Multiscale Finite Element Modeling of Left Ventricular Growth in Simulations of Valve Disease.

Multiscale models of the cardiovascular system are emerging as effective tools for investigating the mechanisms that drive ventricular growth and remodeling. These models can predict how molecular-level mechanisms impact organ-level structure and function and could provide new insights that help improve patient care. MyoFE is a multiscale computer framework that bridges molecular and organ-level mechanisms in a finite element model of the left ventricle that is coupled with the systemic circulation. In this study, we extend MyoFE to include a growth algorithm, based on volumetric growth theory, to simulate concentric growth (wall thickening/thinning) and eccentric growth (chamber dilation/constriction) in response to valvular diseases. Specifically in our model, concentric growth is controlled by time-averaged total stress along the fiber direction over a cardiac cycle while eccentric growth responds to time-averaged intracellular myofiber passive stress over a cardiac cycle. The new framework correctly predicted different forms of growth in response to two types of valvular diseases, namely aortic stenosis and mitral regurgitation. Furthermore, the model predicted that LV size and function are nearly restored (reversal of growth) when the disease-mimicking perturbation was removed in the simulations for each valvular disorder. In conclusion, the simulations suggest that time-averaged total stress along the fiber direction and time-averaged intracellular myofiber passive stress can be used to drive concentric and eccentric growth in simulations of valve disease.

A multiscale finite element model of left ventricular mechanics incorporating baroreflex regulation.

Cardiovascular function is regulated by a short-term hemodynamic baroreflex loop, which tries to maintain arterial pressure at a normal level. In this study, we present a new multiscale model of the cardiovascular system named MyoFE. This framework integrates a mechanistic model of contraction at the myosin level into a finite-element-based model of the left ventricle pumping blood through the systemic circulation. The model is coupled with a closed-loop feedback control of arterial pressure inspired by a baroreflex algorithm previously published by our team. The reflex loop mimics the afferent neuron pathway via a normalized signal derived from arterial pressure. The efferent pathway is represented by a kinetic model that simulates the net result of neural processing in the medulla and cell-level responses to autonomic drive. The baroreflex control algorithm modulates parameters such as heart rate and vascular tone of vessels in the lumped-parameter model of systemic circulation. In addition, it spatially modulates intracellular Ca2+ dynamics and molecular-level function of both the thick and the thin myofilaments in the left ventricle. Our study demonstrates that the baroreflex algorithm can maintain arterial pressure in the presence of perturbations such as acute cases of altered aortic resistance, mitral regurgitation, and myocardial infarction. The capabilities of this new multiscale model will be utilized in future research related to computational investigations of growth and remodeling.

An in silico study of the effects of left ventricular assist device on right ventricular function and inter-ventricular interaction.

BACKGROUND: Left ventricular assist device (LVAD) is associated with a high incidence of right ventricular (RV) failure, which is hypothesized to be caused by the occurring inter-ventricular interactions when the LV is unloaded. Factors contributing to these interactions are unknown. METHODS: We used computer modeling to investigate the impact of the HeartMate 3 LVAD on RV functions. The model was first calibrated against pressure-volume (PV) loops associated with a heart failure (HF) patient and validated against measurements of inter-ventricular interactions in animal experiments. The model was then applied to investigate the effects of LVAD on (1) RV chamber contractility indexed by V 60 derived from its end-systolic PV relationship, and (2) RV diastolic function indexed by V 20 derived from its end-diastolic PV relationship. We also investigated how septal wall thickness and regional contractility affect the impact of LVAD on RV function. RESULTS: The impact of LVAD on RV chamber contractility is small at a pump speed lower than 4k rpm. At a higher pump speed between 4k and 9k rpm, however, RV chamber contractility is reduced (by ~3% at 6k rpm and ~10% at 9k rpm). The reduction of RV chamber contractility is greater with a thinner septal wall or with a lower myocardial contractility at the LV free wall, septum, or RV free wall. CONCLUSION: RV chamber contractility is reduced at a pump speed higher than 4k rpm, and this reduction is greater with a thinner septal wall or lower regional myocardial contractility. Findings here may have clinical implications in identifying LVAD patients who may suffer from RV failure.

Utilization of Engineering Advances for Detailed Biomechanical Characterization of the Mitral-Ventricular Relationship to Optimize Repair Strategies: A Comprehensive Review.

The geometrical details and biomechanical relationships of the mitral valve-left ventricular apparatus are very complex and have posed as an area of research interest for decades. These characteristics play a major role in identifying and perfecting the optimal approaches to treat diseases of this system when the restoration of biomechanical and mechano-biological conditions becomes the main target. Over the years, engineering approaches have helped to revolutionize the field in this regard. Furthermore, advanced modelling modalities have contributed greatly to the development of novel devices and less invasive strategies. This article provides an overview and narrative of the evolution of mitral valve therapy with special focus on two diseases frequently encountered by cardiac surgeons and interventional cardiologists: ischemic and degenerative mitral regurgitation.

Computational analysis of ventricular mechanics in hypertrophic cardiomyopathy patients.

Hypertrophic cardiomyopathy (HCM) is a genetic heart disease that is associated with many pathological features, such as a reduction in global longitudinal strain (GLS), myofiber disarray and hypertrophy. The effects of these features on left ventricle (LV) function are, however, not clear in two phenotypes of HCM, namely, obstructive and non-obstructive. To address this issue, we developed patient-specific computational models of the LV using clinical measurements from 2 female HCM patients and a control subject. Left ventricular mechanics was described using an active stress formulation and myofiber disarray was described using a structural tensor in the constitutive models. Unloaded LV configuration for each subject was first determined from their respective end-diastole LV geometries segmented from the cardiac magnetic resonance images, and an empirical single-beat estimation of the end-diastolic pressure volume relationship. The LV was then connected to a closed-loop circulatory model and calibrated using the clinically measured LV pressure and volume waveforms, peak GLS and blood pressure. Without consideration of myofiber disarray, peak myofiber tension was found to be lowest in the obstructive HCM subject (60 kPa), followed by the non-obstructive subject (242 kPa) and the control subject (375 kPa). With increasing myofiber disarray, we found that peak tension has to increase in the HCM models to match the clinical measurements. In the obstructive HCM patient, however, peak tension was still depressed (cf. normal subject) at the largest degree of myofiber disarray found in the clinic. The computational modeling workflow proposed here can be used in future studies with more HCM patient data.

A multiscale model of the cardiovascular system that regulates arterial pressure via closed loop baroreflex control of chronotropism, cell-level contractility, and vascular tone.

Multiscale models of the cardiovascular system can provide new insights into physiological and pathological processes. PyMyoVent is a computer model that bridges from molecular- to organ-level function and which simulates a left ventricle pumping blood through the systemic circulation. Initial work with PyMyoVent focused on the end-systolic pressure volume relationship and ranked potential therapeutic strategies by their impact on contractility. This manuscript extends the PyMyoVent framework by adding closed-loop feedback control of arterial pressure. The control algorithm mimics important features of the physiological baroreflex and was developed as part of a long-term program that focuses on growth and biological remodeling. Inspired by the underlying biology, the reflex algorithm uses an afferent signal derived from arterial pressure to drive a kinetic model that mimics the net result of neural processing in the medulla and cell-level responses to autonomic drive. The kinetic model outputs control signals that are constrained between limits that represent maximum parasympathetic and maximum sympathetic drive and which modulate heart rate, intracellular Ca2+ dynamics, the molecular-level function of both the thick and the thin myofilaments, and vascular tone. Simulations show that the algorithm can regulate mean arterial pressure at user-defined setpoints as well as maintaining arterial pressure when challenged by changes in blood volume and/or valve resistance. The reflex also regulates arterial pressure when cell-level contractility is modulated to mimic the idealized impact of myotropes. These capabilities will be important for future work that uses computer modeling to investigate clinical conditions and treatments.

Reproducibility of Systolic Strain in Mice Using Cardiac Magnetic Resonance Feature Tracking of Black-Blood Cine Images.

PURPOSE: Mouse models are widely utilized to enhance our understanding of cardiac disease. The goal of this study is to investigate the reproducibility of strain parameters that were measured in mice using cardiac magnetic resonance (CMR) feature-tracking (CMR42, Canada). METHODS: We retrospectively analyzed black-blood CMR datasets from thirteen C57BL/6 B6.SJL-CD45.1 mice (N = 10 female, N = 3 male) that were imaged previously. The circumferential, longitudinal, and radial (Ecc, Ell, and Err, respectively) parameters of strain were measured in the mid-ventricular region of the left ventricle. Intraobserver and interobserver reproducibility were assessed for both the end-systolic (ES) and peak strain. RESULTS: The ES strain had larger intraclass correlation coefficient (ICC) values when compared to peak strain, for both the intraobserver and interobserver reproducibility studies. Specifically, the intraobserver study showed excellent reproducibility for all three ES strain parameters, namely, Ecc (ICC 0.95, 95% CI 0.83-0.98), Ell (ICC 0.90, 95% CI 0.59-0.97), and Err (ICC 0.92, 95% CI 0.73-0.97). This was also the case for the interobserver study, namely, Ecc (ICC 0.92, 95% CI 0.60-0.98), Ell (ICC 0.76, 95% CI 0.33-0.93), and Err (ICC 0.93, 95% CI 0.68-0.98). Additionally, the coefficient of variation values were all < 10%. CONCLUSION: The results of this preliminary study showed excellent reproducibility for all ES strain parameters, with good to excellent reproducibility for the peak strain parameters. Moreover, all ES strain parameters had larger ICC values than the peak strain. In general, these results imply that feature-tracking with CMR42 software and black-blood cine images can be reliably used to assess strain patterns in mice.

In Vitro Mitral Valve Model with Unrestricted Ventricular Access: Using Vacuum to Close the Valve and Enable Static Trans-Mitral Pressure.

Current in vitro models of the left heart establish the pressure difference required to close the mitral valve by sealing and pressurizing the ventricular side of the valve, limiting important access to the subvalvular apparatus. This paper describes and evaluates a system that establishes physiological pressure differences across the valve using vacuum on the atrial side. The subvalvular apparatus is open to atmospheric pressure and accessible by tools and sensors, establishing a novel technique for experimentation on atrioventricular valves. Porcine mitral valves were excised and closed by vacuum within the atrial chamber. Images were used to document and analyze closure of the leaflets. Papillary muscle force and regurgitant flow rate were measured to be 4.07 N at 120 mmHg and approximately 12.1 ml/s respectively, both of which are within clinically relevant ranges. The relative ease of these measurements demonstrates the usefulness of improved ventricular access at peak pressure/force closure.

Multiscale simulations of left ventricular growth and remodeling.

Cardiomyocytes can adapt their size, shape, and orientation in response to altered biomechanical or biochemical stimuli. The process by which the heart undergoes structural changes-affecting both geometry and material properties-in response to altered ventricular loading, altered hormonal levels, or mutant sarcomeric proteins is broadly known as cardiac growth and remodeling (G&R). Although it is likely that cardiac G&R initially occurs as an adaptive response of the heart to the underlying stimuli, prolonged pathological changes can lead to increased risk of atrial fibrillation, heart failure, and sudden death. During the past few decades, computational models have been extensively used to investigate the mechanisms of cardiac G&R, as a complement to experimental measurements. These models have provided an opportunity to quantitatively study the relationships between the underlying stimuli (primarily mechanical) and the adverse outcomes of cardiac G&R, i.e., alterations in ventricular size and function. State-of-the-art computational models have shown promise in predicting the progression of cardiac G&R. However, there are still limitations that need to be addressed in future works to advance the field. In this review, we first outline the current state of computational models of cardiac growth and myofiber remodeling. Then, we discuss the potential limitations of current models of cardiac G&R that need to be addressed before they can be utilized in clinical care. Finally, we briefly discuss the next feasible steps and future directions that could advance the field of cardiac G&R.

Regional end-systolic circumferential strain demonstrates compensatory segmental contractile function in patients with ST-segment elevation myocardial infarction.

Myocardial strain has shown tremendous promise as a potential diagnostic tool for characterizing ventricular function. With regards to myocardial infarction, global circumferential strain (CS) can be used to assess overall function, while regional CS can identify local alterations in contractility. Currently, there is a lack of data related to regional strain in patients with ST-segment elevation myocardial infarction (STEMI). Thus, the goal of this study was to quantify regional strain patterns in STEMI and normal control patients, measuring both peak CS and end-systolic (ES) CS in the mid-ventricular region. This was done by conducting cardiac magnetic resonance (CMR) imaging acutely after STEMI patients underwent primary percutaneous coronary intervention. The CMR datasets were then analyzed using feature-tracking of the cine images. The patients were broken into three groups: (1) control patients (N = 18), (2) STEMI patients with ejection fraction (EF) ≥ 50% (N = 20), and (3) STEMI patients with EF < 50% (N = 20). The key result of the analysis was that ES CS detected a significant increase in the magnitude of strain in the non-infarcted tissue of STEMI patients with EF ≥ 50% when compared to STEMI patients with EF < 50%, whereas peak CS did not detect any differences. This implies that the tissue in this region is contracting more strongly compared to non-infarcted tissue in STEMI patients with EF < 50%. Thus, regional ES CS could potentially be utilized as a diagnostic tool for assessing STEMI patients, by detecting regional changes in contractility after PCI, which could assist in treatment planning.

Impact of regulatory light chain mutation K104E on the ATPase and motor properties of cardiac myosin.

Mutations in the cardiac myosin regulatory light chain (RLC, MYL2 gene) are known to cause inherited cardiomyopathies with variable phenotypes. In this study, we investigated the impact of a mutation in the RLC (K104E) that is associated with hypertrophic cardiomyopathy (HCM). Previously in a mouse model of K104E, older animals were found to develop cardiac hypertrophy, fibrosis, and diastolic dysfunction, suggesting a slow development of HCM. However, variable penetrance of the mutation in human populations suggests that the impact of K104E may be subtle. Therefore, we generated human cardiac myosin subfragment-1 (M2ß-S1) and exchanged on either the wild type (WT) or K104E human ventricular RLC in order to assess the impact of the mutation on the mechanochemical properties of cardiac myosin. The maximum actin-activated ATPase activity and actin sliding velocities in the in vitro motility assay were similar in M2ß-S1 WT and K104E, as were the detachment kinetic parameters, including the rate of ATP-induced dissociation and the ADP release rate constant. We also examined the mechanical performance of α-cardiac myosin extracted from transgenic (Tg) mice expressing human wild type RLC (Tg WT) or mutant RLC (Tg K104E). We found that α-cardiac myosin from Tg K104E animals demonstrated enhanced actin sliding velocities in the motility assay compared with its Tg WT counterpart. Furthermore, the degree of incorporation of the mutant RLC into α-cardiac myosin in the transgenic animals was significantly reduced compared with wild type. Therefore, we conclude that the impact of the K104E mutation depends on either the length or the isoform of the myosin heavy chain backbone and that the mutation may disrupt RLC interactions with the myosin lever arm domain.

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

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

Quantification of regional right ventricular strain in healthy rats using 3D spiral cine dense MRI.

Statistical data from clinical studies suggests that right ventricular (RV) circumferential strain (Ecc) and longitudinal strain (Ell) are significant biomarkers for many cardiovascular diseases. However, a detailed and regional characterization of these strains in the RV is very limited. In the current study, RV images were obtained with 3D spiral cine DENSE MRI in healthy rats. An algorithm for surface growing was proposed in order to fit irregular topology. Specifically, a new custom plugin for the DENSEanalysis program, called 3D DENSE Plugin for Crescent Organ, was developed for surface reconstruction and precise segmentation of organs with sharp curvature, such as the murine RV. The RV free wall (RVFW) was divided into three longitudinal thirds (i.e., basal, middle, and apical) with each one partitioned into circumferential fourths (i.e., anterior, anteriorlateral, inferiorlateral and inferior). Peak systolic strains were quantified for each segment and comparisons were performed statistically. The inclusion of a new plugin was able to generate global values for Ecc and Ell that are in good agreement with previous findings using MRI. Despite no regional variation found in the peak Ecc, the peak Ell exhibited regional variation at the anterior side of the RV, which is potentially due to differences in biventricular torsion at the RV insertion point and fiber architecture. These results provide fundamental insights into the regional contractile function of the RV in healthy rat and could act as a normative baseline for future studies on regional changes induced by disease or treatment.

Differential Effects of Isoproterenol on Regional Myocardial Mechanics in Rat Using Three-Dimensional Cine DENSE Cardiovascular Magnetic Resonance.

The present study assessed the acute effects of isoproterenol on left ventricular (LV) mechanics in healthy rats with the hypothesis that ß-adrenergic stimulation influences the mechanics of different myocardial regions of the LV wall in different ways. To accomplish this, magnetic resonance images were obtained in the LV of healthy rats with or without isoproterenol infusion. The LV contours were divided into basal, midventricular, and apical regions. Additionally, the midventricular myocardium was divided into three transmural layers with each layer partitioned into four segments (i.e., septal, inferior, lateral, and anterior). Peak systolic strains and torsion were quantified for each region. Isoproterenol significantly increased peak systolic radial strain and circumferential-longitudinal (CL) shear strain, as well as ventricular torsion, throughout the basal, midventricle, and apical regions. In the midventricle, isoproterenol significantly increased peak systolic radial strain, and induced significant increases in peak systolic circumferential strain and longitudinal strain in the septum. Isoproterenol consistently increased peak systolic CL shear strain in all midventricular segments. Ventricular torsion was significantly increased in nearly all segments except the inferior subendocardium. The effects of isoproterenol on LV systolic mechanics (i.e., three-dimensional (3D) strains and torsion) in healthy rats depend on the region. This region dependency is also strain component-specific. These results provide insight into the regional response of LV mechanics to ß-adrenergic stimulation in rats and could act as a baseline for future studies on subclinical abnormalities associated with the inotropic response in heart disease.

Effects of hydrogel injection on borderzone contractility post-myocardial infarction.

Injectable hydrogels are a potential therapy for mitigating adverse left ventricular (LV) remodeling after myocardial infarction (MI). Previous studies using magnetic resonance imaging (MRI) have shown that hydrogel treatment improves systolic strain in the borderzone (BZ) region surrounding the infarct. However, the corresponding contractile properties of the BZ myocardium are still unknown. The goal of the current study was to quantify the in vivo contractile properties of the BZ myocardium post-MI in an ovine model treated with an injectable hydrogel. Contractile properties were determined 8 weeks following posterolateral MI by minimizing the difference between in vivo strains and volume calculated from MRI and finite element model predicted strains and volume. This was accomplished by using a combination of MRI, catheterization, finite element modeling, and numerical optimization. Results show contractility in the BZ of animals treated with hydrogel injection was significantly higher than untreated controls. End-systolic (ES) fiber stress was also greatly reduced in the BZ of treated animals. The passive stiffness of the treated infarct region was found to be greater than the untreated control. Additionally, the wall thickness in the infarct and BZ regions was found to be significantly higher in the treated animals. Treatment with hydrogel injection significantly improved BZ function and reduced LV remodeling, via altered MI properties. These changes are linked to a reduction in the ES fiber stress in the BZ myocardium surrounding the infarct. The current results imply that injectable hydrogels could be a viable therapy for maintaining LV function post-MI.

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

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

Computational sensitivity investigation of hydrogel injection characteristics for myocardial support.

Biomaterial injection is a potential new therapy for augmenting ventricular mechanics after myocardial infarction (MI). Recent in vivo studies have demonstrated that hydrogel injections can mitigate the adverse remodeling due to MI. More importantly, the material properties of these injections influence the efficacy of the therapy. The goal of the current study is to explore the interrelated effects of injection stiffness and injection volume on diastolic ventricular wall stress and thickness. To achieve this, finite element models were constructed with different hydrogel injection volumes (150µL and 300 µL), where the modulus was assessed over a range of 0.1kPa to 100kPa (based on experimental measurements). The results indicate that a larger injection volume and higher stiffness reduce diastolic myofiber stress the most, by maintaining the wall thickness during loading. Interestingly, the efficacy begins to taper after the hydrogel injection stiffness reaches a value of 50kPa. This computational approach could be used in the future to evaluate the optimal properties of the hydrogel.

High resolution imaging of the mitral valve in the natural state with 7 Tesla MRI.

Imaging techniques of the mitral valve have improved tremendously during the last decade, but challenges persist. The delicate changes in annulus shape and papillary muscle position throughout the cardiac cycle have significant impact on the stress distribution in the leaflets and chords, thus preservation of anatomically accurate positioning is critical. The aim of this study was to develop an in vitro method and apparatus for obtaining high-resolution 3D MRI images of porcine mitral valves in both the diastolic and systolic configurations with physiologically appropriate annular shape, papillary muscle positions and orientations, specific to the heart from which the valve was harvested. Positioning and mounting was achieved through novel, customized mounting hardware consisting of papillary muscle and annulus holders with geometries determined via pre-mortem ultrasonic intra-valve measurements. A semi-automatic process was developed and employed to tailor Computer Aided Design models of the holders used to mount the valve. All valve mounting hardware was 3D printed using a stereolithographic printer, and the material of all fasteners used were brass for MRI compatibility. The mounted valves were placed within a clear acrylic case, capable of holding a zero-pressure and pressurized liquid bath of a MRI-compatible fluid. Obtaining images from the valve submerged in liquid fluid mimics the natural environment surrounding the valve, avoiding artefacts due to tissue surface tension mismatch and gravitational impact on tissue shape when not neutrally buoyant. Fluid pressure was supplied by reservoirs held at differing elevations and monitored and controlled to within ±1mmHg to ensure that the valves remained steady. The valves were scanned in a 7 Tesla MRI system providing a voxel resolution of at least 80µm. The systematic approach produced 3D datasets of high quality which, when combined with physiologically accurate positioning by the apparatus, can serve as an important input for validated computational models.