Biomechanical properties and microstructure of human ventricular myocardium

Personalized evaluation of the passive myocardium in ischemic cardiomyopathy via computational modeling using Bayesian optimization

Biomechanics-based patient-specific modeling is a promising approach that has proved invaluable for its clinical potential to assess the adversities caused by ischemic heart disease (IHD). In the present study, we propose a framework to find the passive material properties of the myocardium and the unloaded shape of cardiac ventricles simultaneously in patients diagnosed with ischemic cardiomyopathy (ICM). This was achieved by minimizing the difference between the simulated and the target end-diastolic pressure-volume relationships (EDPVRs) using black-box Bayesian optimization, based on the finite element analysis (FEA). End-diastolic (ED) biventricular geometry and the location of the ischemia were determined from cardiac magnetic resonance (CMR) imaging. We employed our pipeline to model the cardiac ventricles of three patients aged between 57 and 66 years, with and without the inclusion of valves. An excellent agreement between the simulated and the target EDPVRs has been reached. Our results revealed that the incorporation of valvular springs typically leads to lower hyperelastic parameters for both healthy and ischemic myocardium, as well as a higher fiber Green strain in the viable regions compared to models without valvular stiffness. Furthermore, the addition of valve-related effects did not result in significant changes in myofiber stress after optimization. We concluded that more accurate results could be obtained when cardiac valves were considered in modeling ventricles. The present novel and practical methodology paves the way for developing digital twins of ischemic cardiac ventricles, providing a non-invasive assessment for designing optimal personalized therapies in precision medicine.

Role of Microtubule Network in the Passive Anisotropic Viscoelasticity of Healthy Right Ventricle

Cardiomyocytes are viscoelastic and key determinants of right ventricle (RV) mechanics. Intracellularly, microtubules are found to impact the viscoelasticity of isolated cardiomyocytes or trabeculae; whether they contribute to the tissue-level viscoelasticity is unknown. Our goal was to reveal the role of the microtubule network in the passive anisotropic viscoelasticity of the healthy RV. Equibiaxial stress relaxation tests were conducted in healthy RV free wall (RVFW) under early (6%) and end (15%) diastolic strain levels, and at sub- and physiological stretch rates. The viscoelasticity was assessed at baseline and after the removal of microtubule network. Furthermore, a quasi-linear viscoelastic (QLV) model was applied to delineate the contribution of microtubules to the relaxation behavior of RVFW. After removing the microtubule network, RVFW elasticity and viscosity were reduced at the early diastolic strain level and in both directions. The reduction in elasticity was stronger in the longitudinal direction, whereas the degree of changes in viscosity were equivalent between directions. There was insignificant change in RVFW viscoelasticity at late diastolic strain level. Finally, the modeling showed that the tissue's relaxation strength was reduced by the removal of the microtubule network, but the change was present only at a later time scale. These new findings suggest a critical role of cytoskeleton filaments in RVFW passive mechanics in physiological conditions.

The Stiffness of the Ascending Aorta Has a Direct Impact on Left Ventricular Function: An In Silico Model

During systole, longitudinal shortening of the left ventricle (LV) displaces the aortic root toward the apex of the heart and stretches the ascending aorta (AA). An in silico study (Living Left Heart Human Model, Dassault Systèmes Simulia Corporation) demonstrated that stiffening of the AA affects myocardial stress and LV strain patterns. With AA stiffening, myofiber stress increased overall in the LV, with particularly high-stress areas at the septum. The most pronounced reduction in strain was noted along the septal longitudinal region. The pressure-volume loops showed that AA stiffening caused a deterioration in LV function, with increased end-systolic volume, reduced systolic LV pressure, decreased stroke volume and effective stroke work, but elevated end-diastolic pressure. An increase in myofiber contractility indicated that stroke volume and effective stroke work could be recovered, with an increase in LV end-systolic pressure and a decrease in end-diastolic pressure. Longitudinal and radial strains remained reduced, but circumferential strains increased over baseline, compensating for lost longitudinal LV function. Myofiber stress increased overall, with the most dramatic increase in the septal region and the LV apex. We demonstrate a direct mechanical pathophysiologic link between stiff AA and reduced longitudinal left ventricular strain which are common in patients with HFpEF.

Effects of cardiac growth on electrical dyssynchrony in the single ventricle patient

Single ventricle patients, including those with hypoplastic left heart syndrome (HLHS), typically undergo three palliative heart surgeries culminating in the Fontan procedure. HLHS is associated with high rates of morbidity and mortality, and many patients develop arrhythmias, electrical dyssynchrony, and eventually ventricular failure. However, the correlation between ventricular enlargement and electrical dysfunction in HLHS physiology remains poorly understood. Here we characterize the relationship between growth and electrophysiology in HLHS using computational modeling. We integrate a personalized finite element model, a volumetric growth model, and a personalized electrophysiology model to perform controlled in silico experiments. We show that right ventricle enlargement negatively affects QRS duration and interventricular dyssynchrony. Conversely, left ventricle enlargement can partially compensate for this dyssynchrony. These findings have potential implications on our understanding of the origins of electrical dyssynchrony and, ultimately, the treatment of HLHS patients.

Establishment of a Biaxial Testing System for Characterization of Right Ventricle Viscoelasticity Under Physiological Loadings

PURPOSE

Prior studies have indicated an impact of cardiac muscle viscoelasticity on systolic and diastolic functions. However, the studies of ventricular free wall viscoelasticity, particularly for that of right ventricles (RV), are limited. Moreover, investigations on ventricular passive viscoelasticity have been restricted to large animals and there is a lack of data on rodent species. To fill this knowledge gap, this study aims to develop a biaxial tester that induces high-speed physiological deformations to characterize the passive viscoelasticity of rat RVs.

METHODS

The biaxial testing system was fabricated so that planar deformation of rat ventricle tissues at physiological strain rates was possible. The testing system was validated using isotropic polydimethylsiloxane (PDMS) sheets. Next, viscoelastic measurements were performed in healthy rat RV free walls by equibiaxial cyclic sinusoidal loadings and stress relaxation.

RESULTS

The biaxial tester's consistency, accuracy, and stability was confirmed from the PDMS samples measurements. Moreover, significant viscoelastic alterations of the RV were found between sub-physiological (0.1 Hz) and physiological frequencies (1-8 Hz). From hysteresis loop analysis, we found as the frequency increased, the elasticity and viscosity were increased in both directions. Interestingly, the ratio of storage energy to dissipated energy (Wd/Ws) remained constant at 0.1-5 Hz. We did not observe marked differences in healthy RV viscoelasticity between longitudinal and circumferential directions.

CONCLUSION

This work provides a new experimental tool to quantify the passive, biaxial viscoelasticity of ventricle free walls in both small and large animals. The dynamic mechanical tests showed frequency-dependent elastic and viscous behaviors of healthy rat RVs. But the ratio of dissipated energy to stored energy was maintained between frequencies. These findings offer novel baseline information on the passive viscoelasticity of healthy RVs in adult rats.

Role of the microtubule network in the passive anisotropic viscoelasticity of right ventricle with pulmonary hypertension progression

Cardiomyocytes are viscoelastic and contribute significantly to right ventricle (RV) mechanics. Microtubule, a cytoskeletal protein, has been shown to regulate cardiomyocyte viscoelasticity. Additionally, hypertrophied cardiomyocytes from failing myocardium have increased microtubules and cell stiffness. How the microtubules contribute to the tissue-level viscoelastic behavior in RV failure remains unknown. Our aim was to investigate the role of the microtubules in the passive anisotropic viscoelasticity of the RV free wall (RVFW) during pulmonary hypertension (PH) progression. Equibiaxial stress relaxation tests were conducted in the RVFW from healthy and PH rats under early (6%) and end (15%) diastolic strains, and at sub- (1Hz) and physiological (5Hz) stretch-rates. The RVFW viscoelasticity was also measured before and after the depolymerization of microtubules at 5Hz. In intact tissues, PH increased RV viscosity and elasticity at both stretch rates and strain levels, and the increase was stronger in the circumferential than longitudinal direction. At 6% of strain, the removal of microtubules reduced elasticity, viscosity, and the ratio of viscosity to elasticity in both directions and for both healthy and diseased RVs. However, at 15% of strain, the effect of microtubules was different between groups - both viscosity and elasticity were reduced in healthy RVs, but in the diseased RVs only the circumferential viscosity and the ratio of viscosity to elasticity were reduced. These data suggest that, at a large strain with collagen recruitment, microtubules play more significant roles in healthy RV tissue elasticity and diseased RV tissue viscosity. Our findings suggest cardiomyocyte cytoskeletons are critical to RV passive viscoelasticity under pressure overload. STATEMENT OF SIGNIFICANCE: This study investigated the impact of microtubules on the passive anisotropic viscoelasticity of the right ventricular (RV) free wall at healthy and pressure-overloaded states. We originally found that the microtubules contribute significantly to healthy and diseased RV viscoelasticity in both (longitudinal and circumferential) directions at early diastolic strains. At end diastolic strains (with the engagement of collagen fibers), microtubules contribute more to the tissue elasticity of healthy RVs and tissue viscosity of diseased RVs. Our findings reveal the critical role of microtubules in the anisotropic viscoelasticity of the RV tissue, and the altered contribution from healthy to diseased state suggests that therapies targeting microtubules may have potentials for RV failure patients.

Biomechanical characterization of the passive porcine stomach

The complex mechanics of the gastric wall facilitates the main digestive tasks of the stomach. However, the interplay between the mechanical properties of the stomach, its microstructure, and its vital functions is not yet fully understood. Importantly, the pig animal model is widely used in biomedical research for preliminary or ethically prohibited studies of the human digestion system. Therefore, this study aims to thoroughly characterize the mechanical behavior and microstructure of the porcine stomach. For this purpose, multiple quasi-static mechanical tests were carried out with three different loading modes, i.e., planar biaxial extension, radial compression, and simple shear. Stress-relaxation tests complemented the quasi-static experiments to evaluate the deformation and strain-dependent viscoelastic properties. Each experiment was conducted on specimens of the complete stomach wall and two separate layers, mucosa and muscularis, from each of the three gastric regions, i.e., fundus, body, and antrum. The significant preconditioning effects and the considerable regional and layer-specific differences in the tissue response were analyzed. Furthermore, the mechanical experiments were complemented with histology to examine the influence of the microstructural composition on the macrostructural mechanical response and vice versa. Importantly, the shear tests showed lower stresses in the complete wall compared to the single layers which the loose network of submucosal collagen might explain. Also, the stratum arrangement of the muscularis might explain mechanical anisotropy during tensile tests. This study shows that gastric tissue is characterized by a highly heterogeneous microstructure with regional variations in layer composition reflecting not only functional differences but also diverse mechanical behavior. STATEMENT OF SIGNIFICANCE: Unfortunately, only few experimental data on gastric tissue are available for an adequate material parameter and model estimation. The present study therefore combines layer- and region-specific stomach wall mechanics obtained under multiple loading conditions with histological insights into the heterogeneous microstructure. On the one hand, the extensive data sets of this study expand our understanding of the interplay between gastric mechanics, motility and functionality, which could help to identify and treat associated pathologies. On the other hand, such data sets are of high relevance for the constitutive modeling of stomach tissue, and its application in the field of medical engineering, e.g., in the development of surgical staplers and the improvement of bariatric surgical interventions.

A homogenized constrained mixture model of cardiac growth and remodeling: analyzing mechanobiological stability and reversal

Cardiac growth and remodeling (G&R) patterns change ventricular size, shape, and function both globally and locally. Biomechanical, neurohormonal, and genetic stimuli drive these patterns through changes in myocyte dimension and fibrosis. We propose a novel microstructure-motivated model that predicts organ-scale G&R in the heart based on the homogenized constrained mixture theory. Previous models, based on the kinematic growth theory, reproduced consequences of G&R in bulk myocardial tissue by prescribing the direction and extent of growth but neglected underlying cellular mechanisms. In our model, the direction and extent of G&R emerge naturally from intra- and extracellular turnover processes in myocardial tissue constituents and their preferred homeostatic stretch state. We additionally propose a method to obtain a mechanobiologically equilibrated reference configuration. We test our model on an idealized 3D left ventricular geometry and demonstrate that our model aims to maintain tensional homeostasis in hypertension conditions. In a stability map, we identify regions of stable and unstable G&R from an identical parameter set with varying systolic pressures and growth factors. Furthermore, we show the extent of G&R reversal after returning the systolic pressure to baseline following stage 1 and 2 hypertension. A realistic model of organ-scale cardiac G&R has the potential to identify patients at risk of heart failure, enable personalized cardiac therapies, and facilitate the optimal design of medical devices.

Mechanical testing and comparison of porcine tissue, silicones and 3D-printed materials for cardiovascular phantoms

Background: Cardiovascular phantoms for patient education, pre-operative planning, surgical training, haemodynamic simulation, and device testing may help improve patient care. However, currently used materials may have different mechanical properties compared to biological tissue. Methods/Aim: The aim of this study was to investigate the mechanical properties of 3D-printing and silicone materials in comparison to biological cardiovascular tissues. Uniaxial cyclic tension testing was performed using dumbbell samples from porcine tissue (aorta, pulmonary artery, right and left ventricle). Flexible testing materials included 15 silicone (mixtures) and three 3D-printing materials. The modulus of elasticity was calculated for different deformation ranges. Results: The modulus of elasticity (0%-60%) for the aorta ranged from 0.16 to 0.18 N/mm2, for the pulmonary artery from 0.07 to 0.09 N/mm2, and for the right ventricle as well as the left ventricle short-axis from 0.1 to 0.16 N/mm2. For silicones the range of modulus of elasticity was 0.02-1.16 N/mm2, and for the 3D-printed materials from 0.85 to 1.02 N/mm2. The stress-strain curves of all tissues showed a non-linear behaviour in the cyclic tensile testing, with a distinct toe region, followed by exponential strain hardening behaviour towards the peak elongation. The vessel samples showed a more linear behaviour comparted to myocardial samples. The silicones and 3D printing materials exhibited near-linearity at higher strain ranges, with a decrease in stiffness following the initial deformation. All samples showed a deviation between the loading and unloading curves (hysteresis), and a reduction in peak force over the first few cycles (adaptation effect) at constant deformation. Conclusion: The modulus of elasticity of silicone mixtures is more in agreement to porcine cardiovascular tissues than 3D-printed materials. All synthetic materials showed an almost linear behaviour in the mechanical testing compared to the non-linear behaviour of the biological tissues, probably due to fibre recruitment mechanism in the latter.

Simulating and Predicting the Mechanical Behavior of Electrospun Scaffolds for Cardiac Patches Fabrication

Fabricating helical scaffolds using electrospinning is a common approach for cardiac implantation, aiming to achieve properties similar to native tissue. However, this process requires multiple experimental attempts to select suitable electrospun properties and validate resulting mechanical responses. To overcome the time and cost constraints associated with this iterative procedure, Finite Element Analysis (FEA) can be applied using stable hyperelastic and viscoelastic models that describe the response of electrospun scaffolds under different conditions. In this study, we aim to create accurate simulations of the viscoelastic behavior of electrospun helical scaffolds. We fabricated helical fibers from Poly (3-caprolactone) (PCL) using the electrospinning process to achieve this. The electrospun samples were subjected to uniaxial deformation, and their response was modelled using existing hyperelastic and stress relaxation models. The simulations were built on experimental data for specific deformation speed and maximum strain conditions. The FEM results were evaluated by accounting for the stress-softening phenomenon, which significantly impacted the models. The electrospun scaffolds' predictions were performed in other than the initial experimental conditions to verify our simulations' accuracy and reliability.

Quantifying the microstructural and biomechanical changes in the porcine ventricles during growth and remodelling

Cardiac tissue growth and remodelling (G & R) occur in response to the changing physiological demands of the heart after birth. The early shift to pulmonary circulation produces an immediate increase in ventricular workload, causing microstructural and biomechanical changes that serve to maintain overall physiological homoeostasis. Such cardiac G & R continues throughout life. Quantifying the tissue's mechanical and microstructural changes because of G & R is of increasing interest, dovetailing with the emerging fields of personalised and precision solutions. This study aimed to determine equibiaxial, and non-equibiaxial extension, stress-relaxation, and the underlying microstructure of the passive porcine ventricles tissue at four time points spanning from neonatal to adulthood. The three-dimensional microstructure was investigated via two-photon excited fluorescence and second-harmonic generation microscopy on optically cleared tissues, describing the 3D orientation, rotation and dispersion of the cardiomyocytes and collagen fibrils. The results revealed that during biomechanical testing, myocardial ventricular tissue possessed non-linear, anisotropic, and viscoelastic behaviour. An increase in stiffness and viscoelasticity was noted for the left and right ventricular free walls from neonatal to adulthood. Microstructural analyses revealed concomitant increases in cardiomyocyte rotation and dispersion. This study provides baseline data, describing the biomechanical and microstructural changes in the left and right ventricular myocardial tissue during G & R, which should prove valuable to researchers in developing age-specific, constitutive models for more accurate computational simulations. STATEMENT OF SIGNIFICANCE: There is a dearth of experimental data describing the growth and remodelling of left and right ventricular tissue. The published literature is fragmented, with data reported via different experimental techniques using tissues harvested from a variety of animals, with different gender and ages. This prevents developing a continuum of data spanning birth to death, so limiting the potential that can be leveraged to aid computational modelling and simulations. In this study, equibiaxial, non-equibiaxial, and stress-relaxation data are presented, describing directional-dependent material responses. The biomechanical data is consolidated with equivalent microstructural data, an important element for the development of future material models. Combined, these data describe microstructural and biomechanical changes in the ventricles, spanning G &R from neonatal to adulthood.

Optimal assist strategy exploration for a direct assist device under stress‒strain dynamics

OBJECTIVES

The aim of this paper is to introduce a new assist strategy for a direct assist device that can enhance the heart's pumping efficiency and decrease the chances of myocardial injury in contrast to the conventional assist strategy.

METHODS

We established a finite element model of a biventricular heart, divided the ventricles into several regions, and applied pressure to each region separately in order to identify the primary and secondary assist areas. Then combined and tested these areas to obtain the optimal assist strategy.

RESULTS

The results indicate that our method exhibits an assist efficiency approximately ten times higher than that of the traditional assist method. Additionally, the stress distribution in the ventricles is more uniform after assistance.

CONCLUSIONS

In summary, this approach can result in a more homogenous stress distribution within the heart while also minimizing the contact area with it, which can reduce the incidence of allergic reactions and the likelihood of myocardial injury.

Physical model of end-diastolic and end-systolic pressure-volume relationships of a heart

Left ventricular stiffness and contractility, characterized by the end-diastolic pressure-volume relationship (EDPVR) and the end-systolic pressure-volume relationship (ESPVR), are two important indicators of the performance of the human heart. Although much research has been conducted on EDPVR and ESPVR, no model with physically interpretable parameters combining both relationships has been presented, thereby impairing the understanding of cardiac physiology and pathology. Here, we present a model that evaluates both EDPVR and ESPVR with physical interpretations of the parameters in a unified framework. Our physics-based model fits the available experimental data and in silico results very well and outperforms existing models. With prescribed parameters, the new model is used to predict the pressure-volume relationships of the left ventricle. Our model provides a deeper understanding of cardiac mechanics and thus will have applications in cardiac research and clinical medicine.

An updated Lagrangian constrained mixture model of pathological cardiac growth and remodelling

Progressive left ventricular (LV) growth and remodelling (G&R) is often induced by volume and pressure overload, characterized by structural and functional adaptation through myocyte hypertrophy and extracellular matrix remodelling, which are dynamically regulated by biomechanical factors, inflammation, neurohormonal pathways, etc. When prolonged, it can eventually lead to irreversible heart failure. In this study, we have developed a new framework for modelling pathological cardiac G&R based on constrained mixture theory using an updated reference configuration, which is triggered by altered biomechanical factors to restore biomechanical homeostasis. Eccentric and concentric growth, and their combination have been explored in a patient-specific human LV model under volume and pressure overload. Eccentric growth is triggered by overstretching of myofibres due to volume overload, i.e. mitral regurgitation, whilst concentric growth is driven by excessive contractile stress due to pressure overload, i.e. aortic stenosis. Different biological constituent's adaptations under pathological conditions are integrated together, which are the ground matrix, myofibres and collagen network. We have shown that this constrained mixture-motivated G&R model can capture different phenotypes of maladaptive LV G&R, such as chamber dilation and wall thinning under volume overload, wall thickening under pressure overload, and more complex patterns under both pressure and volume overload. We have further demonstrated how collagen G&R would affect LV structural and functional adaption by providing mechanistic insight on anti-fibrotic interventions. This updated Lagrangian constrained mixture based myocardial G&R model has the potential to understand the turnover processes of myocytes and collagen due to altered local mechanical stimuli in heart diseases, and in providing mechanistic links between biomechanical factors and biological adaption at both the organ and cellular levels. Once calibrated with patient data, it can be used for assessing heart failure risk and designing optimal treatment therapies. STATEMENT OF SIGNIFICANCE: Computational modelling of cardiac G&R has shown high promise to provide insight into heart disease management when mechanistic understandings are quantified between biomechanical factors and underlying cellular adaptation processes. The kinematic growth theory has been dominantly used to phenomenologically describe the biological G&R process but neglecting underlying cellular mechanisms. We have developed a constrained mixture based G&R model with updated reference by taking into account different mechanobiological processes in the ground matrix, myocytes and collagen fibres. This G&R model can serve as a basis for developing more advanced myocardial G&R models further informed by patient data to assess heart failure risk, predict disease progression, select the optimal treatment by hypothesis testing, and eventually towards a truly precision cardiology using in-silico models.

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 mesenchymal stem cells and heparan sulfate mimetics on urethral function and vaginal wall biomechanics in a simulated rat childbirth injury model

INTRODUCTION AND HYPOTHESIS

New treatments are needed for pelvic floor disorders. ReGeneraTing Agent® (RGTA®) is a promising regenerative therapy. Therefore, the objective of this study was to compare regenerative abilities of mesenchymal stem cells (MSCs) and RGTA® on regeneration after simulated childbirth injury in rats.

METHODS

Rats underwent pudendal nerve crush and vaginal distension (PNC+VD) or sham injury. Rats that underwent PNC+VD were treated intravenously with vehicle, MSCs or RGTA® 1 h, 7 days, and 14 days after surgery. Sham rats received 1 ml vehicle at all time points. After 21 days, urethral function and pudendal nerve function were tested. Vaginal tissues were harvested for biomechanical testing and histology. Biaxial testing was performed to measure tissue stiffness.

RESULTS

PNC+VD decreased urethral and pudendal nerve function compared with sham. Vaginal wall stiffness was significantly decreased in longitudinal and transverse tissue axes after PNC+VD compared with sham. MSC or RGTA® did not restore urethral or pudendal nerve function. However, MSC treatment resolved loss in vaginal wall stiffness in both tissue axes and improved collagen content within the vaginal wall. RGTA® treatment increased vaginal wall anisotropy by increasing relative stiffness in the longitudinal direction. PNC+VD (with vehicle or MSCs) enhanced elastogenesis, which was not observed after RGTA® treatment.

CONCLUSIONS

Treatment with MSCs facilitated recovery of vaginal wall biomechanical properties and connective tissue composition after PNC+VD, whereas treatment with RGTA® resulted in anisotropic biomechanical changes. This indicates that MSCs and RGTA® promote different aspects of vaginal tissue regeneration after simulated childbirth injury.

A multi-scale computational model for the passive mechanical behavior of right ventricular myocardium

We have previously demonstrated the importance of myofiber-collagen mechanical interactions in modeling the passive mechanical behavior of right ventricle free wall (RVFW) myocardium. To gain deeper insights into these coupling mechanisms, we developed a high-fidelity, micro-anatomically realistic 3D finite element model of right ventricle free wall (RVFW) myocardium by combining high-resolution imaging and supercomputer-based simulations. We first developed a representative tissue element (RTE) model at the sub-tissue scale by specializing the hyperelastic anisotropic structurally-based constitutive relations for myofibers and ECM collagen, and equi-biaxial and non-equibiaxial loading conditions were simulated using the open-source software FEniCS to compute the effective stress-strain response of the RTE. To estimate the model parameters of the RTE model, we first fitted a 'top-down' biaxial stress-strain behavior with our previous structurally based (tissue-scale) model, informed by the measured myofiber and collagen fiber composition and orientation distributions. Next, we employed a multi-scale approach to determine the tissue-level (5 x 5 x 0.7 mm specimen size) RVFW biaxial behavior via 'bottom-up' homogenization of the fitted RTE model, recapitulating the histologically measured myofiber and collagen orientation to the biaxial mechanical data. Our homogenization approach successfully reproduced the tissue-level mechanical behavior of our previous studies in all biaxial deformation modes, suggesting that the 3D micro-anatomical arrangement of myofibers and ECM collagen is indeed a primary mechanism driving myofiber-collagen interactions.

Don't go breakin' my heart: cardioprotective alterations to the mechanical and structural properties of reperfused myocardium during post-infarction inflammation

Myocardial infarctions (MIs) kickstart an intense inflammatory response resulting in extracellular matrix (ECM) degradation, wall thinning, and chamber dilation that leaves the heart susceptible to rupture. Reperfusion therapy is one of the most effective strategies for limiting adverse effects of MIs, but is a challenge to administer in a timely manner. Late reperfusion therapy (LRT; 3 + hours post-MI) does not limit infarct size, but does reduce incidences of post-MI rupture and improves long-term patient outcomes. Foundational studies employing LRT in the mid-twentieth century revealed beneficial reductions in infarct expansion, aneurysm formation, and left ventricle dysfunction. The mechanism by which LRT acts, however, is undefined. Structural analyses, relying largely on one-dimensional estimates of ECM composition, have found few differences in collagen content between LRT and permanently occluded animal models when using homogeneous samples from infarct cores. Uniaxial testing, on the other hand, revealed slight reductions in stiffness early in inflammation, followed soon after by an enhanced resistance to failure for cases of LRT. The use of one-dimensional estimates of ECM organization and gross mechanical function have resulted in a poor understanding of the infarct's spatially variable mechanical and structural anisotropy. To resolve these gaps in literature, future work employing full-field mechanical, structural, and cellular analyses is needed to better define the spatiotemporal post-MI alterations occurring during the inflammatory phase of healing and how they are impacted following reperfusion therapy. In turn, these studies may reveal how LRT affects the likelihood of rupture and inspire novel approaches to guide scar formation.

Machine learning and physical based modeling for cardiac hypertrophy

Background and objective

Predicting the long-term expansion and remodeling of the left ventricle in patients is challenging task but it has the potential to be clinically very useful.

Methods

In our study, we present machine learning models based on random forests, gradient boosting, and neural networks, used to track cardiac hypertrophy. We collected data from multiple patients, and then the model was trained using the patient's medical history and present level of cardiac health. We also demonstrate a physical-based model, using the finite element procedure to simulate the development of cardiac hypertrophy.

Results

Our models were used to forecast the evolution of hypertrophy over six years. The machine learning model and finite element model provided similar results.

Conclusions

The finite element model is much slower, but it's more accurate compared to the machine learning model since it's based on physical laws guiding the hypertrophy process. On the other hand, the machine learning model is fast but the results can be less trustworthy in some cases. Both of our models, enable us to monitor the development of the disease. Because of its speed machine learning model is more likely to be used in clinical practice. Further improvements to our machine learning model could be achieved by collecting data from finite element simulations, adding them to the dataset, and retraining the model. This can result in a fast and more accurate model combining the advantages of physical-based and machine learning modeling.

Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations

We develop a fully data-driven model of anisotropic finite viscoelasticity using neural ordinary differential equations as building blocks. We replace the Helmholtz free energy function and the dissipation potential with data-driven functions that a priori satisfy physics-based constraints such as objectivity and the second law of thermodynamics. Our approach enables modeling viscoelastic behavior of materials under arbitrary loads in three-dimensions even with large deformations and large deviations from the thermodynamic equilibrium. The data-driven nature of the governing potentials endows the model with much needed flexibility in modeling the viscoelastic behavior of a wide class of materials. We train the model using stress-strain data from biological and synthetic materials including humain brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.

Alterations of biaxial viscoelastic properties of the right ventricle in pulmonary hypertension development in rest and acute stress conditions

Introduction: The right ventricle (RV) mechanical property is an important determinant of its function. However, compared to its elasticity, RV viscoelasticity is much less studied, and it remains unclear how pulmonary hypertension (PH) alters RV viscoelasticity. Our goal was to characterize the changes in RV free wall (RVFW) anisotropic viscoelastic properties with PH development and at varied heart rates. Methods: PH was induced in rats by monocrotaline treatment, and the RV function was quantified by echocardiography. After euthanasia, equibiaxial stress relaxation tests were performed on RVFWs from healthy and PH rats at various strain-rates and strain levels, which recapitulate physiological deformations at varied heart rates (at rest and under acute stress) and diastole phases (at early and late filling), respectively. Results and Discussion: We observed that PH increased RVFW viscoelasticity in both longitudinal (outflow tract) and circumferential directions. The tissue anisotropy was pronounced for the diseased RVs, not healthy RVs. We also examined the relative change of viscosity to elasticity by the damping capacity (ratio of dissipated energy to total energy), and we found that PH decreased RVFW damping capacity in both directions. The RV viscoelasticity was also differently altered from resting to acute stress conditions between the groups-the damping capacity was decreased only in the circumferential direction for healthy RVs, but it was reduced in both directions for diseased RVs. Lastly, we found some correlations between the damping capacity and RV function indices and there was no correlation between elasticity or viscosity and RV function. Thus, the RV damping capacity may be a better indicator of RV function than elasticity or viscosity alone. These novel findings on RV dynamic mechanical properties offer deeper insights into the role of RV biomechanics in the adaptation of RV to chronic pressure overload and acute stress.

Recent Advances in Tissue-Engineered Cardiac Scaffolds-The Progress and Gap in Mimicking Native Myocardium Mechanical Behaviors

Heart failure is the leading cause of death in the US and worldwide. Despite modern therapy, challenges remain to rescue the damaged organ that contains cells with a very low proliferation rate after birth. Developments in tissue engineering and regeneration offer new tools to investigate the pathology of cardiac diseases and develop therapeutic strategies for heart failure patients. Tissue -engineered cardiac scaffolds should be designed to provide structural, biochemical, mechanical, and/or electrical properties similar to native myocardium tissues. This review primarily focuses on the mechanical behaviors of cardiac scaffolds and their significance in cardiac research. Specifically, we summarize the recent development of synthetic (including hydrogel) scaffolds that have achieved various types of mechanical behavior-nonlinear elasticity, anisotropy, and viscoelasticity-all of which are characteristic of the myocardium and heart valves. For each type of mechanical behavior, we review the current fabrication methods to enable the biomimetic mechanical behavior, the advantages and limitations of the existing scaffolds, and how the mechanical environment affects biological responses and/or treatment outcomes for cardiac diseases. Lastly, we discuss the remaining challenges in this field and suggestions for future directions to improve our understanding of mechanical control over cardiac function and inspire better regenerative therapies for myocardial restoration.

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.

Backscatter tensor imaging and 3D speckle tracking for simultaneous ex vivo structure and deformation measurement of myocardium

OBJECTIVE

Biaxial mechanical testing is a common method for elucidation of mechanical properties of excised ventricular myocardium, especially in the context of structural remodeling that accompanies heart disease. Current imaging strategies in biaxial testing are based on optical camera imaging of the tissue surface, thus providing no information about the tissue microstructure and limiting strain measurements to two dimensions. Here, these limitations are overcome by replacing the camera with ultrasound imaging in order to measure both transmural fiber orientation and 3D tissue deformation during biaxial testing.

METHODS

Quasi-static biaxial mechanical testing is applied to four samples of excised porcine ventricular myocardium (two left- and two right-ventricular tissues). During testing, a rotational scan of an ultrasound linear array provides data for both backscatter tensor imaging and 3D speckle tracking, from which transmural fiber orientation and tissue deformation are computed, respectively. Ultrasound-derived fiber orientation and tissue strain are validated against histology and camera surface imaging, respectively.

DISCUSSION

Ultrasound-derived fiber angle and tissue strain exhibit good accuracy, with root-mean-square errors of 9.9° and 1.2% strain, respectively. Further investigation into the optimization of backscatter tensor imaging is warranted. Replacing the rotational scan of a linear array with volume imaging with a matrix array will improve the technique.

CONCLUSION

Ultrasound imaging can replace the optical camera measurement during biaxial mechanical testing of ventricular myocardium in order to accurately provide measurements of transmural fiber orientation and tissue strain. In situ knowledge of transmural fiber structure and tissue deformation can enhance the inverse problem used to determine tissue mechanical properties from biaxial testing.

Dynamic morphology imaging of cardiomyocytes based on AFM

A cardiomyocyte is the basic structural and functional unit of the heart, which is the actual executor of the systolic function. The study of the contraction and relaxation characteristics of cardiomyocyte is of great significance to the physiological behavior and pathology of the heart. How to dynamically express its contraction and relaxation behaviors in 3D has become a challenging issue. Although the video analysis method under the optical microscope can observe the changes in the horizontal direction, it is difficult to describe the changes in the vertical direction. The atomic force microscope (AFM) can accurately express the mechanical and morphological characteristics of the changes in the vertical direction, but it cannot be fully expressed in real time because it is acquired by scanning with a single probe. In order to express the contraction and relaxation characteristics of cardiomyocyte accurately and three dimensionally, a dynamic imaging method in this study is proposed using the periodicity of AFM acquisition and the periodicity of cardiomyocyte contraction. Compared with the optical experiment, it is proven that this method can dynamically represent the contraction and relaxation processes of cardiomyocyte and solve the problem of how to express it in 3D. It brings a new way for the study of physiological characteristics of cardiomyocytes and dynamic imaging by AFM.

Cardiac hypertrophy simulations using parametric and echocardiography-based left ventricle model with shell finite elements

In our paper, we simulated cardiac hypertrophy with the use of shell elements in parametric and echocardiography-based left ventricle (LV) models. The hypertrophy has an impact on the change in the wall thickness, displacement field and the overall functioning of the heart. We computed both eccentric and concentric hypertrophy effects and tracked changes in the ventricle shape and wall thickness. Thickening of the wall was developed under the influence of concentric hypertrophy, while the eccentric hypertrophy produces wall thinning. To model passive stresses we used the recently developed material modal based on the Holzapfel experiments. Also, our specific shell composite finite element models for heart mechanics are much smaller and simpler to use with respect to conventional 3D models. Furthermore, the presented modeling approach of the echocardiography-based LV can serve as the basis for practical applications since it relies on the true patient-specific geometry and experimental constitutive relationships. Our model gives an insight into hypertrophy development in realistic heart geometries, and it has the potential to test medical hypotheses regarding hypertrophy evolution in a healthy and heart with a disease, under the influence of different conditions and parameters.

The risk of fragment penetrating injury to the heart

Injury due to the penetration of fragments into parts of the body has been the major cause of morbidity and mortality after an explosion. Penetrating injuries into the heart present very high mortality, yet the risk associated with such injuries has not been quantified. Quantifying this risk is key in the design of personal protection and the design of infrastructure. This study is the first quantitative assessment of cardiac penetrating injuries from energised fragments. Typical fragments (5-mm sphere, 0.78-g right-circular cylinder and 1.1-g chisel-nosed cylinder) were accelerated to a range of target striking velocities using a bespoke gas-gun system and impacted ventricular and atrial walls of lamb hearts. The severity of injury was shown to not depend on location (ventricular or atrial wall). The striking velocity with 50% probability of critical injury (Abbreviated Injury Scale (AIS) 5 score) ranged between 31 and 36 m/s across all 3 fragments used. These findings can help directly in reducing morbidity and mortality from explosive events as they can be implemented readily into models that aim to predict casualties in an explosive event, inform protocols for first responders, and improve design of infrastructure and personal protective equipment.

On the structural origin of the anisotropy in the myocardium: Multiscale modeling and analysis

Due to structural heterogeneities within the tissue, the myocardium displays an orthotropic material behavior. However, the link between the microstructure and the macroscopic mechanical properties is still not fully established. In particular, if it is admitted that the cardiomyocyte organization induces a transversely isotropic symmetry, the relative role in the observed orthotropic symmetry of cardiomyocyte orientation variation and perimysium collagen "sheetlet" structure, two mechanisms occurring at different scales, is still a matter of debate. In order to shed light on this question, we designed a multiscale model of the myocardium, bridging the cell, sheetlet and tissue scales. More precisely, we compared the macroscopic anisotropy obtained by homogenization of different mesostructures consisting in cardiomyocytes and extracellular collageneous layers, also taking into account the variation of cardiomyocyte and sheetlet orientations on the macroscale, to available experimental data. This study confirms the importance of sheetlets layers in assuring the tissue's anisotropic response, as cardiomyocytes-only mesostructures cannot reproduce the observed anisotropy. Moreover, our model shows the existence of a size effect in the myocardial tissue shear properties, which will require further experimental analysis.

Computational analysis of ventricular mechanics in hypertrophic cardiomyopathy patients

Hypertrophic cardiomyopathy (HCM) is a genetic heart disease that is associated with many pathological features, such as a reduction in global longitudinal strain (GLS), myofiber disarray and hypertrophy. The effects of these features on left ventricle (LV) function are, however, not clear in two phenotypes of HCM, namely, obstructive and non-obstructive. To address this issue, we developed patient-specific computational models of the LV using clinical measurements from 2 female HCM patients and a control subject. Left ventricular mechanics was described using an active stress formulation and myofiber disarray was described using a structural tensor in the constitutive models. Unloaded LV configuration for each subject was first determined from their respective end-diastole LV geometries segmented from the cardiac magnetic resonance images, and an empirical single-beat estimation of the end-diastolic pressure volume relationship. The LV was then connected to a closed-loop circulatory model and calibrated using the clinically measured LV pressure and volume waveforms, peak GLS and blood pressure. Without consideration of myofiber disarray, peak myofiber tension was found to be lowest in the obstructive HCM subject (60 kPa), followed by the non-obstructive subject (242 kPa) and the control subject (375 kPa). With increasing myofiber disarray, we found that peak tension has to increase in the HCM models to match the clinical measurements. In the obstructive HCM patient, however, peak tension was still depressed (cf. normal subject) at the largest degree of myofiber disarray found in the clinic. The computational modeling workflow proposed here can be used in future studies with more HCM patient data.

Tissue Clearing and Its Application in the Musculoskeletal System

The musculoskeletal system is an integral part of the human body. Currently, most skeletal muscle research is conducted through conventional histological sections due to technological limitations and the structure of skeletal muscles. For studying and observing bones and muscles, there is an urgent need for three-dimensional, objective imaging technologies. Optical tissue-clearing technologies seem to offer a novel and accessible approach to research of the musculoskeletal system. Using this approach, the components which cause refraction or prevent light from penetrating into the tissue are physically and chemically eliminated; then the liquid in the tissue is replaced with high-refractive-index chemicals. This innovative method, which allows three-dimensional reconstruction at the cellular and subcellular scale, significantly improves imaging depth and resolution. Nonetheless, this technology was not originally developed to image bones or muscles. When compared with brain and nerve organs which have attracted considerable attention in this field, the musculoskeletal system contains fewer lipids and has high levels of hemoglobin, collagen fibers, and inorganic hydroxyapatite crystals. Currently, three-dimensional imaging methods are widely used in the diagnosis and treatment of skeletal and muscular illnesses. In this regard, it is vitally important to review and evaluate the optical tissue-clearing technologies currently employed in the musculoskeletal system, so that researchers may make an informed decision. In the meantime, this study offers guidelines and recommendations for expanding the use of this technology in the musculoskeletal system.

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.

An introduction to the Ogden model in biomechanics: benefits, implementation tools and limitations

Constitutive models are important to biomechanics for two key reasons. First, constitutive modelling is an essential component of characterizing tissues' mechanical properties for informing theoretical and computational models of biomechanical systems. Second, constitutive models can be used as a theoretical framework for extracting and comparing key quantities of interest from material characterization experiments. Over the past five decades, the Ogden model has emerged as a popular constitutive model in soft tissue biomechanics with relevance to both informing theoretical and computational models and to comparing material characterization experiments. The goal of this short review is threefold. First, we will discuss the broad relevance of the Ogden model to soft tissue biomechanics and the general characteristics of soft tissues that are suitable for approximating with the Ogden model. Second, we will highlight exemplary uses of the Ogden model in brain tissue, blood clot and other tissues. Finally, we offer a tutorial on fitting the one-term Ogden model to pure shear experimental data via both an analytical approximation of homogeneous deformation and a finite-element model of the tissue domain. Overall, we anticipate that this short review will serve as a practical introduction to the use of the Ogden model in biomechanics. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

An introduction to the Ogden model in biomechanics: benefits, implementation tools and limitations

Constitutive models are important to biomechanics for two key reasons. First, constitutive modelling is an essential component of characterizing tissues' mechanical properties for informing theoretical and computational models of biomechanical systems. Second, constitutive models can be used as a theoretical framework for extracting and comparing key quantities of interest from material characterization experiments. Over the past five decades, the Ogden model has emerged as a popular constitutive model in soft tissue biomechanics with relevance to both informing theoretical and computational models and to comparing material characterization experiments. The goal of this short review is threefold. First, we will discuss the broad relevance of the Ogden model to soft tissue biomechanics and the general characteristics of soft tissues that are suitable for approximating with the Ogden model. Second, we will highlight exemplary uses of the Ogden model in brain tissue, blood clot and other tissues. Finally, we offer a tutorial on fitting the one-term Ogden model to pure shear experimental data via both an analytical approximation of homogeneous deformation and a finite-element model of the tissue domain. Overall, we anticipate that this short review will serve as a practical introduction to the use of the Ogden model in biomechanics. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Direct Observation of Adhesion and Mechanical Behavior of a Single Poly(lactic-co-glycolic acid) (PLGA) Fiber Using an In Situ Technique for Tissue Engineering

Nanometer- and submicrometer-sized fiber have been used as scaffolds for tissue engineering, because of their fundamental load-bearing properties in synergy with mechano-transduction. This study investigates a single biodegradable poly(lactic-co-glycolic acid) (PLGA) fiber's load-displacement behavior utilizing the nanoindentation technique coupled with a high-resolution in situ imaging system. It is demonstrated that a maximum force of ∼3 μN in the radial direction and displacement of at least 150% of fiber diameter should be applied to acquire the fiber's macroscopic mechanical properties for tissue engineering. The adhesion behavior of a single fiber is captured using a high-resolution camera. The digital image correlation (DIC) technique is adopted to quantify the adhesion force (∼25 μN) between the fiber and the tip. Adhesion force has also been quantified for the fiber after immersing in phosphate-buffered saline (PBS) to mimic the bioenvironment. A 4-fold increase in adhesion force after PBS treatment was observed due to water penetration and hydrolysis on the fiber's surface. A high similarity between mechanical properties of a single fiber and native tissues (elastic modulus of 10-25 kPa) and superior adhesion force (25-107.25 μN) was observed, which is excellent for promoting cell-matrix communication. Overall, this study examines the mechanics of a single fiber using innovative indentation and imaging processing techniques, disclosing its profound and striking roles in tissue engineering.

Data-driven computational models of ventricular-arterial hemodynamics in pediatric pulmonary arterial hypertension

Pulmonary arterial hypertension (PAH) is a complex disease involving increased resistance in the pulmonary arteries and subsequent right ventricular (RV) remodeling. Ventricular-arterial interactions are fundamental to PAH pathophysiology but are rarely captured in computational models. It is important to identify metrics that capture and quantify these interactions to inform our understanding of this disease as well as potentially facilitate patient stratification. Towards this end, we developed and calibrated two multi-scale high-resolution closed-loop computational models using open-source software: a high-resolution arterial model implemented using CRIMSON, and a high-resolution ventricular model implemented using FEniCS. Models were constructed with clinical data including non-invasive imaging and invasive hemodynamic measurements from a cohort of pediatric PAH patients. A contribution of this work is the discussion of inconsistencies in anatomical and hemodynamic data routinely acquired in PAH patients. We proposed and implemented strategies to mitigate these inconsistencies, and subsequently use this data to inform and calibrate computational models of the ventricles and large arteries. Computational models based on adjusted clinical data were calibrated until the simulated results for the high-resolution arterial models matched within 10% of adjusted data consisting of pressure and flow, whereas the high-resolution ventricular models were calibrated until simulation results matched adjusted data of volume and pressure waveforms within 10%. A statistical analysis was performed to correlate numerous data-derived and model-derived metrics with clinically assessed disease severity. Several model-derived metrics were strongly correlated with clinically assessed disease severity, suggesting that computational models may aid in assessing PAH severity.

How viscous is the beating heart?: Insights from a computational study

Understanding tissue rheology is critical to accurately model the human heart. While the elastic properties of cardiac tissue have been extensively studied, its viscous properties remain an issue of ongoing debate. Here we adopt a viscoelastic version of the classical Holzapfel Ogden model to study the viscous timescales of human cardiac tissue. We perform a series of simulations and explore stress-relaxation curves, pressure-volume loops, strain profiles, and ventricular wall strains for varying viscosity parameters. We show that the time window for model calibration strongly influences the parameter identification. Using a four-chamber human heart model, we observe that, during the physiologically relevant time scales of the cardiac cycle, viscous relaxation has a negligible effect on the overall behavior of the heart. While viscosity could have important consequences in pathological conditions with compromised contraction or relaxation properties, we conclude that, for simulations within the physiological range of a human heart beat, we can reasonably approximate the human heart as hyperelastic.

Investigating the influence of the viscoelastic material as a heart muscle simulator on the powering leadless pacemaker from heartbeats by using a piezoelectric beam

This paper studies experimentally and analytically the influence of the viscoelastic cardiac muscle on the energy harvesting from heartbeats for powering the leadless pacemakers by using a piezoelectric beam. An appropriate representative gel-type viscoelastic material that mimics the heart tissue is used in the tests. The piezoelectric beam coupled with a gel-type material is analytically modeled, and experimentally tested. By considering a combination of the translational standard linear solid model and a rotational spring component for the gel-type material, the analytical model of the coupled system is developed utilizing the generalized Hamilton’s principle. The system is attached on top of a shaker and excited harmonically, and the time history of output voltage and accelerations are measured. The analytical model is verified by experimental results for the tip displacement, voltage, generated power, phase-portraits histories, and voltage FRF with harmonic base excitations. Transmissibility analysis by the analytical model shows that for excitation frequencies beyond a specific frequency, the viscoelastic material can magnify the amplitude of the excitation and incredibly improve the power generation. Experimental results demonstrate that by coupling the gel into the harvester, oscillations of the tip are increased into high energy orbits and large tip deflections around the resonance frequency. The significantly widened frequency bandwidth and the increased power output at specific input frequencies are the other results of considering the viscoelastic characteristics of the heart wall in the dynamic investigations. By simulating the response of the energy harvesting system to the heartbeat impulsive rhythm, when the energy harvesting system is attached to the viscoelastic material, the output power is increased from 18 to 55 µW. The obtained results reveal that influence of the viscoelastic properties of the heart muscle is crucial in the accurate design of the energy harvesting system for the self-powered medical leadless pacemaker.

Strain-Dependent Stress Relaxation Behavior of Healthy Right Ventricular Free Wall

The increasing evidence of stress-strain hysteresis in large animal or human myocardium calls for extensive characterizations of the passive viscoelastic behavior of the myocardium. Several recent studies have investigated and modeled the viscoelasticity of the left ventricle while the right ventricle (RV) viscoelasticity remains poorly understood. Our goal was to characterize the biaxial viscoelastic behavior of RV free wall (RVFW) using two modeling approaches. We applied both quasi-linear viscoelastic (QLV) and nonlinear viscoelastic (NLV) theories to experimental stress relaxation data from healthy adult ovine. A three-term Prony series relaxation function combined with an Ogden strain energy density function were used in the QLV modeling, while a power-law formulation was adopted in the NLV approach. The ovine RVFW exhibited an anisotropic and strain-dependent viscoelastic behavior relative to anatomical coordinates, and the NLV model showed a higher capacity in predicting strain-dependent stress relaxation than the QLV model. From the QLV fitting, the relaxation term associated with the largest time constant played the dominant role in the overall relaxation behavior at all strains from early to late diastole, whereas the term associated with the smallest time constant was pronounced only at low strains at early diastole. From the NLV fitting, the parameters showed a nonlinear dependence on the strain. Overall, our study characterized the anisotropic, nonlinear viscoelasticity to capture the elastic and viscous resistances of the RVFW during diastole. These findings deepen our understanding of RV myocardium dynamic mechanical properties. STATEMENT OF SIGNIFICANCE: Although significant progress has been made to understand the passive elastic behavior of the right ventricle free wall (RVFW), its viscoelastic behavior remains poorly understood. In this study, we originally applied both quasi-linear viscoelastic (QLV) and nonlinear viscoelastic (NLV) models to published experimental data from healthy ovine RVFW. Our results revealed an anisotropic and strain-dependent viscoelastic behavior of the RVFW. The parameters from the NLV fitting showed nonlinear relationships with the strain, and the NLV model showed a higher capacity in predicting strain-dependent stress relaxation than the QLV model. These findings characterize the anisotropic, nonlinear viscoelasticity of RVFW to fully capture the total (elastic and viscous) resistance that is critical to diastolic function.

Electrospun electroconductive constructs of aligned fibers for cardiac tissue engineering

Myocardial infarction remains the leading cause of death in the western world. Since the heart has limited regenerative capabilities, several cardiac tissue engineering (CTE) strategies have been proposed to repair the damaged myocardium. A novel electrospun construct with aligned and electroconductive fibers combining gelatin, poly(lactic-co-glycolic) acid and polypyrrole that may serve as a cardiac patch is presented. Constructs were characterized for fiber alignment, surface wettability, shrinkage and swelling behavior, porosity, degradation rate, mechanical properties, and electrical properties. Cell-biomaterial interactions were studied using three different types of cells, Neonatal Rat Ventricular Myocytes (NRVM), human lung fibroblasts (MRC-5) and induced pluripotent stem cells (iPSCs). All cell types showed good viability and unique organization on construct surfaces depending on their phenotype. Finally, we assessed the maturation status of NRVMs after 14 days by confocal images and qRT-PCR. Overall evidence supports a proof-of-concept that this novel biomaterial construct could be a good candidate patch for CTE applications.

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.

Robust and efficient fixed-point algorithm for the inverse elastostatic problem to identify myocardial passive material parameters and the unloaded reference configuration

Image-based computational models of the heart represent a powerful tool to shed new light on the mechanisms underlying physiological and pathological conditions in cardiac function and to improve diagnosis and therapy planning. However, in order to enable the clinical translation of such models, it is crucial to develop personalized models that are able to reproduce the physiological reality of a given patient. There have been numerous contributions in experimental and computational biomechanics to characterize the passive behavior of the myocardium. However, most of these studies suffer from severe limitations and are not applicable to high-resolution geometries. In this work, we present a novel methodology to perform an automated identification of in vivo properties of passive cardiac biomechanics. The highly-efficient algorithm fits material parameters against the shape of a patient-specific approximation of the end-diastolic pressure-volume relation (EDPVR). Simultaneously, an unloaded reference configuration is generated, where a novel line search strategy to improve convergence and robustness is implemented. Only clinical image data or previously generated meshes at one time point during diastole and one measured data point of the EDPVR are required as an input. The proposed method can be straightforwardly coupled to existing finite element (FE) software packages and is applicable to different constitutive laws and FE formulations. Sensitivity analysis demonstrates that the algorithm is robust with respect to initial input parameters.

Hearts by design

Scalable biofabrication of heart helical tissue pattern augments pumping function

Integration of Surrogate Huxley Muscle Model into Finite Element Solver for Simulation of the Cardiac Cycle

Clinicians can use biomechanical simulations of cardiac functioning to evaluate various real and fictional events. Our present understanding of the molecular processes behind muscle contraction has inspired Huxley-like muscle models. Huxley-type muscle models, unlike Hill-type muscle models, are capable of modeling non-uniform and unstable contractions. Huxley's computational requirements, on the other hand, are substantially higher than those of Hill-type models, making large-scale simulations impractical to use. We created a data-driven surrogate model that acts similarly to the original Huxley muscle model but requires substantially less processing power in order to make the Huxley muscle models easier to use in computer simulations. We gathered data from multiple numerical simulations and trained a deep neural network based on gated-recurrent units. Once we accomplished satisfying precision, we integrated the surrogate model into our finite element solver and simulated a full cardiac cycle. Clinical Relevance- This enables clinicians to track the effects of changes in muscles at the microscale to the cardiac contraction (macroscale).

Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics

Personalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.

An accurate, robust, and efficient finite element framework with applications to anisotropic, nearly and fully incompressible elasticity

Fiber-reinforced soft biological tissues are typically modeled as hyperelastic, anisotropic, and nearly incompressible materials. To enforce incompressibility a multiplicative split of the deformation gradient into a volumetric and an isochoric part is a very common approach. However, the finite element analysis of such problems often suffers from severe volumetric locking effects and numerical instabilities. In this paper, we present novel methods to overcome volumetric locking phenomena for using stabilized P1-P1 elements. We introduce different stabilization techniques and demonstrate the high robustness and computational efficiency of the chosen methods. In two benchmark problems from the literature as well as an advanced application to cardiac electromechanics, we compare the approach to standard linear elements and show the accuracy and versatility of the methods to simulate anisotropic, nearly and fully incompressible materials. We demonstrate the potential of this numerical framework to accelerate accurate simulations of biological tissues to the extent of enabling patient-specific parameterization studies, where numerous forward simulations are required.

Multiscale Contrasts Between the Right and Left Ventricle Biomechanics in Healthy Adult Sheep and Translational Implications

Cardiac biomechanics play a significant role in the progression of structural heart diseases (SHDs). SHDs alter baseline myocardial biomechanics leading to single or bi-ventricular dysfunction. But therapies for left ventricle (LV) failure patients do not always work well for right ventricle (RV) failure patients. This is partly because the basic knowledge of baseline contrasts between the RV and LV biomechanics remains elusive with limited discrepant findings. The aim of the study was to investigate the multiscale contrasts between LV and RV biomechanics in large animal species. We hypothesize that the adult healthy LV and RV have distinct passive anisotropic biomechanical properties. Ex vivo biaxial tests were performed in fresh sheep hearts. Histology and immunohistochemistry were performed to measure tissue collagen. The experimental data were then fitted to a Fung type model and a structurally informed model, separately. We found that the LV was stiffer in the longitudinal (outflow tract) than circumferential direction, whereas the RV showed the opposite anisotropic behavior. The anisotropic parameter K from the Fung type model accurately captured contrasting anisotropic behaviors in the LV and RV. When comparing the elasticity in the same direction, the LV was stiffer than the RV longitudinally and the RV was stiffer than the LV circumferentially, suggesting different filling patterns of these ventricles during diastole. Results from the structurally informed model suggest potentially stiffer collagen fibers in the LV than RV, demanding further investigation. Finally, type III collagen content was correlated with the low-strain elastic moduli in both ventricles. In summary, our findings provide fundamental biomechanical differences between the chambers. These results provide valuable insights for guiding cardiac tissue engineering and regenerative studies to implement chamber-specific matrix mechanics, which is particularly critical for identifying biomechanical mechanisms of diseases or mechanical regulation of therapeutic responses. In addition, our results serve as a benchmark for image-based inverse modeling technologies to non-invasively estimate myocardial properties in the RV and LV.

Sex Matters: A Comprehensive Comparison of Female and Male Hearts

Cardiovascular disease in women remains under-diagnosed and under-treated. Recent studies suggest that this is caused, at least in part, by the lack of sex-specific diagnostic criteria. While it is widely recognized that the female heart is smaller than the male heart, it has long been ignored that it also has a different microstructural architecture. This has severe implications on a multitude of cardiac parameters. Here, we systematically review and compare geometric, functional, and structural parameters of female and male hearts, both in the healthy population and in athletes. Our study finds that, compared to the male heart, the female heart has a larger ejection fraction and beats at a faster rate but generates a smaller cardiac output. It has a lower blood pressure but produces universally larger contractile strains. Critically, allometric scaling, e.g., by lean body mass, reduces but does not completely eliminate the sex differences between female and male hearts. Our results suggest that the sex differences in cardiac form and function are too complex to be ignored: the female heart is not just a small version of the male heart. When using similar diagnostic criteria for female and male hearts, cardiac disease in women is frequently overlooked by routine exams, and it is diagnosed later and with more severe symptoms than in men. Clearly, there is an urgent need to better understand the female heart and design sex-specific diagnostic criteria that will allow us to diagnose cardiac disease in women equally as early, robustly, and reliably as in men.

Systematic Review Registration

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