A computationally efficient formal optimization of regional myocardial contractility in a sheep with left ventricular aneurysm

Assessment of the elastic stiffness of human cardiac fibres after an apical infarction using finite element simulation

Several research works in the literature have focused on understanding the post-infarction ventricular remodelling phenomenon, but few works have considered the evaluation of the elastic behaviour of the cardiac tissue after a myocardial infarction. This paper presents an investigation focused on predicting the elastic performance of the human heart after a left ventricular apical infarction. The aim is to understand the elastic alterations of the cardiac fibres at different periods after an apical infarct. For this purpose, a hybrid method based on pressure and volume measurements of the left ventricle (LV) at different periods of ventricular remodelling, and the Finite Element Method (FEM), is developed. In addition, several performance indexes are defined to evaluate the heart performance during the ventricular remodelling process. The results show that during the first 2 weeks after a heart infarction, the cardiac fibres must support a much higher structural overload than during normal conditions. This structural overload is proportional to the aneurysm size but diminishes with the time, together with a significant reduction of the ventricular pumping capacity.

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.

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.

A kinematic model-based analysis framework for 3D Cine-DENSE-validation with an axially compressed gel phantom and application in sheep before and after antero-apical myocardial infarction

PURPOSE

Myocardial strain is increasingly used to assess left ventricular (LV) function. Incorporation of LV deformation into finite element (FE) modeling environment with subsequent strain calculation will allow analysis to reach its full potential. We describe a new kinematic model-based analysis framework (KMAF) to calculate strain from 3D cine-DENSE (displacement encoding with stimulated echoes) MRI.

METHODS

Cine-DENSE allows measurement of 3D myocardial displacement with high spatial accuracy. The KMAF framework uses cine cardiovascular magnetic resonance (CMR) to facilitate cine-DENSE segmentation, interpolates cine-DENSE displacement, and kinematically deforms an FE model to calculate strain. This framework was validated in an axially compressed gel phantom and applied in 10 healthy sheep and 5 sheep after myocardial infarction (MI).

RESULTS

Excellent Bland-Altman agreement of peak circumferential (E_cc ) and longitudinal (E_ll ) strain (mean difference = 0.021 ± 0.04 and -0.006 ± 0.03, respectively), was found between KMAF estimates and idealized FE simulation. E_rr had a mean difference of -0.014 but larger variation (±0.12). Cine-DENSE estimated end-systolic (ES) E_cc , E_ll and E_rr exhibited significant spatial variation for healthy sheep. Displacement magnitude was reduced on average by 27%, 42%, and 56% after MI in the remote, adjacent and MI regions, respectively.

CONCLUSIONS

The KMAF framework allows accurate calculation of 3D LV E_cc and E_ll from cine-DENSE.

Finite-element based optimization of left ventricular passive stiffness in normal volunteers and patients after myocardial infarction: Utility of an inverse deformation gradient calculation of regional diastolic strain

INTRODUCTION

Left ventricular (LV) diastolic dysfunction (DD) is common after myocardial infarction (MI). Whereas current clinical assessment of DD relies on indirect markers including LV filling, finite element (FE) -based computational modeling directly measures regional diastolic stiffness. We hypothesized that an inverse deformation gradient (DG) method calculation of diastolic strain (IDGDS) allows the FE model-based calculation of regional diastolic stiffness (material parameters; MP) in post-MI patients with DD.

METHODS

Cardiac magnetic resonance (CMR) with tags (CSPAMM) and late gadolinium enhancement (LGE) was performed in 10 patients with post-MI DD and 10 healthy volunteers. The 3-dimensional (3D) LV DG from end-diastole (ED) to early diastolic filling (EDF; DG_ED→EDF) was calculated from CSPAMM. Diastolic strain was calculated from DG_EDF→ED by inverting the DG_ED→EDF. FE models were created with MI and non-MI (remote; RM) regions determined by LGE. Guccione MPs C, and exponential fiber, b_f, and transverse, b_t , terms were optimized with IDGDS strain.

RESULTS

3D circumferential and longitudinal diastolic strain (E_cc;E_ll) calculated using IDGDS in CSPAMM obtained in volunteers and MI patients were [Formula: see text]  = 0.27 ± 0.01, [Formula: see text]  = 0.24 ± 0.03 and [Formula: see text]  = 0.21 ± 0.02, and [Formula: see text]  = 0.15 ± 0.02, respectively. MPs in the volunteer group were C_H = 0.013 [0.001, 0.235] kPa, [Formula: see text]  = 20.280 ± 4.994, and [Formula: see text]  = 7.460 ± 2.171 and C_RM = 0.0105 [0.010, 0.011] kPa, [Formula: see text]  = 50.786 ± 13.511 (p = 0.0846), and [Formula: see text]  = 17.355 ± 2.743 (p = 0.0208) in the remote myocardium of post-MI patients.

CONCLUSION

Diastolic strain, calculated from CSPAMM with IDGDS, enables calculation of FE model-based regional diastolic material parameters. Transverse stiffness of the remote myocardium, , may be a valuable new metric for determination of DD in patients after MI.

In vivo estimation of normal left ventricular stiffness and contractility based on routine cine MR acquisition

Post-myocardial infarction remodeling process is known to alter the mechanical properties of the heart. Biomechanical parameters, such as tissue stiffness and contractility, would be useful for clinicians to better assess the severity of the diseased heart. However, these parameters are difficult to obtain in the current clinical practice. In this paper, we estimated subject-specific in vivo myocardial stiffness and contractility from 21 healthy volunteers, based on left ventricle models constructed from data acquired from routine cardiac MR acquisition only. The subject-specific biomechanical parameters were quantified using an inverse finite-element modelling approach. The personalized models were evaluated against relevant clinical metrics extracted from the MR data, such as circumferential strain, wall thickness and fractional thickening. We obtained the ranges of healthy biomechanical indices of 1.60 ± 0.22 kPa for left ventricular stiffness and 95.13 ± 14.56 kPa for left ventricular contractility. These reference normal values can be used for future model-based investigation on the stiffness and contractility of ischemic myocardium.

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.

Left ventricular geometry during unloading and the end-systolic pressure volume relationship: Measurement with a modified real-time MRI-based method in normal sheep

The left ventricular (LV) end-systolic (ES) pressure volume relationship (ESPVR) is the cornerstone of systolic LV function analysis. We describe a 2D real-time (RT) MRI-based method (RTPVR) with separate software tools for 1) semi-automatic level set-based shape prior method (LSSPM) of the LV, 2) generation of synchronized pressure area loops and 3) calculation of the ESPVR. We used the RTPVR method to measure ventricular geometry, ES pressure area relationship (ESPAR) and ESPVR during vena cava occlusion (VCO) in normal sheep. 14 adult sheep were anesthetized and underwent measurement of LV systolic function. Ten of the 14 sheep underwent RTMRI and eight of the 14 underwent measurement with conductance catheter; 4 had both RTMRI and conductance measurements. 2D cross sectional RTMRI were performed at apex, mid-ventricle and base levels during separate VCOs. The Dice similarity coefficient was used to compare LSSPM and manual image segmentation and thus determine LSSPM accuracy. LV cross-sectional area, major and minor axis length, axis ratio, major axis orientation angle and ESPAR were measured at each LV level. ESPVR was calculated with a trapezoidal rule. The Dice similarity coefficient between LSSPM and manual segmentation by two readers was 87.31±2.51% and 88.13±3.43%. All cross sections became more elliptical during VCO. The major axis orientation shifted during VCO but remained in the septo-lateral direction. LV chamber obliteration at the apical level occurred during VCO in 7 of 10 sheep that underwent RTMRI. ESPAR was non-linear at all levels. Finally, ESPVR was non-linear because of apical collapse. ESPVR measured by conductance catheter (E_ES,Index = 2.23±0.66 mmHg/ml/m²) and RT (E_ES,Index = 2.31±0.31 mmHg/ml/m²) was not significantly different. LSSPM segmentation of 2D RT MRI images is accurate and allows calculation of LV geometry, ESPAR and ESPVR during VCO. In the future, RTPVR will facilitate determination of regional systolic material parameters underlying ESPVR.

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.

Longitudinal Reinforcement of Acute Myocardial Infarcts Improves Function by Transmurally Redistributing Stretch and Stress

A wide range of emerging therapies, from surgical restraint to biomaterial injection to tissue engineering, aim to improve heart function and limit adverse remodeling following myocardial infarction (MI). We previously showed that longitudinal surgical reinforcement of large anterior infarcts in dogs could significantly enhance systolic function without restricting diastolic function, but the underlying mechanisms for this improvement are poorly understood. The goal of this study was to construct a finite element model that could match our previously published data on changes in regional strains and left ventricular function following longitudinal surgical reinforcement, then use the model to explore potential mechanisms for the improvement in systolic function we observed. The model presented here, implemented in febio, matches all the key features of our experiments, including diastolic remodeling strains in the ischemic region, small shifts in the end-diastolic pressure-volume relationship (EDPVR), and large changes in the end-systolic pressure-volume relationship (ESPVR) in response to ischemia and to patch application. Detailed examination of model strains and stresses suggests that longitudinal reinforcement reduces peak diastolic fiber stretch and systolic fiber stress in the remote myocardium and shifts those peaks away from the endocardial surface by reshaping the left ventricle (LV). These findings could help to guide the development of novel therapies to improve post-MI function by providing specific design objectives.

Mechanical effects of MitraClip on leaflet stress and myocardial strain in functional mitral regurgitation - A finite element modeling study

Purpose

MitraClip is the sole percutaneous device approved for functional mitral regurgitation (MR; FMR) but MR recurs in over one third of patients. As device-induced mechanical effects are a potential cause for MR recurrence, we tested the hypothesis that MitraClip increases leaflet stress and procedure-related strain in sub-valvular left ventricular (LV) myocardium in FMR associated with coronary disease (FMR-CAD).

Methods

Simulations were performed using finite element models of the LV + mitral valve based on MRI of 5 sheep with FMR-CAD. Models were modified to have a 20% increase in LV volume (↑LV_VOLUME) and MitraClip was simulated with contracting beam elements (virtual sutures) placed between nodes in the center edge of the anterior (AL) and posterior (PL) mitral leaflets. Effects of MitraClip on leaflet stress in the peri-MitraClip region of AL and PL, septo-lateral annular diameter (SLAD), and procedure-related radial strain (E_rr) in the sub-valvular myocardium were calculated.

Results

MitraClip increased peri-MitraClip leaflet stress at end-diastole (ED) by 22.3±7.1 kPa (p<0.0001) in AL and 14.8±1.2 kPa (p<0.0001) in PL. MitraClip decreased SLAD by 6.1±2.2 mm (p<0.0001) and increased E_rr in the sub-valvular lateral LV myocardium at ED by 0.09±0.04 (p<0.0001)). Furthermore, MitraClip in ↑LV_VOLUME was associated with persistent effects at ED but also at end-systole where peri-MitraClip leaflet stress was increased in AL by 31.9±14.4 kPa (p = 0.0268) and in PL by 22.5±23.7 kPa (p = 0.0101).

Conclusions

MitraClip for FMR-CAD increases mitral leaflet stress and radial strain in LV sub-valvular myocardium. Mechanical effects of MitraClip are augmented by LV enlargement.

Fast parameter inference in a biomechanical model of the left ventricle by using statistical emulation

A central problem in biomechanical studies of personalized human left ventricular modelling is estimating the material properties and biophysical parameters from in vivo clinical measurements in a timeframe that is suitable for use within a clinic. Understanding these properties can provide insight into heart function or dysfunction and help to inform personalized medicine. However, finding a solution to the differential equations which mathematically describe the kinematics and dynamics of the myocardium through numerical integration can be computationally expensive. To circumvent this issue, we use the concept of emulation to infer the myocardial properties of a healthy volunteer in a viable clinical timeframe by using in vivo magnetic resonance image data. Emulation methods avoid computationally expensive simulations from the left ventricular model by replacing the biomechanical model, which is defined in terms of explicit partial differential equations, with a surrogate model inferred from simulations generated before the arrival of a patient, vastly improving computational efficiency at the clinic. We compare and contrast two emulation strategies: emulation of the computational model outputs and emulation of the loss between the observed patient data and the computational model outputs. These strategies are tested with two interpolation methods, as well as two loss functions. The best combination of methods is found by comparing the accuracy of parameter inference on simulated data for each combination. This combination, using the output emulation method, with local Gaussian process interpolation and the Euclidean loss function, provides accurate parameter inference in both simulated and clinical data, with a reduction in the computational cost of about three orders of magnitude compared with numerical integration of the differential equations by using finite element discretization techniques.

Method for Calibration of Left Ventricle Material Properties using 3D Echocardiography Endocardial Strains

We sought to calibrate mechanical properties of left ventricle (LV) based on 3D speckle tracking echocardiographic imaging data recorded from 16 segments defined by American Heart Association (AHA). The in vivo data were used to create finite element (FE) LV and biventricular (BV) models. The orientation of the fibers in the LV model was rule-based, but diffusion tensor magnetic resonance imaging (DT-MRI) data were used for the fiber directions in the BV model. A nonlinear fiber-reinforced constitutive equation was used to describe the passive behavior of the myocardium, whereas the active tension was described by a model based on tissue contraction (Tmax). Isight was used for optimization, which used Abaqus as the forward solver (Simulia, Providence, USA). The calibration of passive properties based on the end diastolic pressure volume relation (ED PVR) curve resulted in relatively good agreement (mean error = -0.04 ml). The difference between experimental and computational strains decreased after segmental strain metrics, rather than global metrics, were used for calibration: for the LV model, the mean difference reduced from 0.129 to 0.046 (circumferential) and from 0.076 to 0.059 (longitudinal); for the BV model, the mean difference nearly did not change in the circumferential direction (0.061) but reduced in the longitudinal direction from 0.076 to 0.055. The calibration of mechanical properties for myocardium can be improved using segmental strain metrics. The importance of realistic fiber orientation and geometry for modeling of the LV was shown.

Kinematic boundary conditions substantially impact in silico ventricular function

Computational cardiac mechanical models, individualized to the patient, have the potential to elucidate the fundamentals of cardiac (patho-)physiology, enable non-invasive quantification of clinically significant metrics (eg, stiffness, active contraction, work), and anticipate the potential efficacy of therapeutic cardiovascular intervention. In a clinical setting, however, the available imaging resolution is often limited, which limits cardiac models to focus on the ventricles, without including the atria, valves, and proximal arteries and veins. In such models, the absence of surrounding structures needs to be accounted for by imposing realistic kinematic boundary conditions, which, for prognostic purposes, are preferably generic and thus non-image derived. Unfortunately, the literature on cardiac models shows no consistent approach to kinematically constrain the myocardium. The impact of different approaches (eg, fully constrained base, constrained epi-ring) on the predictive capacity of cardiac mechanical models has not been thoroughly studied. For that reason, this study first gives an overview of current approaches to kinematically constrain (bi) ventricular models. Next, we developed a patient-specific in silico biventricular model that compares well with literature and in vivo recorded strains. Alternative constraints were introduced to assess the influence of commonly used mechanical boundary conditions on both the predicted global functional behavior of the in-silico heart (cavity volumes, stroke volume, ejection fraction) and local strain distributions. Meaningful differences in global functioning were found between different kinematic anchoring strategies, which brought forward the importance of selecting appropriate boundary conditions for biventricular models that, in the near future, may inform clinical intervention. However, whilst statistically significant differences were also found in local strain distributions, these differences were minor and mostly confined to the region close to the applied boundary conditions.

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

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

In vivo estimation of elastic heterogeneity in an infarcted human heart

In myocardial infarction, muscle tissue of the heart is damaged as a result of ceased or severely impaired blood flow. Survivors have an increased risk of further complications, possibly leading to heart failure. Material properties play an important role in determining post-infarction outcome. Due to spatial variation in scarring, material properties can be expected to vary throughout the tissue of a heart after an infarction. In this study we propose a data assimilation technique that can efficiently estimate heterogeneous elastic material properties in a personalized model of cardiac mechanics. The proposed data assimilation is tested on a clinical dataset consisting of regional left ventricular strains and in vivo pressures during atrial systole from a human with a myocardial infarction. Good matches to regional strains are obtained, and simulated equi-biaxial tests are carried out to demonstrate regional heterogeneities in stress–strain relationships. A synthetic data test shows a good match of estimated versus ground truth material parameter fields in the presence of no to low levels of noise. This study is the first to apply adjoint-based data assimilation to the important problem of estimating cardiac elastic heterogeneities in 3-D from medical images.

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.

In vivo estimation of passive biomechanical properties of human myocardium

Identification of in vivo passive biomechanical properties of healthy human myocardium from regular clinical data is essential for subject-specific modelling of left ventricle (LV). In this work, myocardium was defined by Holzapfel-Ogden constitutive law. Therefore, the objectives of the study were (a) to estimate the ranges of the constitutive parameters for healthy human myocardium using non-invasive routine clinical data, and (b) to investigate the effect of geometry, LV end-diastolic pressure (EDP) and fibre orientations on estimated values. In order to avoid invasive measurements and additional scans, LV cavity volume, measured from routine MRI, and empirical pressure-normalised-volume relation (Klotz-curve) were used as clinical data. Finite element modelling, response surface method and genetic algorithm were used to inversely estimate the constitutive parameters. Due to the ill-posed nature of the inverse optimisation problem, the myocardial properties was extracted by identifying the ranges of the parameters, instead of finding unique values. Additional sensitivity studies were carried out to identify the effect of LV EDP, fibre orientation and geometry on estimated parameters. Although uniqueness of the solution cannot be achieved, the normal ranges of the parameters produced similar mechanical responses within the physiological ranges. These information could be used in future computational studies for designing heart failure treatments. Graphical abstract.

In vivo estimation of passive biomechanical properties of human myocardium

Identification of in vivo passive biomechanical properties of healthy human myocardium from regular clinical data is essential for subject-specific modelling of left ventricle (LV). In this work, myocardium was defined by Holzapfel-Ogden constitutive law. Therefore, the objectives of the study were (a) to estimate the ranges of the constitutive parameters for healthy human myocardium using non-invasive routine clinical data, and (b) to investigate the effect of geometry, LV end-diastolic pressure (EDP) and fibre orientations on estimated values. In order to avoid invasive measurements and additional scans, LV cavity volume, measured from routine MRI, and empirical pressure-normalised-volume relation (Klotz-curve) were used as clinical data. Finite element modelling, response surface method and genetic algorithm were used to inversely estimate the constitutive parameters. Due to the ill-posed nature of the inverse optimisation problem, the myocardial properties was extracted by identifying the ranges of the parameters, instead of finding unique values. Additional sensitivity studies were carried out to identify the effect of LV EDP, fibre orientation and geometry on estimated parameters. Although uniqueness of the solution cannot be achieved, the normal ranges of the parameters produced similar mechanical responses within the physiological ranges. These information could be used in future computational studies for designing heart failure treatments.

Right Ventricular Fiber Structure as a Compensatory Mechanism in Pressure Overload: A Computational Study

Right ventricular failure (RVF) is a lethal condition in diverse pathologies. Pressure overload is the most common etiology of RVF, but our understanding of the tissue structure remodeling and other biomechanical factors involved in RVF is limited. Some remodeling patterns are interpreted as compensatory mechanisms including myocyte hypertrophy, extracellular fibrosis, and changes in fiber orientation. However, the specific implications of these changes, especially in relation to clinically observable measurements, are difficult to investigate experimentally. In this computational study, we hypothesized that, with other variables constant, fiber orientation alteration provides a quantifiable and distinct compensatory mechanism during RV pressure overload (RVPO). Numerical models were constructed using a rabbit model of chronic pressure overload RVF based on intraventricular pressure measurements, CINE magnetic resonance imaging (MRI), and diffusion tensor MRI (DT-MRI). Biventricular simulations were conducted under normotensive and hypertensive boundary conditions using variations in RV wall thickness, tissue stiffness, and fiber orientation to investigate their effect on RV pump function. Our results show that a longitudinally aligned myocardial fiber orientation contributed to an increase in RV ejection fraction (RVEF). This effect was more pronounced in response to pressure overload. Likewise, models with longitudinally aligned fiber orientation required a lesser contractility for maintaining a target RVEF against elevated pressures. In addition to increased wall thickness and material stiffness (diastolic compensation), systolic mechanisms in the forms of myocardial fiber realignment and changes in contractility are likely involved in the overall compensatory responses to pressure overload.

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.

A finite element model of myocardial infarction using a composite material approach

Computational models are effective tools to study cardiac mechanics under normal and pathological conditions. They can be used to gain insight into the physiology of the heart under these conditions while they are adaptable to computer assisted patient-specific clinical diagnosis and therapeutic procedures. Realistic cardiac mechanics models incorporate tissue active/passive response in conjunction with hyperelasticity and anisotropy. Conventional formulation of such models leads to mathematically-complex problems usually solved by custom-developed non-linear finite element (FE) codes. With a few exceptions, such codes are not available to the research community. This article describes a computational cardiac mechanics model developed such that it can be implemented using off-the-shelf FE solvers while tissue pathologies can be introduced in the model in a straight-forward manner. The model takes into account myocardial hyperelasticity, anisotropy, and active contraction forces. It follows a composite tissue modeling approach where the cardiac tissue is decomposed into two major parts: background and myofibers. The latter is modelled as rebars under initial stresses mimicking the contraction forces. The model was applied in silico to study the mechanics of infarcted left ventricle (LV) of a canine. End-systolic strain components, ejection fraction, and stress distribution attained using this LV model were compared quantitatively and qualitatively to corresponding data obtained from measurements as well as to other corresponding LV mechanics models. This comparison showed very good agreement.

Computational Investigation of Transmural Differences in Left Ventricular Contractility

Myocardial contractility of the left ventricle (LV) plays an essential role in maintaining normal pump function. A recent ex vivo experimental study showed that cardiomyocyte force generation varies across the three myocardial layers of the LV wall. However, the in vivo distribution of myocardial contractile force is still unclear. The current study was designed to investigate the in vivo transmural distribution of myocardial contractility using a noninvasive computational approach. For this purpose, four cases with different transmural distributions of maximum isometric tension (Tmax) and/or reference sarcomere length (lR) were tested with animal-specific finite element (FE) models, in combination with magnetic resonance imaging (MRI), pressure catheterization, and numerical optimization. Results of the current study showed that the best fit with in vivo MRI-derived deformation was obtained when Tmax assumed different values in the subendocardium, midmyocardium, and subepicardium with transmurally varying lR. These results are consistent with recent ex vivo experimental studies, which showed that the midmyocardium produces more contractile force than the other transmural layers. The systolic strain calculated from the best-fit FE model was in good agreement with MRI data. Therefore, the proposed noninvasive approach has the capability to predict the transmural distribution of myocardial contractility. Moreover, FE models with a nonuniform distribution of myocardial contractility could provide a better representation of LV function and be used to investigate the effects of transmural changes due to heart disease.

High-resolution data assimilation of cardiac mechanics applied to a dyssynchronous ventricle

Computational models of cardiac mechanics, personalized to a patient, offer access to mechanical information above and beyond direct medical imaging. Additionally, such models can be used to optimize and plan therapies in-silico, thereby reducing risks and improving patient outcome. Model personalization has traditionally been achieved by data assimilation, which is the tuning or optimization of model parameters to match patient observations. Current data assimilation procedures for cardiac mechanics are limited in their ability to efficiently handle high-dimensional parameters. This restricts parameter spatial resolution, and thereby the ability of a personalized model to account for heterogeneities that are often present in a diseased or injured heart. In this paper, we address this limitation by proposing an adjoint gradient-based data assimilation method that can efficiently handle high-dimensional parameters. We test this procedure on a synthetic data set and provide a clinical example with a dyssynchronous left ventricle with highly irregular motion. Our results show that the method efficiently handles a high-dimensional optimization parameter and produces an excellent agreement for personalized models to both synthetic and clinical data.

Estimating prognosis in patients with acute myocardial infarction using personalized computational heart models

Biomechanical computational models have potential prognostic utility in patients after an acute ST-segment-elevation myocardial infarction (STEMI). In a proof-of-concept study, we defined two groups (1) an acute STEMI group (n = 6, 83% male, age 54 ± 12 years) complicated by left ventricular (LV) systolic dysfunction; (2) an age- and sex- matched hyper-control group (n = 6, 83% male, age 46 ± 14 years), no prior history of cardiovascular disease and normal systolic blood pressure (SBP < 130 mmHg). Cardiac MRI was performed in the patients (2 days & 6 months post-STEMI) and the volunteers, and biomechanical heart models were synthesized for each subject. The candidate parameters included normalized active tension (AT norm) and active tension at the resting sarcomere length (T req, reflecting required contractility). Myocardial contractility was inversely determined from personalized heart models by matching CMR-imaged LV dynamics. Compared with controls, patients with recent STEMI exhibited increased LV wall active tension when normalized by SBP. We observed a linear relationship between T req 2 days post-MI and global longitudinal strain 6 months later (r = 0.86; p = 0.03). T req may be associated with changes in LV function in the longer term in STEMI patients complicated by LV dysfunction. Further studies seem warranted.

Regional assessment of in vivo myocardial stiffness using 3D magnetic resonance elastography in a porcine model of myocardial infarction

PURPOSE

The stiffness of a myocardial infarct affects the left ventricular pump function and remodeling. Magnetic resonance elastography (MRE) is a noninvasive imaging technique for measuring soft-tissue stiffness in vivo. The purpose of this study was to investigate the feasibility of assessing in vivo regional myocardial stiffness with high-frequency 3D cardiac MRE in a porcine model of myocardial infarction, and compare the results with ex vivo uniaxial tensile testing.

METHODS

Myocardial infarct was induced in a porcine model by embolizing the left circumflex artery. Fourteen days postinfarction, MRE imaging was performed in diastole using an echocardiogram-gated spin-echo echo-planar-imaging sequence with 140-Hz vibrations and 3D MRE processing. The MRE stiffness and tensile modulus from uniaxial testing were compared between the remote and infarcted myocardium.

RESULTS

Myocardial infarcts showed increased in vivo MRE stiffness compared with remote myocardium (4.6 ± 0.7 kPa versus 3.0 ± 0.6 kPa, P = 0.02) within the same pig. Ex vivo uniaxial mechanical testing confirmed the in vivo MRE results, showing that myocardial infarcts were stiffer than remote myocardium (650 ± 80 kPa versus 110 ± 20 kPa, P = 0.01).

CONCLUSIONS

These results demonstrate the feasibility of assessing in vivo regional myocardial stiffness with high-frequency 3D cardiac MRE. Magn Reson Med 79:361-369, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Passive diastolic modelling of human ventricles: Effects of base movement and geometrical heterogeneity

Left-ventricular (LV) remodelling, associated with diastolic heart failure, is driven by an increase in myocardial stress. Therefore, normalisation of LV wall stress is the cornerstone of many therapeutic treatments. However, information regarding such regional stress-strain for human LV is still limited. Thus, the objectives of our study were to determine local diastolic stress-strain field in healthy LVs, and consequently, to identify the regional variations amongst them due to geometric heterogeneity. Effects of LV base movement on diastolic model predictions, which were ignored in the literature, were further explored. Personalised finite-element modelling of five normal human bi-ventricles was carried out using subject-specific myocardium properties. Model prediction was validated individually through comparison with end-diastolic volume and a new shape-volume based measurement of LV cavity, extracted from magnetic resonance imaging. Results indicated that incorporation of LV base movement improved the model predictions (shape-volume relevancy of LV cavity), and therefore, it should be considered in future studies. The LV endocardium always experienced higher fibre stress compared to the epicardium for all five subjects. The LV wall near base experienced higher stress compared to equatorial and apical locations. The lateral LV wall underwent greater stress distribution (fibre and sheet stress) compared to other three regions. In addition, normal ranges of different stress-strain components in different regions of LV wall were reported for five healthy ventricles. This information could be used as targets for future computational studies to optimise diastolic heart failure treatments or design new therapeutic interventions/devices.

Undersized Mitral Annuloplasty Increases Strain in the Proximal Lateral Left Ventricular Wall

BACKGROUND

Recurrence of mitral regurgitation (MR) after undersized mitral annuloplasty (MA) for ischemic MR is as high as 60%, with the recurrence rate likely due to continued dilation of the left ventricle (LV). To better understand the causes of recurrent MR, we studied the effect of undersized MA on strain in the LV wall. We hypothesize that the acute change in ventricular shape induced by MA will cause increased strain in regions nearest the mitral valve.

METHODS

Finite element models were previously reported, based on cardiac magnetic resonance images of 5 sheep with mild to moderate ischemic MR. A 24-mm saddle-shaped rigid annuloplasty ring was modeled and used to simulate virtual MA. Longitudinal and myofiber strains were calculated at end-diastole and end-systole, with preoperative early diastolic geometry as the reference state.

RESULTS

The undersized MA significantly increased longitudinal strain at end-diastole in the lateral LV wall. The effect was greatest in the proximal-lateral endocardial surface, where longitudinal strain after MA was approximately triple the preoperative strain (11.17% ± 2.15% vs 3.45% ± 0.92%, p = 0.0057). In contrast, postoperative end-diastolic fiber strain decreased in this same region (2.53% ± 2.14% vs 7.72% ± 1.79%, p = 0.0060). There were no significant changes in either strain type at end-systole.

CONCLUSIONS

Undersized MA increased longitudinal strain in the proximal lateral LV wall at end-diastole. This procedure-related strain at the proximal-lateral LV wall may foster continued LV enlargement and subsequent recurrence of mitral regurgitation.

Computational Modeling of Healthy Myocardium in Diastole

In order to better understand the mechanics of the heart and its disorders, engineers increasingly make use of the finite element method (FEM) to investigate healthy and diseased cardiac tissue. However, FEM is only as good as the underlying constitutive model, which remains a major challenge to the biomechanics community. In this study, a recently developed structurally based constitutive model was implemented to model healthy left ventricular myocardium during passive diastolic filling. This model takes into account the orthotropic response of the heart under loading. In-vivo strains were measured from magnetic resonance images (MRI) of porcine hearts, along with synchronous catheterization pressure data, and used for parameter identification of the passive constitutive model. Optimization was performed by minimizing the difference between MRI measured and FE predicted strains and cavity volumes. A similar approach was followed for the parameter identification of a widely used phenomenological constitutive law, which is based on a transversely isotropic material response. Results indicate that the parameter identification with the structurally based constitutive law is more sensitive to the assigned fiber architecture and the fit between the measured and predicted strains is improved with more realistic sheet angles. In addition, the structurally based model is capable of generating a more physiological end-diastolic pressure-volume relationship in the ventricle.

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.

Finite-Element Extrapolation of Myocardial Structure Alterations Across the Cardiac Cycle in Rats

Myocardial microstructures are responsible for key aspects of cardiac mechanical function. Natural myocardial deformation across the cardiac cycle induces measurable structural alteration, which varies across disease states. Diffusion tensor magnetic resonance imaging (DT-MRI) has become the tool of choice for myocardial structural analysis. Yet, obtaining the comprehensive structural information of the whole organ, in 3D and time, for subject-specific examination is fundamentally limited by scan time. Therefore, subject-specific finite-element (FE) analysis of a group of rat hearts was implemented for extrapolating a set of initial DT-MRI to the rest of the cardiac cycle. The effect of material symmetry (isotropy, transverse isotropy, and orthotropy), structural input, and warping approach was observed by comparing simulated predictions against in vivo MRI displacement measurements and DT-MRI of an isolated heart preparation at relaxed, inflated, and contracture states. Overall, the results indicate that, while ventricular volume and circumferential strain are largely independent of the simulation strategy, structural alteration predictions are generally improved with the sophistication of the material model, which also enhances torsion and radial strain predictions. Moreover, whereas subject-specific transversely isotropic models produced the most accurate descriptions of fiber structural alterations, the orthotropic models best captured changes in sheet structure. These findings underscore the need for subject-specific input data, including structure, to extrapolate DT-MRI measurements across the cardiac cycle.

MRI evaluation of injectable hyaluronic acid-based hydrogel therapy to limit ventricular remodeling after myocardial infarction

Injectable biomaterials are an attractive therapy to attenuate left ventricular (LV) remodeling after myocardial infarction (MI). Although studies have shown that injectable hydrogels improve cardiac structure and function in vivo, temporal changes in infarct material properties after treatment have not been assessed. Emerging imaging and modeling techniques now allow for serial, non-invasive estimation of infarct material properties. Specifically, cine magnetic resonance imaging (MRI) assesses global LV structure and function, late-gadolinium enhancement (LGE) MRI enables visualization of infarcted tissue to quantify infarct expansion, and spatial modulation of magnetization (SPAMM) tagging provides passive wall motion assessment as a measure of tissue strain, which can all be used to evaluate infarct properties when combined with finite element (FE) models. In this work, we investigated the temporal effects of degradable hyaluronic acid (HA) hydrogels on global LV remodeling, infarct thinning and expansion, and infarct stiffness in a porcine infarct model for 12 weeks post-MI using MRI and FE modeling. Hydrogel treatment led to decreased LV volumes, improved ejection fraction, and increased wall thickness when compared to controls. FE model simulations demonstrated that hydrogel therapy increased infarct stiffness for 12 weeks post-MI. Thus, evaluation of myocardial tissue properties through MRI and FE modeling provides insight into the influence of injectable hydrogel therapies on myocardial structure and function post-MI.

Ascending thoracic aortic aneurysm wall stress analysis using patient-specific finite element modeling of in vivo magnetic resonance imaging

OBJECTIVES

Rupture/dissection of ascending thoracic aortic aneurysms (aTAAs) carries high mortality and occurs in many patients who did not meet size criteria for elective surgery. Elevated wall stress may better predict adverse events, but cannot be directly measured in vivo, rather determined from finite element (FE) simulations. Current computational models make assumptions that limit accuracy, most commonly using in vivo imaging geometry to represent zero-pressure state. Accurate patient-specific wall stress requires models with zero-pressure three-dimensional geometry, material properties, wall thickness and residual stress. We hypothesized that wall stress calculated from in vivo imaging geometry at systemic pressure underestimates that using zero-pressure geometry. We developed a novel method to derive zero-pressure geometry from in vivo imaging at systemic pressure. The purpose of this study was to develop the first patient-specific aTAA models using magnetic resonance imaging (MRI) to assess material properties and zero-pressure geometry. Wall stress results from FE models using systemic pressure were compared with those from models using zero-pressure correction.

METHODS

Patients with aTAAs <5 cm underwent ECG-gated computed tomography angiography (CTA) and displacement encoding with stimulated echo (DENSE)-MRI. CTA lumen geometry was used to create surface contour meshes of aTAA geometry. DENSE-MRI measured cyclic aortic wall strain from which wall material property was derived. Zero- and systemic pressure geometries were created. Simulations were loaded to systemic pressure using the ABAQUS FE software. Wall stress analyses were compared between zero-pressure-corrected and systemic pressure geometry FE models.

RESULTS

Peak first principal wall stress (primarily aligned in the circumferential direction) at systolic pressure for the zero-pressure correction models was 430.62 ± 69.69 kPa, whereas that without zero-pressure correction was 312.55 ± 39.65 kPa (P = 0.004). Peak second principal wall stress (primarily aligned in the longitudinal direction) at systolic pressure for the zero-pressure correction models was 200.77 ± 43.13 kPa, whereas that without zero-stress correction was 156.25 ± 25.55 kPa (P = 0.02).

CONCLUSIONS

Previous FE aTAA models from in vivo CT and MRI have not accounted for zero-pressure geometry or patient-specific material property. We demonstrated that zero-pressure correction significantly impacts wall stress results. Future computational models that use wall stress to predict aTAA adverse events must take into account zero-pressure geometry and patient material property for accurate wall stress determination.

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.

Parameter estimation in a Holzapfel-Ogden law for healthy myocardium

A central problem in biomechanical studies of personalized human left ventricular (LV) modelling is to estimate material properties from in vivo clinical measurements. In this work we evaluate the passive myocardial mechanical properties inversely from the in vivo LV chamber pressure-volume and strain data. The LV myocardium is described using a structure-based orthotropic Holzapfel-Ogden constitutive law with eight parameters. In the first part of the paper we demonstrate how to use a multi-step non-linear least-squares optimization procedure to inversely estimate the parameters from the pressure-volume and strain data obtained from a synthetic LV model in diastole. In the second part, we show that to apply this procedure to clinical situations with limited in vivo data, additional constraints are required in the optimization procedure. Our study, based on three different healthy volunteers, demonstrates that the parameters of the Holzapfel-Ogden law could be extracted from pressure-volume and strain data with a suitable multi-step optimization procedure. Although the uniqueness of the solution cannot be addressed using our approaches, the material response is shown to be robustly determined.

Analysis of passive cardiac constitutive laws for parameter estimation using 3D tagged MRI

An unresolved issue in patient-specific models of cardiac mechanics is the choice of an appropriate constitutive law, able to accurately capture the passive behavior of the myocardium, while still having uniquely identifiable parameters tunable from available clinical data. In this paper, we aim to facilitate this choice by examining the practical identifiability and model fidelity of constitutive laws often used in cardiac mechanics. Our analysis focuses on the use of novel 3D tagged MRI, providing detailed displacement information in three dimensions. The practical identifiability of each law is examined by generating synthetic 3D tags from in silico simulations, allowing mapping of the objective function landscape over parameter space and comparison of minimizing parameter values with original ground truth values. Model fidelity was tested by comparing these laws with the more complex transversely isotropic Guccione law, by characterizing their passive end-diastolic pressure–volume relation behavior, as well as by considering the in vivo case of a healthy volunteer. These results show that a reduced form of the Holzapfel–Ogden law provides the best balance between identifiability and model fidelity across the tests considered.

Estimating passive mechanical properties in a myocardial infarction using MRI and finite element simulations

Myocardial infarction (MI) triggers a series of maladaptive events that lead to structural and functional changes in the left ventricle. It is crucial to better understand the progression of adverse remodeling, in order to develop effective treatment. In addition, being able to assess changes in vivo would be a powerful tool in the clinic. The goal of the current study is to quantify the in vivo material properties of infarcted and remote myocardium 1 week after MI, as well as the orientation of collagen fibers in the infarct. This will be accomplished by using a combination of magnetic resonance imaging (MRI), catheterization, finite element modeling, and numerical optimization to analyze a porcine model ([Formula: see text]) of posterolateral myocardial infarction. Specifically, properties will be determined by minimizing the difference between in vivo strains and volume calculated from MRI and finite element model predicted strains and volume. The results indicate that the infarct region is stiffer than the remote region and that the infarct collagen fibers become more circumferentially oriented 1 week post-MI. These findings are consistent with previous studies, which employed ex vivo techniques. The proposed methodology will ultimately provide a means of predicting remote and infarct mechanical properties in vivo at any time point post-MI.

Estimating passive mechanical properties in a myocardial infarction using MRI and finite element simulations

Myocardial infarction (MI) triggers a series of maladaptive events that lead to structural and functional changes in the left ventricle. It is crucial to better understand the progression of adverse remodeling, in order to develop effective treatment. In addition, being able to assess changes in vivo would be a powerful tool in the clinic. The goal of the current study is to quantify the in vivo material properties of infarcted and remote myocardium 1 week after MI, as well as the orientation of collagen fibers in the infarct. This will be accomplished by using a combination of magnetic resonance imaging (MRI), catheterization, finite element modeling, and numerical optimization to analyze a porcine model ([Formula: see text]) of posterolateral myocardial infarction. Specifically, properties will be determined by minimizing the difference between in vivo strains and volume calculated from MRI and finite element model predicted strains and volume. The results indicate that the infarct region is stiffer than the remote region and that the infarct collagen fibers become more circumferentially oriented 1 week post-MI. These findings are consistent with previous studies, which employed ex vivo techniques. The proposed methodology will ultimately provide a means of predicting remote and infarct mechanical properties in vivo at any time point post-MI.

Continuous flow left ventricular pump support and its effect on regional left ventricular wall stress: finite element analysis study

Left ventricular assist device (LVAD) support unloads left ventricular (LV) pressure and volume and decreases wall stress. This study investigated the effect of systematic LVAD unloading on the 3-dimensional myocardial wall stress by employing finite element models containing layered fiber structure, active contractility, and passive stiffness. The HeartMate II(®) (Thoratec, Inc., Pleasanton, CA) was used for LV unloading. The model geometries and hemodynamic conditions for baseline (BL) and LVAD support (LVsupport) were acquired from the Penn State mock circulatory cardiac simulator. Myocardial wall stress of BL was compared with that of LVsupport at 8,000, 9,000, 10,000 RPM, providing mean pump flow (Q(mean)) of 2.6, 3.2, and 3.7 l/min, respectively. LVAD support was more effective at unloading during diastole as compared to systole. Approximately 40, 50, and 60% of end-diastolic wall stress reduction were achieved at Q(mean) of 2.6, 3.2, and 3.7 l/min, respectively, as compared to only a 10% reduction of end-systolic wall stress at Q(mean) of 3.7 l/min. In addition, there was a stress concentration during systole at the apex due to the cannulation and reduced boundary motion. This modeling study can be used to further understand optimal unloading, pump control, patient management, and cannula design.

Dynamic finite-strain modelling of the human left ventricle in health and disease using an immersed boundary-finite element method

Detailed models of the biomechanics of the heart are important both for developing improved interventions for patients with heart disease and also for patient risk stratification and treatment planning. For instance, stress distributions in the heart affect cardiac remodelling, but such distributions are not presently accessible in patients. Biomechanical models of the heart offer detailed three-dimensional deformation, stress and strain fields that can supplement conventional clinical data. In this work, we introduce dynamic computational models of the human left ventricle (LV) that are derived from clinical imaging data obtained from a healthy subject and from a patient with a myocardial infarction (MI). Both models incorporate a detailed invariant-based orthotropic description of the passive elasticity of the ventricular myocardium along with a detailed biophysical model of active tension generation in the ventricular muscle. These constitutive models are employed within a dynamic simulation framework that accounts for the inertia of the ventricular muscle and the blood that is based on an immersed boundary (IB) method with a finite element description of the structural mechanics. The geometry of the models is based on data obtained non-invasively by cardiac magnetic resonance (CMR). CMR imaging data are also used to estimate the parameters of the passive and active constitutive models, which are determined so that the simulated end-diastolic and end-systolic volumes agree with the corresponding volumes determined from the CMR imaging studies. Using these models, we simulate LV dynamics from enddiastole to end-systole. The results of our simulations are shown to be in good agreement with subject-specific CMR-derived strain measurements and also with earlier clinical studies on human LV strain distributions.

Posterior papillary muscle anchoring affects remote myofiber stress and pump function: finite element analysis

BACKGROUND

The role of posterior papillary muscle anchoring (PPMA) in the management of chronic ischemic mitral regurgitation (CIMR) is controversial. We studied the effect of anchoring point direction and relocation displacement on left ventricular (LV) regional myofiber stress and pump function.

METHODS

Previously described finite element models of sheep 16 weeks after posterolateral myocardial infarction (MI) were used. True-sized mitral annuloplasty (MA) ring insertion plus different PPM anchoring techniques were simulated. Anchoring points tested included both commissures and the central anterior mitral annulus; relocation displacement varied from 10% to 40% of baseline diastolic distance from the PPM to the anchor points on the annulus. For each reconstruction scenario, myofiber stress in the MI, border zone, and remote myocardium as well as pump function were calculated.

RESULTS

PPMA caused reductions in myofiber stress at end-diastole and end-systole in all regions of the left ventricle that were proportional to the relocation displacement. Although stress reduction was greatest in the MI region, it also occurred in the remote region. The maximum 40% displacement caused a slight reduction in LV pump function. However, with the correction of regurgitation by MA plus PPMA, there was an overall increase in forward stroke volume. Finally, anchoring point direction had no effect on myofiber stress or pump function.

CONCLUSIONS

PPMA reduces remote myofiber stress, which is proportional to the absolute distance of relocation and independent of anchoring point. Aggressive use of PPMA techniques to reduce remote myofiber stress may accelerate reverse LV remodeling without impairing LV function.

A computational pipeline for quantification of mouse myocardial stiffness parameters

The mouse is an important model for theoretical-experimental cardiac research, and biophysically based whole organ models of the mouse heart are now within reach. However, the passive material properties of mouse myocardium have not been much studied. We present an experimental setup and associated computational pipeline to quantify these stiffness properties. A mouse heart was excised and the left ventricle experimentally inflated from 0 to 1.44kPa in eleven steps, and the resulting deformation was estimated by echocardiography and speckle tracking. An in silico counterpart to this experiment was built using finite element methods and data on ventricular tissue microstructure from diffusion tensor MRI. This model assumed a hyperelastic, transversely isotropic material law to describe the force-deformation relationship, and was simulated for many parameter scenarios, covering the relevant range of parameter space. To identify well-fitting parameter scenarios, we compared experimental and simulated outcomes across the whole range of pressures, based partly on gross phenotypes (volume, elastic energy, and short- and long-axis diameter), and partly on node positions in the geometrical mesh. This identified a narrow region of experimentally compatible values of the material parameters. Estimation turned out to be more precise when based on changes in gross phenotypes, compared to the prevailing practice of using displacements of the material points. We conclude that the presented experimental setup and computational pipeline is a viable method that deserves wider application.

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

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

Patient-specific finite element modeling of the Cardiokinetix Parachute(®) device: effects on left ventricular wall stress and function

The Parachute(®) (Cardiokinetix, Inc., Menlo Park, California) is a catheter-based device intended to reverse left ventricular (LV) remodeling after antero-apical myocardial infarction. When deployed, the device partitions the LV into upper and lower chambers. To simulate its mechanical effects, we created a finite element LV model based on computed tomography (CT) images from a patient before and 6 months after Parachute(®) implantation. Acute mechanical effects were determined by in silico device implantation (VIRTUAL-Parachute). Chronic effects of the device were determined by adjusting the diastolic and systolic material parameters to better match the 6-month post-implantation CT data and LV pressure data at end-diastole (ED) (POST-OP). Regional myofiber stress and pump function were calculated in each case. The principal finding is that VIRTUAL-Parachute was associated with a 61.2 % reduction in the lower chamber myofiber stress at ED. The POST-OP model was associated with a decrease in LV diastolic stiffness and a larger reduction in myofiber stress at the upper (27.1%) and lower chamber (78.4%) at ED. Myofiber stress at end-systole and stroke volume was little changed in the POST-OP case. These results suggest that the primary mechanism of Parachute(®) is a reduction in ED myofiber stress, which may reverse eccentric post-infarct LV hypertrophy.

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.

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.

Measurement of mitral leaflet and annular geometry and stress after repair of posterior leaflet prolapse: virtual repair using a patient-specific finite element simulation

BACKGROUND

Recurrent mitral regurgitation after mitral valve (MV) repair for degenerative disease occurs at a rate of 2.6% per year and reoperation rate progressively reaches 20% at 19.5 years. We believe that MV repair durability is related to initial postoperative leaflet and annular geometry with subsequent leaflet remodeling due to stress. We tested the hypothesis that MV leaflet and annular stress is increased after MV repair.

METHODS

Magnetic resonance imaging was performed before and intraoperative three-dimensional (3D) transesophageal echocardiography was performed before and after repair of posterior leaflet prolapse in a single patient. The repair consisted of triangular resection and annuloplasty band placement. Images of the heart were manually co-registered. The left ventricle and MV were contoured, surfaced, and a 3D finite element (FE) model was created. Elements of the posterior leaflet region were removed to model leaflet resection and virtual sutures were used to repair the leaflet defect and attach the annuloplasty ring.

RESULTS

The principal findings of the current study are the following: (1) FE simulation of MV repair is able to accurately predict changes in MV geometry including changes in annular dimensions and leaflet coaptation; (2) average posterior leaflet stress is increased; and (3) average anterior leaflet and annular stress are reduced after triangular resection and mitral annuloplasty.

CONCLUSIONS

We successfully conducted virtual mitral valve prolapse repair using FE modeling methods. Future studies will examine the effects of leaflet resection type as well as annuloplasty ring size and shape.

Outcomes of myocardial infarction hydrogel injection therapy in the human left ventricle dependent on injectate distribution

Myocardial infarction therapies involving biomaterial injections have shown benefits in inhibiting progression towards heart failure. However, the underlying mechanisms remain unclear. A finite element model of the human left ventricle was developed from magnetic resonance images. An anteroapical infarct was represented at acute (AI) and fibrotic (FI) stage. Hydrogel injections in the infarct region were modelled with layered (L) and bulk (B) distribution. In the FI, injectates reduced end-systolic myofibre stresses from 291.6% to 117.6% (FI-L) and 115.3% (FI-B) of the healthy value, whereas all AI models exhibited sub-healthy stress levels (AI: 90.9%, AI-L: 20.9%, AI-B: 30.5%). Reduction in end-diastolic infarct stress were less pronounced for both FI (FI: 294.1%, FI-L: 176.5%, FI-B: 188.2%) and AI (AI: 94.1%, AI-L: 35.3%, AI-B: 41.2%). In the border zone, injectates reduced end-systolic fibre stress by 8-10% and strain from positive (AI) and zero (FI) to negative. Layered and bulk injectates increased ejection fraction by 7.4% and 8.4% in AI and 14.1% and 13.7% in FI. The layered injectate had a greater impact on infarct stress and strain at acute stage, whereas the bulk injectate exhibited greater benefits at FI stage. These findings were confirmed by our previous in vivo results.