Dependence of local left ventricular wall mechanics on myocardial fiber orientation: a model study

Multiscale fiber remodeling in the infarcted left ventricle using a stress-based reorientation law

The organization of myofibers and extra cellular matrix within the myocardium plays a significant role in defining cardiac function. When pathological events occur, such as myocardial infarction (MI), this organization can become disrupted, leading to degraded pumping performance. The current study proposes a multiscale finite element (FE) framework to determine realistic fiber distributions in the left ventricle (LV). This is achieved by implementing a stress-based fiber reorientation law, which seeks to align the fibers with local traction vectors, such that contractile force and load bearing capabilities are maximized. By utilizing the total stress (passive and active), both myofibers and collagen fibers are reoriented. Simulations are conducted to predict the baseline fiber configuration in a normal LV as well as the adverse fiber reorientation that occurs due to different size MIs. The baseline model successfully captures the transmural variation of helical fiber angles within the LV wall, as well as the transverse fiber angle variation from base to apex. In the models of MI, the patterns of fiber reorientation in the infarct, border zone, and remote regions closely align with previous experimental findings, with a significant increase in fibers oriented in a left-handed helical configuration and increased dispersion in the infarct region. Furthermore, the severity of fiber reorientation and impairment of pumping performance both showed a correlation with the size of the infarct. The proposed multiscale modeling framework allows for the effective prediction of adverse remodeling and offers the potential for assessing the effectiveness of therapeutic interventions in the future. STATEMENT OF SIGNIFICANCE: The organization of muscle and collagen fibers within the heart plays a significant role in defining cardiac function. This organization can become disrupted after a heart attack, leading to degraded pumping performance. In the current study, we implemented a stress-based fiber reorientation law into a computer model of the heart, which seeks to realign the fibers such that contractile force and load bearing capabilities are maximized. The primary goal was to evaluate the effects of different sized heart attacks. We observed substantial fiber remodeling in the heart, which matched experimental observations. The proposed computational framework allows for the effective prediction of adverse remodeling and offers the potential for assessing the effectiveness of therapeutic interventions in the future.

Review of cardiac-coronary interaction and insights from mathematical modeling

Cardiac-coronary interaction is fundamental to the function of the heart. As one of the highest metabolic organs in the body, the cardiac oxygen demand is met by blood perfusion through the coronary vasculature. The coronary vasculature is largely embedded within the myocardial tissue which is continually contracting and hence squeezing the blood vessels. The myocardium-coronary vessel interaction is two-ways and complex. Here, we review the different types of cardiac-coronary interactions with a focus on insights gained from mathematical models. Specifically, we will consider the following: (1) myocardial-vessel mechanical interaction; (2) metabolic-flow interaction and regulation; (3) perfusion-contraction matching, and (4) chronic interactions between the myocardium and coronary vasculature. We also provide a discussion of the relevant experimental and clinical studies of different types of cardiac-coronary interactions. Finally, we highlight knowledge gaps, key challenges, and limitations of existing mathematical models along with future research directions to understand the unique myocardium-coronary coupling in the heart. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Contractile Adaptation of the Left Ventricle Post-myocardial Infarction: Predictions by Rodent-Specific Computational Modeling

Myocardial infarction (MI) results in cardiac myocyte death and the formation of a fibrotic scar in the left ventricular free wall (LVFW). Following an acute MI, LVFW remodeling takes place consisting of several alterations in the structure and properties of cellular and extracellular components with a heterogeneous pattern across the LVFW. The normal function of the heart is strongly influenced by the passive and active biomechanical behavior of the LVFW, and progressive myocardial structural remodeling can have a detrimental effect on both diastolic and systolic functions of the LV leading to heart failure. Despite important advances in understanding LVFW passive remodeling in the setting of MI, heterogeneous remodeling in the LVFW active properties and its relationship to organ-level LV function remain understudied. To address these gaps, we developed high-fidelity finite-element (FE) rodent computational cardiac models (RCCMs) of MI using extensive datasets from MI rat hearts representing the heart remodeling from one-week (1-wk) to four-week (4-wk) post-MI timepoints. The rat-specific models (n = 2 for each timepoint) integrate detailed imaging data of the heart geometry, myocardial fiber architecture, and infarct zone determined using late gadolinium enhancement prior to terminal measurements. The computational models predicted a significantly higher level of active tension in remote myocardium in early post-MI hearts (1-wk post-MI) followed by a return to near the control level in late-stage MI (3- and 4-wk post-MI). The late-stage MI rats showed smaller myofiber ranges in the remote region and in-silico experiments using RCCMs suggested that the smaller fiber helicity is consistent with lower contractile forces needed to meet the measured ejection fractions in late-stage MI. In contrast, in-silico experiments predicted that collagen fiber transmural orientation in the infarct region has little influence on organ-level function. In addition, our MI RCCMs indicated that reduced and potentially positive circumferential strains in the infarct region at end-systole can be used to infer information about the time-varying properties of the infarct region. The detailed description of regional passive and active remodeling patterns can complement and enhance the traditional measures of LV anatomy and function that often lead to a gross and limited assessment of cardiac performance. The translation and implementation of our model in patient-specific organ-level simulations offer to advance the investigation of individualized prognosis and intervention for MI.

Oscillation of the orientation of cardiomyocyte aggregates in human left ventricle free wall

Orientation of local cardiomyocyte aggregates in the human left ventricle free wall experiences an oscillation in the laminar structure regions, besides its gradual change trend. We described this oscillation using five transmural samples imaged at the European Synchrotron Radiation Facility with an isotropic voxel size of 3.5 × 3.5 × 3.5 μm³ . In the reconstructed volume of each sample, we manually selected a region containing a regular laminar structure as the region of interest and measured the distribution of the orientation of local cardiomyocyte aggregates inside using a Fourier-based method. Then, we extracted the gradual change part of the orientation of cardiomyocyte aggregates with a three-dimensional centered Gaussian filter and measured the angle between the original orientation vector of local cardiomyocyte aggregates and its gradual change part. Further, we assessed the measured angles in different local coordinates. The results indicate that the oscillation amplitude of the orientation of cardiomyocyte aggregates is regional in the left ventricle wall, which may promote our understanding of the rearrangement mechanism of the cardiomyocyte aggregates and provide a new biomarker to study the heart physiological status.

SILICOFCM platform, multiscale modeling of left ventricle from echocardiographic images and drug influence for cardiomyopathy disease

BACKGROUND AND OBJECTIVE

In silico clinical trials are the future of medicine and virtual testing and simulation are the future of medical engineering. The use of a computational platform can reduce costs and time required for developing new models of medical devices and drugs. The computational platform, which is one of the main results of the SILICOFCM project, was developed using state-of-the-art finite element modeling for macro simulation of fluid-structure interaction with micro modeling at the molecular level for drug interaction with the cardiac cells. SILICOFCM platform is using for risk prediction and optimal drug therapy of familial cardiomyopathy in a specific patient.

METHODS

In order to obtain 3D image reconstruction, the U-net architecture was used to determine geometric parameters for the left ventricle which were extracted from the echocardiographic apical and M-mode views. A micro-mechanics cellular model which includes three kinetic processes of sarcomeric proteins interactions was developed. It allows simulation of the drugs which are divided into three major groups defined by the principal action of each drug. Fluid-solid coupling for the left ventricle was presented. A nonlinear material model of the heart wall that was developed by using constitutive curves which include the stress-strain relationship was used.

RESULTS

The results obtained with the parametric model of the left ventricle where pressure-volume (PV) diagrams depend on the change of Ca2+ were presented. It directly affects the ejection fraction. The presented approach with the variation of the left ventricle (LV) geometry and simulations which include the influence of different parameters on the PV diagrams are directly interlinked with drug effects on the heart function. It includes different drugs such as Entresto and Digoxin that directly affect the cardiac PV diagrams and ejection fraction.

CONCLUSIONS

Computational platforms such as the SILICOFCM platform are novel tools for risk prediction of cardiac disease in a specific patient that will certainly open a new avenue for in silico clinical trials in the future.

Geometry Does Impact on the Plane Strain Directions of the Human Left Ventricle, Irrespective of Disease

The directions of primary strain lines of local deformation in Epicardial and Endocardial layers have been the subject of debate in recent years. Different methods led to different conclusions and a complete assessment of strain direction patterns in large and variable (in terms of pathology) cohorts of healthy and diseased patients is still lacking. Here, we use local deformation tensors in order to evaluate the angle of strain lines with respect to the horizontal circumferential direction in both Epi- and Endo-layers. We evaluated this on a large group of 193 subjects including 82 healthy control and 111 patients belonging to a great variety of pathological conditions. We found that Epicardial strain lines obliquely directed while those of Endocardium are almost circumferential. This result occurs irrespective of pathological condition. We propose that the geometric vinculum characterizing Endocardium and Epicardium in terms of different lever arm length and orientation of muscular fibers during contraction inescapably requires Endocardial strain lines to be circumferentially oriented and this is corroborated by experimental results. Further investigations on transmural structure of myocytes could couple results presented here in order to furnish additional experimental explanations.

Hearts by design

Scalable biofabrication of heart helical tissue pattern augments pumping function

Transmural Distribution of Coronary Perfusion and Myocardial Work Density Due to Alterations in Ventricular Loading, Geometry and Contractility

Myocardial supply changes to accommodate the variation of myocardial demand across the heart wall to maintain normal cardiac function. A computational framework that couples the systemic circulation of a left ventricular (LV) finite element model and coronary perfusion in a closed loop is developed to investigate the transmural distribution of the myocardial demand (work density) and supply (perfusion) ratio. Calibrated and validated against measurements of LV mechanics and coronary perfusion, the model is applied to investigate changes in the transmural distribution of passive coronary perfusion, myocardial work density, and their ratio in response to changes in LV contractility, preload, afterload, wall thickness, and cavity volume. The model predicts the following: (1) Total passive coronary flow varies from a minimum value at the endocardium to a maximum value at the epicardium transmurally that is consistent with the transmural distribution of IMP; (2) Total passive coronary flow at different transmural locations is increased with an increase in either contractility, afterload, or preload of the LV, whereas is reduced with an increase in wall thickness or cavity volume; (3) Myocardial work density at different transmural locations is increased transmurally with an increase in either contractility, afterload, preload or cavity volume of the LV, but is reduced with an increase in wall thickness; (4) Myocardial work density-perfusion mismatch ratio at different transmural locations is increased with an increase in contractility, preload, wall thickness or cavity volume of the LV, and the ratio is higher at the endocardium than the epicardium. These results suggest that an increase in either contractility, preload, wall thickness, or cavity volume of the LV can increase the vulnerability of the subendocardial region to ischemia.

Multiscale simulations of left ventricular growth and remodeling

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

A finite element model of the cardiac ventricles with coupled circulation: Biventricular mesh generation with hexahedral elements, airbags and a functional mockup interface to the circulation

INTRODUCTION

Finite element (FE) mechanics models of the heart are becoming more sophisticated. However, there is lack of consensus about optimal element type and coupling of FE models to the circulation. We describe biventricular (left (LV) and right (RV) ventricles) FE mechanics model creation using hexahedral elements, airbags and a functional mockup interface (FMI) to lumped-parameter models of the circulation.

METHODS

Cardiac MRI (CMR) was performed in two healthy volunteers and a single patient with ischemic heart disease (IHD). CMR images were segmented and surfaced, meshing with hexahedral elements was performed with a "thin butterfly with septum" topology. LV and RV inflow and outflow airbags were coupled to lumped-parameter circulation models with an FMI interface. Pulmonary constriction (PAC) and vena cava occlusion (VCO) were simulated and end-systolic pressure-volume relations (ESPVR) were calculated.

RESULTS

Mesh construction was prompt with representative contouring and mesh adjustment requiring 32 and 26 min Respectively. The numbers of elements ranged from 4104 to 5184 with a representative Jacobian of 1.0026 ± 0.4531. Agreement between CMR-based surfaces and mesh was excellent with root-mean-squared error of 0.589 ± 0.321 mm. The LV ESPVR slope was 3.37 ± 0.09 in volunteers but 2.74 in the IHD patient. The effect of PAC and VCO on LV ESPVR was consistent with ventricular interaction (p = 0.0286).

CONCLUSION

Successful co-simulation using a biventricular FE mechanics model with hexahedral elements, airbags and an FMI interface to lumped-parameter model of the circulation was demonstrated. Future studies will include comparison of element type and study of cardiovascular pathologies and device therapies.

A 3D personalized cardiac myocyte aggregate orientation model using MRI data-driven low-rank basis functions

Cardiac myocyte aggregate orientation has a strong impact on cardiac electrophysiology and mechanics. Studying the link between structural characteristics, strain, and stresses over the cardiac cycle and cardiac function requires a full volumetric representation of the microstructure. In this work, we exploit the structural similarity across hearts to extract a low-rank representation of predominant myocyte orientation in the left ventricle from high-resolution magnetic resonance ex-vivo cardiac diffusion tensor imaging (cDTI) in porcine hearts. We compared two reduction methods, Proper Generalized Decomposition combined with Singular Value Decomposition and Proper Orthogonal Decomposition. We demonstrate the existence of a general set of basis functions of aggregated myocyte orientation which defines a data-driven, personalizable, parametric model featuring higher flexibility than existing atlas and rule-based approaches. A more detailed representation of microstructure matching the available patient data can improve the accuracy of personalized computational models. Additionally, we approximate the myocyte orientation of one ex-vivo human heart and demonstrate the feasibility of transferring the basis functions to humans.

Characterizing regional myofiber damage post acute myocardial infarction using global optimization

Medical imaging derived cardiac biomechanical models offer a wealth of new information to be used in diagnosis and prognosis of cardiovascular disease. A noteworthy feature of such models is the ability to predict myofiber contraction stresses during acute or chronic ischemic events. Current techniques for heterogeneous contraction models require tissue motion tracking capabilities which are neither available on all imaging modalities, nor currently used in the clinic. Proposed in this article is a proof of concept of a tissue tracking independent technique focused on shape optimization to predict the contraction stresses of in-silico left ventricle models simulating various acute myocardial infarction events. The technique involves three variables defined in the left ventricle muscle. Two of the variables represent the contraction stresses in the healthy and infarct regions while the third is a novel periinfarct variable defining a non-contracting myofiber state allowing finer classification of local myofiber damage. Results indicate that the contraction stress reconstruction errors are overall smaller than 12% when considering standard errors associated with population modelling for the new variable of interest.

The study of border zone formation in ischemic heart using electro-chemical coupled computational model

Myocardial infarction (MI) is the most common cause of a heart failure, which occurs due to myocardial ischemia leading to left ventricular (LV) remodeling. LV remodeling particularly occurs at the ischemic area and the region surrounds it, known as the border zone. The role of the border zone in initiating LV remodeling process urges the investigation on the correlation between early border zone changes and remodeling outcome. Thus, this study aims to simulate a preliminary conceptual work of the border zone formation and evolution during onset of MI and its effect towards early LV remodeling processes by incorporating the oxygen concentration effect on the electrophysiology of an idealized three-dimensional LV through electro-chemical coupled mathematical model. The simulation result shows that the region of border zone, represented by the distribution of electrical conductivities, keeps expanding over time. Based on this result, the border zone is also proposed to consist of three sub-regions, namely mildly, moderately, and seriously impaired conductivity regions, which each region categorized depending on its electrical conductivities. This division could be used as a biomarker for classification of reversible and irreversible myocardial injury and will help to identify the different risks for the survival of patient. Larger ischemic size and complete occlusion of the coronary artery can be associated with an increased risk of developing irreversible injury, in particular if the reperfusion treatment is delayed. Increased irreversible injury area can be related with cardiovascular events and will further deteriorate the LV function over time.

Assessing Myocardial Architecture: The Challenges and Controversies

In recent decades, investigators have strived to describe and quantify the orientation of the cardiac myocytes in an attempt to classify their arrangement in healthy and diseased hearts. There are, however, striking differences between the investigations from both a technical and methodological standpoint, thus limiting their comparability and impeding the drawing of appropriate physiological conclusions from the structural assessments. This review aims to elucidate these differences, and to propose guidance to establish methodological consensus in the field. The review outlines the theory behind myocyte orientation analysis, and importantly has identified pronounced differences in the definitions of otherwise widely accepted concepts of myocytic orientation. Based on the findings, recommendations are made for the future design of studies in the field of myocardial morphology. It is emphasised that projection of myocyte orientations, before quantification of their angulation, introduces considerable bias, and that angles should be assessed relative to the epicardial curvature. The transmural orientation of the cardiomyocytes should also not be neglected, as it is an important determinant of cardiac function. Finally, there is considerable disagreement in the literature as to how the orientation of myocardial aggregates should be assessed, but to do so in a mathematically meaningful way, the normal vector of the aggregate plane should be utilised.

The study of myocardial ischemia-reperfusion treatment through computational modelling

Reperfusion of the blood flow to ischemic myocardium is the standard treatment for patients suffering myocardial infarction. However, the reperfusion itself can also induce myocardial injury, in which the actual mechanism and its risk factors remain unclear. This work aims to study the mechanism of ischemia-reperfusion treatment using a three-dimensional (3D) oxygen diffusion model. An electrical model is then coupled to an oxygen model to identify the possible region of myocardial damage. Our findings show that the value of oxygen exceeds its optimum (>1.0) at the ischemic area during early reperfusion period. This complication was exacerbated in a longer ischemic period. While a longer reperfusion time causes a continuous excessive oxygen supply to the ischemic area throughout the reperfusion time. This work also suggests the use of less than 0.8 of initial oxygen concentration in the reperfusion treatment to prevent undesired upsurge at the early reperfusion period and further myocardial injury. We also found the region at risk for myocardial injury is confined in the ischemic vicinity revealed by its electrical conductivity impairment. Although there is a risk that reperfusion leads to myocardial injury for excessive oxygen accumulation, the reperfusion treatment is helpful in reducing the infarct size.

Structural Responses of Integrated Parametric Aortic Valve in an Electro-Mechanical Full Heart Model

The aortic valve (AV) is located between the left ventricle and the aorta and responsible for maintaining an outward unidirectional flow. Many AV hemodynamic and structural aspects of have been extensively studied, however, more sophisticated models are needed to better understand the AV biomechanical behavior. This study deals with integrating a new parametric AV structural model with the electro-mechanical Living Heart Human Model® (LHHM). The LHHM is a finite element model simulating human heart capable of realistic electro-mechanical simulations. Different geometric metrics of AV have been examined. New integrated structural AV model within the LHHM better predict local stresses during the cardiac cycle due to the realistic boundary condition derived from the LHHM. It was found that ellipticity index (EI), calculated as the ratio between the maximal (Max) and minimal (Min) aortic annulus (AA) diameters, well correlates with measured clinical data obtained from patients undergoing computed tomography (CT) while the annular perimeter (Perim) matches the same trend. This increases the confidence in the predicted kinematic behavior, leaflets coaptation, and the overall stresses. From the clinical aspect, the new proposed coupled and integrated AV modeling can serve as a platform for design and implementation of pre-transcatheter aortic valve replacement (TAVR) procedures.

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

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

Regional variations in ex-vivo diffusion tensor anisotropy are associated with cardiomyocyte remodeling in rats after left ventricular pressure overload

BACKGROUND

Pressure overload left ventricular (LV) hypertrophy is characterized by increased cardiomyocyte width and ventricle wall thickness, however the regional variation of this remodeling is unclear. Cardiovascular magnetic resonance (CMR) diffusion tensor imaging (DTI) may provide a non-invasive, comprehensive, and geometrically accurate method to detect regional differences in structural remodeling in hypertrophy. We hypothesized that DTI parameters, such as fractional and planar anisotropy, would reflect myocyte remodeling due to pressure overload in a regionally-dependent manner.

METHODS

We investigated the regional distributions of myocyte remodeling in rats with or without transverse aortic constriction (TAC) via direct measurement of myocyte dimensions with confocal imaging of thick tissue sections, and correlated myocyte cross-sectional area and other geometric features with parameters of diffusivity from ex-vivo DTI in the same regions of the same hearts.

RESULTS

We observed regional differences in several parameters from DTI between TAC hearts and SHAM controls. Consistent with previous studies, helix angles from DTI correlated strongly with those measured directly from histological sections (p < 0.001, R2 = 0.71). There was a transmural gradient in myocyte cross-sectional area in SHAM hearts that was diminished in the TAC group. We also found several regions of significantly altered DTI parameters in TAC LV compared to SHAM, especially in myocyte sheet angle dispersion and planar anisotropy. Among others, these parameters correlated significantly with directly measured myocyte aspect ratios.

CONCLUSIONS

These results show that structural remodeling in pressure overload LV hypertrophy is regionally heterogeneous, especially transmurally, with a greater degree of remodeling in the sub-endocardium compared to the sub-epicardium. Additionally, several parameters derived from DTI correlated significantly with measurements of myocyte geometry from direct measurement in histological sections. We suggest that DTI may provide a non-invasive, comprehensive method to detect regional structural myocyte LV remodeling during disease.

Anatomically correct assessment of the orientation of the cardiomyocytes using diffusion tensor imaging

Diffusion tensor imaging has been used for assessing the orientation of cardiac myocytes for decades. Striking methodological differences exist between studies when quantifying these orientations. This limits the comparability between studies, and impedes collaboration and the drawing of appropriate physiological conclusions. We have sought to elucidate these differences, permitting us to propose a standardised "tool set" that might better establish consensus in future studies. We fixed hearts from seven 25 kg pigs in formalin, and scanned them using diffusion tensor imaging. Using various angle definitions as found in literature, we assessed the orientations of cardiomyocytes, comparing them in terms of helical and intrusion angles, along with the orientation of their aggregations. The difference between assessment of the helical angle with and without relation to the epicardial curvature was 25.2° (SD: 7.9) at the base, 5.8° (1.9) at the equatorial level, and 28.0° (7.0) at the apex, ANOVA P = 0.001. In comparable fashion, the intrusion angle differed by 25.9° (12.9), 7.6° (0.98) and 17.5° (4.7), P = 0.01, and the angle of the aggregates (E3-angle) differed by 25.0° (13.5) at the base, 9.4° (1.7) at the equator, and 23.1° (6.2) apically, P = 0.003. When assessing 14 definitions used in literature to calculate the orientation of aggregates, only 4 rendered identical results. The findings show that any attempt to use projection of eigenvectors introduces considerable bias. The epicardial curvature of the ventricular cone needs to be taken into account when seeking to provide accurate quantification of the orientation of the aggregated cardiomyocytes, especially in the apical and basal regions. This means that projection of eigenvectors should be avoided prior to quantifying myocyte orientation, especially when assessing radial orientation. Based on our results, we suggest appropriate methods for valid assessment of myocyte orientation using diffusion tensor imaging.

Ventricle stress/strain comparisons between Tetralogy of Fallot patients and healthy using models with different zero-load diastole and systole morphologies

Patient-specific in vivo ventricle mechanical wall stress and strain conditions are important for cardiovascular investigations and should be calculated from correct zero-load ventricle morphologies. Cardiac magnetic resonance (CMR) data were obtained from 6 healthy volunteers and 12 Tetralogy of Fallot (TOF) patients with consent obtained. 3D patient-specific CMR-based ventricle models with different zero-load diastole and systole geometries due to myocardium contraction and relaxation were constructed to qualify right ventricle (RV) diastole and systole stress and strain values at begin-filling, end-filling, begin-ejection, and end-ejection, respectively. Our new models (called 2G models) can provide end-diastole and end-systole stress/strain values which models with one zero-load geometries (called 1G models) could not provide. 2G mean end-ejection stress value from the 18 participants was 321.4% higher than that from 1G models (p = 0.0002). 2G mean strain values was 230% higher than that of 1G models (p = 0.0002). TOF group (TG) end-ejection mean stress value was 105.4% higher than that of healthy group (HG) (17.54±7.42kPa vs. 8.54±0.92kPa, p = 0.0245). Worse outcome group (WG, n = 6) post pulmonary valve replacement (PVR) begin-ejection mean stress was 57.4% higher than that of better outcome group (BG, 86.94±26.29 vs. 52.93±22.86 kPa; p = 0.041). Among 7 selected parameters, End-filling stress was the best predictor to differentiate BG patients from WG patients with prediction accuracy = 0.8208 and area under receiver operating characteristic curve (AUC) value at 0.8135 (EE stress). Large scale studies are needed to further validate our findings.

Effect of myocardial heterogeneity on ventricular electro-mechanical responses: a computational study

BACKGROUND

The heart wall exhibits three layers of different thicknesses: the outer epicardium, mid-myocardium, and inner endocardium. Among these layers, the mid-myocardium is typically the thickest. As indicated by preliminary studies, heart-wall layers exhibit various characteristics with regard to electrophysiology, pharmacology, and pathology. Construction of an accurate three-dimensional (3D) model of the heart is important for predicting physiological behaviors. However, the wide variability of myocardial shapes and the unclear edges between the epicardium and soft tissues are major challenges in the 3D model segmentation approach for identifying the boundaries of the epicardium, mid-myocardium, and endocardium. Therefore, this results in possible variations in the heterogeneity ratios between the epicardium, mid-myocardium, and endocardium. The objective of this study was to observe the effects of different thickness ratios of the epicardium, mid-myocardium, and endocardium on cardiac arrhythmogenesis, reentry instability, and mechanical responses during arrhythmia.

METHODS

We used a computational method and simulated three heterogeneous ventricular models: Model 1 had the thickest M cell layer and thinnest epicardium and endocardium. Model 2 had intermediate layer thicknesses. Model 3 exhibited the thinnest mid-myocardium and thickest epicardium and endocardium. Electrical and mechanical simulations of the three heterogeneous models were performed under normal sinus rhythm and reentry conditions.

RESULTS

Model 1 exhibited the highest probability of terminating reentrant waves, and Model 3 exhibited to experience greater cardiac arrhythmia. In the reentry simulation, at 8 s, Model 3 generated the largest number of rotors (eight), while Models 1 and 2 produced five and seven rotors, respectively. There was no significant difference in the cardiac output obtained during the sinus rhythm. Under the reentry condition, the highest cardiac output was generated by Model 1 (19 mL/s), followed by Model 2 (9 mL/s) and Model 3 (7 mL/s).

CONCLUSIONS

A thicker mid-myocardium led to improvements in the pumping efficacy and contractility and reduced the probability of cardiac arrhythmia. Conversely, thinner M cell layers generated more unstable reentrant spiral waves and hindered the ventricular pumping.

Patient-specific in vivo right ventricle material parameter estimation for patients with tetralogy of Fallot using MRI-based models with different zero-load diastole and systole morphologies

Patient-specific in vivo ventricle material parameter determination is important for cardiovascular investigations. A new cardiac magnetic image (CMR)-based modeling approach with different zero-load diastole and systole geometries was adopted to estimate right ventricle material parameter values for healthy and patients with Tetralogy of Fallot (TOF) and seeking potential clinical applications. CMR data were obtained from 6 healthy volunteers and 16 TOF patients with consent obtained. CMR-based RV/LV models were constructed using two zero-load geometries (diastole and systole, 2G model). Material parameter values for begin-filling (BF), end-filling (EF), begin-ejection (BE), and end-ejection (EE) were recorded for analyses. Effective Young's moduli (YM) for fiber direction stress-strain curves were calculated for easy comparisons. The mean EE YM value of TOF patients was 78.6% higher than that of the healthy group (HG). The mean end-ejection YM value from worse-outcome TOF group (WG) post pulmonary valve replacement (PVR) surgery was 59.5% higher than that from the better-outcome TOF group (BG). Using begin-filling YM and end-ejection YM as predictors and the classic logistic regression model to different better-outcome group patients from worse-outcome group patients, the areas under Receiver Operating Characteristic (ROC) curves were found to be 0.797 and 0.883 for begin-filling YM and end-ejection YM, respectively. The sensitivity and specificity 0.761 and 0.755 using end-ejection YM as the predictor. This preliminary study suggests that ventricle material stiffness could be a potential parameter to be used to differentiate BG patients from WG patients with further effort and large-scale patient data validations.

Stability of left ventricular longitudinal and circumferential deformation over time and standard loading conditions

Aims

Load dependence is an important source of variation in left ventricular (LV) deformation. This impacts on the precision of information obtained from serial measurements. However, it is clinically important to distinguish actual myocardial dysfunction from changes associated with altered loading conditions. We sought to investigate the association of changes of loading parameters with changes in LV longitudinal (GLS) and circumferential (GCS) strains.

Methods and results

Baseline and a 12-month follow-up 2D echocardiograms were performed in 191 Stage A heart failure patients with uncomplicated hypertension. These patients underwent simultaneous measurement of conventional and central blood pressures (BPs) and haemodynamic measurements by applanation tonometry. Significant, but weak correlations (r = 0.15-0.28) of LV strain parameters and their changes over the follow-up period were shown for the majority of LV afterload-associated variables, including central and brachial systolic, diastolic, and mean BPs; 24-h systolic and diastolic BPs; peak reservoir and excess pressures; central augmented pressure (CAP) and pulse pressure; augmentation index; and arterial elastance index (EaI). Central mean BP, EaI, and changes in CAP and EaI over follow-up were independent contributors to LV deformation in multivariable analysis. No improvement in the Bland-Altman 95% limits of agreement and correlation coefficients was seen with LV afterload correction of GLS and GCS using central BP indices.

Conclusions

LV longitudinal and circumferential strains in a population without apparent heart disease is relatively insusceptible to changes in LV afterload within physiological range, which, therefore, seem unlikely to be a significant confounder in repeated GLS or GCS observations.

Construction and Validation of Subject-Specific Biventricular Finite-Element Models of Healthy and Failing Swine Hearts From High-Resolution DT-MRI

Predictive computational modeling has revolutionized classical engineering disciplines and is in the process of transforming cardiovascular research. This is particularly relevant for investigating emergent therapies for heart failure, which remains a leading cause of death globally. The creation of subject-specific biventricular computational cardiac models has been a long-term endeavor within the biomedical engineering community. Using high resolution (0.3 × 0.3 × 0.8 mm) ex vivo data, we constructed a precise fully subject-specific biventricular finite-element model of healthy and failing swine hearts. Each model includes fully subject-specific geometries, myofiber architecture and, in the case of the failing heart, fibrotic tissue distribution. Passive and active material properties are prescribed using hyperelastic strain energy functions that define a nearly incompressible, orthotropic material capable of contractile function. These materials were calibrated using a sophisticated multistep approach to match orthotropic tri-axial shear data as well as subject-specific hemodynamic ventricular targets for pressure and volume to ensure realistic cardiac function. Each mechanically beating heart is coupled with a lumped-parameter representation of the circulatory system, allowing for a closed-loop definition of cardiovascular flow. The circulatory model incorporates unidirectional fluid exchanges driven by pressure gradients of the model, which in turn are driven by the mechanically beating heart. This creates a computationally meaningful representation of the dynamic beating of the heart coupled with the circulatory system. Each model was calibrated using subject-specific experimental data and compared with independent in vivo strain data obtained from echocardiography. Our methods produced highly detailed representations of swine hearts that function mechanically in a remarkably similar manner to the in vivo subject-specific strains on a global and regional comparison. The degree of subject-specificity included in the models represents a milestone for modeling efforts that captures realism of the whole heart. This study establishes a foundation for future computational studies that can apply these validated methods to advance cardiac mechanics research.

Changes and classification in myocardial contractile function in the left ventricle following acute myocardial infarction

In this research, we hypothesized that novel biomechanical parameters are discriminative in patients following acute ST-segment elevation myocardial infarction (STEMI). To identify these biomechanical biomarkers and bring computational biomechanics ‘closer to the clinic’, we applied state-of-the-art multiphysics cardiac modelling combined with advanced machine learning and multivariate statistical inference to a clinical database of myocardial infarction. We obtained data from 11 STEMI patients (ClinicalTrials.gov NCT01717573) and 27 healthy volunteers, and developed personalized mathematical models for the left ventricle (LV) using an immersed boundary method. Subject-specific constitutive parameters were achieved by matching to clinical measurements. We have shown, for the first time, that compared with healthy controls, patients with STEMI exhibited increased LV wall active tension when normalized by systolic blood pressure, which suggests an increased demand on the contractile reserve of remote functional myocardium. The statistical analysis reveals that the required patient-specific contractility, normalized active tension and the systolic myofilament kinematics have the strongest explanatory power for identifying the myocardial function changes post-MI. We further observed a strong correlation between two biomarkers and the changes in LV ejection fraction at six months from baseline (the required contractility (r = − 0.79, p < 0.01) and the systolic myofilament kinematics (r = 0.70, p = 0.02)). The clinical and prognostic significance of these biomechanical parameters merits further scrutinization.

Right Ventricular Fiber Structure as a Compensatory Mechanism in Pressure Overload: A Computational Study

Right ventricular failure (RVF) is a lethal condition in diverse pathologies. Pressure overload is the most common etiology of RVF, but our understanding of the tissue structure remodeling and other biomechanical factors involved in RVF is limited. Some remodeling patterns are interpreted as compensatory mechanisms including myocyte hypertrophy, extracellular fibrosis, and changes in fiber orientation. However, the specific implications of these changes, especially in relation to clinically observable measurements, are difficult to investigate experimentally. In this computational study, we hypothesized that, with other variables constant, fiber orientation alteration provides a quantifiable and distinct compensatory mechanism during RV pressure overload (RVPO). Numerical models were constructed using a rabbit model of chronic pressure overload RVF based on intraventricular pressure measurements, CINE magnetic resonance imaging (MRI), and diffusion tensor MRI (DT-MRI). Biventricular simulations were conducted under normotensive and hypertensive boundary conditions using variations in RV wall thickness, tissue stiffness, and fiber orientation to investigate their effect on RV pump function. Our results show that a longitudinally aligned myocardial fiber orientation contributed to an increase in RV ejection fraction (RVEF). This effect was more pronounced in response to pressure overload. Likewise, models with longitudinally aligned fiber orientation required a lesser contractility for maintaining a target RVEF against elevated pressures. In addition to increased wall thickness and material stiffness (diastolic compensation), systolic mechanisms in the forms of myocardial fiber realignment and changes in contractility are likely involved in the overall compensatory responses to pressure overload.

Personalised computational cardiology: Patient-specific modelling in cardiac mechanics and biomaterial injection therapies for myocardial infarction

Predictive computational modelling in biomedical research offers the potential to integrate diverse data, uncover biological mechanisms that are not easily accessible through experimental methods and expose gaps in knowledge requiring further research. Recent developments in computing and diagnostic technologies have initiated the advancement of computational models in terms of complexity and specificity. Consequently, computational modelling can increasingly be utilised as enabling and complementing modality in the clinic—with medical decisions and interventions being personalised. Myocardial infarction and heart failure are amongst the leading causes of death globally despite optimal modern treatment. The development of novel MI therapies is challenging and may be greatly facilitated through predictive modelling. Here, we review the advances in patient-specific modelling of cardiac mechanics, distinguishing specificity in cardiac geometry, myofibre architecture and mechanical tissue properties. Thereafter, the focus narrows to the mechanics of the infarcted heart and treatment of myocardial infarction with particular attention on intramyocardial biomaterial delivery.

Torsion Mechanics as an Indicator of More Advanced Left Ventricular Systolic Dysfunction in Secondary Mitral Regurgitation in Patients with Dilated Cardiomyopathy: A 2D Speckle-Tracking Analysis

Left ventricular (LV) twist serves as a compensatory mechanism in systolic dysfunction and its degree of reduction may reflect a more advanced stage of disease. Aim: The aim was to investigate twist alterations depending on the degree of functional mitral regurgitation (MR) by speckle-tracking echocardiography. Methods: Sixty-three patients with symptomatic dilated cardiomyopathy (DCM) were included. Patients were divided according to MR vena contracta width (VCW): group 1 with VCW <7 mm (mild/moderate MR) and group 2 with VCW ≥7 mm (severe MR). Results: There were no differences in LV geometry and function between groups. Group 2 showed lower endocardial basal rotation (BR) (–2.04° ± 1.83° vs. –3.23° ± 1.83°, p = 0.012); epicardial BR (–1.54° ± 1.18° vs. –2.31° ± 1.22°, p = 0.015); endocardial torsion (0.41°/cm ± 0.36°/cm vs. 0.63°/cm ± 0.44°/cm, p = 0.033) and mid-level circumferential strain (CSmid) (–6.12% ± 2.64% vs. –7.75% ± 2.90%, p = 0.028), when compared with group 1. Multivariable linear regression analysis identified endocardial BR, torsion and CSmid, as the best predictors of larger VCW. In the ROC curve analysis, endocardial BR and CSmid values greater than or equal to –3.63° and –9.35%, respectively, can differentiate patients with severe MR. Conclusions: In DCM patients, torsional profile was more altered in severe MR. Endocardial BR, endocardial torsion, and CSmid, can be used as indicators of advanced structural wall architecture damage.

A finite element model of myocardial infarction using a composite material approach

Computational models are effective tools to study cardiac mechanics under normal and pathological conditions. They can be used to gain insight into the physiology of the heart under these conditions while they are adaptable to computer assisted patient-specific clinical diagnosis and therapeutic procedures. Realistic cardiac mechanics models incorporate tissue active/passive response in conjunction with hyperelasticity and anisotropy. Conventional formulation of such models leads to mathematically-complex problems usually solved by custom-developed non-linear finite element (FE) codes. With a few exceptions, such codes are not available to the research community. This article describes a computational cardiac mechanics model developed such that it can be implemented using off-the-shelf FE solvers while tissue pathologies can be introduced in the model in a straight-forward manner. The model takes into account myocardial hyperelasticity, anisotropy, and active contraction forces. It follows a composite tissue modeling approach where the cardiac tissue is decomposed into two major parts: background and myofibers. The latter is modelled as rebars under initial stresses mimicking the contraction forces. The model was applied in silico to study the mechanics of infarcted left ventricle (LV) of a canine. End-systolic strain components, ejection fraction, and stress distribution attained using this LV model were compared quantitatively and qualitatively to corresponding data obtained from measurements as well as to other corresponding LV mechanics models. This comparison showed very good agreement.

Magnetic susceptibility anisotropy outside the central nervous system

Magnetic-susceptibility-based MRI has made important contributions to the characterization of tissue microstructure, chemical composition, and organ function. This has motivated a number of studies to explore the link between microstructure and susceptibility in organs and tissues throughout the body, including the kidney, heart, and connective tissue. These organs and tissues have anisotropic magnetic susceptibility properties and cellular organizations that are distinct from the lipid organization of myelin in the brain. For instance, anisotropy is traced to the epithelial lipid orientation in the kidney, the myofilament proteins in the heart, and the collagen fibrils in the knee cartilage. The magnetic susceptibility properties of these and other tissues are quantified using specific MRI tools: susceptibility tensor imaging (STI), quantitative susceptibility mapping (QSM), and individual QSM measurements with respect to tubular and filament directions determined from diffusion tensor imaging. These techniques provide complementary and supplementary information to that produced by traditional MRI methods. In the kidney, STI can track tubules in all layers including the cortex, outer medulla, and inner medulla. In the heart, STI detected myofibers throughout the myocardium. QSM in the knee revealed three unique layers in articular cartilage by exploiting the anisotropic susceptibility features of collagen. While QSM and STI are promising tools to study tissue susceptibility, certain technical challenges must be overcome in order to realize routine clinical use. This paper reviews essential experimental findings of susceptibility anisotropy in the body, the underlying mechanisms, and the associated MRI methodologies. Copyright © 2016 John Wiley & Sons, Ltd.

Transmural gradients of myocardial structure and mechanics: Implications for fiber stress and strain in pressure overload

Although a truly complete understanding of whole heart activation, contraction, and deformation is well beyond our current reach, a significant amount of effort has been devoted to discovering and understanding the mechanisms by which myocardial structure determines cardiac function to better treat patients with cardiac disease. Several experimental studies have shown that transmural fiber strain is relatively uniform in both diastole and systole, in contrast to predictions from traditional mechanical theory. Similarly, mathematical models have largely predicted uniform fiber stress across the wall. The development of this uniform pattern of fiber stress and strain during filling and ejection is due to heterogeneous transmural distributions of several myocardial structures. This review summarizes these transmural gradients, their contributions to fiber mechanics, and the potential functional effects of their remodeling during pressure overload hypertrophy.

Myocardial torsional deformations in cats with hypertrophic cardiomyopathy using two-dimensional speckle-tracking echocardiography

OBJECTIVES

The objective of our study was to quantitatively measure systolic torsional deformations in cats with hypertrophic cardiomyopathy (HCM) and in controls.

ANIMALS

Twenty-six client-owned cats with HCM and 14 healthy cats. HCM cats were categorized based on their symptoms (asymptomatic and symptomatic) and with or without left ventricular outflow tract obstruction (obstructive and non-obstructive).

METHODS

The cats were examined for myocardial deformations using two-dimensional speckle-tracking echocardiography and were evaluated for peak systolic rotation and the rotation rate at each basal and apical view. Cats were also evaluated for the peak systolic torsion and torsion rate.

RESULTS

The peak systolic apical rotation and torsion were higher in asymptomatic and symptomatic cats with HCM than in control cats. Also, the peak systolic apical rotation, apical rotation rate, torsion, and torsion rate were higher in cats with obstructive HCM than in control cats.

CONCLUSIONS

Myocardial torsional deformations assessed by two-dimensional speckle-tracking echocardiography may be useful for evaluating compensatory myocardial function of HCM.

Multiscale model of the human cardiovascular system: Description of heart failure and comparison of contractility indices

A multiscale model of the cardiovascular system is presented. Hemodynamics is described by a lumped parameter model, while heart contraction is described at the cellular scale. An electrophysiological model and a mechanical model were coupled and adjusted so that the pressure and volume of both ventricles are linked to the force and length of a half-sarcomere. Particular attention was paid to the extreme values of the sarcomere length, which must keep physiological values. This model is able to reproduce healthy behavior, preload variations experiments, and ventricular failure. It also allows to compare the relevance of standard cardiac contractility indices. This study shows that the theoretical gold standard for assessing cardiac contractility, namely the end-systolic elastance, is actually load-dependent and therefore not a reliable index of cardiac contractility.

Parametric Modeling of the Mouse Left Ventricular Myocardial Fiber Structure

Magnetic resonance diffusion tensor imaging (DTI) has greatly facilitated detailed quantifications of myocardial structures. However, structural patterns, such as the distinctive transmural rotation of the fibers, remain incompletely described. To investigate the validity and practicality of pattern-based analysis, 3D DTI was performed on 13 fixed mouse hearts and fiber angles in the left ventricle were transformed and fitted to parametric expressions constructed from elementary functions of the prolate spheroidal spatial variables. It was found that, on average, the myocardial fiber helix angle could be represented to 6.5° accuracy by the equivalence of a product of 10th-order polynomials of the radial and longitudinal variables, and 17th-order Fourier series of the circumferential variable. Similarly, the fiber imbrication angle could be described by 10th-order polynomials and 24th-order Fourier series, to 5.6° accuracy. The representations, while relatively concise, did not adversely affect the information commonly derived from DTI datasets including the whole-ventricle mean fiber helix angle transmural span and atlases constructed for the group. The unique ability of parametric models for predicting the 3D myocardial fiber structure from finite number of 2D slices was also demonstrated. These findings strongly support the principle of parametric modeling for characterizing myocardial structures in the mouse and beyond.

Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate efficient scaling up to 1024, 4096 and 8192 compute cores which allowed the simulation of a single heart beat in 44.3, 87.8 and 235.3 minutes, respectively. The efficiency of the method allows fast simulation cycles without compromising anatomical or biophysical detail.

Multiscale Interactions in a 3D Model of the Contracting Ventricle

A biophysical detailed multiscale model of the myocardium is presented. The model was used to study the contribution of interrelated cellular mechanisms to global myocardial function. The multiscale model integrates cellular electrophysiology, excitation propagation dynamics and force development models into a geometrical fiber based model of the ventricle. The description of the cellular electrophysiology in this study was based on the Ten Tusscher-Noble-Noble-Panfilov heterogeneous model for human ventricular myocytes. A four-state model of the sarcomeric control of contraction developed by Negroni and Lascano was employed to model the intracellular mechanism of force generation. The propagation of electrical excitation was described by a reaction-diffusion equation. The 3D geometrical model of the ventricle, based on single fiber contraction was used as a platform for the evaluation of proposed models. The model represents the myocardium as an anatomically oriented array of contracting fibers with individual fiber parameters such as size, spatial location, orientation and mechanical properties. Moreover, the contracting ventricle model interacts with intraventricular blood elements linking the contractile elements to the heart's preload and afterload, thereby producing the corresponding pressure-volume loop. The results show that the multiscale ventricle model is capable of simulating mechanical contraction, pressure generation and load interactions as well as demonstrating the individual contribution of each ion current.

The cardiac torsion as a sensitive index of heart pathology: A model study

The torsional behaviour of the heart (i.e. the mutual rotation of the cardiac base and apex) was proved to be sensitive to alterations of some cardiovascular parameters, i.e. preload, afterload and contractility. Moreover, pathologies which affect the fibers architecture and cardiac geometry were proved to alter the cardiac torsion pattern. For these reasons, cardiac torsion represents a sensitive index of ventricular performance. The aim of this work is to provide further insight into physiological and pathological alterations of the cardiac torsion by means of computational analyses, combining a structural model of the two ventricles with simple lumped parameter models of both the systemic and the pulmonary circulations. Starting from diagnostic images, a 3D anatomy based geometry of the two ventricles was reconstructed. The myocytes orientation in the ventricles was assigned according to literature data and the myocardium was modelled as an anisotropic hyperelastic material. Both the active and the passive phases of the cardiac cycle were modelled, and different clinical conditions were simulated. The results in terms of alterations of the cardiac torsion in the presence of pathologies are in agreement with experimental literature data. The use of a computational approach allowed the investigation of the stresses and strains in the ventricular wall as well as of the global hemodynamic parameters in the presence of the considered pathologies. Furthermore, the model outcomes highlight how for specific pathological conditions, an altered torsional pattern of the ventricles can be present, encouraging the use of the ventricular torsion in the clinical practice.

Finite-Element Extrapolation of Myocardial Structure Alterations Across the Cardiac Cycle in Rats

Myocardial microstructures are responsible for key aspects of cardiac mechanical function. Natural myocardial deformation across the cardiac cycle induces measurable structural alteration, which varies across disease states. Diffusion tensor magnetic resonance imaging (DT-MRI) has become the tool of choice for myocardial structural analysis. Yet, obtaining the comprehensive structural information of the whole organ, in 3D and time, for subject-specific examination is fundamentally limited by scan time. Therefore, subject-specific finite-element (FE) analysis of a group of rat hearts was implemented for extrapolating a set of initial DT-MRI to the rest of the cardiac cycle. The effect of material symmetry (isotropy, transverse isotropy, and orthotropy), structural input, and warping approach was observed by comparing simulated predictions against in vivo MRI displacement measurements and DT-MRI of an isolated heart preparation at relaxed, inflated, and contracture states. Overall, the results indicate that, while ventricular volume and circumferential strain are largely independent of the simulation strategy, structural alteration predictions are generally improved with the sophistication of the material model, which also enhances torsion and radial strain predictions. Moreover, whereas subject-specific transversely isotropic models produced the most accurate descriptions of fiber structural alterations, the orthotropic models best captured changes in sheet structure. These findings underscore the need for subject-specific input data, including structure, to extrapolate DT-MRI measurements across the cardiac cycle.

Magnetic susceptibility anisotropy of myocardium imaged by cardiovascular magnetic resonance reflects the anisotropy of myocardial filament α-helix polypeptide bonds

BACKGROUND

A key component of evaluating myocardial tissue function is the assessment of myofiber organization and structure. Studies suggest that striated muscle fibers are magnetically anisotropic, which, if measurable in the heart, may provide a tool to assess myocardial microstructure and function.

METHODS

To determine whether this weak anisotropy is observable and spatially quantifiable with cardiovascular magnetic resonance (CMR), both gradient-echo and diffusion-weighted data were collected from intact mouse heart specimens at 9.4 Tesla. Susceptibility anisotropy was experimentally calculated using a voxelwise analysis of myocardial tissue susceptibility as a function of myofiber angle. A myocardial tissue simulation was developed to evaluate the role of the known diamagnetic anisotropy of the peptide bond in the observed susceptibility contrast.

RESULTS

The CMR data revealed that myocardial tissue fibers that were parallel and perpendicular to the magnetic field direction appeared relatively paramagnetic and diamagnetic, respectively. A linear relationship was found between the magnetic susceptibility of the myocardial tissue and the squared sine of the myofiber angle with respect to the field direction. The multi-filament model simulation yielded susceptibility anisotropy values that reflected those found in the experimental data, and were consistent that this anisotropy decreased as the echo time increased.

CONCLUSIONS

Though other sources of susceptibility anisotropy in myocardium may exist, the arrangement of peptide bonds in the myofilaments is a significant, and likely the most dominant source of susceptibility anisotropy. This anisotropy can be further exploited to probe the integrity and organization of myofibers in both healthy and diseased heart tissue.

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.

Hypertrophic and dilated cardiomyopathy: four decades of basic research on muscle lead to potential therapeutic approaches to these devastating genetic diseases

With the advent of technologies to obtain the complete sequence of the human genome in a cost-effective manner, this decade and those to come will see an exponential increase in our understanding of the underlying genetics that lead to human disease. And where we have a deep understanding of the biochemical and biophysical basis of the machineries and pathways involved in those genetic changes, there are great hopes for the development of modern therapeutics that specifically target the actual machinery and pathways altered by individual mutations. Prime examples of such a genetic disease are those classes of hypertrophic and dilated cardiomyopathy that result from single amino-acid substitutions in one of several of the proteins that make up the cardiac sarcomere or from the truncation of myosin binding protein C. Hypertrophic cardiomyopathy alone affects ∼1 in 500 individuals, and it is the leading cause of sudden cardiac death in young adults. Here I describe approaches to understand the molecular basis of the alterations in power output that result from these mutations. Small molecules binding to the mutant sarcomeric protein complex should be able to mitigate the effects of hypertrophic and dilated cardiomyopathy mutations at their sources, leading to possible new therapeutic approaches for these genetic diseases.

Left ventricular twist and shear in patients with primary mitral regurgitation

PURPOSE

To evaluate the relationship between left ventricular (LV) twist, shear, and twist-per-volume and the severity of mitral regurgitation (MR). Primary MR is a valvular disorder that induces LV dysfunction. There exist several measures of LV rotational mechanics, but it remains unclear which measure of LV dysfunction best accords with the severity of MR. We hypothesized that LV systolic twist-per-volume slope would decrease with increasing severity of MR because of both decreases in rotational mechanics and increases in stroke volumes.

MATERIALS AND METHODS

Normal subjects (n = 54), moderate MR patients (n = 29), and severe MR patients (n = 54) were studied. Magnetic resonance imaging (MRI) was performed on a 1.5T scanner and grid-tagged LV images were collected at the LV base and LV apex. Measures of LV rotational mechanics were derived from tagged images using Fourier Analysis of STimulated echoes (FAST).

RESULTS

Peak systolic twist-per-volume slope was significantly different for all pairwise comparisons (P < 0.0001) and compared to normal subjects (-0.14 ± 0.05°/mL) was decreased in moderate MR (-0.12 ± 0.04°/mL) and further decreased in severe MR (-0.07 ± 0.03°/mL).

CONCLUSION

Peak systolic twist-per-volume slope significantly decreased with increasing severity of MR and is therefore a suitable quantitative imaging biomarker for LV dysfunction in patients with MR.

Distribution of normal human left ventricular myofiber stress at end diastole and end systole: a target for in silico design of heart failure treatments

Ventricular wall stress is believed to be responsible for many physical mechanisms taking place in the human heart, including ventricular remodeling, which is frequently associated with heart failure. Therefore, normalization of ventricular wall stress is the cornerstone of many existing and new treatments for heart failure. In this paper, we sought to construct reference maps of normal ventricular wall stress in humans that could be used as a target for in silico optimization studies of existing and potential new treatments for heart failure. To do so, we constructed personalized computational models of the left ventricles of five normal human subjects using magnetic resonance images and the finite-element method. These models were calibrated using left ventricular volume data extracted from magnetic resonance imaging (MRI) and validated through comparison with strain measurements from tagged MRI (950 ± 170 strain comparisons/subject). The calibrated passive material parameter values were C0 = 0.115 ± 0.008 kPa and B0 = 14.4 ± 3.18; the active material parameter value was Tmax = 143 ± 11.1 kPa. These values could serve as a reference for future construction of normal human left ventricular computational models. The differences between the predicted and the measured circumferential and longitudinal strains in each subject were 3.4 ± 6.3 and 0.5 ± 5.9%, respectively. The predicted end-diastolic and end-systolic myofiber stress fields for the five subjects were 2.21 ± 0.58 and 16.54 ± 4.73 kPa, respectively. Thus these stresses could serve as targets for in silico design of heart failure treatments.

Impact of weightlessness on cardiac shape and left ventricular stress/strain distributions

In this paper, a finite element model of the heart is developed to investigate the impact of different gravitational loadings of Earth, Mars, Moon, and microgravity on the cardiac shape and strain/stress distributions in the left ventricle. The finite element model is based on realistic 3D heart geometry, detailed fiber/sheet micro-architecture, and a validated orthotropic cardiac tissue model and constitutive relationship that capture the passive behavior of the heart at end-diastole. The model predicts the trend and magnitude of cardiac shape change at different gravitational levels with great fidelity in comparison to recent cardiac sphericity measurements performed during simulated reduced-gravity parabolic flight experiments. Moreover, the numerical predictions indicate that although the left ventricular strain distributions remain relatively unaltered across the gravitational fields and the strain extrema values occur at the same relative locations, their values change noticeably with decreasing gravity. As for the stress, however, both the magnitude and location of the extrema change with a decrease in the gravitational field. Consequently, tension regions of the heart on Earth can change into compression regions in space.

Effects of activation pattern and active stress development on myocardial shear in a model with adaptive myofiber reorientation

It has been hypothesized that myofiber orientation adapts to achieve a preferred mechanical loading state in the myocardial tissue. Earlier studies tested this hypothesis in a combined model of left ventricular (LV) mechanics and remodeling of myofiber orientation in response to fiber cross-fiber shear, assuming synchronous timing of activation and uniaxial active stress development. Differences between computed and measured patterns of circumferential-radial shear strain Ecr were assumed to be caused by limitations in either the LV mechanics model or the myofiber reorientation model. Therefore, we extended the LV mechanics model with a physiological transmural and longitudinal gradient in activation pattern and with triaxial active stress development. We investigated the effects on myofiber reorientation, LV function, and deformation. The effect on the developed pattern of the transverse fiber angle αt,0 and the effect on global pump function were minor. Triaxial active stress development decreased amplitudes of Ecr towards values within the experimental range and resulted in a similar base-to-apex gradient during ejection in model computed and measured Ecr. The physiological pattern of mechanical activation resulted in better agreement between computed and measured strain in myofiber direction, especially during isovolumic contraction phase and first half of ejection. In addition, remodeling was favorable for LV pump and myofiber function. In conclusion, the outcome of the combined model of LV mechanics and remodeling of myofiber orientation is found to become more physiologic by extending the mechanics model with triaxial active stress development and physiological activation pattern.