure tracings.

Localized targeting of biomaterials following myocardial infarction: a foundation to build on

Acute coronary syndromes can give rise to myocardial injury infarction (MI), which in turn promulgates a series of cellular and extracellular events that result in left ventricular (LV) dilation and dysfunction. Localized strategies focused upon interrupting this inexorable process include delivery of bioactive molecules and stem cell derivatives. These localized treatment strategies are often delivered in a biomaterial complex in order to facilitate elution of the bioactive molecules or stem cell engraftment. However, these biomaterials can impart significant and independent effects upon the MI remodeling process. In addition, significant changes in local cell and interstitial biology within the targeted MI region can occur following injection of certain biomaterials, which may hold important considerations when using these materials as matrices for adjuvant drug/cell therapies.

Multi-parametric MRI as an indirect evaluation tool of the mechanical properties of in-vitro cardiac tissues

Background

Early detection of heart failure is essential to effectively reduce related mortality. The quantification of the mechanical properties of the myocardium, a primordial indicator of the viability of the cardiac tissue, is a key element in patient’s care. Despite an incremental utilization of multi-parametric magnetic resonance imaging (MRI) for cardiac tissue characteristics and function, the link between multi-parametric MRI and the mechanical properties of the heart has not been established. We sought to determine the parametric relationship between the myocardial mechanical properties and the MR parameters. The specific aim was to develop a reproducible evaluative quantitative tool of the mechanical properties of cardiac tissue using multi-parametric MRI associated to principal component analysis.

Methods

Samples from porcine hearts were submitted to a multi-parametric MRI acquisition followed by a uniaxial tensile test. Multi linear regressions were performed between dependent (Young’s modulus E) and independent (relaxation times T1, T2 and T2*, magnetization transfer ratio MTR, apparent diffusion coefficient ADC and fractional anisotropy FA) variables. A principal component analysis was used to convert the set of possibly correlated variables into a set of linearly uncorrelated variables.

Results

Values of 46.1±12.7 MPa for E, 729±21 ms for T1, 61±6 ms for T2, 26±7 for T2*, 35±5% for MTRx100, 33.8±4.7 for FAx10^-2, and 5.85±0.21 mm²/s for ADCx10^-4 were measured. Multi linear regressions showed that only 45% of E can be explained by the MRI parameters. The principal component analysis reduced our seven variables to two principal components with a cumulative variability of 63%, which increased to 80% when considering the third principal component.

Conclusions

The proposed multi-parametric MRI protocol associated to principal component analysis is a promising tool for the evaluation of mechanical properties within the left ventricle in the in vitro porcine model. Our in vitro experiments will now allow us focused in vivo testing on healthy and infracted hearts in order to determine useful quantitative MR-based biomarkers.

The benefit of enhanced contractility in the infarct borderzone: a virtual experiment

OBJECTIVES

Contractile function in the normally perfused infarct borderzone (BZ) is depressed. However, the impact of reduced BZ contractility on left ventricular (LV) pump function is unknown. As a consequence, there have been no therapies specifically designed to improve BZ contractility. We tested the hypothesis that an improvement in borderzone contractility will improve LV pump function.

METHODS

From a previously reported study, magnetic resonance imaging (MRI) images with non-invasive tags were used to calculate 3D myocardial strain in five sheep 16 weeks after anteroapical myocardial infarction. Animal-specific finite element (FE) models were created using MRI data and LV pressure obtained at early diastolic filling. Analysis of borderzone function using those FE models has been previously reported. Chamber stiffness, pump function (Starling's law) and stress in the fiber, cross fiber, and circumferential directions were calculated. Animal-specific FE models were performed for three cases: (a) impaired BZ contractility (INJURED); (b) BZ-contractility fully restored (100% BZ IMPROVEMENT); or (c) BZ-contractility partially restored (50% BZ IMPROVEMENT).

RESULTS

100% BZ IMPROVEMENT and 50% BZ IMPROVEMENT both caused an upward shift in the Starling relationship, resulting in a large (36 and 26%) increase in stroke volume at LVP(ED) = 20 mmHg (8.0 ml, p < 0.001). Moreover, there were a leftward shift in the end-systolic pressure volume relationship, resulting in a 7 and 5% increase in LVP(ES) at 110 mmHg (7.7 ml, p < 0.005). It showed that even 50% BZ IMPROVEMENT was sufficient to drive much of the calculated increase in function.

CONCLUSION

Improved borderzone contractility has a beneficial effect on LV pump function. Partial improvement of borderzone contractility was sufficient to drive much of the calculated increase in function. Therapies specifically designed to improve borderzone contractility should be developed.

The effect of hydrogel injection on cardiac function and myocardial mechanics in a computational post-infarction model

An emerging therapy to limit adverse heart remodelling following myocardial infarction (MI) is the injection of polymers into the infarcted left ventricle (LV). In the few numerical studies carried out in this field, the definition and distribution of the hydrogel in the infarcted myocardium were simplified. In this computational study, a more realistic biomaterial distribution was simulated after which the effect on cardiac function and mechanics was studied. A validated finite element heart model was used in which an antero-apical infarct was defined. Four infarct models were created representing different temporal phases in the progression of a MI. Hydrogel layers were simulated in the infarcted myocardium in each model. Biomechanical and functional improvement of the LV was found after hydrogel inclusion in the ischaemic models representing the early phases of MI. In contrast, only functional but no mechanical restitution was shown in the scar model due to hydrogel presence.