An efficient and accurate method for modeling nonlinear fractional viscoelastic biomaterials.

Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is viscoelastic, current biomechanical models in the computational community often assume hyperelastic material models. Fractional viscoelastic constitutive models have been successfully used in literature to capture viscoelastic material response; however, the translation of these models into computational platforms remains limited. Many experimentally derived viscoelastic constitutive models are not suitable for three-dimensional simulations. Furthermore, the use of fractional derivatives can be computationally prohibitive, with a number of current numerical approximations having a computational cost that is 𝒪 ( N T 2 ) and a storage cost that is 𝒪(NT ) (NT denotes the number of time steps). In this paper, we present a novel numerical approximation to the Caputo derivative which exploits a recurrence relation similar to those used to discretize classic temporal derivatives, giving a computational cost that is 𝒪(NT ) and a storage cost that is fixed over time. The approximation is optimized for numerical applications, and an error estimate is presented to demonstrate the efficacy of the method. The method, integrated into a finite element solid mechanics framework, is shown to be unconditionally stable in the linear viscoelastic case. It was then integrated into a computational biomechanical framework, with several numerical examples verifying the accuracy and computational efficiency of the method, including in an analytic test, in an analytic fractional differential equation, as well as in a computational biomechanical model problem.

On the simulation of mitral valve function in health, disease, and treatment.

The mitral valve (MV) is the heart valve that regulates blood ?ow between the left atrium and left ventricle (LV). In situations where the MV fails to fully cover the left atrioventricular ori?ce during systole, the resulting regurgitation causes pulmonary congestion, leading to heart failure and/or stroke. The causes of MV insuf?ciency can be either primary (e.g. myxomatous degeneration) where the valvular tissue is organically diseased, or secondary (typically inducded by ischemic cardiomyopathy) termed ischemic mitral regurgitation (IMR), is brought on by adverse LV remodeling. IMR is present in up to 40% of patients and more than doubles the probability of cardiovascular morbidity after 3.5 years. There is now agreement that adjunctive procedures are required to treat IMR caused by lea?et tethering. However, there is no consensus regarding the best procedure. Multicenter registries and randomized trials would be necessary to prove which procedure is superior. Given the number of proposed procedures and the complexity and duration of such studies, it is highly unlikely that IMR procedure optimization will be achieved by prospective clinical trials. There is thus an urgent need for cell and tissue physiologically based quantitative assessments of MV function to better design surgical solutions and associated therapies. Novel computational approaches directed towards optimized surgical repair procedures can substantially reduce the need for such trial-and-error approaches. We present the details of our MV modeling techniques, with an emphasis on what is known and investigated at various length scales.

On the presence of affine fibril and fiber kinematics in the mitral valve anterior leaflet.

In this study, we evaluated the hypothesis that the constituent fibers follow an affine deformation kinematic model for planar collagenous tissues. Results from two experimental datasets were utilized, taken at two scales (nanometer and micrometer), using mitral valve anterior leaflet (MVAL) tissues as the representative tissue. We simulated MVAL collagen fiber network as an ensemble of undulated fibers under a generalized two-dimensional deformation state, by representing the collagen fibrils based on a planar sinusoidally shaped geometric model. The proposed approach accounted for collagen fibril amplitude, crimp period, and rotation with applied macroscopic tissue-level deformation. When compared to the small angle x-ray scattering measurements, the model fit the data well, with an r(2) = 0.976. This important finding suggests that, at the homogenized tissue-level scale of ∼1 mm, the collagen fiber network in the MVAL deforms according to an affine kinematics model. Moreover, with respect to understanding its function, affine kinematics suggests that the constituent fibers are largely noninteracting and deform in accordance with the bulk tissue. It also suggests that the collagen fibrils are tightly bounded and deform as a single fiber-level unit. This greatly simplifies the modeling efforts at the tissue and organ levels, because affine kinematics allows a straightforward connection between the macroscopic and local fiber strains. It also suggests that the collagen and elastin fiber networks act independently of each other, with the collagen and elastin forming long fiber networks that allow for free rotations. Such freedom of rotation can greatly facilitate the observed high degree of mechanical anisotropy in the MVAL and other heart valves, which is essential to heart valve function. These apparently novel findings support modeling efforts directed toward improving our fundamental understanding of tissue biomechanics in healthy and diseased conditions.

A generalized method for the analysis of planar biaxial mechanical data using tethered testing configurations.

Simulation of the mechanical behavior of soft tissues is critical for many physiological and medical device applications. Accurate mechanical test data is crucial for both obtaining the form and robust parameter determination of the constitutive model. For incompressible soft tissues that are either membranes or thin sections, planar biaxial mechanical testing configurations can provide much information about the anisotropic stress-strain behavior. However, the analysis of soft biological tissue planar biaxial mechanical test data can be complicated by in-plane shear, tissue heterogeneities, and inelastic changes in specimen geometry that commonly occur during testing. These inelastic effects, without appropriate corrections, alter the stress-traction mapping and violates equilibrium so that the stress tensor is incorrectly determined. To overcome these problems, we presented an analytical method to determine the Cauchy stress tensor from the experimentally derived tractions for tethered testing configurations. We accounted for the measured testing geometry and compensate for run-time inelastic effects by enforcing equilibrium using small rigid body rotations. To evaluate the effectiveness of our method, we simulated complete planar biaxial test configurations that incorporated actual device mechanisms, specimen geometry, and heterogeneous tissue fibrous structure using a finite element (FE) model. We determined that our method corrected the errors in the equilibrium of momentum and correctly estimated the Cauchy stress tensor. We also noted that since stress is applied primarily over a subregion bounded by the tethers, an adjustment to the effective specimen dimensions is required to correct the magnitude of the stresses. Simulations of various tether placements demonstrated that typical tether placements used in the current experimental setups will produce accurate stress tensor estimates. Overall, our method provides an improved and relatively straightforward method of calculating the resulting stresses for planar biaxial experiments for tethered configurations, which is especially useful for specimens that undergo large shear and exhibit substantial inelastic effects.

Insights into regional adaptations in the growing pulmonary artery using a meso-scale structural model: effects of ascending aorta impingement.

As the next step in our investigations into the structural adaptations of the main pulmonary artery (PA) during postnatal growth, we utilized the extensive experimental measurements of the growing ovine PA from our previous study (Fata et al., 2013, "Estimated in vivo Postnatal Surface Growth Patterns of the Ovine Main Pulmonary Artery and Ascending Aorta," J. Biomech. Eng., 135(7), pp. 71010-71012). to develop a structural constitutive model for the PA wall tissue. Novel to the present approach was the treatment of the elastin network as a distributed fiber network rather than a continuum phase. We then utilized this model to delineate structure-function differences in the PA wall at the juvenile and adult stages. Overall, the predicted elastin moduli exhibited minor differences remained largely unchanged with age and region (in the range of 150 to 200 kPa). Similarly, the predicted collagen moduli ranged from ∼1,600 to 2700 kPa in the four regions studied in the juvenile state. Interestingly, we found for the medial region that the elastin and collagen fiber splay underwent opposite changes (collagen standard deviation juvenile = 17 deg to adult = 28 deg, elastin standard deviation juvenile = 35 deg to adult = 27 deg), along with a trend towards more rapid collagen fiber strain recruitment with age, along with a drop in collagen fiber moduli, which went from 2700 kPa for the juvenile stage to 746 kPa in the adult. These changes were likely due to the previously observed impingement of the relatively stiff ascending aorta on the growing PA medial region. Intuitively, the effects of the local impingement would be to lower the local wall stress, consistent with the observed parallel decrease in collagen modulus. These results suggest that during the postnatal somatic growth period local stresses can substantially modulate regional tissue microstructure and mechanical behaviors in the PA. We further underscore that our previous studies indicated an increase in effective PA wall stress with postnatal maturation. When taken together with the fact that the observed changes in mechanical behavior and structure in the growing PA wall were modest in the other three regions studied, our collective results suggest that the majority of the growing PA wall is subjected to increasing stress levels with age without undergoing major structural adaptations. This observation is contrary to the accepted theory of maintenance of homeostatic stress levels in the regulation of vascular function, and suggests alternative mechanisms might regulate postnatal somatic growth. Understanding the underlying mechanisms will help to improve our understanding of congenital defects of the PA and lay the basis for functional duplication in their repair and replacement.

A viscoelastic constitutive model for human femoropopliteal arteries.

High failure rates present challenges for surgical and interventional therapies for peripheral artery disease of the femoropopliteal artery (FPA). The FPA's demanding biomechanical environment necessitates complex interactions with repair devices and materials. While a comprehensive understanding of the FPA's mechanical characteristics could improve medical treatments, the viscoelastic properties of these muscular arteries remain poorly understood, and the constitutive model describing their time-dependent behavior is absent. We introduce a new viscoelastic constitutive model for the human FPA grounded in its microstructural composition. The model is capable of detailing the contributions of each intramural component to the overall viscoelastic response. Our model was developed utilizing fractional viscoelasticity and tested using biaxial experimental data with hysteresis and relaxation collected from 10 healthy human subjects aged 57 to 65 and further optimized for high throughput and automation. The model accurately described the experimental data, capturing significant nonlinearity and hysteresis that were particularly pronounced circumferentially, and tracked the contribution of passive smooth muscle cells to viscoelasticity that was twice that of the collagen fibers. The high-throughput parameter estimation procedure we developed included a specialized objective function and modifications to enhance convergence for the common exponential-type fiber laws, facilitating computational implementation. Our new model delineates the time-dependent behavior of human FPAs, which will improve the fidelity of computational simulations investigating device-artery interactions and contribute to their greater physical accuracy. Moreover, it serves as a useful tool to investigate the contribution of arterial constituents to overall tissue viscoelasticity, thereby expanding our knowledge of arterial mechanophysiology. STATEMENT OF SIGNIFICANCE: The demanding biomechanical environment of the femoropopliteal artery (FPA) necessitates complex interactions with repair devices and materials, but the viscoelastic properties of these muscular arteries remain poorly understood with the constitutive model describing their time-dependent behavior being absent. We hereby introduce the first viscoelastic constitutive model for the human FPA grounded in its microstructures. This model was tested using biaxial mechanical data collected from 10 healthy human subjects between the ages of 57 to 65. It can detail the contributions of each intramural component to the overall viscoelastic response, showing that the contribution of passive smooth muscle cells to viscoelasticity is twice that of collagen fibers. The usefulness of this model as tool to better understand arterial mechanophysiology was demonstrated.

The effects of viscoelasticity on residual strain in aortic soft tissues.

Residual stress is thought to play a critical role in modulating stress distributions in soft biological tissues and in maintaining the mechanobiological stress environment of cells. Residual stresses in arteries and other tissues are classically assessed through opening angle experiments, which demonstrate the continuous release of residual stresses over hours. These results are then assessed through nonlinear biomechanical models to provide estimates of the residual stresses in the intact state. Although well studied, these analyses typically focus on hyperelastic material models despite significant evidence of viscoelastic phenomena over both short and long timescales. In this work, we extended the state-of-the-art structural tensor model for arterial tissues from Holzapfel and Ogden for fractional viscoelasticity. Models were tuned to capture consistent levels of hysteresis observed in biaxial experiments, while also minimizing the fractional viscoelastic weighting and opening angles to correctly capture opening angle dynamics. Results suggest that a substantial portion of the human abdominal aorta is viscoelastic, but exhibits a low fractional order (i.e. more elastically). Additionally, a significantly larger opening angle in the fully unloaded state is necessary to produce comparable hysteresis in biaxial testing. As a consequence, conventional estimates of residual stress using hyperelastic approaches over-estimate their viscoelastic counterparts by a factor of 2. Thus, a viscoelastic approach, such as the one illustrated in this study, in combination with an additional source of rate-controlled viscoelastic data is necessary to accurately analyze the residual stress distribution in soft biological tissues. STATEMENT OF SIGNIFICANCE: Residual stress plays a crucial role in achieving a homeostatic stress environment in soft biological tissues. However, the analysis of residual stress typically focuses on hyperelastic material models despite evidence of viscoelastic behavior. This work is the first attempt at analyzing the effects of viscoelasticity on residual stress. The application of viscoelasticity was crucial for producing realistic opening dynamics in arteries. The overall residual stresses were estimated to be 50% less than those from using hyperelastic material models, while the opening angles were projected to be 25% more than those measured after 16 hours, suggesting underestimated residual strain. This study highlights the importance viscoelasticity in the analysis of residual stress even in weakly dissipative materials like the human aorta.

Simulating the time evolving geometry, mechanical properties, and fibrous structure of bioprosthetic heart valve leaflets under cyclic loading.

Currently, the most common replacement heart valve design is the 'bioprosthetic' heart valve (BHV), which has important advantages in that it does not require permanent anti-coagulation therapy, operates noiselessly, and has blood flow characteristics similar to the native valve. BHVs are typically fabricated from glutaraldehyde-crosslinked pericardial xenograft tissue biomaterials (XTBs) attached to a rigid, semi-flexible, or fully collapsible stent in the case of the increasingly popular transcutaneous aortic valve replacement (TAVR). While current TAVR assessments are positive, clinical results to date are generally limited to <2 years. Since TAVR leaflets are constructed using thinner XTBs, their mechanical demands are substantially greater than surgical BHV due to the increased stresses during in vivo operation, potentially resulting in decreased durability. Given the functional complexity of heart valve operation, in-silico predictive simulations clearly have potential to greatly improve the TAVR development process. As such simulations must start with accurate material models, we have developed a novel time-evolving constitutive model for pericardial xenograft tissue biomaterials (XTB) utilized in BHV (doi: 10.1016/j.jmbbm.2017.07.013). This model was able to simulate the observed tissue plasticity effects that occur in approximately in the first two years of in vivo function (50 million cycles). In the present work, we implemented this model into a complete simulation pipeline to predict the BHV time evolving geometry to 50 million cycles. The pipeline was implemented within an isogeometric finite element formulation that directly integrated our established BHV NURBS-based geometry (doi: 10.1007/s00466-015-1166-x). Simulations of successive loading cycles indicated continual changes in leaflet shape, as indicated by spatially varying increases in leaflet curvature. While the simulation model assumed an initial uniform fiber orientation distribution, anisotropic regional changes in leaflet tissue plastic strain induced a complex changes in regional fiber orientation. We have previously noted in our time-evolving constitutive model that the increases in collagen fiber recruitment with cyclic loading placed an upper bound on plastic strain levels. This effect was manifested by restricting further changes in leaflet geometry past 50 million cycles. Such phenomena was accurately captured in the valve-level simulations due to the use of a tissue-level structural-based modeling approach. Changes in basic leaflet dimensions agreed well with extant experimental studies. As a whole, the results of the present study indicate the complexity of BHV responses to cyclic loading, including changes in leaflet shape and internal fibrous structure. It should be noted that the later effect also influences changes in local mechanical behavior (i.e. changes in leaflet anisotropic tissue stress-strain relationship) due to internal fibrous structure resulting from plastic strains. Such mechanism-based simulations can help pave the way towards the application of sophisticated simulation technologies in the development of replacement heart valve technology.

A viscoelastic model for human myocardium.

Understanding the biomechanics of the heart in health and disease plays an important role in the diagnosis and treatment of heart failure. The use of computational biomechanical models for therapy assessment is paving the way for personalized treatment, and relies on accurate constitutive equations mapping strain to stress. Current state-of-the art constitutive equations account for the nonlinear anisotropic stress-strain response of cardiac muscle using hyperelasticity theory. While providing a solid foundation for understanding the biomechanics of heart tissue, most current laws neglect viscoelastic phenomena observed experimentally. Utilizing experimental data from human myocardium and knowledge of the hierarchical structure of heart muscle, we present a fractional nonlinear anisotropic viscoelastic constitutive model. The model is shown to replicate biaxial stretch, triaxial cyclic shear and triaxial stress relaxation experiments (mean error ∼7.68%), showing improvements compared to its hyperelastic (mean error ∼24%) counterparts. Model sensitivity, fidelity and parameter uniqueness are demonstrated. The model is also compared to rate-dependent biaxial stretch as well as different modes of biaxial stretch, illustrating extensibility of the model to a range of loading phenomena. STATEMENT OF SIGNIFICANCE: The viscoelastic response of human heart tissues has yet to be integrated into common constitutive models describing cardiac mechanics. In this work, a fractional viscoelastic modeling approach is introduced based on the hierarchical structure of heart tissue. From these foundations, the current state-of-the-art biomechanical models of the heart muscle are transformed using fractional viscoelasticity, replicating passive muscle function across multiple experimental tests. Comparisons are drawn with current models to highlight the improvements of this approach and predictive responses show strong qualitative agreement with experimental data. The proposed model presents the first constitutive model aimed at capturing viscoelastic nonlinear response across multiple testing regimes, providing a platform for better understanding the biomechanics of myocardial tissue in health and disease.

A material modeling approach for the effective response of planar soft tissues for efficient computational simulations.

One of the most crucial aspects of biomechanical simulations of physiological systems that seek to predict the outcomes of disease, injury, and surgical interventions is the underlying soft tissue constitutive model. Soft tissue constitutive modeling approaches have become increasingly complex, often utilizing meso- and multi-scale methods for greater predictive capability and linking to the underlying biological mechanisms. However, such modeling approaches are associated with substantial computational costs. One solution is to use effective constitutive models in place of meso- and multi-scale models in numerical simulations but derive their responses by homogenizing the responses of the underlying meso- or multi-scale models. A robust effective constitutive model can thus drastically increase the speed of simulations for a wide range of meso- and multi-scale models. However, there is no consensus on how to develop a single effective constitutive model and optimal methods for parameter estimation for a wide range of soft tissue responses. In the present study, we developed an effective constitutive model which can fully reproduce the response of a wide range of planar soft tissues, along with a method for robust and fast-convergent parameter estimation. We then evaluated our approach and demonstrated its ability to handle materials of widely varying degrees of stiffness and anisotropy. Furthermore, we demonstrated the robutst performance of the meso-structural to effective constitutive model framework in finite element simulations of tri-leaflet heart valves. We conclude that the effective constitutive modeling approach has significant potential for improving the computational efficiency and numerical robustness of multi-scale and meso-scale models, facilitating efficient soft tissue simulations in such demanding applications as inverse modeling and growth.

Modeling the response of exogenously crosslinked tissue to cyclic loading: The effects of permanent set.

Bioprosthetic heart valves (BHVs), fabricated from exogenously crosslinked collagenous tissues, remain the most popular heart valve replacement design. However, the life span of BHVs remains limited to 10-15 years, in part because the mechanisms that underlie BHV failure remain poorly understood. Experimental evidence indicates that BHVs undergo significant changes in geometry with in vivo operation, which lead to stress concentrations that can have significant impact on structural damage. These changes do not appear to be due to plastic deformation, as the leaflets only deform in the elastic regime. Moreover, structural damage was not detected by the 65 million cycle time point. Instead, we found that this nonrecoverable deformation is similar to the permanent set effect observed in elastomers, which allows the reference configuration of the material to evolve over time. We hypothesize that the scission-healing reaction of glutaraldehyde is the underlying mechanism responsible for permanent set in exogenously crosslinked soft tissues. The continuous scission-healing process of glutaraldehyde allows a portion of the exogenously crosslinked matrix, which is considered to be the non-fibrous part of the extra-cellular matrix, to be re-crosslinked in the loaded state. Thus, this mechanism for permanent set can be used to explain the time evolving mechanical response and geometry of BHVs in the early stage. To model the permanent set effect, we assume that the exogenously crosslinked matrix undergoes changes in reference configurations over time. The changes in the collagen fiber architecture due to dimensional changes allow us to predict subsequent changes in mechanical response. Results show that permanent set alone can explain and, more importantly, predict how the mechanical response of the biomaterial change with time. Furthermore, we found is no difference in permanent set rate constants between the strain controlled and the stress controlled cyclic loading studies. An important finding we have is that the collagen fiber architecture has a limiting effect on the maximum changes in geometry that the permanent set effect can induce. This is due to the recruitment of collagen fibers as the changes in geometry due to permanent set increase. This means we can potentially optimize the BHV geometry based on the predicted the final BHV geometry after permanent set has largely ceased. Thus, we have developed the first structural constitutive model for the permanent set effect in exogenously crosslinked soft tissue, which can help to simulate BHV designs and reduce changes in BHV geometry during cyclic loading and thus potentially increasing BHV durability.

A mathematical model for the determination of forming tissue moduli in needled-nonwoven scaffolds.

Formation of engineering tissues (ET) remains an important scientific area of investigation for both clinical translational and mechanobiological studies. Needled-nonwoven (NNW) scaffolds represent one of the most ubiquitous biomaterials based on their well-documented capacity to sustain tissue formation and the unique property of substantial construct stiffness amplification, the latter allowing for very sensitive determination of forming tissue modulus. Yet, their use in more fundamental studies is hampered by the lack of: (1) substantial understanding of the mechanics of the NNW scaffold itself under finite deformations and means to model the complex mechanical interactions between scaffold fibers, cells, and de novo tissue; and (2) rational models with reliable predictive capabilities describing their evolving mechanical properties and their response to mechanical stimulation. Our objective is to quantify the mechanical properties of the forming ET phase in constructs that utilize NNW scaffolds. We present herein a novel mathematical model to quantify their stiffness based on explicit considerations of the modulation of NNW scaffold fiber-fiber interactions and effective fiber stiffness by surrounding de novo ECM. Specifically, fibers in NNW scaffolds are effectively stiffer than if acting alone due to extensive fiber-fiber cross-over points that impart changes in fiber geometry, particularly crimp wavelength and amplitude. Fiber-fiber interactions in NNW scaffolds also play significant role in the bulk anisotropy of the material, mainly due to fiber buckling and large translational out-of-plane displacements occurring to fibers undergoing contraction. To calibrate the model parameters, we mechanically tested impregnated NNW scaffolds with polyacrylamide (PAM) gels with a wide range of moduli with values chosen to mimic the effects of surrounding tissues on the scaffold fiber network. Results indicated a high degree of model fidelity over a wide range of planar strains. Lastly, we illustrated the impact of our modeling approach quantifying the stiffness of engineered ECM after in vitro incubation and early stages of in vivo implantation obtained in a concurrent study of engineered tissue pulmonary valves in an ovine model. STATEMENT OF SIGNIFICANCE: Regenerative medicine has the potential to fully restore diseased tissues or entire organs with engineered tissues. Needled-nonwoven scaffolds can be employed to serve as the support for their growth. However, there is a lack of understanding of the mechanics of these materials and their interactions with the forming tissues. We developed a mathematical model for these scaffold-tissue composites to quantify the mechanical properties of the forming tissues. Firstly, these measurements are pivotal to achieve functional requirements for tissue engineering implants; however, the theoretical development yielded critical insight into particular mechanisms and behaviors of these scaffolds that were not possible to conjecture without the insight given by modeling, let alone describe or foresee a priori.

On the in vivo function of the mitral heart valve leaflet: insights into tissue-interstitial cell biomechanical coupling.

There continues to be a critical need for developing data-informed computational modeling techniques that enable systematic evaluations of mitral valve (MV) function. This is important for a better understanding of MV organ-level biomechanical performance, in vivo functional tissue stresses, and the biosynthetic responses of MV interstitial cells (MVICs) in the normal, pathophysiological, and surgically repaired states. In the present study, we utilized extant ovine MV population-averaged 3D fiducial marker data to quantify the MV anterior leaflet (MVAL) deformations in various kinematic states. This approach allowed us to make the critical connection between the in vivo functional and the in vitro experimental configurations. Moreover, we incorporated the in vivo MVAL deformations and pre-strains into an enhanced inverse finite element modeling framework (Path 1) to estimate the resulting in vivo tissue prestresses [Formula: see text] and the in vivo peak functional tissue stresses [Formula: see text]. These in vivo stress estimates were then cross-verified with the results obtained from an alternative forward modeling method (Path 2), by taking account of the changes in the in vitro and in vivo reference configurations. Moreover, by integrating the tissue-level kinematic results into a downscale MVIC microenvironment FE model, we were able to estimate, for the first time, the in vivo layer-specific MVIC deformations and deformation rates of the normal and surgically repaired MVALs. From these simulations, we determined that the placement of annuloplasty ring greatly reduces the peak MVIC deformation levels in a layer-specific manner. This suggests that the associated reductions in MVIC deformation may down-regulate MV extracellular matrix maintenance, ultimately leading to reduction in tissue mechanical integrity. These simulations provide valuable insight into MV cellular mechanobiology in response to organ- and tissue-level alternations induced by MV disease or surgical repair. They will also assist in the future development of computer simulation tools for guiding MV surgery procedure with enhanced durability and improved long-term surgical outcomes.

A novel constitutive model for passive right ventricular myocardium: evidence for myofiber-collagen fiber mechanical coupling.

The function of right ventricle (RV) is recognized to play a key role in the development of many cardiopulmonary disorders, such as pulmonary arterial hypertension (PAH). Given the strong link between tissue structure and mechanical behavior, there remains a need for a myocardial constitutive model that accurately accounts for right ventricular myocardium architecture. Moreover, most available myocardial constitutive models approach myocardium at the length scale of mean fiber orientation and do not explicitly account for different fibrous constituents and possible interactions among them. In the present work, we developed a fiber-level constitutive model for the passive mechanical behavior of the right ventricular free wall (RVFW). The model explicitly separates the mechanical contributions of myofiber and collagen fiber ensembles, and accounts for the mechanical interactions between them. To obtain model parameters for the healthy passive RVFW, the model was informed by transmural orientation distribution measurements of myo- and collagen fibers and was fit to the mechanical testing data, where both sets of data were obtained from recent experimental studies on non-contractile, but viable, murine RVFW specimens. Results supported the hypothesis that in the low-strain regime, the behavior of the RVFW is governed by myofiber response alone, which does not demonstrate any coupling between different myofiber ensembles. At higher strains, the collagen fibers and their interactions with myofibers begin to gradually contribute and dominate the behavior as recruitment proceeds. Due to the use of viable myocardial tissue, the contribution of myofibers was significant at all strains with the predicted tensile modulus of [Formula: see text]32 kPa. This was in contrast to earlier reports (Horowitz et al. 1988) where the contribution of myofibers was found to be insignificant. Also, we found that the interaction between myo- and collagen fibers was greatest under equibiaxial strain, with its contribution to the total stress not exceeding 20 %. The present model can be applied to organ-level computational models of right ventricular dysfunction for efficient diagnosis and evaluation of pulmonary hypertension disorder.

A novel fibre-ensemble level constitutive model for exogenous cross-linked collagenous tissues.

Exogenous cross-linking of soft collagenous tissues is a common method for biomaterial development and medical therapies. To enable improved applications through computational methods, physically realistic constitutive models are required. Yet, despite decades of research, development and clinical use, no such model exists. In this study, we develop the first rigorous full structural model (i.e. explicitly incorporating various features of the collagen fibre architecture) for exogenously cross-linked soft tissues. This was made possible, in-part, with the use of native to cross-linked matched experimental datasets and an extension to the collagenous structural constitutive model so that the uncross-linked collagen fibre responses could be mapped to the cross-linked configuration. This allowed us to separate the effects of cross-linking from kinematic changes induced in the cross-linking process, which in turn allowed the non-fibrous tissue matrix component and the interaction effects to be identified. It was determined that the matrix could be modelled as an isotropic material using a modified Yeoh model. The most novel findings of this study were that: (i) the effective collagen fibre modulus was unaffected by cross-linking and (ii) fibre-ensemble interactions played a large role in stress development, often dominating the total tissue response (depending on the stress component and loading path considered). An important utility of the present model is its ability to separate the effects of exogenous cross-linking on the fibres from changes due to the matrix. Applications of this approach include the utilization in the design of novel chemical treatments to produce specific mechanical responses and the study of fatigue damage in bioprosthetic heart valve biomaterials.

A meso-scale layer-specific structural constitutive model of the mitral heart valve leaflets.

Fundamental to developing a deeper understanding of pathophysiological remodeling in mitral valve (MV) disease is the development of an accurate tissue-level constitutive model. In the present work, we developed a novel meso-scale (i.e. at the level of the fiber, 10-100 µm in length scale) structural constitutive model (MSSCM) for MV leaflet tissues. Due to its four-layer structure, we focused on the contributions from the distinct collagen and elastin fiber networks within each tissue layer. Requisite collagen and elastin fibrous structural information for each layer were quantified using second harmonic generation microscopy and conventional histology. A comprehensive mechanical dataset was also used to guide model formulation and parameter estimation. Furthermore, novel to tissue-level structural constitutive modeling approaches, we allowed the collagen fiber recruitment function to vary with orientation. Results indicated that the MSSCM predicted a surprisingly consistent mean effective collagen fiber modulus of 162.72 MPa, and demonstrated excellent predictive capability for extra-physiological loading regimes. There were also anterior-posterior leaflet-specific differences, such as tighter collagen and elastin fiber orientation distributions (ODF) in the anterior leaflet, and a thicker and stiffer atrialis in the posterior leaflet. While a degree of angular variance was observed, the tight valvular tissue ODF also left little room for any physically meaningful angular variance in fiber mechanical responses. Finally, a novel fibril-level (0.1-1 µm) validation approach was used to compare the predicted collagen fiber/fibril mechanical behavior with extant MV small angle X-ray scattering data. Results demonstrated excellent agreement, indicating that the MSSCM fully captures the tissue-level function. Future utilization of the MSSCM in computational models of the MV will aid in producing highly accurate simulations in non-physiological loading states that can occur in repair situations, as well as guide the form of simplified models for real-time simulation tools.

Biomechanical Behavior of Bioprosthetic Heart Valve Heterograft Tissues: Characterization, Simulation, and Performance.

The use of replacement heart valves continues to grow due to the increased prevalence of valvular heart disease resulting from an ageing population. Since bioprosthetic heart valves (BHVs) continue to be the preferred replacement valve, there continues to be a strong need to develop better and more reliable BHVs through and improved the general understanding of BHV failure mechanisms. The major technological hurdle for the lifespan of the BHV implant continues to be the durability of the constituent leaflet biomaterials, which if improved can lead to substantial clinical impact. In order to develop improved solutions for BHV biomaterials, it is critical to have a better understanding of the inherent biomechanical behaviors of the leaflet biomaterials, including chemical treatment technologies, the impact of repetitive mechanical loading, and the inherent failure modes. This review seeks to provide a comprehensive overview of these issues, with a focus on developing insight on the mechanisms of BHV function and failure. Additionally, this review provides a detailed summary of the computational biomechanical simulations that have been used to inform and develop a higher level of understanding of BHV tissues and their failure modes. Collectively, this information should serve as a tool not only to infer reliable and dependable prosthesis function, but also to instigate and facilitate the design of future bioprosthetic valves and clinically impact cardiology.

Large strain stimulation promotes extracellular matrix production and stiffness in an elastomeric scaffold model.

Mechanical conditioning of engineered tissue constructs is widely recognized as one of the most relevant methods to enhance tissue accretion and microstructure, leading to improved mechanical behaviors. The understanding of the underlying mechanisms remains rather limited, restricting the development of in silico models of these phenomena, and the translation of engineered tissues into clinical application. In the present study, we examined the role of large strip-biaxial strains (up to 50%) on ECM synthesis by vascular smooth muscle cells (VSMCs) micro-integrated into electrospun polyester urethane urea (PEUU) constructs over the course of 3 weeks. Experimental results indicated that VSMC biosynthetic behavior was quite sensitive to tissue strain maximum level, and that collagen was the primary ECM component synthesized. Moreover, we found that while a 30% peak strain level achieved maximum ECM synthesis rate, further increases in strain level lead to a reduction in ECM biosynthesis. Subsequent mechanical analysis of the formed collagen fiber network was performed by removing the scaffold mechanical responses using a strain-energy based approach, showing that the denovo collagen also demonstrated mechanical behaviors substantially better than previously obtained with small strain training and comparable to mature collagenous tissues. We conclude that the application of large deformations can play a critical role not only in the quantity of ECM synthesis (i.e. the rate of mass production), but also on the modulation of the stiffness of the newly formed ECM constituents. The improved understanding of the process of growth and development of ECM in these mechano-sensitive cell-scaffold systems will lead to more rational design and manufacturing of engineered tissues operating under highly demanding mechanical environments.

A novel crosslinking method for improved tear resistance and biocompatibility of tissue based biomaterials.

Over 300,000 heart valve replacements are performed annually to replace stenotic and regurgitant heart valves. Bioprosthetic heart valves (BHVs), derived from glutaraldehyde crosslinked (GLUT) porcine aortic valve leaflets or bovine pericardium are often used. However, valve failure can occur within 12-15 years due to calcification and/or progressive degeneration. In this study, we have developed a novel fabrication method that utilizes carbodiimide, neomycin trisulfate, and pentagalloyl glucose crosslinking chemistry (TRI) to better stabilize the extracellular matrix of porcine aortic valve leaflets. We demonstrate that TRI treated leaflets show similar biomechanics to GLUT crosslinked leaflets. TRI treated leaflets had better resistance to enzymatic degradation in vitro and demonstrated better tearing toughness after challenged with enzymatic degradation. When implanted subcutaneously in rats for up to 90 days, GLUT control leaflets calcified heavily while TRI treated leaflets resisted calcification, retained more ECM components, and showed better biocompatibility.

Structural and mechanical adaptations of right ventricle free wall myocardium to pressure overload.

Right ventricular (RV) failure in response to pulmonary hypertension (PH) is a severe disease that remains poorly understood. PH-induced pressure overload leads to changes in the RV free wall (RVFW) that eventually results in RV failure. While the development of computational models can benefit our understanding of the onset and progression of PH-induced pressure overload, detailed knowledge of the underlying structural and biomechanical events remains limited. The goal of the present study was to elucidate the structural and biomechanical adaptations of RV myocardium subjected to sustained pressure overload in a rat model. Hemodynamically confirmed severe chronic RV pressure overload was induced in Sprague-Dawley rats via pulmonary artery banding. Extensive tissue-level biaxial mechanical and histomorphological analyses were conducted to assess the remodeling response in the RV free wall. Simultaneous myofiber hypertrophy and longitudinal re-orientation of myo- and collagen fibers were observed, with both fiber types becoming more highly aligned. Transmural myo- and collagen fiber orientations were co-aligned in both the normal and diseased state. The overall tissue stiffness increased, with larger increases in longitudinal vs. circumferential stiffness. The latter was attributed to longitudinal fiber re-orientation, which increased the degree of anisotropy. Increased mechanical coupling between the two axes was attributed to the increased fiber alignment. Interestingly, estimated myofiber stiffness increased while the collagen fiber stiffness remained unchanged. The increased myofiber stiffness was consistent with clinical results showing titin-associated increased sarcomeric stiffening observed in PH patients. These results further our understanding of the underlying adaptive and maladaptive remodeling mechanisms and may lead to improved techniques for prognosis, diagnosis, and treatment for PH.