An inverse modeling approach for semilunar heart valve leaflet mechanics: exploitation of tissue structure

Smooth leaflets with curved belly and attachment edge profiles promote adaptive remodeling in tissue-engineered heart valves: an in silico study

Tissue-engineered heart valves (TEHVs) are promising valve replacements due to their potential to regenerate into living heart valves, capable of growth and adaptation. Previous TEHVs showed promising results, but often developed progressive leaflet retraction in the long term. In a prior proof-of-concept study, we demonstrated that a novel geometry with more native-like mechanical behavior could give rise to more adaptive remodeling, thereby minimizing leaflet retraction in vivo. In the current study, we aimed to systematically analyze the impact of TEHV geometry on in vivo remodeling under both pulmonary and aortic conditions. Using a bio-inspired in silico framework, we predicted cell-driven, mechano-mediated remodeling in TEHVs post-implantation. Two parameterized valve designs were evaluated under both pulmonary and aortic pressure conditions. The results indicate that a valve design with smooth leaflets, a curved belly profile, and medium to wide attachment edge effectively minimizes stress concentrations and reduces the risk of valve insufficiency in both conditions. Additionally, this design should be tailored to specific hemodynamic conditions to prevent retraction in pulmonary applications and excessive stress concentrations in aortic applications. These insights provide essential guidelines for optimizing TEHV designs, aiming to promote functional remodeling and maintain valve functionality over time, thereby advancing the development of next-generation TEHVs with enhanced long-term outcomes.

FEBio FINESSE: An Open-Source Finite Element Simulation Approach to Estimate In Vivo Heart Valve Strains Using Shape Enforcement

PURPOSE

Finite element simulations are an enticing tool to evaluate heart valve function; however, patient-specific simulations derived from 3D echocardiography are hampered by several technical challenges. The objective of this work is to develop an open-source method to enforce matching between finite element simulations and in vivo image-derived heart valve geometry in the absence of patient-specific material properties, leaflet thickness, and chordae tendineae structures.

METHODS

We evaluate FEBio Finite Element Simulations with Shape Enforcement (FINESSE) using three synthetic test cases considering a range of model complexity. FINESSE is then used to estimate the in vivo valve behavior and leaflet strains for three pediatric patients.

RESULTS

Our results suggest that FINESSE can be used to enforce finite element simulations to match an image-derived surface and estimate the first principal leaflet strains within ± 0.03 strain. Key considerations include: (i) defining the user-defined penalty, (ii) omitting the leaflet commissures to improve simulation convergence, and (iii) emulating the chordae tendineae behavior via prescribed leaflet free edge motion or a chordae emulating force. In all patient-specific cases, FINESSE matched the target surface with median errors of approximately the smallest voxel dimension. Further analysis revealed valve-specific findings, such as the tricuspid valve leaflet strains of a 2-day old patient with HLHS being larger than those of two 13-year old patients.

CONCLUSIONS

FEBio FINESSE can be used to estimate patient-specific in vivo heart valve leaflet strains. The development of this open-source pipeline will enable future studies to begin linking in vivo leaflet mechanics with patient outcomes.

In Vivo Three-Dimensional Geometric Reconstruction of the Mouse Aortic Heart Valve

Aortic valve (AV) disease is a common valvular lesion in the United States, present in about 5% of the population at age 65 with increasing prevalence with advancing age. While current replacement heart valves have extended life for many, their long-term use remains hampered by limited durability. Non-surgical treatments for AV disease do not yet exist, in large part because our understanding of AV disease etiology remains incomplete. The direct study of human AV disease remains hampered by the fact that clinical data is only available at the time of treatment, where the disease is at or near end stage and any time progression information has been lost. Large animal models, long used to assess replacement AV devices, cannot yet reproduce AV disease processes. As an important alternative mouse animal models are attractive for their ability to perform genetic studies of the AV disease processes and test potential pharmaceutical treatments. While mouse models have been used for cellular and genetic studies of AV disease, their small size and fast heart rates have hindered their use for tissue- and organ-level studies. We have recently developed a novel ex vivo micro-CT-based methodology to 3D reconstruct murine heart valves and estimate the leaflet mechanical behaviors (Feng et al. in Sci Rep 13(1):12852, 2023). In the present study, we extended our approach to 3D reconstruction of the in vivo functional murine AV (mAV) geometry using high-frequency four-dimensional ultrasound (4DUS). From the resulting 4DUS images we digitized the mAV mid-surface coordinates in the fully closed and fully opened states. We then utilized matched high-resolution µCT images of ex vivo mouse mAV to develop mAV NURBS-based geometric model. We then fitted the mAV geometric model to the in vivo data to reconstruct the 3D in vivo mAV geometry in the closed and open states in n = 3 mAV. Results demonstrated high fidelity geometric results. To our knowledge, this is the first time such reconstruction was ever achieved. This robust assessment of in vivo mAV leaflet kinematics in 3D opens up the possibility for longitudinal characterization of murine models that develop aortic valve disease.

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.

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.

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.

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.

A Computational Framework for Atrioventricular Valve Modeling Using Open-Source Software

Atrioventricular valve regurgitation is a significant cause of morbidity and mortality in patients with acquired and congenital cardiac valve disease. Image-derived computational modeling of atrioventricular valves has advanced substantially over the last decade and holds particular promise to inform valve repair in small and heterogeneous populations, which are less likely to be optimized through empiric clinical application. While an abundance of computational biomechanics studies has investigated mitral and tricuspid valve disease in adults, few studies have investigated its application to vulnerable pediatric and congenital heart populations. Further, to date, investigators have primarily relied upon a series of commercial applications that are neither designed for image-derived modeling of cardiac valves nor freely available to facilitate transparent and reproducible valve science. To address this deficiency, we aimed to build an open-source computational framework for the image-derived biomechanical analysis of atrioventricular valves. In the present work, we integrated an open-source valve modeling platform, SlicerHeart, and an open-source biomechanics finite element modeling software, FEBio, to facilitate image-derived atrioventricular valve model creation and finite element analysis. We present a detailed verification and sensitivity analysis to demonstrate the fidelity of this modeling in application to three-dimensional echocardiography-derived pediatric mitral and tricuspid valve models. Our analyses achieved an excellent agreement with those reported in the literature. As such, this evolving computational framework offers a promising initial foundation for future development and investigation of valve mechanics, in particular collaborative efforts targeting the development of improved repairs for children with congenital heart disease.

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

Patient-Specific Bicuspid Aortic Valve Biomechanics: A Magnetic Resonance Imaging Integrated Fluid-Structure Interaction Approach

Congenital bicuspid aortic valve (BAV) consists of two fused cusps and represents a major risk factor for calcific valvular stenosis. Herein, a fully coupled fluid-structure interaction (FSI) BAV model was developed from patient-specific magnetic resonance imaging (MRI) and compared against in vivo 4-dimensional flow MRI (4D Flow). FSI simulation compared well with 4D Flow, confirming direction and magnitude of the flow jet impinging onto the aortic wall as well as location and extension of secondary flows and vortices developing at systole: the systolic flow jet originating from an elliptical 1.6 cm² orifice reached a peak velocity of 252.2 cm/s, 0.6% lower than 4D Flow, progressively impinging on the ascending aorta convexity. The FSI model predicted a peak flow rate of 22.4 L/min, 6.7% higher than 4D Flow, and provided BAV leaflets mechanical and flow-induced shear stresses, not directly attainable from MRI. At systole, the ventricular side of the non-fused leaflet revealed the highest wall shear stress (WSS) average magnitude, up to 14.6 Pa along the free margin, with WSS progressively decreasing towards the belly. During diastole, the aortic side of the fused leaflet exhibited the highest diastolic maximum principal stress, up to 322 kPa within the attachment region. Systematic comparison with ground-truth non-invasive MRI can improve the computational model ability to reproduce native BAV hemodynamics and biomechanical response more realistically, and shed light on their role in BAV patients' risk for developing complications; this approach may further contribute to the validation of advanced FSI simulations designed to assess BAV biomechanics.

Effect of Residual and Transformation Choice on Computational Aspects of Biomechanical Parameter Estimation of Soft Tissues

Several nonlinear and anisotropic constitutive models have been proposed to describe the biomechanical properties of soft tissues, and reliably estimating the unknown parameters in these models using experimental data is an important step towards developing predictive capabilities. However, the effect of parameter estimation technique on the resulting biomechanical parameters remains under-analyzed. Standard off-the-shelf techniques can produce unreliable results where the parameters are not uniquely identified and can vary with the initial guess. In this study, a thorough analysis of parameter estimation techniques on the resulting properties for four multi-parameter invariant-based constitutive models is presented. It was found that linear transformations have no effect on parameter estimation for the presented cases, and nonlinear transforms are necessary for any improvement. A distinct focus is put on the issue of non-convergence, and we propose simple modifications that not only improve the speed of convergence but also avoid convergence to a wrong solution. The proposed modifications are straightforward to implement and can avoid severe problems in the biomechanical analysis. The results also show that including the fiber angle as an unknown in the parameter estimation makes it extremely challenging, where almost all of the formulations and models fail to converge to the true solution. Therefore, until this issue is resolved, a non-mechanical—such as optical—technique for determining the fiber angle is required in conjunction with the planar biaxial test for a robust biomechanical analysis.

Mechanics of the Tricuspid Valve-From Clinical Diagnosis/Treatment, In-Vivo and In-Vitro Investigations, to Patient-Specific Biomechanical Modeling

Proper tricuspid valve (TV) function is essential to unidirectional blood flow through the right side of the heart. Alterations to the tricuspid valvular components, such as the TV annulus, may lead to functional tricuspid regurgitation (FTR), where the valve is unable to prevent undesired backflow of blood from the right ventricle into the right atrium during systole. Various treatment options are currently available for FTR; however, research for the tricuspid heart valve, functional tricuspid regurgitation, and the relevant treatment methodologies are limited due to the pervasive expectation among cardiac surgeons and cardiologists that FTR will naturally regress after repair of left-sided heart valve lesions. Recent studies have focused on (i) understanding the function of the TV and the initiation or progression of FTR using both in-vivo and in-vitro methods, (ii) quantifying the biomechanical properties of the tricuspid valve apparatus as well as its surrounding heart tissue, and (iii) performing computational modeling of the TV to provide new insight into its biomechanical and physiological function. This review paper focuses on these advances and summarizes recent research relevant to the TV within the scope of FTR. Moreover, this review also provides future perspectives and extensions critical to enhancing the current understanding of the functioning and remodeling tricuspid valve in both the healthy and pathophysiological states.

A Non-Invasive Material Characterization Framework for Bioprosthetic Heart Valves

Computational modeling and simulation has become more common in design and development of bioprosthetic heart valves. To have a reliable computational model, considering accurate mechanical properties of biological soft tissue is one of the most important steps. The goal of this study was to present a non-invasive material characterization framework to determine mechanical propertied of soft tissue employed in bioprosthetic heart valves. Using integrated experimental methods (i.e., digital image correlation measurements and hemodynamic testing in a pulse duplicator system) and numerical methods (i.e., finite element modeling and optimization), three-dimensional anisotropic mechanical properties of leaflets used in two commercially available transcatheter aortic valves (i.e., Edwards SAPIEN 3 and Medtronic CoreValve) were characterized and compared to that of a commonly used and well-examined surgical bioprosthesis (i.e., Carpentier-Edwards PERIMOUNT Magna aortic heart valve). The results of the simulations showed that the highest stress value during one cardiac cycle was at the peak of systole in the three bioprostheses. In addition, in the diastole, the peak of maximum in-plane principal stress was 0.98, 0.96, and 2.95 MPa for the PERIMOUNT Magna, CoreValve, and SAPIEN 3, respectively. Considering leaflet stress distributions, there might be a difference in the long-term durability of different TAV models.

Material characterization of cardiovascular biomaterials using an inverse finite-element method and an explicit solver

The ability to accurately model soft tissue behavior, such as that of heart valve tissue, is essential for developing reliable numerical simulations and determining patient-specific care options. Although several material models can predict soft tissue behavior, complications may arise when these models are implemented into finite element (FE) programs, due to the addition of an arbitrary penalty parameter for numerically enforcing material incompressibility. Herein, an inverse methodology was developed in MATLAB to use previously published stress-strain data from experimental planar equibiaxial testing of five biomaterials used in heart valve cusp replacements, in conjunction with commercial explicit FE solver LS-DYNA, to optimize the material parameters and the penalty parameter for an anisotropic hyperelastic strain energy function. A two-parameter optimization involving the scaling constant of the strain energy function and the penalty parameter proved sufficient to produce acceptable material responses when compared with experimental behaviors under the same testing conditions, as long as analytically derived material constants were available for the other non-optimized parameters and the actual tissue thickness was not much less than 1 mm. Variations in the penalty parameter had a direct effect on the accuracy of the simulated responses, with a practical range determined to be 5×10⁸-9×10⁸ times the scaling constant of the strain energy function.

A Novel Small-Specimen Planar Biaxial Testing System With Full In-Plane Deformation Control

Simulations of soft tissues require accurate and robust constitutive models, whose form is derived from carefully designed experimental studies. For such investigations of membranes or thin specimens, planar biaxial systems have been used extensively. Yet, all such systems remain limited in their ability to: (1) fully prescribe in-plane deformation gradient tensor F2D, (2) ensure homogeneity of the applied deformation, and (3) be able to accommodate sufficiently small specimens to ensure a reasonable degree of material homogeneity. To address these issues, we have developed a novel planar biaxial testing device that overcomes these difficulties and is capable of full control of the in-plane deformation gradient tensor F2D and of testing specimens as small as ∼4 mm × ∼4 mm. Individual actuation of the specimen attachment points, combined with a robust real-time feedback control, enabled the device to enforce any arbitrary F2D with a high degree of accuracy and homogeneity. Results from extensive device validation trials and example tissues illustrated the ability of the device to perform as designed and gather data needed for developing and validating constitutive models. Examples included the murine aortic tissues, allowing for investigators to take advantage of the genetic manipulation of murine disease models. These capabilities highlight the potential of the device to serve as a platform for informing and verifying the results of inverse models and for conducting robust, controlled investigation into the biomechanics of very local behaviors of soft tissues and membrane biomaterials.

A contact formulation based on a volumetric potential: Application to isogeometric simulations of atrioventricular valves

This work formulates frictionless contact between solid bodies in terms of a repulsive potential energy term and illustrates how numerical integration of the resulting forces is computationally similar to the "pinball algorithm" proposed and studied by Belytschko and collaborators in the 1990s. We thereby arrive at a numerical approach that has both the theoretical advantages of a potential-based formulation and the algorithmic simplicity, computational efficiency, and geometrical versatility of pinball contact. The singular nature of the contact potential requires a specialized nonlinear solver and an adaptive time stepping scheme to ensure reliable convergence of implicit dynamic calculations. We illustrate the effectiveness of this numerical method by simulating several benchmark problems and the structural mechanics of the right atrioventricular (tricuspid) heart valve. Atrioventricular valve closure involves contact between every combination of shell surfaces, edges of shells, and cables, but our formulation handles all contact scenarios in a unified manner. We take advantage of this versatility to demonstrate the effects of chordal rupture on tricuspid valve coaptation behavior.

Computational methods for the aortic heart valve and its replacements

INTRODUCTION

Replacement with a prosthetic device remains a major treatment option for the patients suffering from heart valve disease, with prevalence growing resulting from an ageing population. While the most popular replacement heart valve continues to be the bioprosthetic heart valve (BHV), its durability remains limited. There is thus a continued need to develop a general understanding of the underlying mechanisms limiting BHV durability to facilitate development of a more durable prosthesis. In this regard, computational models can play a pivotal role as they can evaluate our understanding of the underlying mechanisms and be used to optimize designs that may not always be intuitive. Areas covered: This review covers recent progress in computational models for the simulation of BHV, with a focus on aortic valve (AV) replacement. Recent contributions in valve geometry, leaflet material models, novel methods for numerical simulation, and applications to BHV optimization are discussed. This information should serve not only to infer reliable and dependable BHV function, but also to establish guidelines and insight for the design of future prosthetic valves by analyzing the influence of design, hemodynamics and tissue mechanics. Expert commentary: The paradigm of predictive modeling of heart valve prosthesis are becoming a reality which can simultaneously improve clinical outcomes and reduce costs. It can also lead to patient-specific valve design.

An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function

Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress–strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.

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.

In-vivo heterogeneous functional and residual strains in human aortic valve leaflets

Residual and physiological functional strains in soft tissues are known to play an important role in modulating organ stress distributions. Yet, no known comprehensive information on residual strains exist, or non-invasive techniques to quantify in-vivo deformations for the aortic valve (AV) leaflets. Herein we present a completely non-invasive approach for determining heterogeneous strains - both functional and residual - in semilunar valves and apply it to normal human AV leaflets. Transesophageal 3D echocardiographic (3DE) images of the AV were acquired from open-heart transplant patients, with each AV leaflet excised after heart explant and then imaged in a flattened configuration ex-vivo. Using an established spline parameterization of both 3DE segmentations and digitized ex-vivo images (Aggarwal et al., 2014), surface strains were calculated for deformation between the ex-vivo and three in-vivo configurations: fully open, just-coapted, and fully-loaded. Results indicated that leaflet area increased by an average of 20% from the ex-vivo to in-vivo open states, with a highly heterogeneous strain field. The increase in area from open to just-coapted state was the highest at an average of 25%, while that from just-coapted to fully-loaded remained almost unaltered. Going from the ex-vivo to in-vivo mid-systole configurations, the leaflet area near the basal attachment shrank slightly, whereas the free edge expanded by ~10%. This was accompanied by a 10° -20° shear along the circumferential-radial direction. Moreover, the principal stretches aligned approximately with the circumferential and radial directions for all cases, with the highest stretch being along the radial direction. Collectively, these results indicated that even though the AV did not support any measurable pressure gradient in the just-coapted state, the leaflets were significantly pre-strained with respect to the excised state. Furthermore, the collagen fibers of the leaflet were almost fully recruited in the just-coapted state, making the leaflet very stiff with marginal deformation under full pressure. Lastly, the deformation was always higher in the radial direction and lower along the circumferential one, the latter direction made stiffer by the preferential alignment of collagen fibers. These results provide significant insight into the distribution of residual strains and the in-vivo strains encountered during valve opening and closing in AV leaflets, and will form an important component of the tool that can evaluate valve׳s functional properties in a non-invasive manner.