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.

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.

Regional quantification of myocardial mechanics in rat using 3D cine DENSE cardiovascular magnetic resonance.

Rat models have assumed an increasingly important role in cardiac research. However, a detailed profile of regional cardiac mechanics, such as strains and torsion, is lacking for rats. We hypothesized that healthy rat left ventricles (LVs) exhibit regional differences in cardiac mechanics, which are part of normal function. In this study, images of the LV were obtained with 3D cine displacement encoding with stimulated echoes (DENSE) cardiovascular magnetic resonance in 10 healthy rats. To evaluate regional cardiac mechanics, the LV was divided into basal, mid-ventricular, and apical regions. The myocardium at the mid-LV was further partitioned into four wall segments (i.e. septal, inferior, lateral, and anterior) and three transmural layers (i.e. sub-endocardium, mid-myocardium, and sub-epicardium). The six Lagrangian strain components (i.e. Err , Ecc , Ell , Ecl , Erl , and Ecr ) were computed from the 3D displacement field and averaged within each region of interest. Torsion was quantified using the circumferential-longitudinal shear angle. While peak systolic Ecl differed between the mid-ventricle and apex, the other five components of peak systolic strain were similar across the base, mid-ventricle, and apex. In the mid-LV myocardium, Ecc decreased gradually from the sub-endocardial to the sub-epicardial layer. Ell demonstrated significant differences between the four wall segments, with the largest magnitude in the inferior segment. Err was uniform among the four wall segments. Ecl varied along the transmural direction and among wall segments, whereas Erl differed only among the wall segments. Erc was not associated with significant variations. Torsion also varied along the transmural direction and among wall segments. These results provide fundamental insights into the regional contractile function of healthy rat hearts, and form the foundation for future studies on regional changes induced by disease or treatments.

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.

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

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

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.

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.

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.

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.

Growth and remodeling of the left ventricle: A case study of myocardial infarction and surgical ventricular restoration.

Cardiac growth and remodeling in the form of chamber dilation and wall thinning are typical hallmarks of infarct-induced heart failure. Over time, the infarct region stiffens, the remaining muscle takes over function, and the chamber weakens and dilates. Current therapies seek to attenuate these effects by removing the infarct region or by providing structural support to the ventricular wall. However, the underlying mechanisms of these therapies are unclear, and the results remain suboptimal. Here we show that myocardial infarction induces pronounced regional and transmural variations in cardiac form. We introduce a mechanistic growth model capable of predicting structural alterations in response to mechanical overload. Under a uniform loading, this model predicts non-uniform growth. Using this model, we simulate growth in a patient-specific left ventricle. We compare two cases, growth in an infarcted heart, pre-operative, and growth in the same heart, after the infarct was surgically excluded, post-operative. Our results suggest that removing the infarct and creating a left ventricle with homogeneous mechanical properties does not necessarily reduce the driving forces for growth and remodeling. These preliminary findings agree conceptually with clinical observations.

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.

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.

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.

Numerical modeling of stress in stenotic arteries with microcalcifications: a parameter sensitivity study.

As a follow-up to the work presented in Wenk et al. (2010, "Numerical Modeling of Stress in Stenotic Arteries With Microcalcifications: A Micromechanical Approximation," ASME J. Biomech. Eng., 132, p. 091011), a formal sensitivity study was conducted in which several model parameters were varied. The previous work only simulated a few combinations of the parameters. In the present study, the fibrous cap thickness, longitudinal position of the region of microcalcifications, and volume fraction of microcalcifications were varied over a broader range of values. The goal of the present work is to investigate the effects of localized regions of microcalcifications on the stress field of atherosclerotic plaque caps in a section of carotid artery. More specifically, the variations in the magnitude and location of the maximum circumferential stress were assessed for a range of parameters using a global sensitivity analysis method known as Sobol' indices. The stress was calculated by performing finite element simulations of three-dimensional fluid-structure interaction models, while the sensitivity indices were computed using a Monte Carlo scheme. The results indicate that cap thickness plays a significant role in the variation in the magnitude of the maximum circumferential stress, with the sensitivity to volume fraction increasing when the region of microcalcification is located at the shoulder. However, the volume fraction played a larger role in the variation in the location of the maximum circumferential stress. This matches the finding of the previous study (Wenk et al., 2010, "Numerical Modeling of Stress in Stenotic Arteries With Microcalcifications: A Micromechanical Approximation," ASME J. Biomech. Eng., 132, p. 091011), which indicates that the maximum circumferential stress always shifts to the region of microcalcification.

Simulation of LV pacemaker lead in marginal vein: potential risk factors for acute dislodgement.

Although left ventricular (LV) coronary sinus lead dislodgement remains a problem, the risk factors for dislodgement have not been clearly defined. In order to identify potential risk factors for acute lead dislodgement, we conducted dynamic finite element simulations of pacemaker lead dislodgement in marginal LV vein. We considered factors such as mismatch in lead and vein diameters, velocity of myocardial motion, branch angle between the insertion vein and the coronary sinus, degree of slack, and depth of insertion. The results show that large lead-to-vein diameter mismatch, rapid myocardial motion, and superficial insertion are potential risk factors for lead dislodgement. In addition, the degree of slack presents either a positive or negative effect on dislodgement risk depending on the branch angle. The prevention of acute lead dislodgment can be enforced by inducing as much static friction force as possible at the lead-vein interface, while reducing the external force. If the latter exceeds the former, dislodgement will occur. The present findings underscore the major risk factors for lead dislodgment, which may improve implantation criterion and future lead design.

Simulation of mechanical environment in active lead fixation: effect of fixation helix size.

The risk of myocardial penetration due to active-fixation screw-in type pacing leads has been reported to increase as the helix electrodes become smaller. In order to understand the contributing factors for lead penetration, we conducted finite element analyses of acute myocardial micro-damage induced by a pacemaker lead screw-in helix electrode. We compared the propensity for myocardial micro-damage of seven lead designs including a baseline model, three modified designs with various helix wire cross-sectional diameters, and three modified designs with different helix diameters. The comparisons show that electrodes with a smaller helix wire diameter cause more severe micro-damage to the myocardium in the early stage. The damage severity, represented by the volume of failed elements, is roughly the same in the middle stage, whereas in the later stage the larger helix wire diameter generally causes more severe damage. The onset of myocardial damage is not significantly affected by the helix diameter. As the helix diameter increases, however, the extent of myocardial damage increases accordingly. The present findings identified several of the major risk factors for myocardial damage whose consideration for lead use and design might improve acute and chronic lead performance.

Regional left ventricular myocardial contractility and stress in a finite element model of posterobasal myocardial infarction.

Recently, a noninvasive method for determining regional myocardial contractility, using an animal-specific finite element (FE) model-based optimization, was developed to study a sheep with anteroapical infarction (Sun et al., 2009, "A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep With Left Ventricular Aneurysm," ASME J. Biomech. Eng., 131(11), p. 111001). Using the methodology developed in the previous study (Sun et al., 2009, "A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep With Left Ventricular Aneurysm," ASME J. Biomech. Eng., 131(11), p. 111001), which incorporates tagged magnetic resonance images, three-dimensional myocardial strains, left ventricular (LV) volumes, and LV cardiac catheterization pressures, the regional myocardial contractility and stress distribution of a sheep with posterobasal infarction were investigated. Active material parameters in the noninfarcted border zone (BZ) myocardium adjacent to the infarct (T(max_B)), in the myocardium remote from the infarct (T(max_R)), and in the infarct (T(max_I)) were estimated by minimizing the errors between FE model-predicted and experimentally measured systolic strains and LV volumes using the previously developed optimization scheme. The optimized T(max_B) was found to be significantly depressed relative to T(max_R), while T(max_I) was found to be zero. The myofiber stress in the BZ was found to be elevated, relative to the remote region. This could cause further damage to the contracting myocytes, leading to heart failure.

A novel method for quantifying in-vivo regional left ventricular myocardial contractility in the border zone of a myocardial infarction.

Homogeneous contractility is usually assigned to the remote region, border zone (BZ), and the infarct in existing infarcted left ventricle (LV) mathematical models. Within the LV, the contractile function is therefore discontinuous. Here, we hypothesize that the BZ may in fact define a smooth linear transition in contractility between the remote region and the infarct. To test this hypothesis, we developed a mathematical model of a sheep LV having an anteroapical infarct with linearly-varying BZ contractility. Using an existing optimization method (Sun et al., 2009, "A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep With Left Ventricular Aneurysm," J. Biomech. Eng., 131(11), pp. 111001), we use that model to extract active material parameter T(max) and BZ width d(n) that "best" predict in-vivo systolic strain fields measured from tagged magnetic resonance images (MRI). We confirm our hypothesis by showing that our model, compared to one that has homogeneous contractility assigned in each region, reduces the mean square errors between the predicted and the measured strain fields. Because the peak fiber stress differs significantly (~15%) between these two models, our result suggests that future mathematical LV models, particularly those used to analyze myocardial infarction treatment, should account for a smooth linear transition in contractility within the BZ.