Transmural left ventricular mechanics underlying torsional recoil during relaxation

Early relaxation in the cardiac cycle is characterized by rapid torsional recoil of the left ventricular (LV) wall. To elucidate the contribution of the transmural arrangement of the myofiber to relaxation, we determined the time course of three-dimensional fiber-sheet strains in the anterior wall of five adult mongrel dogs in vivo during early relaxation with biplane cineangiography (125 Hz) of implanted transmural markers. Fiber-sheet strains were found from transmural fiber and sheet orientations directly measured in the heart tissue. The strain time course was determined during early relaxation in the epicardial, midwall, and endocardial layers referenced to the end-diastolic configuration. During early relaxation, significant circumferential stretch, wall thinning, and in-plane and transverse shear were observed (P < 0.05). We also observed significant stretch along myofibers in the epicardial layers and sheet shortening and shear in the endocardial layers (P < 0.01). Importantly, predominant epicardial stretch along the fiber direction and endocardial sheet shortening occurred during isovolumic relaxation (P < 0.05). We conclude that the LV mechanics during early relaxation involves substantial deformation of fiber and sheet structures with significant transmural heterogeneity. Predominant epicardial stretch along myofibers during isovolumic relaxation appears to drive global torsional recoil to aid early diastolic filling.     

Importance of material parameters and strain energy function on the wall stresses in the left ventricle

Patient-specific estimates of the stress distribution in the left ventricles (LV) may have important applications for therapy planning, but computing the stress generally requires knowledge of the material behaviour. The passive stress-strain relation of myocardial tissue has been characterized by a number of models, but material parameters (MPs) remain difficult to estimate. The aim of this study is to implement a zero-pressure algorithm to reconstruct numerically the stress distribution in the LV without precise knowledge of MPs. We investigate the sensitivity of the stress distribution to variations in the different sets of constitutive parameters. We show that the sensitivity of the LV stresses to MPs can be marginal for an isotropic constitutive model. However, when using a transversely isotropic exponential strain energy function, the LV stresses become sensitive to MPs, especially to the linear elastic coefficient before the exponential function. This indicates that in-vivo identification efforts should focus mostly on this MP for the development of patient-specific finite-element analysis.     

Transmural mechanics at left ventricular epicardial pacing site

Left ventricular (LV) epicardial pacing acutely reduces wall thickening at the pacing site. Because LV epicardial pacing also reduces transverse shear deformation, which is related to myocardial sheet shear, we hypothesized that impaired end-systolic wall thickening at the pacing site is due to reduction in myocardial sheet shear deformation, resulting in a reduced contribution of sheet shear to wall thickening. We also hypothesized that epicardial pacing would reverse the transmural mechanical activation sequence and thereby mitigate normal transmural deformation. To test these hypotheses, we investigated the effects of LV epicardial pacing on transmural fiber-sheet mechanics by determining three-dimensional finite deformation during normal atrioventricular conduction and LV epicardial pacing in the anterior wall of normal dog hearts in vivo. Our measurements indicate that impaired end-systolic wall thickening at the pacing site was not due to selective reduction of sheet shear, but rather resulted from overall depression of fiber-sheet deformation, and relative contributions of sheet strains to wall thickening were maintained. These findings suggest lack of effective end-systolic myocardial deformation at the pacing site, most likely because the pacing site initiates contraction significantly earlier than the rest of the ventricle. Epicardial pacing also induced reversal of the transmural mechanical activation sequence, which depressed sheet extension and wall thickening early in the cardiac cycle, whereas transverse shear and sheet shear deformation were not affected. These findings suggest that normal sheet extension and wall thickening immediately after activation may require normal transmural activation sequence, whereas sheet shear deformation may be determined by local anatomy.     

Modeling left ventricular dynamics with characteristic deformation modes

A computationally efficient method is described for simulating the dynamics of the left ventricle (LV) in three dimensions. LV motion is represented as a combination of a limited number of deformation modes, chosen to represent observed cardiac motions while conserving volume in the LV wall. The contribution of each mode to wall motion is determined by a corresponding time-dependent deformation variable. The principle of virtual work is applied to these deformation variables, yielding a system of ordinary differential equations for LV dynamics, including effects of muscle fiber orientations, active and passive stresses, and surface tractions. Passive stress is governed by a transversely isotropic elastic model. Active stress acts in the fiber direction and incorporates length–tension and force–velocity properties of cardiac muscle. Preload and afterload are represented by lumped vascular models. The variational equations and their numerical solutions are verified by comparison to analytic solutions of the strong form equations. Deformation modes are constructed using Fourier series with an arbitrary number of terms. Greater numbers of deformation modes increase deformable model resolution but at increased computational cost. Simulations of normal LV motion throughout the cardiac cycle are presented using models with 8, 23, or 46 deformation modes. Aggregate quantities that describe LV function vary little as the number of deformation modes is increased. Spatial distributions of stress and strain change as more deformation modes are included, but overall patterns are conserved. This approach yields three-dimensional simulations of the cardiac cycle on a clinically relevant time-scale.

     

Effects of using the unloaded configuration in predicting the in vivo diastolic properties of the heart

Computational models are increasingly being used to investigate the mechanical properties of cardiac tissue. While much insight has been gained from these studies, one important limitation associated with computational modeling arises when using in vivo images of the heart to generate the reference state of the model. An unloaded reference configuration is needed to accurately represent the deformation of the heart. However, it is rare for a beating heart to actually reach a zero-pressure state during the cardiac cycle. To overcome this, a computational technique was adapted to determine the unloaded configuration of an in vivo porcine left ventricle (LV). In the current study, in vivo measurements were acquired using magnetic resonance images (MRI) and synchronous pressure catheterization in the LV (N = 5). The overall goal was to quantify the effects of using early–diastolic filling as the reference configuration (common assumption used in modeling) versus using the unloaded reference configuration for predicting the in vivo properties of LV myocardium. This was accomplished by using optimization to minimize the difference between MRI measured and finite element predicted strains and cavity volumes. The results show that when using the unloaded reference configuration, the computational method predicts material properties for LV myocardium that are softer and less anisotropic than when using the early-diastolic filling reference configuration. This indicates that the choice of reference configuration could have a significant impact on capturing the realistic mechanical response of the heart.     

Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte

We present a three-dimensional computational study of whole-cell equilibrium shape and deformation of human red blood cell (RBC) using spectrin-level energetics. Random network models consisting of degree-2, 3, ..., 9 junction complexes and spectrin links are used to populate spherical and biconcave surfaces and intermediate shapes, and coarse-grained molecular dynamics simulations are then performed with spectrin connectivities fixed. A sphere is first filled with cytosol and gradually deflated while preserving its total surface area, until cytosol volume consistent with the real RBC is reached. The equilibrium shape is determined through energy minimization by assuming that the spectrin tetramer links satisfy the worm-like chain free-energy model. Subsequently, direct stretching by optical tweezers of the initial equilibrium shape is simulated to extract the variation of axial and transverse diameters with the stretch force. At persistence length p = 7.5 nm for the spectrin tetramer molecule and corresponding in-plane shear modulus mu(0) approximately 8.3 microN/m, our models show reasonable agreement with recent experimental measurements on the large deformation of RBC with optical tweezers. We find that the choice of the reference state used for the in-plane elastic energy is critical for determining the equilibrium shape. If a position-independent material reference state such as a full sphere is used in defining the in-plane energy, then the bending modulus kappa needs to be at least a decade larger than the widely accepted value of 2 x 10(-19) J to stabilize the biconcave shape against the cup shape. We demonstrate through detailed computations that this paradox can be avoided by invoking the physical hypothesis that the spectrin network undergoes constant remodeling to always relax the in-plane shear elastic energy to zero at any macroscopic shape, at some slow characteristic timescale. We have devised and implemented a liquefied network structure evolution algorithm that relaxes shear stress everywhere in the network and generates cytoskeleton structures that mimic experimental observations.     

Automatic registration of MRI-based joint models to high-speed biplanar radiographs for precise quantification of in vivo anterior cruciate ligament deformation during gait

Understanding in vivo joint mechanics during dynamic activity is crucial for revealing mechanisms of injury and disease development. To this end, laboratories have utilized computed tomography (CT) to create 3-dimensional (3D) models of bone, which are then registered to high-speed biplanar radiographic data captured during movement in order to measure in vivo joint kinematics. In the present study, we describe a system for measuring dynamic joint mechanics using 3D surface models of the joint created from magnetic resonance imaging (MRI) registered to high-speed biplanar radiographs using a novel automatic registration algorithm. The use of MRI allows for modeling of both bony and soft tissue structures. Specifically, the attachment site footprints of the anterior cruciate ligament (ACL) on the femur and tibia can be modeled, allowing for measurement of dynamic ACL deformation. In the present study, we demonstrate the precision of this system by tracking the motion of a cadaveric porcine knee joint. We then utilize this system to quantify in vivo ACL deformation during gait in four healthy volunteers.     

Sodium current abnormalities and deregulation of Wnt/β-catenin signaling in iPSC-derived cardiomyocytes generated from patient with arrhythmogenic cardiomyopathy harboring compound genetic variants in plakophilin 2 gene

BackgroundMutations in desmosomal genes linked to arrhythmogenic cardiomyopathy are commonly associated with Wnt/β-catenin signaling abnormalities and reduction of the sodium current density. Inhibitors of GSK3B were reported to restore sodium current and improve heart function in various arrhythmogenic cardiomyopathy models, but mechanisms underlying this effect remain unclear. We hypothesized that there is a crosstalk between desmosomal proteins, signaling pathways, and cardiac sodium channels.Methods and resultsTo reveal molecular mechanisms of arrhythmogenic cardiomyopathy, we established human iPSC-based model of this pathology. iPSC-derived cardiomyocytes from patient carrying two genetic variants in PKP2 gene demonstrated that PKP2 haploinsufficiency due to frameshift variant, in combination with the missense variant expressed from the second allele, was associated with decreased Wnt/β-catenin activity and reduced sodium current. Different approaches were tested to restore impaired cardiomyocytes functions, including wild type PKP2 transduction, GSK3B inhibition and Wnt/β-catenin signaling modulation. Inhibition of GSK3B led to the restoration of both Wnt/β-catenin signaling activity and sodium current density in patient-specific cardiomyocytes while GSK3B activation led to the reduction of sodium current density. Moreover, we found that upon inhibition GSK3B sodium current was restored through Wnt/β-catenin-independent mechanism.ConclusionWe propose that alterations in GSK3B-Wnt/β-catenin signaling pathways lead to regulation of sodium current implying its role in molecular pathogenesis of arrhythmogenic cardiomyopathy.     

In Vivo Human Left-to-Right Ventricular Differences in Rate Adaptation Transiently Increase Pro-Arrhythmic Risk following Rate Acceleration

Left-to-right ventricular (LV/RV) differences in repolarization have been implicated in lethal arrhythmias in animal models. Our goal is to quantify LV/RV differences in action potential duration (APD) and APD rate adaptation and their contribution to arrhythmogenic substrates in the in vivo human heart using combined in vivo and in silico studies. Electrograms were acquired from 10 LV and 10 RV endocardial sites in 15 patients with normal ventricles. APD and APD adaptation were measured during an increase in heart rate. Analysis of in vivo electrograms revealed longer APD in LV than RV (207.8±21.5 vs 196.7±20.1 ms; P<0.05), and slower APD adaptation in LV than RV (time constant τ^s = 47.0±14.3 vs 35.6±6.5 s; P<0.05). Following rate acceleration, LV/RV APD dispersion experienced an increase of up to 91% in 12 patients, showing a strong correlation (r² = 0.90) with both initial dispersion and LV/RV difference in slow adaptation. Pro-arrhythmic implications of measured LV/RV functional differences were studied using in silico simulations. Results show that LV/RV APD and APD adaptation heterogeneities promote unidirectional block following rate acceleration, albeit being insufficient for establishment of reentry in normal hearts. However, in the presence of an ischemic region at the LV/RV junction, LV/RV heterogeneity in APD and APD rate adaptation promotes reentrant activity and its degeneration into fibrillatory activity. Our results suggest that LV/RV heterogeneities in APD adaptation cause a transient increase in APD dispersion in the human ventricles following rate acceleration, which promotes unidirectional block and wave-break at the LV/RV junction, and may potentiate the arrhythmogenic substrate, particularly in patients with ischemic heart disease.     

Changes in left ventricular geometry during spontaneous breathing

The purpose of these experiments was to determine the effects of a spontaneously generated inspiration on the size and shape of the left ventricle (LV) in anesthetized supine dogs. We implanted markers in the LV to establish three perpendicular axes and recorded the motion of these markers using biplane cinefluoroscopy at 60 Hz. The primary changes in LV size that accompanied inspiration occurred at end diastole (ED). The largest change in LVED dimension was a 2.46-mm narrowing of the septal-lateral wall dimension, but the apex-base dimension decreased also, by 0.74 mm. The anteroposterior dimension actually widened by 1.07 mm. The septal-lateral narrowing was caused by both a 1.0-mm narrowing of the distance between the septal marker and the apex-base axis, as well as by a 1.4-mm narrowing between the apex-base axis and the lateral wall marker. Narrowing of the septal portion seemed expected because of presumed enhanced right ventricular filling during inspiration. Narrowing of the lateral portion of the LV, while the anteroposterior dimension widened, was surprising because a change in LVEDV shape is implied. Assuming ventricular homogeneity, this change in LVED shape implies that the forces applied to the epicardial surface were not uniform. There must have been a retraction on the anterior and posterior surface that was not experienced by the lateral LV wall. The net effect of these dimensional changes of the LV at end diastole (estimated from the product of the three ED axes) was a 3.5-cm3 reduction in LVED volume.(ABSTRACT TRUNCATED AT 250 WORDS)     

Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations

Patient-specific simulations of heart (dys)function aimed at personalizing cardiac therapy are hampered by the absence of in vivo imaging technology for clinically acquiring myocardial fiber orientations. The objective of this project was to develop a methodology to estimate cardiac fiber orientations from in vivo images of patient heart geometries. An accurate representation of ventricular geometry and fiber orientations was reconstructed, respectively, from high-resolution ex vivo structural magnetic resonance (MR) and diffusion tensor (DT) MR images of a normal human heart, referred to as the atlas. Ventricular geometry of a patient heart was extracted, via semiautomatic segmentation, from an in vivo computed tomography (CT) image. Using image transformation algorithms, the atlas ventricular geometry was deformed to match that of the patient. Finally, the deformation field was applied to the atlas fiber orientations to obtain an estimate of patient fiber orientations. The accuracy of the fiber estimates was assessed using six normal and three failing canine hearts. The mean absolute difference between inclination angles of acquired and estimated fiber orientations was 15.4 °. Computational simulations of ventricular activation maps and pseudo-ECGs in sinus rhythm and ventricular tachycardia indicated that there are no significant differences between estimated and acquired fiber orientations at a clinically observable level.The new insights obtained from the project will pave the way for the development of patient-specific models of the heart that can aid physicians in personalized diagnosis and decisions regarding electrophysiological interventions.     

Signaling via the Tgf-beta type I receptor Alk5 in heart development

Trophic factors secreted both from the endocardium and epicardium regulate appropriate growth of the myocardium during cardiac development. Epicardially-derived cells play also a key role in development of the coronary vasculature. This process involves transformation of epithelial (epicardial) cells to mesenchymal cells (EMT). Similarly, a subset of endocardial cells undergoes EMT to form the mesenchyme of endocardial cushions, which function as primordia for developing valves and septa. While it has been suggested that transforming growth factor-βs (Tgf-β) play an important role in induction of EMT in the avian epi- and endocardium, the function of Tgf-βs in corresponding mammalian tissues is still poorly understood. In this study, we have ablated the Tgf-β type I receptor Alk5 in endo-, myo- and epicardial lineages using the Tie2-Cre, Nkx2.5-Cre, and Gata5-Cre driver lines, respectively. We show that while Alk5-mediated signaling does not play a major role in the myocardium during mouse cardiac development, it is critically important in the endocardium for induction of EMT both in vitro and in vivo. Moreover, loss of epicardial Alk5-mediated signaling leads to disruption of cell-cell interactions between the epicardium and myocardium resulting in a thinned myocardium. Furthermore, epicardial cells lacking Alk5 fail to undergo Tgf-β-induced EMT in vitro. Late term mutant embryos lacking epicardial Alk5 display defective formation of a smooth muscle cell layer around coronary arteries, and aberrant formation of capillary vessels in the myocardium suggesting that Alk5 is controlling vascular homeostasis during cardiogenesis. To conclude, Tgf-β signaling via Alk5 is not required in myocardial cells during mammalian cardiac development, but plays an irreplaceable cell-autonomous role regulating cellular communication, differentiation and proliferation in endocardial and epicardial cells.     

Right and left ventricular wall deformation patterns in normal and left heart hypoplasia chick embryos

The vertebrate embryonic ventricle transforms from a smooth-walled single tube to trabeculated right ventricular (RV) and left ventricular (LV) chambers during cardiovascular morphogenesis. We hypothesized that ventricular contraction patterns change from globally isotropic to chamber-specific anisotropic patterns during normal morphogenesis and that these deformation patterns are influenced by experimentally altered mechanical load produced by chronic left atrial ligation (LAL). We measured epicardial RV and LV wall strains during normal development and left heart hypoplasia produced by LAL in Hamburger-Hamilton stage 21, 24, 27, and 31 chick embryos. Normal RV contracted isotropically until stage 24 and then contracted preferentially in the circumferential direction. Normal LV contracted isotropically at stage 21, preferentially in the longitudinal direction at stages 24 and 27, and then in the circumferential direction at stage 31. LAL altered both RV and LV strain patterns, accelerated the onset of preferential RV circumferential strain patterns, and abolished preferential LV longitudinal strain (P < 0.05 vs. normal). Mature patterns of anisotropic RV and LV deformation develop coincidentally with morphogenesis, and changes in these deformation patterns reflect altered cardiovascular function and/or morphogenesis.     

A novel methodology for generating 3D finite element models of the hip from 2D radiographs

Finite element (FE) modelling has been proposed as a tool for estimating fracture risk and patient-specific FE models are commonly based on computed tomography (CT). Here, we present a novel method to automatically create personalised 3D models from standard 2D hip radiographs. A set of geometrical parameters of the femur were determined from seven a–p hip radiographs and compared to the 3D femoral shape obtained from CT as training material; the error in reconstructing the 3D model from the 2D radiographs was assessed. Using the geometry parameters as the input, the 3D shape of another 21 femora was built and meshed, separating a cortical and trabecular compartment. The material properties were derived from the homogeneity index assessed by texture analysis of the radiographs, with focus on the principal tensile and compressive trabecular systems. The ability of these FE models to predict failure load as determined by experimental biomechanical testing was evaluated and compared to the predictive ability of DXA. The average reconstruction error of the 3D models was 1.77 mm (±1.17 mm), with the error being smallest in the femoral head and neck, and greatest in the trochanter. The correlation of the FE predicted failure load with the experimental failure load was r²=64% for the reconstruction FE model, which was significantly better (p<0.05) than that for DXA (r²=24%). This novel method for automatically constructing a patient-specific 3D finite element model from standard 2D radiographs shows encouraging results in estimating patient-specific failure loads.     

Patient-Specific Artery Shrinkage and 3D Zero-Stress State in Multi-Component 3D FSI Models for Carotid Atherosclerotic Plaques Based on <i>In Vivo</i> MRI Data

Image-based computational models for atherosclerotic plaques have been developed to perform mechanical analysis to quantify critical flow and stress/strain conditions related to plaque rupture which often leads directly to heart attack or stroke. An important modeling issue is how to determine zero stress state from in vivo plaque geometries. This paper presents a method to quantify human carotid artery axial and inner circumferential shrinkages by using patient-specific ex vivo and in vivo MRI images. A shrink-stretch process based on patient-specific in vivo plaque morphology and shrinkage data was introduced to shrink the in vivo geometry first to find the zero-stress state (opening angle was ignored to reduce the complexity), and then stretch and pressurize to recover the in vivo plaque geometry with computed initial stress, strain, flow pressure and velocity conditions. Effects of the shrink-stretch process on plaque stress/strain distributions were demonstrated based on patient-specific data using 3D models with fluid-structure interactions (FSI). The average artery axial and inner circumferential shrinkages were 25% and 7.9%, respectively, based on a data set obtained from 10 patients. Maximum values of maximum principal stress and strain increased 349.8% and 249% respectively with 33% axial stretch. Influence of inner circumferential shrinkage (7.9%) was not very noticeable under 33% axial stretch, but became more noticeable under smaller axial stretch. Our results indicated that accurate knowledge of artery shrinkages and the shrink-stretch process will considerably improve the accuracy of computational predictions made based on results from those in vivo MRI-based FSI models.     

Left ventricular endocardial or triventricular pacing to optimize cardiac resynchronization therapy in a chronic canine model of ischemic heart failure

Cardiac resynchronization therapy (CRT) is a proven treatment for heart failure but ~30% of patients appear to not benefit from the therapy. Left ventricular (LV) endocardial and multisite epicardial [triventricular (TriV)] pacing have been proposed as alternatives to traditional LV transvenous epicardial pacing, but no study has directly compared the hemodynamic effects of these approaches. Left bundle branch block ablation and repeated microembolizations were performed in dogs to induce electrical dysynchrony and to reduce LV ejection fraction to <35%. LVdP/dt(max) and other hemodynamic indexes were measured with a conductance catheter during LV epicardial, LV endocardial, biventricular (BiV) epicardial, BiV endocardial, and TriV pacing performed at three atrioventricular delays. LV endocardial pacing was obtained with a clinically available pacing system. The optimal site was defined as the site that increased dP/dt(max) by the largest percentage. Implantation of the endocardial lead was feasible in all canines (n = 8) without increased mitral regurgitation seen with transesophageal echocardiography and with full access to the different LV endocardial pacing sites. BiV endocardial pacing increased dP/dt(max) more than BiV epicardial and TriV pacing on average (P < 0.01) and at the optimal site (P < 0.01). There were no significant differences between BiV epicardial and TriV pacing. BiV endocardial pacing was superior to BiV epicardial and to TriV pacing in terms of acute hemodynamic response. Further investigation is needed to confirm the chronic benefit of this approach in humans.     

Three-dimensional systolic kinematics of the right ventricle

The right ventricle (RV) of the heart is responsible for pumping blood to the lungs. Its kinematics are not as well understood as that of the left ventricle (LV) due to its thin wall and asymmetric geometry. In this study, the combination of tagged MRI and three-dimensional (3-D) image-processing techniques was used to reconstruct 3-D RV-LV motion and deformation. The reconstructed models were used to quantify the 3-D global and local deformation of the ventricles in a set of normal subjects. When compared with the LV, the RV exhibited a similar twisting pattern, a more longitudinal strain pattern, and a greater amount of displacement.     

Identification of in vivo material and geometric parameters of a human aorta: toward patient-specific modeling of abdominal aortic aneurysm

Recent advances in computational modeling of vascular adaptations and the need for their extension to patient-specific modeling have introduced new challenges to the path toward abdominal aortic aneurysm modeling. First, the fundamental assumption in adaptation models, namely the existence of vascular homeostasis in normal vessels, is not easy to implement in a vessel model built from medical images. Second, subjecting the vessel wall model to the normal pressure often makes the configuration deviate from the original geometry obtained from medical images. To address those technical challenges, in this work, we propose a two-step optimization approach; first, we estimate constitutive parameters of a healthy human aorta intrinsic to the material by using biaxial test data and a weighted nonlinear least-squares parameter estimation method; second, we estimate the distributions of wall thickness and anisotropy using a 2-D parameterization of the vessel wall surface and a global approximation scheme integrated within an optimization routine. A direct search method is implemented to solve the optimization problem. The numerical optimization method results in a considerable improvement in both satisfying homeostatic condition and minimizing the deviation of geometry from the original shape based on in vivo images. Finally, the utility of the proposed technique for patient-specific modeling is demonstrated in a simulation of an abdominal aortic aneurysm enlargement.