Coupled agent-based and hyperelastic modelling of the left ventricle post-myocardial infarction

Simulated Effects of Acute Left Ventricular Myocardial Infarction on Mitral Regurgitation in an Ovine Model

Ischemic mitral regurgitation (IMR) occurs from incomplete coaptation of the mitral valve (MV) after myocardial infarction (MI), typically worsened by continued remodeling of the left ventricular (LV). The importance of LV remodeling is clear as IMR is induced by the post-MI dual mechanisms of mitral annular dilation and leaflet tethering from papillary muscle (PM) distension via the MV chordae tendineae (MVCT). However, the detailed etiology of IMR remains poorly understood, in large part due to the complex interactions of the MV and the post-MI LV remodeling processes. Given the patient-specific anatomical complexities of the IMR disease processes, simulation-based approaches represent an ideal approach to improve our understanding of this deadly disease. However, development of patient-specific models of left ventricle-mitral valve (LV-MV) interactions in IMR are complicated by the substantial variability and complexity of the MR etiology itself, making it difficult to extract underlying mechanisms from clinical data alone. To address these shortcomings, we developed a detailed ovine LV-MV finite element (FE) model based on extant comprehensive ovine experimental data. First, an extant ovine LV FE model (Sci. Rep. 2021 Jun 29;11(1):13466) was extended to incorporate the MV using a high fidelity ovine in vivo derived MV leaflet geometry. As it is not currently possible to image the MVCT in vivo, a functionally equivalent MVCT network was developed to create the final LV-MV model. Interestingly, in pilot studies, the MV leaflet strains did not agree well with known in vivo MV leaflet strain fields. We then incorporated previously reported MV leaflet prestrains (J. Biomech. Eng. 2023 Nov 1;145(11):111002) in the simulations. The resulting LV-MV model produced excellent agreement with the known in vivo ovine MV leaflet strains and deformed shapes in the normal state. We then simulated the effects of regional acute infarctions of varying sizes and anatomical locations by shutting down the local myocardial contractility. The remaining healthy (noninfarcted) myocardium mechanical behaviors were maintained, but allowed to adjust their active contractile patterns to maintain the prescribed pressure-volume loop behaviors in the acute post-MI state. For all cases studied, the LV-MV simulation demonstrated excellent agreement with known LV and MV in vivo strains and MV regurgitation orifice areas. Infarct location was shown to play a critical role in resultant MV leaflet strain fields. Specifically, extensional deformations of the posterior leaflets occurred in the posterobasal and laterobasal infarcts, while compressive deformations of the anterior leaflet were observed in the anterobasal infarct. Moreover, the simulated posterobasal infarct induced the largest MV regurgitation orifice area, consistent with experimental observations. The present study is the first detailed LV-MV simulation that reveals the important role of MV leaflet prestrain and functionally equivalent MVCT for accurate predictions of LV-MV interactions. Importantly, the current study further underscored simulation-based methods in understanding MV function as an integral part of the LV.

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.

An updated Lagrangian constrained mixture model of pathological cardiac growth and remodelling

Progressive left ventricular (LV) growth and remodelling (G&R) is often induced by volume and pressure overload, characterized by structural and functional adaptation through myocyte hypertrophy and extracellular matrix remodelling, which are dynamically regulated by biomechanical factors, inflammation, neurohormonal pathways, etc. When prolonged, it can eventually lead to irreversible heart failure. In this study, we have developed a new framework for modelling pathological cardiac G&R based on constrained mixture theory using an updated reference configuration, which is triggered by altered biomechanical factors to restore biomechanical homeostasis. Eccentric and concentric growth, and their combination have been explored in a patient-specific human LV model under volume and pressure overload. Eccentric growth is triggered by overstretching of myofibres due to volume overload, i.e. mitral regurgitation, whilst concentric growth is driven by excessive contractile stress due to pressure overload, i.e. aortic stenosis. Different biological constituent's adaptations under pathological conditions are integrated together, which are the ground matrix, myofibres and collagen network. We have shown that this constrained mixture-motivated G&R model can capture different phenotypes of maladaptive LV G&R, such as chamber dilation and wall thinning under volume overload, wall thickening under pressure overload, and more complex patterns under both pressure and volume overload. We have further demonstrated how collagen G&R would affect LV structural and functional adaption by providing mechanistic insight on anti-fibrotic interventions. This updated Lagrangian constrained mixture based myocardial G&R model has the potential to understand the turnover processes of myocytes and collagen due to altered local mechanical stimuli in heart diseases, and in providing mechanistic links between biomechanical factors and biological adaption at both the organ and cellular levels. Once calibrated with patient data, it can be used for assessing heart failure risk and designing optimal treatment therapies. STATEMENT OF SIGNIFICANCE: Computational modelling of cardiac G&R has shown high promise to provide insight into heart disease management when mechanistic understandings are quantified between biomechanical factors and underlying cellular adaptation processes. The kinematic growth theory has been dominantly used to phenomenologically describe the biological G&R process but neglecting underlying cellular mechanisms. We have developed a constrained mixture based G&R model with updated reference by taking into account different mechanobiological processes in the ground matrix, myocytes and collagen fibres. This G&R model can serve as a basis for developing more advanced myocardial G&R models further informed by patient data to assess heart failure risk, predict disease progression, select the optimal treatment by hypothesis testing, and eventually towards a truly precision cardiology using in-silico models.

Mechano-biological and bio-mechanical pathways in cutaneous wound healing

Injuries to the skin heal through coordinated action of fibroblast-mediated extracellular matrix (ECM) deposition, ECM remodeling, and wound contraction. Defects involving the dermis result in fibrotic scars featuring increased stiffness and altered collagen content and organization. Although computational models are crucial to unravel the underlying biochemical and biophysical mechanisms, simulations of the evolving wound biomechanics are seldom benchmarked against measurements. Here, we leverage recent quantifications of local tissue stiffness in murine wounds to refine a previously-proposed systems-mechanobiological finite-element model. Fibroblasts are considered as the main cell type involved in ECM remodeling and wound contraction. Tissue rebuilding is coordinated by the release and diffusion of a cytokine wave, e.g. TGF-β, itself developed in response to an earlier inflammatory signal triggered by platelet aggregation. We calibrate a model of the evolving wound biomechanics through a custom-developed hierarchical Bayesian inverse analysis procedure. Further calibration is based on published biochemical and morphological murine wound healing data over a 21-day healing period. The calibrated model recapitulates the temporal evolution of: inflammatory signal, fibroblast infiltration, collagen buildup, and wound contraction. Moreover, it enables in silico hypothesis testing, which we explore by: (i) quantifying the alteration of wound contraction profiles corresponding to the measured variability in local wound stiffness; (ii) proposing alternative constitutive links connecting the dynamics of the biochemical fields to the evolving mechanical properties; (iii) discussing the plausibility of a stretch- vs. stiffness-mediated mechanobiological coupling. Ultimately, our model challenges the current understanding of wound biomechanics and mechanobiology, beside offering a versatile tool to explore and eventually control scar fibrosis after injury.

A Lumped Two-Compartment Model for Simulation of Ventricular Pump and Tissue Mechanics in Ischemic Heart Disease

Introduction: Computational modeling of cardiac mechanics and hemodynamics in ischemic heart disease (IHD) is important for a better understanding of the complex relations between ischemia-induced heterogeneity of myocardial tissue properties, regional tissue mechanics, and hemodynamic pump function. We validated and applied a lumped two-compartment modeling approach for IHD integrated into the CircAdapt model of the human heart and circulation.

Methods: Ischemic contractile dysfunction was simulated by subdividing a left ventricular (LV) wall segment into a hypothetical contractile and noncontractile compartment, and dysfunction severity was determined by the noncontractile volume fraction (NCVF). Myocardial stiffness was determined by the zero-passive stress length (Ls0,pas) and nonlinearity (kECM) of the passive stress-sarcomere length relation of the noncontractile compartment. Simulated end-systolic pressure volume relations (ESPVRs) for 20% acute ischemia were qualitatively compared between a two- and one-compartment simulation, and parameters of the two-compartment model were tuned to previously published canine data of regional myocardial deformation during acute and prolonged ischemia and reperfusion. In six patients with myocardial infarction (MI), the NCVF was automatically estimated using the echocardiographic LV strain and volume measurements obtained acutely and 6 months after MI. Estimated segmental NCVF values at the baseline and 6-month follow-up were compared with percentage late gadolinium enhancement (LGE) at 6-month follow-up.

Results: Simulation of 20% of NCVF shifted the ESPVR rightward while moderately reducing the slope, while a one-compartment simulation caused a leftward shift with severe reduction in the slope. Through tuning of the NCVF, Ls0,pas, and kECM, it was found that manipulation of the NCVF alone reproduced the deformation during acute ischemia and reperfusion, while additional manipulations of Ls0,pas and kECM were required to reproduce deformation during prolonged ischemia and reperfusion. Out of all segments with LGE>25% at the follow-up, the majority (68%) had higher estimated NCVF at the baseline than at the follow-up. Furthermore, the baseline NCVF correlated better with percentage LGE than NCVF did at the follow-up.

Conclusion: We successfully used a two-compartment model for simulation of the ventricular pump and tissue mechanics in IHD. Patient-specific optimizations using regional myocardial deformation estimated the NCVF in a small cohort of MI patients in the acute and chronic phase after MI, while estimated NCVF values closely approximated the extent of the myocardial scar at the follow-up. In future studies, this approach can facilitate deformation imaging–based estimation of myocardial tissue properties in patients with cardiovascular diseases.

Effects of dispersed fibres in myocardial mechanics, Part I: passive response

It is widely acknowledged that an imbalanced biomechanical environment can have significant effects on myocardial pathology, leading to adverse remodelling of cardiac function if it persists. Accurate stress prediction essentially depends on the strain energy function which should have competent descriptive and predictive capabilities. Previous studies have focused on myofibre dispersion, but not on fibres along other directions. In this study, we will investigate how fibre dispersion affects myocardial biomechanical behaviours by taking into account both the myofibre dispersion and the sheet fibre dispersion, with a focus on the sheet fibre dispersion. Fibre dispersion is incorporated into a widely-used myocardial strain energy function using the discrete fibre bundle approach. We first study how different dispersion affects the descriptive capability of the strain energy function when fitting to ex vivo experimental data, and then the predictive capability in a human left ventricle during diastole. Our results show that the chosen strain energy function can achieve the best goodness-of-fit to the experimental data by including both fibre dispersion. Furthermore, noticeable differences in stress can be found in the LV model. Our results may suggest that it is necessary to include both dispersion for myofibres and the sheet fibres for the improved descriptive capability to the ex vivo experimental data and potentially more accurate stress prediction in cardiac mechanics.

Volumetric growth of soft tissues evaluated in the current configuration

The growth and remodelling of soft tissues plays a significant role in many physiological applications, particularly in understanding and managing many diseases. A commonly used approach for soft tissue growth and remodelling is volumetric growth theory, introduced in the framework of finite elasticity. In such an approach, the total deformation gradient tensor is decomposed so that the elastic and growth tensors can be studied separately. A critical element in this approach is to determine the growth tensor and its evolution with time. Most existing volumetric growth theories define the growth tensor in the reference (natural) configuration, which does not reflect the continuous adaptation processes of soft tissues under the current configuration. In a few studies where growth from a loaded configuration was considered, simplifying assumptions, such as compatible deformation or geometric symmetries, were introduced. In this work, we propose a new volumetric growth law that depends on fields evaluated in the current configuration, which is residually stressed and loaded, without any geometrical restrictions. We illustrate our idea using a simplified left ventricle model, which admits inhomogeneous growth in the current configuration. We compare the residual stress distribution of our approach with the traditional volumetric growth theory, that assumes growth occurring from the natural reference configuration. We show that the proposed framework leads to qualitative agreements with experimental measurements. Furthermore, using a cylindrical model, we find an incompatibility index that explains the differences between the two approaches in more depth. We also demonstrate that results from both approaches reach the same steady solution published previously at the limit of a saturated growth. Although we used a left ventricle model as an example, our theory is applicable in modelling the volumetric growth of general soft tissues.

Fluid-structure interaction in a fully coupled three-dimensional mitral-atrium-pulmonary model

This paper aims to investigate detailed mechanical interactions between the pulmonary haemodynamics and left heart function in pathophysiological situations (e.g. atrial fibrillation and acute mitral regurgitation). This is achieved by developing a complex computational framework for a coupled pulmonary circulation, left atrium and mitral valve model. The left atrium and mitral valve are modelled with physiologically realistic three-dimensional geometries, fibre-reinforced hyperelastic materials and fluid–structure interaction, and the pulmonary vessels are modelled as one-dimensional network ended with structured trees, with specified vessel geometries and wall material properties. This new coupled model reveals some interesting results which could be of diagnostic values. For example, the wave propagation through the pulmonary vasculature can lead to different arrival times for the second systolic flow wave (S2 wave) among the pulmonary veins, forming vortex rings inside the left atrium. In the case of acute mitral regurgitation, the left atrium experiences an increased energy dissipation and pressure elevation. The pulmonary veins can experience increased wave intensities, reversal flow during systole and increased early-diastolic flow wave (D wave), which in turn causes an additional flow wave across the mitral valve (L wave), as well as a reversal flow at the left atrial appendage orifice. In the case of atrial fibrillation, we show that the loss of active contraction is associated with a slower flow inside the left atrial appendage and disappearances of the late-diastole atrial reversal wave (AR wave) and the first systolic wave (S1 wave) in pulmonary veins. The haemodynamic changes along the pulmonary vessel trees on different scales from microscopic vessels to the main pulmonary artery can all be captured in this model. The work promises a potential in quantifying disease progression and medical treatments of various pulmonary diseases such as the pulmonary hypertension due to a left heart dysfunction.

Comparisons of simulation results between passive and active fluid structure interaction models for left ventricle in hypertrophic obstructive cardiomyopathy

BACKGROUND

Patient-specific active fluid-structure interactions (FSI) model is a useful approach to non-invasively investigate the hemodynamics in the heart. However, it takes a lot of effort to obtain the proper external force boundary conditions for active models, which heavily restrained the time-sensitive clinical applications of active computational models.

METHODS

The simulation results of 12 passive FSI models based on 6 patients' pre-operative and post-operative CT images were compared with corresponding active models to investigate the differences in hemodynamics and cardiac mechanics between these models.

RESULTS

In comparing the passive and active models, it was found that there was no significant difference in pressure difference and shear stress on mitral valve leaflet (MVL) at the pre-SAM time point, but a significant difference was found in wall stress on the inner boundary of left ventricle (endocardium). It was also found that pressure difference on the coapted MVL and the shear stress on MVL were significantly decreased after successful surgery in both active and passive models.

CONCLUSION

Our results suggested that the passive models may provide good approximated hemodynamic results at 5% RR interval, which is crucial for analyzing the initiation of systolic anterior motion (SAM). Comparing to active models, the passive models decrease the complexity of the modeling construction and the difficulty of convergence significantly. These findings suggest that, with proper boundary conditions and sufficient clinical data, the passive computational model may be a good substitution model for the active model to perform hemodynamic analysis of the initiation of SAM.

Apparent growth tensor of left ventricular post myocardial infarction - In human first natural history study

An outstanding challenge in modelling biomechanics after myocardial infarction (MI) is to estimate the so-called growth tensor. Since it is impossible to track pure growth induced geometry change from in vivo magnetic resonance images alone, in this work, we propose a way of estimating a surrogate or apparent growth tensor of the human left ventricle using cine magnetic resonance (CMR) and late gadolinium enhanced (LGE) images of 16 patients following acute MI. The apparent growth tensor is evaluated at four time-points following myocardial reperfusion: 4-12 h (baseline), 3 days, 10 days and 7 months. We have identified three different growth patterns classified as the Dilation, No-Change and Shrinkage groups defined by the left ventricle end-diastole cavity volume change from baseline. We study the- trends in both the infarct and remote regions. Importantly, although the No-Change group has little change in the ventricular cavity volume, significant remodelling changes are seen within the myocardial wall, both in the infarct and remote regions. Through statistical analysis, we show that the growth tensor invariants can be used as effective biomarkers for adverse and favourable remodelling of the heart from 10 days onwards post-MI with statistically significant changes over time, in contrast to most of the routine clinical indices. We believe this is the first time that the apparent growth tensor has been estimated from in vivo CMR images post-MI. Our study not only provides much-needed information for understanding growth and remodelling in the human heart following acute MI, but also identifies novel biomarker for assessing heart disease progression.

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.

On the AIC-based model reduction for the general Holzapfel-Ogden myocardial constitutive law

Constitutive laws that describe the mechanical responses of cardiac tissue under loading hold the key to accurately model the biomechanical behaviour of the heart. There have been ample choices of phenomenological constitutive laws derived from experiments, some of which are quite sophisticated and include effects of microscopic fibre structures of the myocardium. A typical example is the strain-invariant-based Holzapfel-Ogden 2009 model that is excellently fitted to simple shear tests. It has been widely used and regarded as the state-of-the-art constitutive law for myocardium. However, there has been no analysis to show if it has both adequate descriptive and predictive capabilities for other tissue tests of myocardium. Indeed, such an analysis is important for any constitutive laws for clinically useful computational simulations. In this work, we perform such an analysis using combinations of tissue tests, uniaxial tension, biaxial tension and simple shear from three different sets of myocardial tissue studies. Starting from the general 14-parameter myocardial constitutive law developed by Holzapfel and Ogden, denoted as the general HO model, we show that this model has good descriptive and predictive capabilities for all the experimental tests. However, to reliably determine all 14 parameters of the model from experiments remains a great challenge. Our aim is to reduce the constitutive law using Akaike information criterion, to maintain its mechanical integrity whilst achieving minimal computational cost. A competent constitutive law should have descriptive and predictive capabilities for different tissue tests. By competent, we mean the model has least terms but is still able to describe and predict experimental data. We also investigate the optimal combinations of tissue tests for a given constitutive model. For example, our results show that using one of the reduced HO models, one may need just one shear response (along normal-fibre direction) and one biaxial stretch (ratio of 1 mean fibre : 1 cross-fibre) to satisfactorily describe Sommer et al. human myocardial mechanical properties. Our study suggests that single-state tests (i.e. simple shear or stretching only) are insufficient to determine the myocardium responses. We also found it is important to consider transmural fibre rotations within each myocardial sample of tests during the fitting process. This is done by excluding un-stretched fibres using an "effective fibre ratio", which depends on the sample size, shape, local myofibre architecture and loading conditions. We conclude that a competent myocardium material model can be obtained from the general HO model using AIC analysis and a suitable combination of tissue tests.