Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium

Use of the intrusion angle to describe the radial orientation of local cardiomyocytes in the left ventricle

The projected transverse angle and the nonprojected intrusion angle can be used to describe the radial orientation of local cardiomyocytes in the left ventricle wall, although to date their descriptive relevance has not been demonstrated. This paper compares the evolution of the transverse angle and the intrusion angle in five left ventricle wall samples, and investigates in more detail their respective behaviors when the nonprojected helical angle varies. We show that the intrusion angle avoids the "projection" effect, and contrary to the transverse angle, it remains stable whatever the values taken by the nonprojected helical angle, even when this approaches 90°. The intrusion angle is the better choice, rather than the transverse angle, in describing the radial orientation of local cardiomyocytes. Furthermore, the oscillation of the intrusion angle in the samples is assessed, whose results indicate that the intrusion angle's oscillation amplitude and period are regional and related to the local tissue architecture.

Matrix architecture and mechanics regulate myofibril organization, costamere assembly, and contractility of engineered myocardial microtissues

The mechanical function of the myocardium is defined by cardiomyocyte contractility and the biomechanics of the extracellular matrix (ECM). Understanding this relationship remains an important unmet challenge due to limitations in existing approaches for engineering myocardial tissue. Here, we established arrays of cardiac microtissues with tunable mechanics and architecture by integrating ECM-mimetic synthetic, fiber matrices and induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs), enabling real-time contractility readouts, in-depth structural assessment, and tissue-specific computational modeling. We find that the stiffness and alignment of matrix fibers distinctly affect the structural development and contractile function of pure iPSC-CM tissues. Further examination into the impact of fibrous matrix stiffness enabled by computational models and quantitative immunofluorescence implicates cell-ECM interactions in myofibril assembly and notably costamere assembly, which correlates with improved contractile function of tissues. These results highlight how iPSC-CM tissue models with controllable architecture and mechanics can inform the design of translatable regenerative cardiac therapies.

Transmural fibre orientations based on Laplace-Dirichlet-Rule-Based-Methods and their influence on human heart simulations

It is well known that the orthotropic tissue structure decisively influences the mechanical and electrical properties of the heart. Numerous approaches to compute the orthotropic tissue structure in computational heart models have been developed in the past decades. In this study, we investigate to what extent different Laplace-Dirichlet-Rule-Based-Methods (LDRBMs) influence the local orthotropic tissue structure and thus the electromechanical behaviour of the subsequent cardiac simulation. In detail, we are utilising three Laplace-Dirichlet-Rule-Based-Methods and compare: (i) the local myofibre orientation; (ii) important global characteristics (ejection fraction, peak pressure, apex shortening, myocardial volume reduction, fractional wall thickening); (iii) local characteristics (active fibre stress, fibre strain). We observe that the orthotropic tissue structures for the three LDRBMs show significant differences in the local myofibre orientation. The global characteristics myocardial volume reduction and peak pressure are rather insensitive to a change in local myofibre orientation, while the ejection fraction is moderately influenced by the different LDRBMs. Moreover, the apical shortening and fractional wall thickening exhibit a sensitive behaviour to a change in the local myofibre orientation. The highest sensitivity can be observed for the local characteristics.

Effects of myocardial sheetlet sliding on left ventricular function

Left ventricle myocardium has a complex micro-architecture, which was revealed to consist of myocyte bundles arranged in a series of laminar sheetlets. Recent imaging studies demonstrated that these sheetlets re-orientated and likely slided over each other during the deformations between systole and diastole, and that sheetlet dynamics were altered during cardiomyopathy. However, the biomechanical effect of sheetlet sliding is not well-understood, which is the focus here. We conducted finite element simulations of the left ventricle (LV) coupled with a windkessel lumped parameter model to study sheetlet sliding, based on cardiac MRI of a healthy human subject, and modifications to account for hypertrophic and dilated geometric changes during cardiomyopathy remodeling. We modeled sheetlet sliding as a reduced shear stiffness in the sheet-normal direction and observed that (1) the diastolic sheetlet orientations must depart from alignment with the LV wall plane in order for sheetlet sliding to have an effect on cardiac function, that (2) sheetlet sliding modestly aided cardiac function of the healthy and dilated hearts, in terms of ejection fraction, stroke volume, and systolic pressure generation, but its effects were amplified during hypertrophic cardiomyopathy and diminished during dilated cardiomyopathy due to both sheetlet angle configuration and geometry, and that (3) where sheetlet sliding aided cardiac function, it increased tissue stresses, particularly in the myofibre direction. We speculate that sheetlet sliding is a tissue architectural adaptation to allow easier deformations of the LV walls so that LV wall stiffness will not hinder function, and to provide a balance between function and tissue stresses. A limitation here is that sheetlet sliding is modeled as a simple reduction in shear stiffness, without consideration of micro-scale sheetlet mechanics and dynamics.

Cell-instructive biomaterials in tissue engineering and regenerative medicine

The field of biomaterials aims to improve regenerative outcomes or scientific understanding for a wide range of tissue types and ailments. Biomaterials can be fabricated from natural or synthetic sources and display a plethora of mechanical, electrical, and geometrical properties dependent on their desired application. To date, most biomaterial systems designed for eventual translation to the clinic rely on soluble signaling moieties, such as growth factors, to elicit a specific cellular response. However, these soluble factors are often limited by high cost, convoluted synthesis, low stability, and difficulty in regulation, making the translation of these biomaterials systems to clinical or commercial applications a long and arduous process. In response to this, significant effort has been dedicated to researching cell-directive biomaterials which can signal for specific cell behavior in the absence of soluble factors. Cells of all tissue types have been shown to be innately in tune with their microenvironment, which is a biological phenomenon that can be exploited by researchers to design materials that direct cell behavior based on their intrinsic characteristics. This review will focus on recent developments in biomaterials that direct cell behavior using biomaterial properties such as charge, peptide presentation, and micro- or nano-geometry. These next generation biomaterials could offer significant strides in the development of clinically relevant medical devices which improve our understanding of the cellular microenvironment and enhance patient care in a variety of ailments.

Engineering a conduction-consistent cardiac patch with graphene oxide modified butterfly wings and human pluripotent stem cell-derived cardiomyocytes

Engineering a conduction-consistent cardiac patch has direct implications to biomedical research. However, there is difficulty in obtaining and maintaining a system that allows researchers to study physiologically relevant cardiac development, maturation, and drug screening due to the issues around inconsistent contractions of cardiomyocytes. Butterfly wings have special nanostructures arranged in parallel, which could help generate the alignment of cardiomyocytes to better mimic the natural heart tissue structure. Here, we construct a conduction-consistent human cardiac muscle patch by assembling human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) on graphene oxide (GO) modified butterfly wings. We also show this system functions as a versatile model to study human cardiomyogenesis by assembling human induced pluripotent stem cell-derived cardiac progenitor cells (hiPSC-CPCs) on the GO modified butterfly wings. The GO modified butterfly wing platform facilitated the parallel orientation of hiPSC-CMs, enhanced relative maturation as well as improved conduction consistency of the cardiomyocytes. In addition, GO modified butterfly wings enhanced the proliferation and maturation characteristics of the hiPSC-CPCs. In accordance with data obtained from RNA-sequencing and gene signatures, assembling hiPSC-CPCs on GO modified butterfly wings stimulated the differentiation of the progenitors into relatively mature hiPSC-CMs. These characteristics and capabilities of GO modified butterfly wings make them an ideal platform for heart research and drug screening.

Effect of biomaterial stiffness on cardiac mechanics in a biventricular infarcted rat heart model with microstructural representation of in situ intramyocardial injectate

Intramyocardial delivery of biomaterials is a promising concept for treating myocardial infarction. The delivered biomaterial provides mechanical support and attenuates wall thinning and elevated wall stress in the infarct region. This study aimed at developing a biventricular finite element model of an infarcted rat heart with a microstructural representation of an in situ biomaterial injectate, and a parametric investigation of the effect of the injectate stiffness on the cardiac mechanics. A three-dimensional subject-specific biventricular finite element model of a rat heart with left ventricular infarct and microstructurally dispersed biomaterial delivered 1 week after infarct induction was developed from ex vivo microcomputed tomography data. The volumetric mesh density varied between 303 mm-3 in the myocardium and 3852 mm-3 in the injectate region due to the microstructural intramyocardial dispersion. Parametric simulations were conducted with the injectate's elastic modulus varying from 4.1 to 405,900 kPa, and myocardial and injectate strains were recorded. With increasing injectate stiffness, the end-diastolic median myocardial fibre and cross-fibre strain decreased in magnitude from 3.6% to 1.1% and from -6.0% to -2.9%, respectively. At end-systole, the myocardial fibre and cross-fibre strain decreased in magnitude from -20.4% to -11.8% and from 6.5% to 4.6%, respectively. In the injectate, the maximum and minimum principal strains decreased in magnitude from 5.4% to 0.001% and from -5.4% to -0.001%, respectively, at end-diastole and from 38.5% to 0.06% and from -39.0% to -0.06%, respectively, at end-systole. With the microstructural injectate geometry, the developed subject-specific cardiac finite element model offers potential for extension to cellular injectates and in silico studies of mechanotransduction and therapeutic signalling in the infarcted heart with an infarct animal model extensively used in preclinical research.

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.

A cell-based framework for modeling cardiac mechanics

Cardiomyocytes are the functional building blocks of the heart-yet most models developed to simulate cardiac mechanics do not represent the individual cells and their surrounding matrix. Instead, they work on a homogenized tissue level, assuming that cellular and subcellular structures and processes scale uniformly. Here we present a mathematical and numerical framework for exploring tissue-level cardiac mechanics on a microscale given an explicit three-dimensional geometrical representation of cells embedded in a matrix. We defined a mathematical model over such a geometry and parametrized our model using publicly available data from tissue stretching and shearing experiments. We then used the model to explore mechanical differences between the extracellular and the intracellular space. Through sensitivity analysis, we found the stiffness in the extracellular matrix to be most important for the intracellular stress values under contraction. Strain and stress values were observed to follow a normal-tangential pattern concentrated along the membrane, with substantial spatial variations both under contraction and stretching. We also examined how it scales to larger size simulations, considering multicellular domains. Our work extends existing continuum models, providing a new geometrical-based framework for exploring complex cell-cell and cell-matrix interactions.

Myocardial mesostructure and mesofunction

The complex and highly organized structural arrangement of some five billion cardiomyocytes directs the coordinated electrical activity and mechanical contraction of the human heart. The characteristic transmural change in cardiomyocyte orientation underlies base-to-apex shortening, circumferential shortening, and left ventricular torsion during contraction. Individual cardiomyocytes shorten ∼15% and increase in diameter ∼8%. Remarkably, however, the left ventricular wall thickens by up to 30-40%. To accommodate this, the myocardium must undergo significant structural rearrangement during contraction. At the mesoscale, collections of cardiomyocytes are organized into sheetlets, and sheetlet shear is the fundamental mechanism of rearrangement that produces wall thickening. Herein, we review the histological and physiological studies of myocardial mesostructure that have established the sheetlet shear model of wall thickening. Recent developments in tissue clearing techniques allow for imaging of whole hearts at the cellular scale, whereas magnetic resonance imaging (MRI) and computed tomography (CT) can image the myocardium at the mesoscale (100 µm to 1 mm) to resolve cardiomyocyte orientation and organization. Through histology, cardiac diffusion tensor imaging (DTI), and other modalities, mesostructural sheetlets have been confirmed in both animal and human hearts. Recent in vivo cardiac DTI methods have measured reorientation of sheetlets during the cardiac cycle. We also examine the role of pathological cardiac remodeling on sheetlet organization and reorientation, and the impact this has on ventricular function and dysfunction. We also review the unresolved mesostructural questions and challenges that may direct future work in the field.

Recreating the heart's helical structure-function relationship with focused rotary jet spinning

Helical alignments within the heart's musculature have been speculated to be important in achieving physiological pumping efficiencies. Testing this possibility is difficult, however, because it is challenging to reproduce the fine spatial features and complex structures of the heart's musculature using current techniques. Here we report focused rotary jet spinning (FRJS), an additive manufacturing approach that enables rapid fabrication of micro/nanofiber scaffolds with programmable alignments in three-dimensional geometries. Seeding these scaffolds with cardiomyocytes enabled the biofabrication of tissue-engineered ventricles, with helically aligned models displaying more uniform deformations, greater apical shortening, and increased ejection fractions compared with circumferential alignments. The ability of FRJS to control fiber arrangements in three dimensions offers a streamlined approach to fabricating tissues and organs, with this work demonstrating how helical architectures contribute to cardiac performance.

A Transmural Path Model Improves the Definition of the Orthotropic Tissue Structure in Heart Simulations

In the past decades, the structure of the heart, human as well as other species, has been explored in a detailed way, e.g., via histological studies or diffusion tensor magnetic resonance imaging. Nevertheless, the assignment of the characteristic orthotropic structure in a patient-specific finite element model remains a challenging task. Various types of rule-based models, which define the local fiber and sheet orientation depending on the transmural depth, have been developed. However, the correct assessment of the transmural depth is not trivial. Its accuracy has a substantial influence on the overall mechanical and electrical properties in rule-based models. The main purpose of this study is the development of a finite element-based approach to accurately determine the transmural depth on a general unstructured grid. Instead of directly using the solution of the Laplace problem as the transmural depth, we make use of a well-established model for the assessment of the transmural thickness. It is based on two hyperbolic first-order partial differential equations for the definition of a transmural path, whereby the transmural thickness is defined as the arc length of this path. Subsequently, the transmural depth is determined based on the position on the transmural path. Originally, the partial differential equations were solved via finite differences on structured grids. In order to circumvent the need of two grids and mapping between the structured (to determine the transmural depth) and unstructured (electromechanical heart simulation) grids, we solve the equations directly on the same unstructured tetrahedral mesh. We propose a finite-element-based discontinuous Galerkin approach. Based on the accurate transmural depth, we assign the local material orientation of the orthotropic tissue structure in a usual fashion. We show that this approach leads to a more accurate definition of the transmural depth. Furthermore, for the left ventricle, we propose functions for the transmural fiber and sheet orientation by fitting them to literature-based diffusion tensor magnetic resonance imaging data. The proposed functions provide a distinct improvement compared to existing rules from the literature.

Measurement of local orientation of cardiomyocyte aggregates in human left ventricle free wall samples using X-ray phase-contrast microtomography

Most cardiomyocytes in the left ventricle wall are grouped in aggregates of four to five units that are quasi-parallel to each other. When one or more "cardiomyocyte aggregates" are delimited by two cleavage planes, this defines a "sheetlet" that can be considered as a "work unit" that contributes to the thickening of the wall during the cardiac cycle. In this paper, we introduce the skeleton method to measure the local three-dimensional (3D) orientation of cardiomyocyte aggregates in the sheetlets in three steps: data segmentation; extraction of the skeleton of the sheetlets; and calculation of the local orientation of the cardiomyocyte aggregates inside the sheetlets. These data include a series of virtual tissue volumes and five transmural human left ventricle free wall samples, imaged with 3D synchrotron radiation phase-contrast microtomography, and reconstructed with a 3.5×3.5×3.5μm³ voxel size. We computed the local orientation of the cardiomyocyte aggregates inside the sheetlets with a working window of 112×112×112μm³ in size. These data demonstrate that the skeleton method can provide accurate 3D measurements and reliable screening of the 3D evolution of the orientation of cardiomyocyte aggregates within the sheetlets. We showed that in regions that contain one population of quasi-parallel sheetlets, the orientation of the cardiomyocyte aggregates undergo "oscillations" along the perpendicular direction of the sheetlets. In regions that contain two populations of sheetlets with a different angular range, we demonstrate some discontinuity of the helix angle of the cardiomyocyte aggregates at the interface between the two populations.

Passive myocardial mechanical properties: meaning, measurement, models

Passive mechanical tissue properties are major determinants of myocardial contraction and relaxation and, thus, shape cardiac function. Tightly regulated, dynamically adapting throughout life, and affecting a host of cellular functions, passive tissue mechanics also contribute to cardiac dysfunction. Development of treatments and early identification of diseases requires better spatio-temporal characterisation of tissue mechanical properties and their underlying mechanisms. With this understanding, key regulators may be identified, providing pathways with potential to control and limit pathological development. Methodologies and models used to assess and mimic tissue mechanical properties are diverse, and available data are in part mutually contradictory. In this review, we define important concepts useful for characterising passive mechanical tissue properties, and compare a variety of in vitro and in vivo techniques that allow one to assess tissue mechanics. We give definitions of key terms, and summarise insight into determinants of myocardial stiffness in situ. We then provide an overview of common experimental models utilised to assess the role of environmental stiffness and composition, and its effects on cardiac cell and tissue function. Finally, promising future directions are outlined.

Remodeling of Ion Channel Trafficking and Cardiac Arrhythmias

Both inherited and acquired cardiac arrhythmias are often associated with the abnormal functional expression of ion channels at the cellular level. The complex machinery that continuously traffics, anchors, organizes, and recycles ion channels at the plasma membrane of a cardiomyocyte appears to be a major source of channel dysfunction during cardiac arrhythmias. This has been well established with the discovery of mutations in the genes encoding several ion channels and ion channel partners during inherited cardiac arrhythmias. Fibrosis, altered myocyte contacts, and post-transcriptional protein changes are common factors that disorganize normal channel trafficking during acquired cardiac arrhythmias. Channel availability, described notably for hERG and K_V1.5 channels, could be another potent arrhythmogenic mechanism. From this molecular knowledge on cardiac arrhythmias will emerge novel antiarrhythmic strategies.

Clinical Translation of Three-Dimensional Scar, Diffusion Tensor Imaging, Four-Dimensional Flow, and Quantitative Perfusion in Cardiac MRI: A Comprehensive Review

Cardiovascular magnetic resonance (CMR) imaging is a versatile tool that has established itself as the reference method for functional assessment and tissue characterisation. CMR helps to diagnose, monitor disease course and sub-phenotype disease states. Several emerging CMR methods have the potential to offer a personalised medicine approach to treatment. CMR tissue characterisation is used to assess myocardial oedema, inflammation or thrombus in various disease conditions. CMR derived scar maps have the potential to inform ablation therapy—both in atrial and ventricular arrhythmias. Quantitative CMR is pushing boundaries with motion corrections in tissue characterisation and first-pass perfusion. Advanced tissue characterisation by imaging the myocardial fibre orientation using diffusion tensor imaging (DTI), has also demonstrated novel insights in patients with cardiomyopathies. Enhanced flow assessment using four-dimensional flow (4D flow) CMR, where time is the fourth dimension, allows quantification of transvalvular flow to a high degree of accuracy for all four-valves within the same cardiac cycle. This review discusses these emerging methods and others in detail and gives the reader a foresight of how CMR will evolve into a powerful clinical tool in offering a precision medicine approach to treatment, diagnosis, and detection of disease.

Multiphysics computational modelling of the cardiac ventricles

Development of cardiac multiphysics models has progressed significantly over the decades and simulations combining multiple physics interactions have become increasingly common. In this review, we summarise the progress in this field focusing on various approaches of integrating ventricular structures. electrophysiological properties, myocardial mechanics, as well as incorporating blood hemodynamics and the circulatory system. Common coupling approaches are discussed and compared, including the advantages and shortcomings of each. Currently used strategies for patient-specific implementations are highlighted and potential future improvements considered.

3D MRI of explanted sheep hearts with submillimeter isotropic spatial resolution: comparison between diffusion tensor and structure tensor imaging

Objective

The aim of the study is to compare structure tensor imaging (STI) with diffusion tensor imaging (DTI) of the sheep heart (approximately the same size as the human heart).

Materials and methods

MRI acquisition on three sheep ex vivo hearts was performed at 9.4 T/30 cm with a seven-element RF coil. 3D FLASH with an isotropic resolution of 150 µm and 3D spin-echo DTI at 600 µm were performed. Tensor analysis, angles extraction and segments divisions were performed on both volumes.

Results

A 3D FLASH allows for visualization of the detailed structure of the left and right ventricles. The helix angle determined using DTI and STI exhibited a smooth transmural change from the endocardium to the epicardium. Both the helix and transverse angles were similar between techniques. Sheetlet organization exhibited the same pattern in both acquisitions, but local angle differences were seen and identified in 17 segments representation.

Discussion

This study demonstrated the feasibility of high-resolution MRI for studying the myocyte and myolaminar architecture of sheep hearts. We presented the results of STI on three whole sheep ex vivo hearts and demonstrated a good correspondence between DTI and STI.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10334-021-00913-4.

Estimating cardiomyofiber strain in vivo by solving a computational model

Since heart contraction results from the electrically activated contraction of millions of cardiomyocytes, a measure of cardiomyocyte shortening mechanistically underlies cardiac contraction. In this work we aim to measure preferential aggregate cardiomyocyte ("myofiber") strains based on Magnetic Resonance Imaging (MRI) data acquired to measure both voxel-wise displacements through systole and myofiber orientation. In order to reduce the effect of experimental noise on the computed myofiber strains, we recast the strains calculation as the solution of a boundary value problem (BVP). This approach does not require a calibrated material model, and consequently is independent of specific myocardial material properties. The solution to this auxiliary BVP is the displacement field corresponding to assigned values of myofiber strains. The actual myofiber strains are then determined by minimizing the difference between computed and measured displacements. The approach is validated using an analytical phantom, for which the ground-truth solution is known. The method is applied to compute myofiber strains using in vivo displacement and myofiber MRI data acquired in a mid-ventricular left ventricle section in N=8 swine subjects. The proposed method shows a more physiological distribution of myofiber strains compared to standard approaches that directly differentiate the displacement field.

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.

Impact of 2 different aerobic periodization training protocols on left ventricular function in patients with stable coronary artery disease: an exploratory study

We compared the impacts of linear (LP) and nonlinear (NLP) aerobic training periodizations on left ventricular (LV) function and geometry in coronary artery disease (CAD) patients. Thirty-nine CAD patients were randomized to either a 3-month isoenergetic supervised LP or NLP. All underwent standard echocardiography with assessment of 3D LV ejection fraction (LVEF), diastolic function, strain (global longitudinal, radial, and circumferential), and strain rate at baseline and study end. Training was performed 3 times/week and included high-intensity interval and moderate-intensity continuous training sessions. Training load was progressively increased in the LP group, while it was deeply increased and intercepted with a recovery week each fourth week in the NLP group. For the 34 analyzed patients, we found similar improvements for 3D LVEF (effect size (ES): LP, 0.29; NLP, 0.77), radial strain (ES: LP, 0.58; NLP, 0.48), and radial strain rate (ES: LP, 0.87; NLP, 0.17) in both groups (time for all: p ≤ 0.01). All other parameters of cardiac function remained similar. In conclusion, NLP and LP led to similar improvements in 3D LVEF and radial strain, suggesting a favourable positive cardiac remodelling through myofibers reorganization. These findings must be investigated in patients with more severe cardiac dysfunction. The study was registered on ClinicalTrials.gov (NCT03443193). Novelty: Linear and nonlinear periodization programs improved radial strain, accompanied by improvement of ejection fraction. Both aerobic periodization programs did not negatively impact cardiac function in coronary artery disease patients.

Effect of myofibre architecture on ventricular pump function by using a neonatal porcine heart model: from DT-MRI to rule-based methods

Myofibre architecture is one of the essential components when constructing personalized cardiac models. In this study, we develop a neonatal porcine bi-ventricle model with three different myofibre architectures for the left ventricle (LV). The most realistic one is derived from ex vivo diffusion tensor magnetic resonance imaging, and other two simplifications are based on rule-based methods (RBM): one is regionally dependent by dividing the LV into 17 segments, each with different myofibre angles, and the other is more simplified by assigning a set of myofibre angles across the whole ventricle. Results from different myofibre architectures are compared in terms of cardiac pump function. We show that the model with the most realistic myofibre architecture can produce larger cardiac output, higher ejection fraction and larger apical twist compared with those of the rule-based models under the same pre/after-loads. Our results also reveal that when the cross-fibre contraction is included, the active stress seems to play a dual role: its sheet-normal component enhances the ventricular contraction while its sheet component does the opposite. We further show that by including non-symmetric fibre dispersion using a general structural tensor, even the most simplified rule-based myofibre model can achieve similar pump function as the most realistic one, and cross-fibre contraction components can be determined from this non-symmetric dispersion approach. Thus, our study highlights the importance of including myofibre dispersion in cardiac modelling if RBM are used, especially in personalized models.

Computational modeling of cardiac growth and remodeling in pressure overloaded hearts-Linking microstructure to organ phenotype

Cardiac growth and remodeling (G&R) refers to structural changes in myocardial tissue in response to chronic alterations in loading conditions. One such condition is pressure overload where elevated wall stresses stimulate the growth in cardiomyocyte thickness, associated with a phenotype of concentric hypertrophy at the organ scale, and promote fibrosis. The initial hypertrophic response can be considered adaptive and beneficial by favoring myocyte survival, but over time if pressure overload conditions persist, maladaptive mechanisms favoring cell death and fibrosis start to dominate, ultimately mediating the transition towards an overt heart failure phenotype. The underlying mechanisms linking biological factors at the myocyte level to biomechanical factors at the systemic and organ level remain poorly understood. Computational models of G&R show high promise as a unique framework for providing a quantitative link between myocardial stresses and strains at the organ scale to biological regulatory processes at the cellular level which govern the hypertrophic response. However, microstructurally motivated, rigorously validated computational models of G&R are still in their infancy. This article provides an overview of the current state-of-the-art of computational models to study cardiac G&R. The microstructure and mechanosensing/mechanotransduction within cells of the myocardium is discussed and quantitative data from previous experimental and clinical studies is summarized. We conclude with a discussion of major challenges and possible directions of future research that can advance the current state of cardiac G&R computational modeling. STATEMENT OF SIGNIFICANCE: The mechanistic links between organ-scale biomechanics and biological factors at the cellular size scale remain poorly understood as these are largely elusive to investigations using experimental methodology alone. Computational G&R models show high promise to establish quantitative links which allow more mechanistic insight into adaptation mechanisms and may be used as a tool for stratifying the state and predict the progression of disease in the clinic. This review provides a comprehensive overview of research in this domain including a summary of experimental data. Thus, this study may serve as a basis for the further development of more advanced G&R models which are suitable for making clinical predictions on disease progression or for testing hypotheses on pathogenic mechanisms using in-silico models.

Multi-Band Surgery for Repaired Tetralogy of Fallot Patients With Reduced Right Ventricle Ejection Fraction: A Pilot Study

Introduction

Right ventricle (RV) failure is one of the most common symptoms among patients with repaired tetralogy of Fallot (TOF). The current surgery treatment approach including pulmonary valve replacement (PVR) showed mixed post-surgery outcomes. A novel PVR surgical strategy using active contracting bands is proposed to improve the post-PVR outcome. In lieu of testing the risky surgical procedures on real patients, computational simulations (virtual surgery) using biomechanical ventricle models based on patient-specific cardiac magnetic resonance (CMR) data were performed to test the feasibility of the PVR procedures with active contracting bands. Different band combination and insertion options were tested to identify optimal surgery designs.

Method

Cardiac magnetic resonance data were obtained from one TOF patient (male, age 23) whose informed consent was obtained. A total of 21 finite element models were constructed and solved following our established procedures to investigate the outcomes of the band insertion surgery. The non-linear anisotropic Mooney–Rivlin model was used as the material model. Five different band insertion plans were simulated (three single band models with different band locations, one model with two bands, and one model with three bands). Three band contraction ratios (10, 15, and 20%) and passive bands (0% contraction ratio) were tested. RV ejection fraction was used as the measure for cardiac function.

Results

The RV ejection fraction from the three-band model with 20% contraction increased to 41.58% from the baseline of 37.38%, a 4.20% absolute improvement. The RV ejection fractions from the other four band models with 20% contraction rate were 39.70, 39.45, and 40.70% (two-band) and 39.17%, respectively. The mean RV stress and strain values from all of the 21 models showed only modest differences (5–11%).

Conclusion

This pilot study demonstrated that the three-band model with 20% band contraction ratio led to 4.20% absolute improvement in the RV ejection fraction, which is considered as clinically significant. The passive elastic bands led to the reduction of the RV ejection fractions. The modeling results and surgical strategy need to be further developed and validated by a multi-patient study and animal experiments before clinical trial could become possible. Tissue regeneration techniques are needed to produce materials for the contracting bands.

Efficient estimation of load-free left ventricular geometry and passive myocardial properties using principal component analysis

Models of cardiac mechanics require a well-defined reference geometry from which deformations and hence myocardial strain and stress can be calculated. In the in vivo beating heart, the load-free (LF) geometry generally cannot be measured directly, since, in many cases, there is no stage at which the lumen pressures and contractile state are all zero. Therefore, there is a need for an efficient method to estimate the LF geometry, which is essential for an accurate mechanical simulation of left ventricular (LV) mechanics, and for estimations of passive and contractile constitutive parameters of the heart muscle. In this paper, we present a novel method for estimating both the LF geometry and the passive stiffness of the myocardium. A linear combination of principal components from a population of diastolic displacements is used to construct the LF geometry. For each estimate of the LF geometry and tissue stiffness, LV inflation is simulated, and the model predictions are compared with surface data at multiple stages during passive diastolic filling. The feasibility of this method was demonstrated using synthetically deformation data that were generated using LV models derived from clinical magnetic resonance image data, and the identifiability of the LF geometry and passive stiffness parameters were analysed using Hessian metrics. Applications of this method to clinical data would improve the accuracy of constitutive parameter estimation and allow a better simulation of LV wall strains and stresses.

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.

A Contemporary Look at Biomechanical Models of Myocardium

Understanding and predicting the mechanical behavior of myocardium under healthy and pathophysiological conditions are vital to developing novel cardiac therapies and promoting personalized interventions. Within the past 30 years, various constitutive models have been proposed for the passive mechanical behavior of myocardium. These models cover a broad range of mathematical forms, microstructural observations, and specific test conditions to which they are fitted. We present a critical review of these models, covering both phenomenological and structural approaches, and their relations to the underlying structure and function of myocardium. We further explore the experimental and numerical techniques used to identify the model parameters. Next, we provide a brief overview of continuum-level electromechanical models of myocardium, with a focus on the methods used to integrate the active and passive components of myocardial behavior. We conclude by pointing to future directions in the areas of optimal form as well as new approaches for constitutive modeling of myocardium.

[The antagonistic function of the heart muscle sustains the autoregulation according to Frank and Starling : Part I: Structure and function of heart muscle]

In the tradition of Harvey and according to Otto Frank the heart muscle structure is arranged in a strictly tangential fashion hence all contractile forces act in the direction of ventricular ejection. In contrast, morphology confirms that the heart consists of a 3-dimensional network of muscle fibers with up to two fifths of the chains of aggregated myocytes deviating from a tangential alignment at variable angles. Accordingly, the myocardial systolic forces contain, in addition to a constrictive also a (albeit smaller) radially acting component. Using needle force probes we have correspondingly measured an unloading type of force in a tangential direction and an auxotonic type in dilatative transversal direction of the ventricular walls to show that the myocardial body contracts actively in a 3-dimensional pattern. This antagonism supports the autoregulation of heart muscle function according to Frank and Starling, preserving ventricular shape, enhances late systolic fast dilation and attenuates systolic constriction of the ventricle wall. Auxotonic dilating forces are particularly sensitive to inotropic medication. Low dose beta-blocker is able to attenuate the antagonistic activity. All myocardial components act against four components of afterload, the hemodynamic, the myostructural, the stromatogenic and the hydraulic component. This complex interplay critically complicates clinical diagnostics. Clinical implications are far-reaching (see Part II, https://doi.org/10.1007/s00059-018-4735-x).

A tissue-engineered scale model of the heart ventricle

Laboratory studies of the heart use cell and tissue cultures to dissect heart function yet rely on animal models to measure pressure and volume dynamics. Here, we report tissue-engineered scale models of the human left ventricle, made of nanofibrous scaffolds that promote native-like anisotropic myocardial tissue genesis and chamber-level contractile function. Incorporating neonatal rat ventricular myocytes or cardiomyocytes derived from human induced pluripotent stem cells, the tissue-engineered ventricles have a diastolic chamber volume of ~500 μL (comparable to that of the native rat ventricle and approximately 1/250 the size of the human ventricle), and ejection fractions and contractile work 50–250 times smaller and 10⁴–10⁸ times smaller than the corresponding values for rodent and human ventricles, respectively. We also measured tissue coverage and alignment, calcium-transient propagation and pressure/volume loops in the presence or absence of test compounds. Moreover, we describe an instrumented bioreactor with ventricular-assist capabilities, and provide a proof-of-concept disease model of structural arrhythmia. The model ventricles can be evaluated with the same assays used in animal models and in clinical settings.

Will the real ventricular architecture please stand up?

Ventricular twisting, essential for cardiac function, is attributed to the contraction of myocardial helical fibers. The exact relationship between ventricular anatomy and function remains to be determined, but one commonly used explanatory model is the helical ventricular myocardial band (HVMB) model of Torrent‐Guasp. This model has been successful in explaining many aspects of ventricular function, (Torrent‐Guasp et al. Eur. J. Cardiothorac. Surg., 25, 376, 2004; Buckberg et al. Eur. J. Cardiothorac. Surg., 47, 587, 2015; Buckberg et al. Eur. J. Cardiothorac. Surg. 47, 778, 2015) but the model ignores important aspects of ventricular anatomy and should probably be replaced. The purpose of this review is to compare the HVMB model with a different model (nested layers). A complication when interpreting experimental observations that relate anatomy to function is that, in the myocardium, shortening does not always imply activation and lengthening does not always imply inactivation.

Patient-specific CT-based 3D passive FSI model for left ventricle in hypertrophic obstructive cardiomyopathy

Left ventricular outflow tract obstruction is observed in 70% of patients with hypertrophic cardiomyopathy, which occurs in about 1 of every 500 adults in the general population. It has been widely believed that the motion of the mitral valve, in particular, its systolic anterior motion (SAM), attributes significantly to such obstruction. For a better understanding of the mitral valve motion, a 3D patient-specific fluid-structure interaction model of the left ventricle from a patient with hypertrophic obstructive cardiomyopathy based on computed tomography (CT) scan images was proposed in this study. Displacement, structural stress, pressure, flow velocity and shear stress within the left ventricle and mitral valve were extracted to characterize their behavior. The maximum shear stress on mitral valve was 9.68 [Formula: see text]. The pressure on its posterior leaflet was higher than that on the anterior leaflet and the peak pressure on the mitral valve was 93.5 mm Hg which occurred at pre-SAM time. High angles of attack (54.3 ± 22.4°) were found in this patient. The methodology established in this study may have the potential to clarify the mechanisms of SAM and ultimately optimize surgical planning by comparing the mechanical results obtained from preoperative and postoperative models.

Fluid flow modulates electrical activity in cardiac hERG potassium channels

Fluid movement within the heart generates substantial shear forces, but the effect of this mechanical stress on the electrical activity of the human heart has not been examined. The fast component of the delayed rectifier potassium currents responsible for repolarization of the cardiac action potential, Ikr, is encoded by the human ether-a-go-go related gene (hERG) channel. Here, we exposed hERG1a channel-expressing HEK293T cells to laminar shear stress (LSS) and observed that this mechanical stress increased the whole-cell current by 30-40%. LSS shifted the voltage dependence of steady-state activation of the hERG channel to the hyperpolarizing direction, accelerated the time course of activation and recovery from inactivation, slowed down deactivation, and shifted the steady-state inactivation to the positive direction, all of which favored the hERG open state. In contrast, the time course of inactivation was faster, favoring the closed state. Using specific inhibitors of focal adhesion kinase, a regulator of mechano-transduction via the integrin pathway, we also found that the LSS-induced modulation of the whole-cell current depended on the integrin pathway. The hERG1b channel variant, which lacks the Per-Arnt-Sim (PAS) domain, and long QT syndrome-associated variants having point mutations in the PAS domain were unaffected by LSS, suggesting that the PAS domain in hERG1a channel may be involved in sensing mechanical shear stress. We conclude that a mechano-electric feedback pathway modulates hERG channel activity through the integrin pathway, indicating that mechanical forces in the heart influence its electrical activity.

Ion Channel Trafficking: Control of Ion Channel Density as a Target for Arrhythmias?

The shape of the cardiac action potential (AP) is determined by the contributions of numerous ion channels. Any dysfunction in the proper function or expression of these ion channels can result in a change in effective refractory period (ERP) and lead to arrhythmia. The processes underlying the correct targeting of ion channels to the plasma membrane are complex, and have not been fully characterized in cardiac myocytes. Emerging evidence highlights ion channel trafficking as a potential causative factor in certain acquired and inherited arrhythmias, and therapies which target trafficking as opposed to pore block are starting to receive attention. In this review we present the current evidence for the mechanisms which underlie precise control of cardiac ion channel trafficking and targeting.

Evaluation of the impact of strain correction on the orientation of cardiac diffusion tensors with in vivo and ex vivo porcine hearts

PURPOSE

To evaluate the importance of strain-correcting stimulated echo acquisition mode echo-planar imaging cardiac diffusion tensor imaging.

METHODS

Healthy pigs (n = 11) were successfully scanned with a 3D cine displacement-encoded imaging with stimulated echoes and a monopolar-stimulated echo-planar imaging diffusion tensor imaging sequence at 3 T during diastasis, peak systole, and strain sweet spots in a midventricular short-axis slice. The same diffusion tensor imaging sequence was repeated ex vivo after arresting the hearts in either a relaxed (KCl-induced) or contracted (BaCl₂ -induced) state. The displacement-encoded imaging with stimulated echoes data were used to strain-correct the in vivo cardiac diffusion tensor imaging in diastole and systole. The orientation of the primary (helix angles) and secondary (E2A) diffusion eigenvectors was compared with and without strain correction and to the strain-free ex vivo data.

RESULTS

Strain correction reduces systolic E2A significantly when compared without strain correction and ex vivo (median absolute E2A = 34.3° versus E2A = 57.1° (P = 0.01), E2A = 60.5° (P = 0.006), respectively). The systolic distribution of E2A without strain correction is closer to the contracted ex vivo distribution than with strain correction, root mean square deviation of 0.027 versus 0.038.

CONCLUSIONS

The current strain-correction model amplifies the contribution of microscopic strain to diffusion resulting in an overcorrection of E2A. Results show that a new model that considers cellular rearrangement is required. Magn Reson Med 79:2205-2215, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Myocardial Architecture, Mechanics, and Fibrosis in Congenital Heart Disease

Congenital heart disease (CHD) is the most common category of birth defect, affecting 1% of the population and requiring cardiovascular surgery in the first months of life in many patients. Due to advances in congenital cardiovascular surgery and patient management, most children with CHD now survive into adulthood. However, residual and postoperative defects are common resulting in abnormal hemodynamics, which may interact further with scar formation related to surgical procedures. Cardiovascular magnetic resonance (CMR) has become an important diagnostic imaging modality in the long-term management of CHD patients. It is the gold standard technique to assess ventricular volumes and systolic function. Besides this, advanced CMR techniques allow the acquisition of more detailed information about myocardial architecture, ventricular mechanics, and fibrosis. The left ventricle (LV) and right ventricle have unique myocardial architecture that underpins their mechanics; however, this becomes disorganized under conditions of volume and pressure overload. CMR diffusion tensor imaging is able to interrogate non-invasively the principal alignments of microstructures in the left ventricular wall. Myocardial tissue tagging (displacement encoding using stimulated echoes) and feature tracking are CMR techniques that can be used to examine the deformation and strain of the myocardium in CHD, whereas 3D feature tracking can assess the twisting motion of the LV chamber. Late gadolinium enhancement imaging and more recently T1 mapping can help in detecting fibrotic myocardial changes and evolve our understanding of the pathophysiology of CHD patients. This review not only gives an overview about available or emerging CMR techniques for assessing myocardial mechanics and fibrosis but it also describes their clinical value and how they can be used to detect abnormalities in myocardial architecture and mechanics in CHD patients.

Imaging the dynamics of cardiac fiber orientation in vivo using 3D Ultrasound Backscatter Tensor Imaging

The assessment of myocardial fiber disarray is of major interest for the study of the progression of myocardial disease. However, time-resolved imaging of the myocardial structure remains unavailable in clinical practice. In this study, we introduce 3D Backscatter Tensor Imaging (3D-BTI), an entirely novel ultrasound-based imaging technique that can map the myocardial fibers orientation and its dynamics with a temporal resolution of 10 ms during a single cardiac cycle, non-invasively and in vivo in entire volumes. 3D-BTI is based on ultrafast volumetric ultrasound acquisitions, which are used to quantify the spatial coherence of backscattered echoes at each point of the volume. The capability of 3D-BTI to map the fibers orientation was evaluated in vitro in 5 myocardial samples. The helicoidal transmural variation of fiber angles was in good agreement with the one obtained by histological analysis. 3D-BTI was then performed to map the fiber orientation dynamics in vivo in the beating heart of an open-chest sheep at a volume rate of 90 volumes/s. Finally, the clinical feasibility of 3D-BTI was shown on a healthy volunteer. These initial results indicate that 3D-BTI could become a fully non-invasive technique to assess myocardial disarray at the bedside of patients.

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.

Patient-Specific MRI-Based Right Ventricle Models Using Different Zero-Load Diastole and Systole Geometries for Better Cardiac Stress and Strain Calculations and Pulmonary Valve Replacement Surgical Outcome Predictions

Background

Accurate calculation of ventricular stress and strain is critical for cardiovascular investigations. Sarcomere shortening in active contraction leads to change of ventricular zero-stress configurations during the cardiac cycle. A new model using different zero-load diastole and systole geometries was introduced to provide more accurate cardiac stress/strain calculations with potential to predict post pulmonary valve replacement (PVR) surgical outcome.

Methods

Cardiac magnetic resonance (CMR) data were obtained from 16 patients with repaired tetralogy of Fallot prior to and 6 months after pulmonary valve replacement (8 male, 8 female, mean age 34.5 years). Patients were divided into Group 1 (n = 8) with better post PVR outcome and Group 2 (n = 8) with worse post PVR outcome based on their change in RV ejection fraction (EF). CMR-based patient-specific computational RV/LV models using one zero-load geometry (1G model) and two zero-load geometries (diastole and systole, 2G model) were constructed and RV wall thickness, volume, circumferential and longitudinal curvatures, mechanical stress and strain were obtained for analysis. Pairwise T-test and Linear Mixed Effect (LME) model were used to determine if the differences from the 1G and 2G models were statistically significant, with the dependence of the pair-wise observations and the patient-slice clustering effects being taken into consideration. For group comparisons, continuous variables (RV volumes, WT, C- and L- curvatures, and stress and strain values) were summarized as mean ± SD and compared between the outcome groups by using an unpaired Student t-test. Logistic regression analysis was used to identify potential morphological and mechanical predictors for post PVR surgical outcome.

Results

Based on results from the 16 patients, mean begin-ejection stress and strain from the 2G model were 28% and 40% higher than that from the 1G model, respectively. Using the 2G model results, RV EF changes correlated negatively with stress (r = -0.609, P = 0.012) and with pre-PVR RV end-diastole volume (r = -0.60, P = 0.015), but did not correlate with WT, C-curvature, L-curvature, or strain. At begin-ejection, mean RV stress of Group 2 was 57.4% higher than that of Group 1 (130.1±60.7 vs. 82.7±38.8 kPa, P = 0.0042). Stress was the only parameter that showed significant differences between the two groups. The combination of circumferential curvature, RV volume and the difference between begin-ejection stress and end-ejection stress was the best predictor for post PVR outcome with an area under the ROC curve of 0.855. The begin-ejection stress was the best single predictor among the 8 individual parameters with an area under the ROC curve of 0.782.

Conclusion

The new 2G model may be able to provide more accurate ventricular stress and strain calculations for potential clinical applications. Combining morphological and mechanical parameters may provide better predictions for post PVR outcome.

Resolving Fine Cardiac Structures in Rats with High-Resolution Diffusion Tensor Imaging

Cardiac architecture is fundamental to cardiac function and can be assessed non-invasively with diffusion tensor imaging (DTI). Here, we aimed to overcome technical challenges in ex vivo DTI in order to extract fine anatomical details and to provide novel insights in the 3D structure of the heart. An integrated set of methods was implemented in ex vivo rat hearts, including dynamic receiver gain adjustment, gradient system scaling calibration, prospective adjustment of diffusion gradients, and interleaving of diffusion-weighted and non-diffusion-weighted scans. Together, these methods enhanced SNR and spatial resolution, minimised orientation bias in diffusion-weighting, and reduced temperature variation, enabling detection of tissue structures such as cell alignment in atria, valves and vessels at an unprecedented level of detail. Improved confidence in eigenvector reproducibility enabled tracking of myolaminar structures as a basis for segmentation of functional groups of cardiomyocytes. Ex vivo DTI facilitates acquisition of high quality structural data that complements readily available in vivo cardiac functional and anatomical MRI. The improvements presented here will facilitate next generation virtual models integrating micro-structural and electro-mechanical properties of the heart.

Ventricular fiber optimization utilizing the branching structure

In this paper, we propose an algorithm that optimizes the ventricular fiber structure of the human heart. A number of histological studies and diffusion tensor magnetic resonance imaging analyses have revealed that the myocardial fiber forms a right-handed helix at the endocardium. However, the fiber formation changes its orientation as a function of transmural depth, becoming a left-handed helix at the epicardium. To determine how nature can construct such a structure, which obtains surprising pumping performance, we introduce macroscopic modeling of the branching structure of cardiac myocytes in our finite element ventricular model and utilize this in an optimization process. We put a set of multidirectional fibers around a central fiber orientation at each point of the ventricle walls and simulate heartbeats by generating contraction forces along each of these directions. We examine two optimization processes using the workloads or impulses measured in these directions to update the central fiber orientation. Both processes improve the pumping performance towards an optimal value within several tens of heartbeats, starting from an almost-flat fiber orientation. However, compared with the workload optimization, the impulse optimization produces better agreement with experimental studies on transmural changes of fiber helix angle, streamline patterns of characteristic helical structures, and temporal changes in strain. Furthermore, the impulse optimization is robust under geometrical changes of the heart and tends to homogenize various mechanical factors such as the stretch and stretch rate along the fiber orientation, the contraction force, and energy consumption. Copyright © 2015 John Wiley & Sons, Ltd.

Mapping cardiac microstructure of rabbit heart in different mechanical states by high resolution diffusion tensor imaging: A proof-of-principle study

Myocardial microstructure and its macroscopic materialisation are fundamental to the function of the heart. Despite this importance, characterisation of cellular features at the organ level remains challenging, and a unifying description of the structure of the heart is still outstanding. Here, we optimised diffusion tensor imaging data to acquire high quality data in ex vivo rabbit hearts in slack and contractured states, approximating diastolic and systolic conditions. The data were analysed with a suite of methods that focused on different aspects of the myocardium. In the slack heart, we observed a similar transmural gradient in helix angle of the primary eigenvector of up to 23.6°/mm in the left ventricle and 24.2°/mm in the right ventricle. In the contractured heart, the same transmural gradient remained largely linear, but was offset by up to +49.9° in the left ventricle. In the right ventricle, there was an increase in the transmural gradient to 31.2°/mm and an offset of up to +39.0°. The application of tractography based on each eigenvector enabled visualisation of streamlines that depict cardiomyocyte and sheetlet organisation over large distances. We observed multiple V- and N-shaped sheetlet arrangements throughout the myocardium, and insertion of sheetlets at the intersection of the left and right ventricle. This study integrates several complementary techniques to visualise and quantify the heart's microstructure, projecting parameter representations across different length scales. This represents a step towards a more comprehensive characterisation of myocardial microstructure at the whole organ level.

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics

With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.

Material stiffness parameters as potential predictors of presence of left ventricle myocardial infarction: 3D echo-based computational modeling study

Background

Ventricle material properties are difficult to obtain under in vivo conditions and are not readily available in the current literature. It is also desirable to have an initial determination if a patient had an infarction based on echo data before more expensive examinations are recommended. A noninvasive echo-based modeling approach and a predictive method were introduced to determine left ventricle material parameters and differentiate patients with recent myocardial infarction (MI) from those without.

Methods

Echo data were obtained from 10 patients, 5 with MI (Infarct Group) and 5 without (Non-Infarcted Group). Echo-based patient-specific computational left ventricle (LV) models were constructed to quantify LV material properties. All patients were treated equally in the modeling process without using MI information. Systolic and diastolic material parameter values in the Mooney-Rivlin models were adjusted to match echo volume data. The equivalent Young’s modulus (YM) values were obtained for each material stress–strain curve by linear fitting for easy comparison. Predictive logistic regression analysis was used to identify the best parameters for infract prediction.

Results

The LV end-systole material stiffness (ES-YM_f) was the best single predictor among the 12 individual parameters with an area under the receiver operating characteristic (ROC) curve of 0.9841. LV wall thickness (WT), material stiffness in fiber direction at end-systole (ES-YM_f) and material stiffness variation (∆YM_f) had positive correlations with LV ejection fraction with correlation coefficients r = 0.8125, 0.9495 and 0.9619, respectively. The best combination of parameters WT + ∆YM_f was the best over-all predictor with an area under the ROC curve of 0.9951.

Conclusion

Computational modeling and material stiffness parameters may be used as a potential tool to suggest if a patient had infarction based on echo data. Large-scale clinical studies are needed to validate these preliminary findings.

Biomechanics Simulations Using Cubic Hermite Meshes with Extraordinary Nodes for Isogeometric Cardiac Modeling

Cubic Hermite hexahedral finite element meshes have some well-known advantages over linear tetrahedral finite element meshes in biomechanical and anatomic modeling using isogeometric analysis. These include faster convergence rates as well as the ability to easily model rule-based anatomic features such as cardiac fiber directions. However, it is not possible to create closed complex objects with only regular nodes; these objects require the presence of extraordinary nodes (nodes with 3 or >= 5 adjacent elements in 2D) in the mesh. The presence of extraordinary nodes requires new constraints on the derivatives of adjacent elements to maintain continuity. We have developed a new method that uses an ensemble coordinate frame at the nodes and a local-to-global mapping to maintain continuity. In this paper, we make use of this mapping to create cubic Hermite models of the human ventricles and a four-chamber heart. We also extend the methods to the finite element equations to perform biomechanics simulations using these meshes. The new methods are validated using simple test models and applied to anatomically accurate ventricular meshes with valve annuli to simulate complete cardiac cycle simulations.

Shear stress activates monovalent cation channel transient receptor potential melastatin subfamily 4 in rat atrial myocytes via type 2 inositol 1,4,5-trisphosphate receptors and Ca(2+) release

KEY POINTS

During each contraction and haemodynamic disturbance, cardiac myocytes are subjected to fluid shear stress as a result of blood flow and the relative movement of sheets of myocytes. The present study aimed to characterize the shear stress-sensitive membrane current in atrial myocytes using the whole-cell patch clamp technique, combined with pressurized fluid flow, as well as pharmacological and genetic interventions of specific proteins. The data obtained suggest that shear stress indirectly activates the monovalent cation current carried by transient receptor potential melastatin subfamily 4 channels via type 2 inositol 1,4,5-trisphosphate receptor-mediated Ca(2+) release in subsarcolemmal domains of atrial myocytes. Ca(2+) -mediated interactions between these two proteins under shear stress may be an important mechanism by which atrial cells measure mechanical stress and translate it to alter their excitability.

ABSTRACT

Atrial myocytes are subjected to shear stress during the cardiac cycle under physiological or pathological conditions. The ionic currents regulated by shear stress remain poorly understood. We report the characteristics, molecular identity and activation mechanism of the shear stress-sensitive current (Ishear ) in rat atrial myocytes. A shear stress of ∼16 dyn cm(-2) was applied to single myocytes using a pressurized microflow system, and the current was measured by whole-cell patch clamp. In symmetrical CsCl solutions with minimal concentrations of internal EGTA, Ishear showed an outwardly rectifying current-voltage relationship (reversal at -2 mV). The current was conducted primarily (∼80%) by monovalent cations but not Ca(2+) . It was suppressed by intracellular Ca(2+) buffering at a fixed physiological level, inhibitors of transient receptor potential melastatin subfamily 4 (TRPM4), intracellular introduction of TRPM4 antibodies or knockdown of TRPM4 expression, suggesting that TRPM4 carries most of this current. A notable reduction in Ishear occurred upon inhibition of Ca(2+) release through the ryanodine receptors or inositol 1,4,5-trisphosphate receptors (IP3 R) and upon depletion of sarcoplasmic reticulum Ca(2+) . In type 2 IP3 R (IP3 R2) knockout atrial myocytes, Ishear was 10-20% of that in wild-type myocytes. Immunocytochemistry and proximity ligation assays revealed that TRPM4 and IP3 R2 were expressed at peripheral sites with co-localization, although they are not localized within 40 nm. Peripheral localization of TRPM4 was intact in IP3 R2 knockout cells. The data obtained in the present study suggest that shear stress activates TRPM4 current by triggering Ca(2+) release from the IP3 R2 in the peripheral domains of atrial myocytes.

Modeling Active Contraction and Relaxation of Left Ventricle Using Different Zero-load Diastole and Systole Geometries for Better Material Parameter Estimation and Stress/Strain Calculations

Modeling ventricle active contraction based on in vivo data is extremely challenging because of complex ventricle geometry, dynamic heart motion and active contraction where the reference geometry (zero-stress geometry) changes constantly. A new modeling approach using different diastole and systole zero-load geometries was introduced to handle the changing zero-load geometries for more accurate stress/strain calculations. Echo image data were acquired from 5 patients with infarction (Infarct Group) and 10 without (Non-Infarcted Group). Echo-based computational two-layer left ventricle models using one zero-load geometry (1G) and two zero-load geometries (2G) were constructed. Material parameter values in Mooney-Rivlin models were adjusted to match echo volume data. Effective Young's moduli (YM) were calculated for easy comparison. For diastole phase, begin-filling (BF) mean YM value in the fiber direction (YM_f) was 738% higher than its end-diastole (ED) value (645.39 kPa vs. 76.97 kPa, p=3.38E-06). For systole phase, end-systole (ES) YM_f was 903% higher than its begin-ejection (BE) value (1025.10 kPa vs. 102.11 kPa, p=6.10E-05). Comparing systolic and diastolic material properties, ES YM_f was 59% higher than its BF value (1025.10 kPa vs. 645.39 kPa. p=0.0002). BE mean stress value was 514% higher than its ED value (299.69 kPa vs. 48.81 kPa, p=3.39E-06), while BE mean strain value was 31.5% higher than its ED value (0.9417 vs. 0.7162, p=0.004). Similarly, ES mean stress value was 562% higher than its BF value (19.74 kPa vs. 2.98 kPa, p=6.22E-05), and ES mean strain value was 264% higher than its BF value (0.1985 vs. 0.0546, p=3.42E-06). 2G models improved over 1G model limitations and may provide better material parameter estimation and stress/strain calculations.

Shear stress induces a longitudinal Ca(2+) wave via autocrine activation of P2Y1 purinergic signalling in rat atrial myocytes

Atrial myocytes are exposed to shear stress during the cardiac cycle and haemodynamic disturbance. In response, they generate a longitudinally propagating global Ca(2+) wave. Here, we investigated the cellular mechanisms underlying the shear stress-mediated Ca(2+) wave, using two-dimensional confocal Ca(2+) imaging combined with a pressurized microflow system in single rat atrial myocytes. Shear stress of ∼16 dyn cm(-2) for 8 s induced ∼1.2 aperiodic longitudinal Ca(2+) waves (∼79 μm s(-1)) with a delay of 0.2-3 s. Pharmacological blockade of ryanodine receptors (RyRs) or inositol 1,4,5-trisphosphate receptors (IP3 Rs) abolished shear stress-induced Ca(2+) wave generation. Furthermore, in atrial myocytes from type 2 IP3R (IP3R2) knock-out mice, shear stress failed to induce longitudinal Ca(2+) waves. The phospholipase C (PLC) inhibitor U73122, but not its inactive analogue U73343, abolished the shear-induced longitudinal Ca(2+) wave. However, pretreating atrial cells with blockers for stretch-activated channels, Na(+)-Ca(2+) exchanger, transient receptor potential melastatin subfamily 4, or nicotinamide adenine dinucleotide phosphate oxidase did not suppress wave generation under shear stress. The P2 purinoceptor inhibitor suramin, and the potent P2Y1 receptor antagonist MRS 2179, both suppressed the Ca(2+) wave, whereas the P2X receptor antagonist, iso-PPADS, did not alter it. Suppression of gap junction hemichannels permeable to ATP or extracellular application of ATP-metabolizing apyrase inhibited the wave. Removal of external Ca(2+) to enhance hemichannel opening facilitated the wave generation. Our data suggest that longitudinally propagating, regenerative Ca(2+) release through RyRs is triggered by P2Y1-PLC-IP3R2 signalling that is activated by gap junction hemichannel-mediated ATP release in atrial myocytes under shear stress.

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.

Spin echo versus stimulated echo diffusion tensor imaging of the in vivo human heart

Purpose

To compare signal‐to‐noise ratio (SNR) efficiency and diffusion tensor metrics of cardiac diffusion tensor mapping using acceleration‐compensated spin‐echo (SE) and stimulated echo acquisition mode (STEAM) imaging.

Methods

Diffusion weighted SE and STEAM sequences were implemented on a clinical 1.5 Tesla MR system. The SNR efficiency of SE and STEAM was measured (b = 50–450 s/mm²) in isotropic agar, anisotropic diffusion phantoms and the in vivo human heart. Diffusion tensor analysis was performed on mean diffusivity, fractional anisotropy, helix and transverse angles.

Results

In the isotropic phantom, the ratio of SNR efficiency for SE versus STEAM, SNR_t(SE/STEAM), was 2.84 ± 0.08 for all tested b‐values. In the anisotropic diffusion phantom the ratio decreased from 2.75 ± 0.05 to 2.20 ± 0.13 with increasing b‐value, similar to the in vivo decrease from 2.91 ± 0.43 to 2.30 ± 0.30. Diffusion tensor analysis revealed reduced deviation of helix angles from a linear transmural model and reduced transverse angle standard deviation for SE compared with STEAM. Mean diffusivity and fractional anisotropy were measured to be statistically different (P < 0.001) between SE and STEAM.

Conclusion

Cardiac DTI using motion‐compensated SE yields a 2.3–2.9× increase in SNR efficiency relative to STEAM and improved accuracy of tensor metrics. The SE method hence presents an attractive alternative to STEAM based approaches. Magn Reson Med 76:862–872, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.