Method for Calibration of Left Ventricle Material Properties Using Three-Dimensional Echocardiography Endocardial Strains.

We sought to calibrate mechanical properties of left ventricle (LV) based on three-dimensional (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 (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, RI). The calibration of passive properties based on the end diastolic pressure volume relation (EDPVR) curve resulted in relatively good agreement (mean error = -0.04 ml). The difference between the 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.

Tricuspid Valve Regurgitation Decreases after MitraClip Implantation: Fluid Structure Interaction Simulation.

Untreated tricuspid valve regurgitation (TR) is associated with increased rates of mortality, morbidity, and hospitalization. Current pharmacological and surgical treatment options for TR are limited. MitraClip (MC), an edge-to-edge percutaneous intervention, has been reported to be effective for treatment of TR. The goal of this study was to examine the effects of MC position on TR, using a multiphysics fluid-structure-interaction (FSI) analysis. The computational set up included the tricuspid valve (TV), the chordae tendineae, the blood particles, and a tube that surrounded the leaflets and blood particles. The leaflets and chordae were modeled as hyperelastic materials, and blood was modeled using smoothed particle hydrodynamics. FSI analysis was conducted for blood flow through the closed valve for multiple simulations that account for normal, diseased, and treated conditions of the TV. To simulate the diseased TV, a group of chordae between septal and pulmonary leaflets were removed from the normal TV, which produced increased regurgitation. Four MC treated scenarios were considered: i) one MC near the annulus, ii) one MC approximately midway between the annulus and leaflet tip, iii) one MC near the leaflet tip, iv) two MCs: one approximately midway between the annulus and leaflet tip, and one close to the leaflet tip. The TR increased in diseased TV (7.5%) compared to normal TV (2.5%). All MC treated scenarios decreased TR. The MC located near the midway point between the annulus and leaflet tip led to largest decrease in TR (75.2% compared to the untreated condition). The MC located near the leaflet tip was associated with lowest reduction in TR (2.2% compared to the untreated condition). When two MCs were used, reduction in TR was relatively high (68.7%), but TR was not improved compared to the optimal single MC. MC caused high stresses in the vicinity of the clipping area in all conditions; the highest occurred when the MC was near the leaflet tips. Using a quantitative computational approach, we confirm previous clinical reports on the efficacy of MC for treatment of TR. The results of this study could lead to the design of more efficient MC interventions for TR.

Time in Range, Time in Tight Range, and Average Glucose Relationships Are Modulated by Glycemic Variability: Identification of a Glucose Distribution Model Connecting Glycemic Parameters Using Real-World Data.

Background: Time in range (TIR), time in tight range (TITR), and average glucose (AG) are used to adjust glycemic therapies in diabetes. However, TIR/TITR and AG can show a disconnect, which may create management difficulties. We aimed to understand the factors influencing the relationships between these glycemic markers. Materials and Methods: Real-world glucose data were collected from self-identified diabetes type 1 and type 2 diabetes (T1D and T2D) individuals using flash continuous glucose monitoring (FCGM). The effects of glycemic variability, assessed as glucose coefficient of variation (CV), on the relationship between AG and TIR/TITR were investigated together with the best-fit glucose distribution model that addresses these relationships. Results: Of 29,164 FCGM users (16,367 T1D, 11,061 T2D, and 1736 others), 38,259 glucose readings/individual were available. Comparing low and high CV tertiles, TIR at AG of 150 mg/dL varied from 80% ± 5.6% to 62% ± 6.8%, respectively (P < 0.001), while TITR at AG of 130 mg/dL varied from 65% ± 7.5% to 49% ± 7.0%, respectively (P < 0.001). In contrast, higher CV was associated with increased TIR and TITR at AG levels outside the upper limit of these ranges. Gamma distribution was superior to six other models at explaining AG and TIR/TITR interactions and demonstrated nonlinear interplay between these metrics. Conclusions: The gamma model accurately predicts interactions between CGM-derived glycemic metrics and reveals that glycemic variability can significantly influence the relationship between AG and TIR with opposing effects according to AG levels. Our findings potentially help with clinical diabetes management, particularly when AG and TIR appear mismatched.

Machine learning used for simulation of MitraClip intervention: A proof-of-concept study.

Introduction: Severe mitral regurgitation (MR) is a mitral valve disease that can lead to lifethreatening complications. MitraClip (MC) therapy is a percutaneous solution for patients who cannot tolerate surgical solutions. In MC therapy, a clip is implanted in the heart to reduce MR. To achieve optimal MC therapy, the cardiologist needs to foresee the outcomes of different scenarios for MC implantation, including the location of the MC. Although finite element (FE) modeling can simulate the outcomes of different MC scenarios, it is not suitable for clinical usage because it requires several hours to complete. Methods: In this paper, we used machine learning (ML) to predict the outcomes of MC therapy in less than 1 s. Two ML algorithms were used: XGBoost, which is a decision tree model, and a feed-forward deep learning (DL) model. The MC location, the geometrical attributes of the models and baseline stress and MR were the features of the ML models, and the predictions were performed for MR and maximum von Mises stress in the leaflets. The parameters of the ML models were determined to achieve the minimum errors obtained by applying the ML models on the validation set. Results: The results for the test set (not used during training) showed relative agreement between ML predictions and ground truth FE predictions. The accuracy of the XGBoost models were better than DL models. Mean absolute percentage error (MAPE) for the XGBoost predictions were 0.115 and 0.231, and the MAPE for DL predictions were 0.154 and 0.310, for MR and stress, respectively. Discussion: The ML models reduced the FE runtime from 6 hours (on average) to less than 1 s. The accuracy of ML models can be increased by increasing the dataset size. The results of this study have important implications for improving the outcomes of MC therapy by providing information about the outcomes of MC implantation in real-time.

A Simulation Study of the Effects of Number and Location of MitraClips on Mitral Regurgitation.

Background: MitraClip (MC) is a device that is implanted on the mitral valve (MV) percutaneously to treat severe mitral regurgitation (MR). It is common practice to place the MCs at the site of the most significant MR jets identified by echocardiography. Objectives: We used computational modeling to examine changes in MR after MC placement. Methods: Echocardiographic images from 29 patients with MR were analyzed to reconstruct geometries for finite element simulations and created fluid structure interaction models of the MV with deformable hyperelastic material, the left ventricle as the surrounding geometry, and blood flow. Blood flow was modelled with smoothed particle hydrodynamics. The number of blood particles on the atrial side of MV was used to estimate MR. MC placement was based on the MR jets (jet-based strategy using primary and secondary jets) and simulation models using various MCs locations. Results: Computational modelling was able to quantitate reductions in MR after MC placement. Reduction in MR was related to the number of MCs used: 42% reduction with 1 MC, 62% with 2 MCs, and 88% with 3 MCs. Using 2 MCs did not always result in an MR reduction greater than with a single MC. In 31% (9 of 29) of patients, the jet-based strategy did not lead to maximum MR reduction. The majority of patients (89%) who did not have maximal MR reduction with the MC placement using the jet-based strategy, had wide jets, and/or had multiple jets. Conclusions: Subject-specific simulation models may be helpful to identify optimal locations for MC placement in patients with MR.

Mitral Valve Atlas for Artificial Intelligence Predictions of MitraClip Intervention Outcomes.

Severe mitral regurgitation (MR) is a cardiac disease that can lead to fatal consequences. MitraClip (MC) intervention is a percutaneous procedure whereby the mitral valve (MV) leaflets are connected along the edge using MCs. The outcomes of the MC intervention are not known in advance, i.e., the outcomes are quite variable. Artificial intelligence (AI) can be used to guide the cardiologist in selecting optimal MC scenarios. In this study, we describe an atlas of shapes as well as different scenarios for MC implantation for such an AI analysis. We generated the MV geometrical data from three different sources. First, the patients' 3-dimensional echo images were used. The pixel data from six key points were obtained from three views of the echo images. Using PyGem, an open-source morphing library in Python, these coordinates were used to create the geometry by morphing a template geometry. Second, the dimensions of the MV, from the literature were used to create data. Third, we used machine learning methods, principal component analysis, and generative adversarial networks to generate more shapes. We used the finite element (FE) software ABAQUS to simulate smoothed particle hydrodynamics in different scenarios for MC intervention. The MR and stresses in the leaflets were post-processed. Our physics-based FE models simulated the outcomes of MC intervention for different scenarios. The MR and stresses in the leaflets were computed by the FE models for a single clip at different locations as well as two and three clips. Results from FE simulations showed that the location and number of MCs affect subsequent residual MR, and that leaflet stresses do not follow a simple pattern. Furthermore, FE models need several hours to provide the results, and they are not applicable for clinical usage where the predicted outcomes of MC therapy are needed in real-time. In this study, we generated the required dataset for the AI models which can provide the results in a matter of seconds.

Application of feed forward and recurrent neural networks in simulation of left ventricular mechanics.

An understanding of left ventricle (LV) mechanics is fundamental for designing better preventive, diagnostic, and treatment strategies for improved heart function. Because of the costs of clinical and experimental studies to treat and understand heart function, respectively, in-silico models play an important role. Finite element (FE) models, which have been used to create in-silico LV models for different cardiac health and disease conditions, as well as cardiac device design, are time-consuming and require powerful computational resources, which limits their use when real-time results are needed. As an alternative, we sought to use deep learning (DL) for LV in-silico modeling. We used 80 four-chamber heart FE models for feed forward, as well as recurrent neural network (RNN) with long short-term memory (LSTM) models for LV pressure and volume. We used 120 LV-only FE models for training LV stress predictions. The active material properties of the myocardium and time were features for the LV pressure and volume training, and passive material properties and element centroid coordinates were features of the LV stress prediction models. For six test FE models, the DL error for LV volume was 1.599 ± 1.227 ml, and the error for pressure was 1.257 ± 0.488 mmHg; for 20 LV FE test examples, the mean absolute errors were, respectively, 0.179 ± 0.050 for myofiber, 0.049 ± 0.017 for cross-fiber, and 0.039 ± 0.011 kPa for shear stress. After training, the DL runtime was in the order of seconds whereas equivalent FE runtime was in the order of several hours (pressure and volume) or 20 min (stress). We conclude that using DL, LV in-silico simulations can be provided for applications requiring real-time results.

Numerical Simulations of MitraClip Placement: Clinical Implications.

Mitral regurgitation (MR) is the most common type of valvular heart disease in patients over the age of 75 in the US. Despite the prevalence of mitral regurgitation in the elderly population, however, almost half of patients identified with moderate-severe MR are turned down for traditional open heart surgery due to frailty and other existing co-morbidities. MitraClip (MC) is a recent percutaneous approach to treat mitral regurgitation by placement of MC in the center of the mitral valve to reduce MR. There are currently no computational simulations to elucidate the role of MC on both the fluid and solid mechanics of the mitral valve. Here, we use the Smoothed Particle Hydrodynamics (SPH) approach to study various positional placements of the MC in the mitral valve and its impact on reducing MR. SPH is a particle based (meshless) approach that handles flow through narrow regions quite efficiently. Fluid and surrounding anatomical structure interactions is handled via contact and hence can be used for studying fluid-structure interaction problems such as blood flow with surrounding tissues/structure. This method is available as part of the Abaqus/Explicit solver. Regurgitation was initiated by removing targeted chordae tendineae that are attached to specified leaflets of the mitral valve and, subsequently, MC implants are placed in various locations, starting from the region near where the chordae tendineae were removed and moving away from the location towards the center of the valve. The MC implant location closest to where the chordae tendineae were removed showed the least amount of residual MR post-clip implantation amongst all other locations of MC implant considered. These findings have important implications for strategic placement of the MC depending on the etiology of MR to optimize clinical outcome.

Prediction of Left Ventricular Mechanics Using Machine Learning.

The goal of this paper was to provide a real-time left ventricular (LV) mechanics simulator using machine learning (ML). Finite element (FE) simulations were conducted for the LV with different material properties to obtain a training set. A hyperelastic fiber-reinforced material model was used to describe the passive behavior of the myocardium during diastole. The active behavior of the heart resulting from myofiber contractions was added to the passive tissue during systole. The active and passive properties govern the LV constitutive equation. These mechanical properties were altered using optimal Latin hypercube design of experiments to obtain training FE models with varied active properties (volume and pressure predictions) and varied passive properties (stress predictions). For prediction of LV pressures, we used eXtreme Gradient Boosting (XGboost) and Cubist, and XGBoost was used for predictions of LV pressures, volumes as well as LV stresses. The LV pressure and volume results obtained from ML were similar to FE computations. The ML results could capture the shape of LV pressure as well as LV pressure-volume loops. The results predicted by Cubist were smoother than those from XGBoost. The mean absolute errors were as follows: XGBoost volume: 1.734 ± 0.584 ml, XGBoost pressure: 1.544 ± 0.298 mmHg, Cubist volume: 1.495 ± 0.260 ml, Cubist pressure: 1.623 ± 0.191 mmHg, myofiber stress: 0.334 ± 0.228 kPa, cross myofiber stress: 0.075 ± 0.024 kPa, and shear stress: 0.050 ± 0.032 kPa. The simulation results show ML can predict LV mechanics much faster than the FE method. The ML model can be used as a tool to predict LV behavior. Training of our ML model based on a large group of subjects can improve its predictability for real world applications.

Intramyocardial Injections to De-Stiffen the Heart: A Subject-Specific in Silico Approach.

We hypothesized that minimally invasive injections of a softening agent at strategic locations in stiff myocardium could de-stiffen the left ventricle (LV) globally. Physics-based finite element models of the LV were created from LV echocardiography images and pressures recorded during experiments in four swine. Results confirmed animal models of LV softening by systemic agents. Regional de-stiffening of myocardium led to global de-stiffening of LV. The mathematical set up was used to design LV global de-stiffening by regional softening of myocardium. At an end diastolic pressure of 23 mmHg, when 8 ml of the free wall was covered by intramyocardial injections, end diastolic volume (EDV) increased by 15.0%, whereas an increase up to 11 ml due to intramyocardial injections in the septum and free wall led to a 26.0% increase in EDV. Although the endocardial intramyocardial injections occupied a lower LV wall volume, they led to an EDV (44 ml) that was equal compared to intramyocardial injections in the mid-wall (44 ml) and larger compared to intramyocardial injections in the epicardium (41 ml). Using an in silico set up, sites of regional myocardium de-stiffening could be planned in order to globally soften overly stiff LV in heart failure with preserved ejection fraction. This novel treatment is built on subject-specific data. Hypothesis-testing of these simulation findings in animal models is warranted.

Relationship of Transmural Variations in Myofiber Contractility to Left Ventricular Ejection Fraction: Implications for Modeling Heart Failure Phenotype With Preserved Ejection Fraction.

The pathophysiological mechanisms underlying preserved left ventricular (LV) ejection fraction (EF) in patients with heart failure and preserved ejection fraction (HFpEF) remain incompletely understood. We hypothesized that transmural variations in myofiber contractility with existence of subendocardial dysfunction and compensatory increased subepicardial contractility may underlie preservation of LVEF in patients with HFpEF. We quantified alterations in myocardial function in a mathematical model of the human LV that is based on the finite element method. The fiber-reinforced material formulation of the myocardium included passive and active properties. The passive material properties were determined such that the diastolic pressure-volume behavior of the LV was similar to that shown in published clinical studies of pressure-volume curves. To examine changes in active properties, we considered six scenarios: (1) normal properties throughout the LV wall; (2) decreased myocardial contractility in the subendocardium; (3) increased myocardial contractility in the subepicardium; (4) myocardial contractility decreased equally in all layers, (5) myocardial contractility decreased in the midmyocardium and subepicardium, (6) myocardial contractility decreased in the subepicardium. Our results indicate that decreased subendocardial contractility reduced LVEF from 53.2 to 40.5%. Increased contractility in the subepicardium recovered LVEF from 40.5 to 53.2%. Decreased contractility transmurally reduced LVEF and could not be recovered if subepicardial and midmyocardial contractility remained depressed. The computational results simulating the effects of transmural alterations in the ventricular tissue replicate the phenotypic patterns of LV dysfunction observed in clinical practice. In particular, data for LVEF, strain and displacement are consistent with previous clinical observations in patients with HFpEF, and substantiate the hypothesis that increased subepicardial contractility may compensate for subendocardial dysfunction and play a vital role in maintaining LVEF.

Investigating the Role of Interventricular Interdependence in Development of Right Heart Dysfunction During LVAD Support: A Patient-Specific Methods-Based Approach.

Predictive computation models offer the potential to uncover the mechanisms of treatments whose actions cannot be easily determined by experimental or imaging techniques. This is particularly relevant for investigating left ventricular mechanical assistance, a therapy for end-stage heart failure, which is increasingly used as more than just a bridge-to-transplant therapy. The high incidence of right ventricular failure following left ventricular assistance reflects an undesired consequence of treatment, which has been hypothesized to be related to the mechanical interdependence between the two ventricles. To investigate the implication of this interdependence specifically in the setting of left ventricular assistance device (LVAD) support, we introduce a patient-specific finite-element model of dilated chronic heart failure. The model geometry and material parameters were calibrated using patient-specific clinical data, producing a mechanical surrogate of the failing in vivo heart that models its dynamic strain and stress throughout the cardiac cycle. The model of the heart was coupled to lumped-parameter circulatory systems to simulate realistic ventricular loading conditions. Finally, the impact of ventricular assistance was investigated by incorporating a pump with pressure-flow characteristics of an LVAD (HeartMate II™ operating between 8 and 12 k RPM) in parallel to the left ventricle. This allowed us to investigate the mechanical impact of acute left ventricular assistance at multiple operating-speeds on right ventricular mechanics and septal wall motion. Our findings show that left ventricular assistance reduces myofiber stress in the left ventricle and, to a lesser extent, right ventricle free wall, while increasing leftward septal-shift with increased operating-speeds. These effects were achieved with secondary, potentially negative effects on the interventricular septum which showed that support from LVADs, introduces unnatural bending of the septum and with it, increased localized stress regions. Left ventricular assistance unloads the left ventricle significantly and shifts the right ventricular pressure-volume-loop toward larger volumes and higher pressures; a consequence of left-to-right ventricular interactions and a leftward septal shift. The methods and results described in the present study are a meaningful advancement of computational efforts to investigate heart-failure therapies in silico and illustrate the potential of computational models to aid understanding of complex mechanical and hemodynamic effects of new therapies.

Effects of Leaflet Design on Transvalvular Gradients of Bioprosthetic Heart Valves.

Bioprosthetic aortic valves (BAVs) are becoming the prostheses of choice in heart valve replacement. The objective of this paper is to assess the effects of leaflet geometry on the mechanics and hemodynamics of BAVs in a fluid structure interaction model. The curvature and angle of leaflets were varied in 10 case studies whereby the following design parameters were altered: a circular arch, a line, and a parabola for the radial curvature, and a circular arch, a spline, and a parabola for the circumferential curvature. Six different leaflet angles (representative of the inclination of the leaflets toward the surrounding aortic wall) were analyzed. The 3-dimensional geometry of the models were created using SolidWorks, Pointwise was used for meshing, and Comsol Multiphysics was used for implicit finite element calculations. Realistic loading was enforced by considering the time-dependent strongly-coupled interaction between blood flow and leaflets. Higher mean pressure gradients as well as von Mises stresses were obtained with a parabolic or circular curvature for radial curvature or a parabolic or spline curvature for the circumferential curvature. A smaller leaflet angle was associated with a lower pressure gradient, and, a lower von Mises stress. The leaflet curvature and angle noticeably affected the speed of valve opening, and closing. When a parabola was used for circumferential or radial curvature, leaflets displacements were asymmetric, and they opened and closed more slowly. A circular circumferential leaflet curvature, a linear leaflet radial curvature, and leaflet inclination toward the surrounding aortic wall were associated with superior BAVs mechanics.

Focal cartilage defect compromises fluid-pressure dependent load support in the knee joint.

A focal cartilage defect involves tissue loss or rupture. Altered mechanics in the affected joint may play an essential role in the onset and progression of osteoarthritis. The objective of the present study was to determine the compromised load support in the human knee joint during defect progression from the cartilage surface to the cartilage-bone interface. Ten normal and defect cases were simulated with a previously tested 3D finite element model of the knee. The focal defects were considered in both condyles within high load-bearing regions. Fluid pressurization, anisotropic fibril-reinforcement, and depth-dependent mechanical properties were considered for the articular cartilages and menisci. The results showed that a small cartilage defect could cause 25% reduction in the load support of the knee joint due to a reduced capacity of fluid pressurization in the defect cartilage. A partial-thickness defect could cause a fluid pressure decrease or increase in the remaining underlying cartilage depending on the defect depth. A cartilage defect also increased the shear strain at the cartilage-bone interface, which was more significant with a full-thickness defect. The effect of cartilage defect on the fluid pressurization also depended on the defect sites and contact conditions. In conclusion, a focal cartilage defect causes a fluid-pressure dependent load reallocation and a compromised load support in the joint, which depend on the defect depth, site, and contact condition.

Effects of mass and momentum of inertia alternation on individual muscle forces during swing phase of transtibial amputee gait.

A computer simulation was carried out to investigate the forces of lower extremity muscles in the swing phase of a transtibial amputee gait. With each muscle as an ideal force generator, the lower extremity was simulated as a two-degrees of freedom linkage with the hip and knee as its joints. Kinematic data of hip and knee joints were recorded by a motion analysis system. Through a static optimization approach, the forces exerted by muscles were determined so that recorded hip and knee joint angles were produced. Simulation results showed that when the mass of prosthetic foot is increased, muscle forces increase, too. This result is in accord with experimental and theoretical studies that reported an increase in leg mass lead to higher electromyography activity of muscles, and energetic of walking. However, since prosthetic foot moment of inertia is smaller than that of thigh and prosthetic shank, its alternation does not have noticeable effect on muscle forces.

A computer simulation of blood flow in arterial networks, including blood non-newtonian models and arterial stenosis.

The goals of this research are: 1. To construct a software that can determine pressure and flow at different points of an arbitrary arterial network; 2. To investigate the effect of non-Newtonian model on pressure and flow waves in comparison with Newtonian model. The main assumptions in our physical model are: 1- Blood flow is one dimensional and in axial direction; 2- Arteries are elastic cylindrical tubes; 3-Blood flow is laminar. The method of analysis is finite element technique. Three element types have been used: 1- Artery element for an unobstructed healthy artery, 2- Branch element for three or more artery element connections and 3- Stenosis element for an artery stenosis. Arterioles and capillary beds at the ends of arteries have been electrically modeled as a "developed Windkessel model" that includes a capacitance and a resistance in series and a resistance parallel with them. The numerical solvers were written in C++ computer language.