Bayesian Optimization-Based Inverse Finite Element Analysis for Atrioventricular Heart Valves.

Inverse finite element analysis (iFEA) of the atrioventricular heart valves (AHVs) can provide insights into the in-vivo valvular function, such as in-vivo tissue strains; however, there are several limitations in the current state-of-the-art that iFEA has not been widely employed to predict the in-vivo, patient-specific AHV leaflet mechanical responses. In this exploratory study, we propose the use of Bayesian optimization (BO) to study the AHV functional behaviors in-vivo. We analyzed the efficacy of Bayesian optimization to estimate the isotropic Lee-Sacks material coefficients in three benchmark problems: (i) an inflation test, (ii) a simplified leaflet contact model, and (iii) an idealized AHV model. Then, we applied the developed BO-iFEA framework to predict the leaflet properties for a patient-specific tricuspid valve under a congenital heart defect condition. We found that the BO could accurately construct the objective function surface compared to the one from a [Formula: see text] grid search analysis. Additionally, in all cases the proposed BO-iFEA framework yielded material parameter predictions with average element errors less than 0.02 mm/mm (normalized by the simulation-specific characteristic length). Nonetheless, the solutions were not unique due to the presence of a long-valley minima region in the objective function surfaces. Parameter sets along this valley can yield functionally equivalent outcomes (i.e., closing behavior) and are typically observed in the inverse analysis or parameter estimation for the nonlinear mechanical responses of the AHV. In this study, our key contributions include: (i) a first-of-its-kind demonstration of the BO method used for the AHV iFEA; and (ii) the evaluation of a candidate AHV in-silico modeling approach wherein the chordae could be substituted with equivalent displacement boundary conditions, rendering the better iFEA convergence and a smoother objective surface.

An investigation of how specimen dimensions affect biaxial mechanical characterizations with CellScale BioTester and constitutive modeling of porcine tricuspid valve leaflets.

Biaxial mechanical characterizations are the accepted approach to determine the mechanical response of many biological soft tissues. Although several computational and experimental studies have examined how experimental factors (e.g., clamped vs. suture mounting) affect the acquired tissue mechanical behavior, little is known about the role of specimen dimensions in data acquisition and the subsequent modeling. In this study, we combined our established mechanical characterization framework with an iterative size-reduction protocol to test the hypothesis that specimen dimensions affect the observed mechanical behavior of biaxial characterizations. Our findings indicated that there were non-significant differences in the peak equibiaxial stretches of tricuspid valve leaflets across four specimen dimensions ranging from 4.5×4.5mm to 9 × 9mm. Further analyses revealed that there were significant differences in the low-tensile modulus of the circumferential tissue direction. These differences resulted in significantly different constitutive model parameters for the Tong-Fung model between different specimen dimensions of the posterior and septal leaflets. Overall, our findings demonstrate that specimen dimensions play an important role in experimental characterizations, but not necessarily in constitutive modeling of soft tissue mechanical behavior during biaxial testing with the commercial CellScale BioTester.

Modulation of Smooth Muscle Cell Phenotype for Translation of Tissue-Engineered Vascular Grafts.

Translation of small-diameter tissue-engineered vascular grafts (TEVGs) for the treatment of coronary artery disease (CAD) remains an unfulfilled promise. This is largely due to the limited integration of TEVGs into the native vascular wall-a process hampered by the insufficient smooth muscle cell (SMC) infiltration and extracellular matrix deposition, and low vasoactivity. These processes can be promoted through the judicious modulation of the SMC toward a synthetic phenotype to promote remodeling and vascular integration; however, the expression of synthetic markers is often accompanied by a decrease in the expression of contractile proteins. Therefore, techniques that can precisely modulate the SMC phenotypical behavior could have the potential to advance the translation of TEVGs. In this review, we describe the phenotypic diversity of SMCs and the different environmental cues that allow the modulation of SMC gene expression. Furthermore, we describe the emerging biomaterial approaches to modulate the SMC phenotype in TEVG design and discuss the limitations of current techniques. In addition, we found that current studies in tissue engineering limit the analysis of the SMC phenotype to a few markers, which are often the characteristic of early differentiation only. This limited scope has reduced the potential of tissue engineering to modulate the SMC toward specific behaviors and applications. Therefore, we recommend using the techniques presented in this review, in addition to modern single-cell proteomics analysis techniques to comprehensively characterize the phenotypic modulation of SMCs. Expanding the holistic potential of SMC modulation presents a great opportunity to advance the translation of living conduits for CAD therapeutics.

Finite Element Modeling of Residual Hearing after Cochlear Implant Surgery in Chinchillas.

Cochlear implant (CI) surgery is one of the most utilized treatments for severe hearing loss. However, the effects of a successful scala tympani insertion on the mechanics of hearing are not yet fully understood. This paper presents a finite element (FE) model of the chinchilla inner ear for studying the interrelationship between the mechanical function and the insertion angle of a CI electrode. This FE model includes a three-chambered cochlea and full vestibular system, accomplished using µ-MRI and µ-CT scanning technologies. This model's first application found minimal loss of residual hearing due to insertion angle after CI surgery, and this indicates that it is a reliable and helpful tool for future applications in CI design, surgical planning, and stimuli setup.

Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: application to planar soft tissues.

Data-based approaches are promising alternatives to the traditional analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar, hyperelastic and incompressible soft tissues. The strain energy density of soft tissues is modeled as a GP, which can be regressed to experimental stress-strain data obtained from biaxial experiments. Moreover, the GP model can be weakly constrained to be convex. A key advantage of a GP-based model is that, in addition to the mean value, it provides a probability density (i.e. associated uncertainty) for the strain energy density. To simulate the effect of this uncertainty, a non-intrusive stochastic finite element analysis (SFEA) framework is proposed. The proposed framework is verified against an artificial dataset based on the Gasser-Ogden-Holzapfel model and applied to a real experimental dataset of a porcine aortic valve leaflet tissue. Results show that the proposed framework can be trained with limited experimental data and fits the data better than several existing models. The SFEA framework provides a straightforward way of using the experimental data and quantifying the resulting uncertainty in simulation-based predictions.

Tricuspid Valve Regurgitation in Hypoplastic Left Heart Syndrome: Current Insights and Future Perspectives.

Hypoplastic Left Heart Syndrome (HLHS) is a congenital heart defect that requires a three-stage surgical palliation to create a single ventricle system in the right side of the heart. Of patients undergoing this cardiac palliation series, 25% will develop tricuspid regurgitation (TR), which is associated with an increased mortality risk. Valvular regurgitation in this population has been extensively studied to understand indicators and mechanisms of comorbidity. In this article, we review the current state of research on TR in HLHS, including identified valvular anomalies and geometric properties as the main reasons for the poor prognosis. After this review, we present some suggestions for future TR-related studies to answer the central question: What are the predictors of TR onset during the three palliation stages? These studies involve (i) the use of engineering-based metrics to evaluate valve leaflet strains and predict tissue material properties, (ii) perform multivariate analyses to identify TR predictors, and (iii) develop predictive models, particularly using longitudinally tracked patient cohorts to foretell patient-specific trajectories. Regarded together, these ongoing and future efforts will result in the development of innovative tools that can aid in surgical timing decisions, in prophylactic surgical valve repair, and in the refinement of current intervention techniques.

The Lasso Suture: Ex Vivo Testing of an Alternative to the High-Tension Deep Dermal Stitch.

SUMMARY: Wound dehiscence, with an estimated occurrence rate greater than 4% in plastic surgery, is generally underreported, and can be an indicator of increased mortality and remission rates. The authors developed the lasso suture as a stronger alternative to the current standard patterns. The lasso suture takes less time to perform than the standard high-tension wound repair method. The authors dissected caprine skin specimens to create full-thickness wounds for suture repair using simple interrupted, vertical mattress, horizontal mattress, and deep dermal with running intradermal (DDR) sutures ( n = 10) and lasso sutures ( n = 9). They then conducted uniaxial failure testing to quantify the suture rupture stresses and strains. They also measured the suture operating time with medical students and residents (PGY or MS programs) performing wound repair (10-cm wide, 2-cm deep, 2-0 polydioxanone sutures) on soft-fixed human cadaver skin. The lasso stitch had a greater first-suture rupture stress compared with all other patterns ( P < 0.001): 2.46 ± 0.27 MPa for lasso versus 0.69 ± 0.14 MPa for simple interrupted, 0.68 ± 0.13 MPa for vertical mattress, 0.50 ± 0.10 MPa for horizontal mattress, and 1.17 ± 0.28 MPa for DDR sutures. Performing the lasso suture was 28% faster than performing standard DDR (264 ± 21 versus 349 ± 25 seconds; P = 0.027). In summary, the authors showed that the lasso has superior mechanical properties compared with the studied traditional sutures, and that the new technique can be performed more quickly than the current standard (DDR stitch) for high-tension wounds. Future animal and in-clinic studies will be helpful to confirm the authors' findings in this proof-of-concept study. CLINICAL RELEVANCE STATEMENT: The authors propose the lasso suture, a new suturing method with improved tensile performance compared with traditional techniques and a faster operative time than the deep dermal stitch typically used for high-tension wounds in reconstructive surgery to prevent wound dehiscence.

A Bayesian constitutive model selection framework for biaxial mechanical testing of planar soft tissues: Application to porcine aortic valves.

A variety of constitutive models have been developed for soft tissue mechanics. However, there is no established criterion to select a suitable model for a specific application. Although the model that best fits the experimental data can be deemed the most suitable model, this practice often can be insufficient given the inter-sample variability of experimental observations. Herein, we present a Bayesian approach to calculate the relative probabilities of constitutive models based on biaxial mechanical testing of tissue samples. Forty-six samples of porcine aortic valve tissue were tested using a biaxial stretching setup. For each sample, seven ratios of stresses along and perpendicular to the fiber direction were applied. The probabilities of eight invariant-based constitutive models were calculated based on the experimental data using the proposed model selection framework. The calculated probabilities showed that, out of the considered models and based on the information available through the utilized experimental dataset, the May-Newman model was the most probable model for the porcine aortic valve data. When the samples were further grouped into different cusp types, the May-Newman model remained the most probable for the left- and right-coronary cusps, whereas for non-coronary cusps two models were found to be equally probable: the Lee-Sacks model and the May-Newman model. This difference between cusp types was found to be associated with the first principal component analysis (PCA) mode, where this mode's amplitudes of the non-coronary and right-coronary cusps were found to be significantly different. Our results show that a PCA-based statistical model can capture significant variations in the mechanical properties of soft tissues. The presented framework is applicable to other tissue types, and has the potential to provide a structured and rational way of making simulations population-based.

MetaNO: How to Transfer Your Knowledge on Learning Hidden Physics.

Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important impact on learning and predicting the response of a complex physical system directly from observational data. Taking the material modeling problems for example, the neural operator approach learns a surrogate mapping from the loading field to the corresponding material response field, which can be seen as learning the solution operator of a hidden PDE. The microstructure and mechanical parameters of each material specimen correspond to the (possibly heterogeneous) parameter field in this hidden PDE. Due to the limitation on experimental measurement techniques, the data acquisition for each material specimen is commonly challenging and costly. This fact calls for the utilization and transfer of existing knowledge to new and unseen material specimens, which corresponds to sampling efficient learning of the solution operator of a hidden PDE with a different parameter field. Herein, we propose a novel meta-learning approach for neural operators, which can be seen as transferring the knowledge of solution operators between governing (unknown) PDEs with varying parameter fields. Our approach is a provably universal solution operator for multiple PDE solving tasks, with a key theoretical observation that underlying parameter fields can be captured in the first layer of neural operator models, in contrast to typical final-layer transfer in existing meta-learning methods. As applications, we demonstrate the efficacy of our proposed approach on PDE-based datasets and a real-world material modeling problem, illustrating that our method can handle complex and nonlinear physical response learning tasks while greatly improving the sampling efficiency in unseen tasks.

A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues From Digital Image Correlation Measurements.

We present a data-driven workflow to biological tissue modeling, which aims to predict the displacement field based on digital image correlation (DIC) measurements under unseen loading scenarios, without postulating a specific constitutive model form nor possessing knowledge of the material microstructure. To this end, a material database is constructed from the DIC displacement tracking measurements of multiple biaxial stretching protocols on a porcine tricuspid valve anterior leaflet, with which we build a neural operator learning model. The material response is modeled as a solution operator from the loading to the resultant displacement field, with the material microstructure properties learned implicitly from the data and naturally embedded in the network parameters. Using various combinations of loading protocols, we compare the predictivity of this framework with finite element analysis based on three conventional constitutive models. From in-distribution tests, the predictivity of our approach presents good generalizability to different loading conditions and outperforms the conventional constitutive modeling at approximately one order of magnitude. When tested on out-of-distribution loading ratios, the neural operator learning approach becomes less effective. To improve the generalizability of our framework, we propose a physics-guided neural operator learning model via imposing partial physics knowledge. This method is shown to improve the model's extrapolative performance in the small-deformation regime. Our results demonstrate that with sufficient data coverage and/or guidance from partial physics constraints, the data-driven approach can be a more effective method for modeling biological materials than the traditional constitutive modeling.

Benchtop characterization of the tricuspid valve leaflet pre-strains.

The pre-strains of biological soft tissues are important when relating their in vitro and in vivo mechanical behaviors. In this study, we present the first-of-its-kind experimental characterization of the tricuspid valve leaflet pre-strains. We use 3D photogrammetry and the reproducing kernel method to calculate the pre-strains within the central 10×10 mm region of the tricuspid valve leaflets from n=8 porcine hearts. In agreement with previous pre-strain studies for heart valve leaflets, our results show that all the three tricuspid valve leaflets shrink after being explanted from the ex vivo heart. These calculated strains are leaflet-specific and the septal leaflet experiences the most compressive changes. Furthermore, the strains observed after dissection of the central 10×10 mm region of the leaflet are smaller than when the valve is explanted, suggesting that our computed pre-strains are mainly due to the release of in situ annulus and chordae connections. The leaflets are then mounted on a biaxial testing device and preconditioned using force-controlled equibiaxial loading. We show that the employed preconditioning protocol does not 100% restore the leaflet pre-strains as removed during tissue dissection, and future studies are warranted to explore alternative preconditioning methods. Finally, we compare the calculated biomechanically oriented metrics considering five stress-free reference configurations. Interestingly, the radial tissue stretches and material anisotropies are significantly smaller compared to the post-preconditioning configuration. Extensions of this work can further explore the role of this unique leaflet-specific leaflet pre-strains on in vivo valve behavior via high-fidelity in-silico models. STATEMENT OF SIGNIFICANCE: This study provides a first of its kind benchtop characterization of tricuspid valve leaflet pre-strains. We used 3D photogrammetry to reconstruct the central region of the tricuspid valve leaflets in three configurations. The associated configurational changes revealed compressive, leaflet-specific strains after dissection of the valve from its in situ environment. Interestingly, we found that biaxial preconditioning did not restore the measured pre-strains of the leaflets. Depending on the selection of the stress-free reference configuration, this led to substantial differences in the leaflet mechanics. Our findings and methodology are crucial when it comes to relating in vitro mechanical behaviors to valve function in vivo. Future studies can integrate our quantified pre-strains into in-silico simulations to get more realistic predictions about the valve function.

A pilot investigation of the tricuspid valve annulus in newborns with hypoplastic left heart syndrome.

Objective: Hypoplastic left heart syndrome (HLHS) is a congenital disease characterized by an underdevelopment of the anatomical components inside the left heart. Approximately 30% of HLHS newborns will develop tricuspid regurgitation (TR), and it is currently unknown how the valve annulus mechanics and geometry are associated with regurgitation. Thus, we present an engineering mechanics-based analysis approach to quantify the mechanics and geometry of the HLHS-afflicted tricuspid valve (TV), using 4-dimensional echocardiograms. Methods: Infants born with hypoplastic left heart syndrome (n=8) and healthy newborns (n=4) had their tricuspid valves imaged, and the data was imported to the 3D Slicer. The annular curves were defined at five points in the cardiac cycle. The geometry and deformation (strain) of the TV annulus were calculated to elucidate the mechanics of this critical structure, and compare them between HLHS and normal neonates. Results: For the annular geometry, HLHS-afflicted newborns had significantly larger annular circumferences (20-30%) and anterior-posterior diameters (35-45%) than the healthy patients. From a biomechanics perspective, the HLHS patients had significantly smaller strains in the anterior segments (-0.1±2.6%) during end diastolic and end isovolumetric relaxation (1.7±3.0%) compared to the healthy counterparts (-13.3±2.9% and 6.8±0.9%, respectively). Conclusions: The image-based analysis in this study may provide novel insights into the geometric and mechanistic differences in the TV annulus between healthy and HLHS newborns. Future longitudinal studies of the biomechanics of TV annulus and other subvalvular structures may inform our understanding of the initiation and development of TR and the design of optimal repairs in this challenging population.

Ex vivo experimental characterizations for understanding the interrelationship between tissue mechanics and collagen microstructure of porcine mitral valve leaflets.

Unidirectional blood flow in the left side of the heart is regulated by the mitral valve. To better understand the mitral valve function, researchers have examined the structural and mechanical properties of the mitral valve leaflets; however, limitations of the previous studies include the use of mechanics- and structure-altering tissue modifications (e.g., optical clearing) that limit the ability to quantify the unique load-dependent reorientation and realignment of the collagen fibers as well as their interrelation with the valve tissue mechanics. Herein, we aimed to circumvent these limitations by utilizing an integrated polarized-light imaging and biaxial testing system for understanding the mechanics-microstructure interrelationship for porcine mitral valve leaflets. We further performed constitutive modeling and evaluated the accuracy of the affine fiber kinematics theory. From the tissue mechanics perspective, the posterior leaflet was more extensible in the radial direction than the anterior leaflet (14.2% difference in radial tissue stretch), while exhibiting smaller collagen and elastin moduli based on the determined constitutive model parameters. From the collagen microstructure's standpoint, the posterior leaflet had smaller increases in optical anisotropy (closely related to the degree of fiber alignment) than the anterior leaflet (32.8±7.7% vs. 50.0±19.7%). Further, the leaflets were found to possess two distinct fiber families - one family oriented along the circumferential tissue direction, and another more disperse family with a 30°-40° offset from the first fiber family. Finally, affine fiber kinematics consistently underpredicted the collagen fiber reorientations Overall, this study improved our understanding of the mitral valve leaflets that is essential for facilitating tissue-emulated valve replacement and cardiac valve modeling frameworks.

Linking the region-specific tissue microstructure to the biaxial mechanical properties of the porcine left anterior descending artery.

Coronary atherosclerosis is the main cause of death worldwide. Advancing the understanding of coronary microstructure-based mechanics is fundamental for the development of therapeutic tools and surgical procedures. Although the passive biaxial properties of the coronary arteries have been extensively explored, their regional differences and the relationship between tissue microstructure and mechanics have not been fully characterized. In this study, we characterized the passive biaxial mechanical properties and microstructural properties of the proximal, medial, and distal regions of the porcine left anterior descending artery (LADA). We also attempted to relate the biaxial stress-stretch response of the LADA and its respective birefringent responses to the polarized light for obtaining information about the load-dependent microstructural variations. We found that the LADA extensibility is reduced in the proximal-to-distal direction and that the medial region exhibits more heterogeneous mechanical behavior than the other two regions. We have also observed highly dynamic microstructural behavior where fiber families realign themselves depending on loading. In addition, we found that the microstructure of the distal region exhibited highly aligned fibers along the longitudinal axis of the artery. To verify this microstructural feature, we imaged the LADA specimens with multi-photon microscopy and observed that the adventitia microstructure transitioned from a random fiber network in the proximal region to highly aligned fibers in the distal region. Our findings could offer new perspectives for understanding coronary mechanics and aid in the development of tissue-engineered vascular grafts, which are currently limited due to their mismatch with native tissue in terms of mechanical properties and microstructural features. STATEMENT OF SIGNIFICANCE: The tissue biomechanics of coronary arteries is fundamental for the development of revascularization techniques such as coronary artery bypass. These therapeutics require a deep understanding of arterial mechanics, microstructure, and mechanobiology to prevent graft failure and reoperation. The present study characterizes the unique regional mechanical and microstructural properties of the porcine left anterior descending artery using biaxial testing, polarized-light imaging, and confocal microscopy. This comprehensive characterization provides an improved understanding of the collagen/elastin architecture in response to mechanical loads using a region-specific approach. The unique tissue properties obtained from this study will provide guidance for the selection of anastomotic sites in coronary artery bypass grafting and for the design of tissue-engineered vascular grafts.

Shape Memory Polymer-Based Endovascular Devices: Design Criteria and Future Perspective.

Devices for the endovascular embolization of intracranial aneurysms (ICAs) face limitations related to suboptimal rates of lasting complete occlusion. Incomplete occlusion frequently leads to residual flow within the aneurysm sac, which subsequently causes aneurysm recurrence needing surgical re-operation. An emerging method for improving the rates of complete occlusion both immediately after implant and in the longer run can be the fabrication of patient-specific materials for ICA embolization. Shape memory polymers (SMPs) are materials with great potential for this application, owing to their versatile and tunable shape memory properties that can be tailored to a patient's aneurysm geometry and flow condition. In this review, we first present the state-of-the-art endovascular devices and their limitations in providing long-term complete occlusion. Then, we present methods for the fabrication of SMPs, the most prominent actuation methods for their shape recovery, and the potential of SMPs as endovascular devices for ICA embolization. Although SMPs are a promising alternative for the patient-specific treatment of ICAs, there are still limitations that need to be addressed for their application as an effective coil-free endovascular therapy.

The role of elastin on the mechanical properties of the anterior leaflet in porcine tricuspid valves.

Elastin is present in the extracellular matrix (ECM) of connective tissues, and its mechanical properties are well documented. In Marfan syndrome, however, the inability to properly code for the protein fibrillin-1 prematurely leads to the degradation and loss of elastin fiber integrity in the ECM. In this study, the role of elastin in the ECM of the anterior leaflet of the tricuspid valve was investigated by examining the biomechanical behavior of porcine leaflets before and after the application of the enzyme elastase. Five loading protocols were applied to the leaflet specimens in two groups (elastase-treated and control samples). The mechanical response following elastase application yielded a significantly stiffer material in both the radial and circumferential directions. At a physiological level of stress (85 kPa), the elastase group had an average strain of 26.21% and 6.32% in the radial and circumferential directions, respectively, at baseline prior to elastase application. Following elastase treatment, the average strain was 5.28% and 0.97% in the radial and circumferential directions, respectively. No statistically significant change was found in the control group following sham treatment with phosphate-buffered saline (PBS). Two-photon microscopy images confirmed that after the removal of elastin, the collagen fibers displayed a loss of undulation. With a significant reduction in radial compliance, the ability to withstand physiological loads may be compromised. As such, an extracellular matrix that is structurally deficient in elastin may hinder normal tricuspid valve function.

Layer Microdissection of Tricuspid Valve Leaflets for Biaxial Mechanical Characterization and Microstructural Quantification.

The tricuspid valve (TV) regulates the unidirectional flow of unoxygenated blood from the right atrium to the right ventricle. The TV consists of three leaflets, each with unique mechanical behaviors. These variations among the three TV leaflets can be further understood by examining their four anatomical layers, which are the atrialis (A), spongiosa (S), fibrosa (F), and ventricularis (V). While these layers are present in all three TV leaflets, there are differences in their thicknesses and microstructural constituents that further influence their respective mechanical behaviors. This protocol includes four steps to elucidate the layer-specific differences: (i) characterize the mechanical and collagen fiber architectural behaviors of the intact TV leaflet, (ii) separate the composite layers (A/S and F/V) of the TV leaflet, (iii) carry out the same characterizations for the composite layers, and (iv) perform post-hoc histology assessment. This experimental framework uniquely allows the direct comparison of the intact TV tissue to each of its composite layers. As a result, detailed information regarding the microstructure and biomechanical function of the TV leaflets can be collected with this protocol. Such information can potentially be used to develop TV computational models that seek to provide guidance for the clinical treatment of TV disease.

Multiscale modeling of passive material influences on deformation and force output of skeletal muscles.

Passive materials in human skeletal muscle tissues play an important role in force output of skeletal muscles. This paper introduces a multiscale modeling framework to investigate how age-associated variations on microscale passive muscle components, including microstructural geometry (e.g., connective tissue thickness) and material properties (e.g., anisotropy), influence the force output and deformations of the continuum skeletal muscle. We first define a representative volume element (RVE) for the microstructure of muscle and determine the homogenized macroscale mechanical properties of the RVE from the separate mechanical properties of the individual components of the RVE, including muscle fibers and connective tissue with its associated collagen fibers. The homogenized properties of the RVE are then used to define the elements of the continuum muscle model to evaluate the force output and deformations of the whole muscle. Conversely, the regional deformations of the continuum model are fed back to the RVE model to determine the responses of the individual microscale components. Simulations of muscle isometric contractions at a range of muscle lengths are performed to investigate the effects of muscle architectural changes (e.g., pennation angles) due to aging on force output and muscle deformation. The correlations between the pennation angle, the shear deformation in the microscale connective tissue (an indicator for the lateral force transmission), the angle difference between the fiber direction and principal strain direction and the resulting shear deformation at the continuum scale, as well as the force output of the skeletal muscle are also discussed.

Linking collagen fiber architecture to tissue-level biaxial mechanical behaviors of porcine semilunar heart valve cusps.

The semilunar heart valves regulate the blood flow from the ventricles to the major arteries through the opening and closing of the scallop shaped cusps. These cusps are composed of collagen fibers that act as the primary loading-bearing component. The load-dependent collagen fiber architecture has been previously examined in the existing literature; however, these studies relied on chemical clearing and tissue modifications to observe the underlying changes in response to mechanical loads. In the present study, we address this gap in knowledge by quantifying the collagen fiber orientations and alignments of the aortic and pulmonary cusps through a multi-scale, non-destructive experimental approach. This opto-mechanical approach, which combines polarized spatial frequency domain imaging and biaxial mechanical testing, provides a greater field of view (10-25mm) and faster imaging time (45-50s) than other traditional collagen imaging techniques. The birefringent response of the collagen fibers was fit with a von Mises distribution, while the biaxial mechanical testing data was implemented into a modified full structural model for further analysis. Our results showed that the semilunar heart valve cusps are more extensible in the tissue's radial direction than the circumferential direction under all the varied biaxial testing protocols, together with greater material anisotropy among the pulmonary valve cusps compared to the aortic valve cusps. The collagen fibers were shown to reorient towards the direction of the greatest applied loading and incrementally realign with the increased applied stress. The collagen fiber architecture within the aortic valve cusps were found to be more homogeneous than the pulmonary valve counterparts, reflecting the differences in the physiological environments experienced by these two semilunar heart valves. Further, the von Mises distribution fitting highlighted the presence and contribution of two distinct fiber families for each of the two semilunar heart valves. The results from this work would provide valuable insight into connecting tissue-level mechanics to the underlying collagen fiber architecture-an essential information for the future development of high-fidelity aortic/pulmonary valve computational models.

An in-silico benchmark for the tricuspid heart valve - Geometry, finite element mesh, Abaqus simulation, and result data set.

This article provides Abaqus input files and user subroutines for performing finite element simulations of the tricuspid heart valve with an idealized geometry. Additional post-processing steps to obtain a ParaView visualization file (*.vtk) of the deformed geometry are also provided to allow the readers to use the included ParaView state file (*.pvsm) for customizable visualization and evaluation of the simulation results. We expect this first-of-its-kind in-silico benchmark dataset will facilitate user-friendly simulations considering material nonlinearity, leaflet-to-leaflet contact, and large deformations. Additionally, the information included herein can be used to rapidly evaluate other novel in-silico approaches developed for simulating cardiac valve function. The benchmark can be expanded to consider more complex features of the tricuspid valve function, such as the dynamic annulus motion or the time-varying transvalvular pressure. Interested readers are referred to the companion article (Johnson et al., 2021) for an example application of this in-silico tool for isogeometric analysis of tricuspid valves.