Torsion of the human left ventricle: experimental analysis and computational modeling

Simulating the effect of sodium channel blockage on cardiac electromechanics

There is growing interest to better understand drug-induced cardiovascular complications and to predict undesirable side effects at as early a stage in the drug development process as possible. The purpose of this paper is to investigate computationally the influence of sodium ion channel blockage on cardiac electromechanics. To do so, we implement a myofiber orientation dependent passive stress model (Holzapfel-Ogden) in the multiphysics solver Chaste to simulate an imaged physiological model of the human ventricles. A dosage of a sodium channel blocker was then applied and its inhibitory effects on the electrical propagation across ventricles were modeled. We employ the Kerckhoffs active stress model to generate electrically excited contractile behavior of myofibers. Our predictions indicate that a delay in the electrical activation of ventricular tissue caused by the sodium channel blockage translates to a delay in the mechanical biomarkers that were investigated. Moreover, sodium channel blockage was found to increase left ventricular twist. A multiphysics computational framework from the cell level to the organ level was thus used to predict the effect of sodium channel blocking drugs on cardiac electromechanics.

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

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

Improved identifiability of myocardial material parameters by an energy-based cost function

Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were [Formula: see text] and [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]) for the HF cases and [Formula: see text] and [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]) for the healthy case.

Improved identifiability of myocardial material parameters by an energy-based cost function

Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were [Formula: see text] and [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]) for the HF cases and [Formula: see text] and [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]) for the healthy case.

Modeling and simulation of fish swimming with active muscles

Our goal is to reproduce the key features of carangiform swimming by modeling muscle functioning using the notion of active distortions, thus emphasizing the kinematical role of muscle, the generation of movement, rather than the dynamical one, the production of force. This approach, already proposed to model the action of muscles in different contexts, is here tested again for the problem of developing an effective and reliable framework to model and simulate swimming. A proper undulatory movement of a fish-like body is reproduced by defining a pattern of distortions, tuned in both space and time, meant to model the muscles activation which produce the flexural motion of body fish; eventually, interactions with the surrounding water yields the desired thrust. Carangiform swimmers have a relatively inflexible anterior body section and a generally flat, flexible posterior section. Because of this configuration, undulations sent rearward along the body attain a significant amplitude only in the posterior section. We compare the performances of different swimming gaits, and we are able to find some important relations between key parameters such as frequencies, wavelength, tail amplitude, and the achieved swim velocity, or the generated thrust, which summarize the swimming performance. In particular, an interesting relation is found between the Strouhal number and the wavelength of muscles activation. We highlight the muscle function during fish locomotion describing the activation of muscles and the relation between the force production and the shortening-lengthening cycle of muscle. We found a great accordance between results and empirical relations, giving an implicit validation of our models.

A new 4D trajectory-based approach unveils abnormal LV revolution dynamics in hypertrophic cardiomyopathy

The assessment of left ventricular shape changes during cardiac revolution may be a new step in clinical cardiology to ease early diagnosis and treatment. To quantify these changes, only point registration was adopted and neither Generalized Procrustes Analysis nor Principal Component Analysis were applied as we did previously to study a group of healthy subjects. Here, we extend to patients affected by hypertrophic cardiomyopathy the original approach and preliminarily include genotype positive/phenotype negative individuals to explore the potential that incumbent pathology might also be detected. Using 3D Speckle Tracking Echocardiography, we recorded left ventricular shape of 48 healthy subjects, 24 patients affected by hypertrophic cardiomyopathy and 3 genotype positive/phenotype negative individuals. We then applied Generalized Procrustes Analysis and Principal Component Analysis and inter-individual differences were cleaned by Parallel Transport performed on the tangent space, along the horizontal geodesic, between the per-subject consensuses and the grand mean. Endocardial and epicardial layers were evaluated separately, different from many ecocardiographic applications. Under a common Principal Component Analysis, we then evaluated left ventricle morphological changes (at both layers) explained by first Principal Component scores. Trajectories' shape and orientation were investigated and contrasted. Logistic regression and Receiver Operating Characteristic curves were used to compare these morphometric indicators with traditional 3D Speckle Tracking Echocardiography global parameters. Geometric morphometrics indicators performed better than 3D Speckle Tracking Echocardiography global parameters in recognizing pathology both in systole and diastole. Genotype positive/phenotype negative individuals clustered with patients affected by hypertrophic cardiomyopathy during diastole, suggesting that incumbent pathology may indeed be foreseen by these methods. Left ventricle deformation in patients affected by hypertrophic cardiomyopathy compared to healthy subjects may be assessed by modern shape analysis better than by traditional 3D Speckle Tracking Echocardiography global parameters. Hypertrophic cardiomyopathy pathophysiology was unveiled in a new manner whereby also diastolic phase abnormalities are evident which is more difficult to investigate by traditional ecocardiographic techniques.

Active contraction of the cardiac ventricle and distortion of the microstructural architecture

The shortening of the myocardial fibers is the microstructural engine that produces the contraction of the cardiac muscle. The complex interplay between fibers shortening and elastic macroscopic strain is functional to the ejection of blood into the pulmonary and arterial networks. Here, we address the contraction of the left ventricle in a finite elasticity framework, adopting the 'prolate ellipsoid' geometry and the invariants-based strain energy proposed by Holzapfel and Ogden, where the mechanical role of fibers and sheets is accounted for. We show that a microstructurally motivated mathematical model of active strain type reproduces the main indicators of normal cardiac function along the whole PV-loop without introduction of any further ad hoc law. The bare-bones mathematical model depends on one measurable parameter only, that is, the shortening ratio of the sarcomere units, which we assume to be nearly independent on the prestretch. Strict enforcement of incompressibility and novel treatment of boundary conditions are shown to be crucial to simulate the correct muscle torsion.

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.

4D-analysis of left ventricular heart cycle using procrustes motion analysis

The aim of this study is to investigate human left ventricular heart morphological changes in time among 17 healthy subjects. Preliminarily, 2 patients with volumetric overload due to aortic insufficiency were added to our analyses. We propose a special strategy to compare the shape, orientation and size of cardiac cycle's morphological trajectories in time. We used 3D data obtained by Speckle Tracking Echocardiography in order to detect semi-automated and homologous landmarks clouds as proxies of left ventricular heart morphology. An extended Geometric Morphometrics toolkit in order to distinguish between intra- and inter-individual shape variations was used. Shape of trajectories with inter-individual variation were compared under the assumption that trajectories attributes, estimated at electrophysiologically homologous times are expressions of left ventricular heart function. We found that shape analysis as commonly applied in Geometric Morphometrics studies fails in identifying a proper morpho-space to compare the shape of morphological trajectories in time. To overcome this problem, we performed a special type of Riemannian Parallel Transport, called "linear shift". Whereas the two patients with aortic insufficiency were not differentiated in the static shape analysis from the healthy subjects, they set apart significantly in the analyses of motion trajectory's shape and orientation. We found that in healthy subjects, the variations due to inter-individual morphological differences were not related to shape and orientation of morphological trajectories. Principal Component Analysis showed that volumetric contraction, torsion and twist are differently distributed on different axes. Moreover, global shape change appeared to be more correlated with endocardial shape change than with the epicardial one. Finally, the total shape variation occurring among different subjects was significantly larger than that observable across properly defined morphological trajectories.

An inverse finite element method for determining the tissue compressibility of human left ventricular wall during the cardiac cycle

The determination of the myocardium's tissue properties is important in constructing functional finite element (FE) models of the human heart. To obtain accurate properties especially for functional modeling of a heart, tissue properties have to be determined in vivo. At present, there are only few in vivo methods that can be applied to characterize the internal myocardium tissue mechanics. This work introduced and evaluated an FE inverse method to determine the myocardial tissue compressibility. Specifically, it combined an inverse FE method with the experimentally-measured left ventricular (LV) internal cavity pressure and volume versus time curves. Results indicated that the FE inverse method showed good correlation between LV repolarization and the variations in the myocardium tissue bulk modulus K (K = 1/compressibility), as well as provided an ability to describe in vivo human myocardium material behavior. The myocardium bulk modulus can be effectively used as a diagnostic tool of the heart ejection fraction. The model developed is proved to be robust and efficient. It offers a new perspective and means to the study of living-myocardium tissue properties, as it shows the variation of the bulk modulus throughout the cardiac cycle.

Evaluation of the strain-line patterns in a human left ventricle: a simulation study

The aim of this paper is to emphasise the role of the primary strain-line patterns in a human left ventricle (LV) within the complex system that is the heart. In particular, a protocol is proposed for the measurement of the principal strain lines (PSL) in the walls of the LV; this protocol is tested by means of a computational model which resembles a human LV. When the analysis is focused on the epicardial surface, PSL can be used to derive information on the directions of muscle fibres during the entire cardiac cycle, not only the systolic phase.

Myosin light chain phosphorylation is critical for adaptation to cardiac stress

BACKGROUND

Cardiac hypertrophy is a common response to circulatory or neurohumoral stressors as a mechanism to augment contractility. When the heart is under sustained stress, the hypertrophic response can evolve into decompensated heart failure, although the mechanism(s) underlying this transition remain largely unknown. Because phosphorylation of cardiac myosin light chain 2 (MLC2v), bound to myosin at the head-rod junction, facilitates actin-myosin interactions and enhances contractility, we hypothesized that phosphorylation of MLC2v plays a role in the adaptation of the heart to stress. We previously identified an enzyme that predominantly phosphorylates MLC2v in cardiomyocytes, cardiac myosin light-chain kinase (cMLCK), yet the role(s) played by cMLCK in regulating cardiac function in health and disease remain to be determined.

METHODS AND RESULTS

We found that pressure overload induced by transaortic constriction in wild-type mice reduced phosphorylated MLC2v levels by ≈40% and cMLCK levels by ≈85%. To examine how a reduction in cMLCK and the corresponding reduction in phosphorylated MLC2v affect function, we generated Mylk3 gene-targeted mice and transgenic mice overexpressing cMLCK specifically in cardiomyocytes. Pressure overload led to severe heart failure in cMLCK knockout mice but not in mice with cMLCK overexpression in which cMLCK protein synthesis exceeded degradation. The reduction in cMLCK protein during pressure overload was attenuated by inhibition of ubiquitin-proteasome protein degradation systems.

CONCLUSIONS

Our results suggest the novel idea that accelerated cMLCK protein turnover by the ubiquitin-proteasome system underlies the transition from compensated hypertrophy to decompensated heart failure as a result of reduced phosphorylation of MLC2v.

Orthotropic active strain models for the numerical simulation of cardiac biomechanics

A model for the active deformation of cardiac tissue considering orthotropic constitutive laws is introduced and studied. In particular, the passive mechanical properties of the myocardium are described by the Holzapfel-Ogden relation, whereas the activation model is based on the concept of active strain. There, an incompatible intermediate configuration is considered, which entails a multiplicative decomposition between active and passive deformation gradients. The underlying Euler-Lagrange equations for minimizing the total energy are written in terms of these deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiomyocytes. The active strain formulation is compared with the classical active stress model from both numerical and modeling perspectives. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed, and different mechanical activation functions are considered. Taylor-Hood and MINI finite elements are used in the discretization of the overall mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main features of the phenomenon, while allowing savings in computational costs.

Patient-specific modeling of dyssynchronous heart failure: a case study

The development and clinical use of patient-specific models of the heart is now a feasible goal. Models have the potential to aid in diagnosis and support decision-making in clinical cardiology. Several groups are now working on developing multi-scale models of the heart for understanding therapeutic mechanisms and better predicting clinical outcomes of interventions such as cardiac resynchronization therapy. Here we describe the methodology for generating a patient-specific model of the failing heart with a myocardial infarct and left ventricular bundle branch block. We discuss some of the remaining challenges in developing reliable patient-specific models of cardiac electromechanical activity, and identify some of the main areas for focusing future research efforts. Key challenges include: efficiently generating accurate patient-specific geometric meshes and mapping regional myofiber architecture to them; modeling electrical activation patterns based on cellular alterations in human heart failure, and estimating regional tissue conductivities based on clinically available electrocardiographic recordings; estimating unloaded ventricular reference geometry and material properties for biomechanical simulations; and parameterizing systemic models of circulatory dynamics from available hemodynamic measurements.

Contribution of mechanical factors to arrhythmogenesis in calcium overloaded cardiomyocytes: model predictions and experiments

It is well-known that Ca²⁺ overload in cardiomyocytes may underlie arrhythmias. However, the possible contribution of mechanical factors to rhythm disturbances in Ca²⁺ overloaded myocytes has not been sufficiently investigated. We used a mathematical model of the electrical and mechanical activity of cardiomyocytes to reveal an essential role of the mechanisms of cardiac mechano-electric feedback in arrhythmogenesis in Ca²⁺ overloaded myocardium. In the model, the following mechanical factors increased Ca²⁺ overload in contracting cardiomyocytes and promoted rhythm disturbances: i) a decrease in the mechanical load for afterloaded contractions; and ii) a decrease in the initial length of sarcomeres for isometric twitches. In exact accordance with the model predictions, in experiments on papillary muscles from the right ventricle of guinea pigs with Ca²⁺ overloaded cardiomyocytes (using 0.5-1 μM of ouabain), we found that emergence of rhythm disturbances and extrasystoles depends on the mechanical conditions of muscle contraction.