Mechanical Behavior Of Soft Tissues Research Articles

Development of a Multi-Material 3D Printer for Functional Anatomic Models.

Anatomic models are important in medical education and pre-operative planning as they help students or doctors prepare for real scenarios in a risk-free way. Several experimental anatomic models were made with additive manufacturing techniques to improve geometric, radiological, or mechanical realism. However, reproducing the mechanical behavior of soft tissues remains a challenge. To solve this problem, multi-material structuring of soft and hard materials was proposed in this study, and a three-dimensional (3D) printer was built to make such structuring possible. The printer relies on extrusion to deposit certain thermoplastic and silicone rubber materials. Various objects were successfully printed for testing the feasibility of geometric features such as thin walls, infill structuring, overhangs, and multi-material interfaces. Finally, a small medical image-based ribcage model was printed as a proof of concept for anatomic model printing. The features enabled by this printer offer a promising outlook on mimicking the mechanical properties of various soft tissues.

Experimental Protocols to Test Aortic Soft Tissues: A Systematic Review.

Experimental protocols are fundamental for quantifying the mechanical behaviour of soft tissue. These data are crucial for advancing the understanding of soft tissue mechanics, developing and calibrating constitutive models, and informing the development of more accurate and predictive computational simulations and artificial intelligence tools. This paper offers a comprehensive review of experimental tests conducted on soft aortic tissues, employing the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology, based on the Scopus, Web of Science, IEEE, Google Scholar and PubMed databases. This study includes a detailed overview of the test method protocols, providing insights into practical methodologies, specimen preparation and full-field measurements. The review also briefly discusses the post-processing methods applied to extract material parameters from experimental data. In particular, the results are analysed and discussed providing representative domains of stress-strain curves for both uniaxial and biaxial tests on human aortic tissue.

Nondestructively identifying the mechanical behavior of soft tissues using surface deformation with an explicit inverse approach

Identifying the spatial variation of stiffness properties in soft tissues nondestructively, with limited surface measurements, poses significant challenges. In this paper, we present a novel explicit inverse approach designed to characterize the nonhomogeneous elastic property distribution of soft tissues using only surface displacement datasets. In contrast to the prevalent implicit inverse approach, which focuses on optimizing the elastic properties of individual pixels, our proposed method optimizes the geometric parameters of deformable and movable components, as well as shear moduli of each component. As a result, the proposed approach requires far fewer optimization variables, streamlining the process. Numerical tests conducted in this study demonstrate the superiority of the explicit inverse method over the implicit inverse method, providing much-improved reconstructed results. In particular for a ring structure, while the average relative error of reconstruction using the implicit inverse method can exceed 40 %, the explicit inverse method achieves a remarkable average relative error of only 5 %. Given that surface displacements are easily measurable, the integration of our proposed explicit inverse method with low-cost imaging techniques shows great potential in accurately mapping the elastic property distribution of biological tissues.

Characterization of the layer, direction and time-dependent mechanical behaviour of the human oesophagus and the effects of formalin preservation.

The mechanical characterization of the oesophagus is essential for applications such as medical device design, surgical simulations and tissue engineering, as well as for investigating the organ's pathophysiology. However, the material response of the oesophagus has not been established ex vivo in regard to the more complex aspects of its mechanical behaviour using fresh, human tissue: as of yet, in the literature, only the hyperelastic response of the intact wall has been studied. Therefore, in this study, the layer-dependent, anisotropic, visco-hyperelastic behaviour of the human oesophagus was investigated through various mechanical tests. For this, cyclic tests, with increasing stretch levels, were conducted on the layers of the human oesophagus in the longitudinal and circumferential directions and at two different strain rates. Additionally, stress-relaxation tests on the oesophageal layers were carried out in both directions. Overall, the results show discrete properties in each layer and direction, highlighting the importance of treating the oesophagus as a multi-layered composite material with direction-dependent behaviour. Previously, the authors conducted layer-dependent cyclic experimentation on formalin-embalmed human oesophagi. A comparison between the fresh and embalmed tissue response was carried out and revealed surprising similarities in terms of anisotropy, strain-rate dependency, stress-softening and hysteresis, with the main difference between the two preservation states being the magnitude of these properties. As formalin fixation is known to notably affect the formation of cross-links between the collagen of biological materials, the differences may reveal the influence of cross-links on the mechanical behaviour of soft tissues.

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.

A custom-built planar biaxial system for soft tissue material testing

Accurate material characterization of soft tissues is crucial for understanding the physiopathology of cardiovascular diseases. However, commercial biaxial testing systems are expensive, prompting the need for affordable custom solutions. This study aimed to develop a low-cost custom biaxial system capable of accurately characterizing the mechanical behavior of soft tissues. The biaxial system was constructed using 3D printing technology and non-captive linear actuators for precise displacement control. A real-time marker tracking system was implemented to estimate dis-placements without the need for costly hardware. The system's performance was evaluated through tests on a calibration spring and frozen porcine aorta samples. The linear actuators demonstrated excellent response to user position input after motor tuning, showing no discrepancies between commands and actual positions. The experimental testing of the calibration spring showed good agreement with the analytical solution, validating the system's ability to accurately test materials. Testing on porcine aorta samples revealed stress–strain responses consistent with existing literature, accounting for potential variations due to tissue preservation and regional material property heterogeneity. Overall, this custom biaxial system demonstrates promising performance in accurately assessing the mechanical behavior of soft tissues, providing researchers with a valuable tool for cardiovascular disease research and tissue engineering applications.

Characterisation of the soft tissue viscous and elastic properties using ultrasound elastography and rheological models: validation and applications in plantar soft tissue assessment

Objective. The mechanical behaviour of soft tissue is influenced by its elastic and viscous characteristics. Therefore, the aim of this study was to develop a validated method to characterise the viscoelastic properties of soft tissues based on ultrasound elastography data. Approach. Plantar soft tissue was chosen as the tissue of interest, and gelatine-phantoms replicating its mechanical properties were manufactured for validation of the protocol. Both plantar soft tissue and the phantom were scanned using Reverberant shear wave ultrasound (US) elastography at 400–600 Hz. Shear wave speed was estimated using the US particle velocity data. The viscoelastic parameters were extracted by fitting the Young’s modulus as a function of frequency derived from the constitutive equations of the eight rheological models (four classic and their fractional-derivative versions) to the shear wave dispersion data. Furthermore, stress-time functions derived from the eight rheological models were fitted to the phantom stress-relaxation data. Main results. The viscoelastic parameters estimated using elastography data based on the fractional-derivative (FD) models, compared to the classic models, were closer to those quantified using the mechanical test. In addition, the FD-Maxwell and FD-Kelvin–Voigt models showed to more effectively replicate the viscoelastic behaviour of the plantar soft tissue with minimum number of model parameters ( = 0.72 for both models) . Hence the FD-KV and FD-Maxwell models can more effectively quantify the viscoelastic characteristics of the soft tissue compared to other models. Significance. In this study, a method for mechanical characterisation of the viscoelastic properties of soft tissue in ultrasound elastography was developed and fully validated. An investigation into the most valid rheological model and its applications in plantar soft tissue assessment were also presented. This proposed approach for the characterisation of viscous and elastic mechanical properties of soft tissue has implications in assessing the soft tissue function where those can be used as markers for diagnosis or prognosis of tissue status.

Development of an ultra-low-cost planar biaxial tester for soft tissue characterization

Nowadays, the research in the arena of biomedical engineering or specifically soft tissue characterization is rapidly increasing. Due to the complex properties of soft tissues such as, anisotropy and viscoelasticity, it is difficult to predict the deformation behaviour. Hence, soft tissue characterization is essential to analyze these metrics. Soft tissue characterization, specifically, can be done by implementing a planar biaxial tester. Currently, available biaxial testers are mostly developed with respect to other mechanical components such as metals, and not for the soft tissues. Also, these devices are very costly, which makes it difficult for the low and middle income countries to perform this characterization. To solve this problem, in this work, an extremely low-cost biaxial tester was designed and developed. The design of the biaxial tester was simple and modular to allow device modifications according to the applications. The device has a force capability of less than 0.4 kN and a variable speed of 18 mm min−1 to 300 mm min−1. The biaxial tester was validated using a standard test material with mechanical testing machine and was further tested on several wound geometries including circular, square, diamond shaped, L-Plasty, and elliptical. The developed fully automated device exhibited high accuracy with real-time monitoring. Furthermore, test results on the wounds showed the device’s capability to differentiate amongst the considered wound geometries. This device can be helpful to medical students and doctors in understanding the mechanical behaviour of soft tissues during injury induced damage, disease, wounds healing and also for plethora of applications such as expansion testing of skin grafts.

Data-driven Modeling of the Mechanical Behavior of Anisotropic Soft Biological Tissue.

Closed-form constitutive models are the standard to describe soft tissue mechanical behavior. However, inherent pitfalls of an explicit functional form include poor fits to the data, non-uniqueness of fit, and sensitivity to parameters. Here we design deep neural networks (DNN) that satisfy desirable physics constraints in order to replace expert models of tissue mechanics. To guarantee stress-objectivity, the DNN takes strain (pseudo)-invariants as inputs, and outputs the strain energy and its derivatives. Polyconvexity of strain energy is enforced through the loss function. Direct prediction of both energy and derivative functions enables the computation of the elasticity tensor needed for a finite element implementation. We showcase the DNN ability to learn the anisotropic mechanical behavior of porcine and murine skin from biaxial test data. A multi-fidelity scheme that combines high fidelity experimental data with a low fidelity analytical approximation yields the best performance. Finite element simulations of tissue expansion with the DNN model illustrate the potential of this method to impact medical device design for skin therapeutics. We expect that the open data and software from this work will broaden the use of data-driven constitutive models of tissue mechanics.

Effects of cryo-preservation on skeletal muscle tissues mechanical behavior under tensile and peeling tests until rupture

The most common method to study the mechanical behavior of soft tissue is to test animal specimens, which should be prepared as soon as possible after the death to avoid biological deterioration effects such as rigor mortis. Freezing and cryo-preservation could allow extending the time between procurement and implantation. From a mechanical perspective, tissue preservation could influence mechanical testing results.Therefore, this study focuses on the influence of cryo-preserved samples on their mechanical behavior, especially at the rupture.In order to analyze this aspect, two tests were performed on the porcine abdominal wall. A tensile test to study the elastic behavior of samples and the tensile strength until rupture. A peeling test to more finely investigate the cohesion between muscle fibers.No statistical difference could be observed following tensile test. However, peeling tests between cryo-preserved and control samples showed a clear statistical difference with a p-value of 0.0097 for Gp. Indeed, energy release rate was higher for the Cryo-preserve group than the Control group with Gp = 0.36 ± 0.07 N/mm vs 0.26 ± 0.10 N/mm. This difference suggests that the characterization of rupture energies for muscular tissue should be done without having frozen the samples, even with a cryopreservative agent.These results could also indicate that even if the rupture mode is the same between mechanical tests, a different rupture direction could imply different mechanical preservations for soft tissues.This study could help to understand the difficult mechanical preservation of soft tissues, especially on the rupture behavior. Future studies on skeletal muscles will be necessary to compare our results, especially in peeling.

Soft Tissue Hybrid Model for Real-Time Simulations.

In this article, a recent formulation for real-time simulation is developed combining the strain energy density of the Spring Mass Model (SMM) with the equivalent representation of the Strain Energy Density Function (SEDF). The resulting Equivalent Energy Spring Model (EESM) is expected to provide information in real-time about the mechanical response of soft tissue when subjected to uniaxial deformations. The proposed model represents a variation of the SMM and can be used to predict the mechanical behavior of biological tissues not only during loading but also during unloading deformation states. To assess the accuracy achieved by the EESM, experimental data was collected from liver porcine samples via uniaxial loading and unloading tensile tests. Validation of the model through numerical predictions achieved a refresh rate of 31 fps (31.49 ms of computation time for each frame), achieving a coefficient of determination R2 from 93.23% to 99.94% when compared to experimental data. The proposed hybrid formulation to characterize soft tissue mechanical behavior is fast enough for real-time simulation and captures the soft material nonlinear virgin and stress-softened effects with high accuracy.

Characterizing and Engineering Biomimetic Materials for Viscoelastic Mechanotransduction Studies.

The mechanical behavior of soft tissue extracellular matrix is time dependent. Moreover, it evolves over time due to physiological processes as well as aging and disease. Measuring and quantifying the time-dependent mechanical behavior of soft tissues and materials pose a challenge, not only because of their labile and hydrated nature but also because of the lack of a common definition of terms and understanding of models for characterizing viscoelasticity. Here, we review the most important measurement techniques and models used to determine the viscoelastic properties of soft hydrated materials—or hydrogels—underlining the difference between viscoelastic behavior and the properties and descriptors used to quantify viscoelasticity. We then discuss the principal factors, which determine tissue viscoelasticity in vivo and summarize what we currently know about cell response to time-dependent materials, outlining fundamental factors that have to be considered when interpreting results. Particular attention is given to the relationship between the different time scales involved (mechanical, cellular and observation time scales), as well as scaling principles, all of which must be considered when designing viscoelastic materials and performing experiments for biomechanics or mechanobiology applications. From this overview, key considerations and directions for furthering insights and applications in the emergent field of cell viscoelastic mechanotransduction are provided.Impact statementOur tissues are viscoelastic: they respond to mechanical stresses and strains in a time-dependent manner. Their mechanical behavior also evolves over time due to growth, aging, remodeling and disease. Understanding cell response to time-dependent and time-evolving mechanical cues is important for a better comprehension of a wide number of pathophysiological processes and for the design of biomimetic substrates, which can be used as physiologically relevant in vitro models and in regenerative medicine applications. This review highlights the importance of a more rigorous approach toward viscoelastic material design and testing for cell mechanobiology studies, which embrace the entire spectrum of elasto- and viscotransduction.

A hyperelastic model to capture the mechanical behaviour and histological aspects of the soft tissues

It is well established that the soft connective tissues show a nonlinear elastic response that comes from their microstructural arrangement. Tissues' microstructure alters with various physiological conditions and may affect their mechanical responses. Therefore, the accurate prediction of tissue's mechanical response is crucial for clinical diagnosis and treatments. Thus, a physically motivated and mathematically simplified model is required for the accurate prediction of tissues' mechanical and structural responses. This study explored the ‘Exp-Ln’ hyperelastic model (Khajehsaeid et al., 2013) to capture soft tissues' mechanical and histological behaviour. In this work, uniaxial tensile test data for the belly and back pig skin were extracted from the experiments performed in our laboratory, whereas uniaxial test data for other soft tissues (human skin, tendon, ligament, and aorta) were extracted from the literature. The ‘Exp-Ln; and other hyperelastic models (e.g. Money Rivlin, Ogden, Yeoh, and Gent models) were fitted with these experimental data, and obtained results were compared between the models. These results show that the ‘Exp-Ln’ model could capture the mechanical behaviour of soft tissues more accurately than other hyperelastic models. This model was also found numerically stable for all modes and ranges of deformation. This study also investigated the link between ‘Exp-Ln’ material parameters and tissue's histological parameters. The histological parameters such as collagen content, fibre free length, crosslink density, and collagen arrangement were measured using staining and ATR-FTIR techniques. The material parameters were found statistically correlated with the histological parameters. Further, ‘Exp-Ln’ model was implemented in ABAQUS through the VUMAT subroutine, where the mechanical behaviour of various soft tissues was simulated for different modes of deformation. The finite element analysis results obtained using the ‘Exp-Ln’ model agreed with the experiments and were more accurate than other hyperelastic models. Overall, these results demonstrate the capability of ‘Exp-Ln’ model to predict the mechanical and structural responses of the soft tissues.

Fiber Rearrangement and Matrix Compression in Soft Tissues: Multiscale Hypoelasticity and Application to Tendon.

It is widely accepted that the nonlinear macroscopic mechanical behavior of soft tissue is governed by fiber straightening and re-orientation. Here, we provide a quantitative assessment of this phenomenon, by means of a continuum micromechanics approach. Given the negligibly small bending stiffness of crimped fibers, the latter are represented through a number of hypoelastic straight fiber phases with different orientations, being embedded into a hypoelastic matrix phase. The corresponding representative volume element (RVE) hosting these phases is subjected to “macroscopic” strain rates, which are downscaled to fiber and matrix strain rates on the one hand, and to fiber spins on the other hand. This gives quantitative access to the fiber decrimping (or straightening) phenomenon under non-affine conditions, i.e. in the case where the fiber orientations cannot be simply linked to the macroscopic strain state. In the case of tendinous tissue, such an RVE relates to the fascicle material with 50 μm characteristic length, made up of crimped collagen bundles and a gel-type matrix in-between. The fascicles themselves act as parallel fibers in a similar matrix at the scale of a tissue-related RVE with 500 μm characteristic length. As evidenced by a sensitivity analysis and confirmed by various mechanical tests, it is the initial crimping angle which drives both the degree of straightening and the shape of the macroscopic stress-strain curve, while the final linear portion of this curve depends almost exclusively on the collagen bundle elasticity. Our model also reveals the mechanical cooperation of the tissue’s key microstructural components: while the fibers carry tensile forces, the matrices undergo hydrostatic pressure.

Surface wave elastography is a reliable method to correlate muscle elasticity, torque, and electromyography activity level.

The shear elastic modulus is one of the most important parameters to characterize the mechanical behavior of soft tissues. In biomechanics, ultrasound elastography is the gold standard for measuring and mapping it locally in skeletal muscle in vivo. However, their applications are limited to the laboratory or clinic. Thus, low‐frequency elastography methods have recently emerged as a novel alternative to ultrasound elastography. Avoiding the use of high frequencies, these methods allow obtaining a mean value of bulk shear elasticity. However, they are frequently susceptible to diffraction, guided waves, and near field effects, which introduces biases in the estimates. The goal of this work is to test the performance of the non‐ultrasound surface wave elastography (NU‐SWE), which is portable and is based on new algorithms designed to correct the incidence of such effects. Thus, we show its first application to muscle biomechanics. We performed two experiments to assess the relationships of muscle shear elasticity versus joint torque (experiment 1) and the electromyographic activity level (experiment 2). Our results were comparable regarding previous works using the reference ultrasonic methods. Thus, the NU‐SWE showed its potentiality to get wide the biomechanical applications of elastography in many areas of health and sports sciences.

SPH-based simulation of micro-impacts in human-tissue surrogate: A preliminary study on multilayered structure

Microparticle impact responses into soft tissue is of interest in various framework like transdermal durg delivery in pharmaceuticals. In order to investigate this phenomenon, experimental devices have been developed using human surrogate such as ballistic gelatin, rubber, or polymers, such as SEBS gel (styrene-ethylenebutylenestyrene), which is considered as an interesting simulant because of its properties (environmental stability, reproducibility, mechanical consistency, transparency), and its ability to represent correctly the mechanical behavior of soft tissues. Considering the perforation mechanical behavior of this surrogate, this paper investigates the multilayered SEBS gel structure of various concentration submitted to high velocity micro-penetrating impact at a numerical level using smoothed particle hydrodynamics formulation. Different concentrations of SEBS gels have been modeled, and the numerical results have been compared to analytical data and existing experimental results, which show a very good correlation, in terms of penetration time history for a single SEBS concentration, as well as a for superimposition of several layers of various concentration of SEBS gel. This paper is a first step in the understanding of penetration of microprojectiles into soft tissue surrogate at various concentrations, allowing further investigations of multilayered target, approaching the human epidermal with several different layers.

Reliability and discriminative validity of real-time ultrasound elastography in the assessment of tissue stiffness after calf muscle injury

ObjectiveTo investigate the reliability and discriminative validity of real-time ultrasound elastography (RTE) measures of soft-tissue elasticity after calf muscle tear. DesignCross-sectional, intra/inter-examiner reliability and comparative validity study. SettingDepartment of Physical Therapy. ParticipantsTwenty-one recreational athletes were included and examined 6 weeks after sustaining a grade I-II calf musculature tear. Main outcome measuresSoft-tissue elasticity was measured by two experienced assessors using RTE assessments in both the longitudinal and transverse planes of the athletes’ injured and uninjured calf muscles. Elasticity was estimated by using the strain ratio (SR), which was calculated by dividing the strain (displacement) value taken at the medial gastrocnemius-soleus myotendinous junction (reference) by the strain value taken at the centre of the injury (index) as visualized on B-mode sonogram. Intra- and inter-observer reliability was estimated calculating intra-class correlation coefficients (ICCs) and standard error of measurement (SEM). Differences in elasticity between injured and healthy legs were assessed using t-tests or Wilcoxon tests for repeated measures. ResultsAll RTE assessments in both planes showed ICC values ranging from 0.77 to 0.95 and SEM values ranging from 0.72 to 0.99. Additionally, RTE enabled both assessors to determine differences in elastic properties between injured and control legs (p < 0.001). ConclusionRTE measures of calf muscles demonstrated good reliability and were able to differentiate injured from non-injured muscle tissue. RTE may provide a fast and objective measure in sports medicine to improve the detection of risk factors for muscle injury related to alterations of the mechanical behaviour of soft tissues during healing process.

Dynamic Tensile Response of Caprine Muscles Using Split Hopkinson Pressure Bar

Computer modeling and numerical simulation has become an efficient diagnostic tool to predict the human body injuries caused due to high speed automotive impacts, blast and ballistic impacts. Soft tissues such as muscles and skin in human body are exposed to varying strain rates under dynamic loadings during impacts. The prediction of impact-induced injuries requires a thorough understanding of mechanical behaviour of soft tissues for computational modeling of human body. In the present study, uniaxial tensile tests were conducted on caprine lower extremity muscles in the strain rate range of (500s^-1-3500s^-1) using custom-made split Hopkinson pressure bar (SHPB) apparatus. The challenges in the dynamic testing of soft tissues such as measurement of weak transmitted signals, use of viscoelastic pressure bars, tensile loading of specimen and generation of constant strain rate were addressed in dynamic tensile testing of soft tissues using polymeric SHPB. The attenuation and dispersion in waves are corrected using isolated incident bar tests. The stress-strain results were determined from the reconstructed waves for the tests conducted on lower extremity caprine muscles. The muscle specimens were tested along and perpendicular to the fiber direction to study the directional dependency of tissue behaviour. The stress-strain response was found to be non-linear and significant dependant on strain rate when tested along and perpendicular to fiber direction at same strain rates. It is also observed that at the same strain rate, the specimen stress of caprine muscle along the perpendicular fiber direction is higher than that along the fiber direction. The obtained results may further be used to develop finite element human body models and safety systems for human body in high rate scenario.

Childbirth Computational Models: Characteristics and Applications.

The biomechanical process of childbirth is necessary to usher in new lives-but it can also result in trauma. This physically intense process can put both the mother and the child at risk of injuries and complications that have life-long impact. Computational models, as a powerful tool to simulate and explore complex phenomena, have been used to improve our understanding of childbirth processes and related injuries since the 1990s. The goal of this paper is to review and summarize the breadth and current state of the computational models of childbirth in the literature-focusing on those that investigate the mechanical process and effects. We first summarize the state of critical characteristics that have been included in computational models of childbirth (i.e., maternal anatomy, fetal anatomy, cardinal movements, and maternal soft tissue mechanical behavior). We then delve into the findings of the past studies of birth processes and mechanical injuries in an effort to bridge the gap between the theoretical, numerical assessment and the empirical, clinical observations and practices. These findings are from applications of childbirth computational models in four areas: (1) the process of childbirth itself, (2) maternal injuries, (3) fetal injuries, and (4) protective measures employed by clinicians during delivery. Finally, we identify some of the challenges that computational models still face and suggest future directions through which more biofidelic simulations of childbirth might be achieved, with the goal that advancing models may provide more efficient and accurate, patient-specific assessment to support future clinical decision-making.

Isogeometric finite element-based simulation of the aortic heart valve: Integration of neural network structural material model and structural tensor fiber architecture representations.

The functional complexity of native and replacement aortic heart valves (AVs) is well known, incorporating such physical phenomenons as time-varying non-linear anisotropic soft tissue mechanical behavior, geometric non-linearity, complex multi-surface time varying contact, and fluid-structure interactions to name a few. It is thus clear that computational simulations are critical in understanding AV function and for the rational basis for design of their replacements. However, such approaches continued to be limited by ad-hoc approaches for incorporating tissue fibrous structure, high-fidelity material models, and valve geometry. To this end, we developed an integrated tri-leaflet valve pipeline built upon an isogeometric analysis framework. A high-order structural tensor (HOST)-based method was developed for efficient storage and mapping the two-dimensional fiber structural data onto the valvular 3D geometry. We then developed a neural network (NN) material model that learned the responses of a detailed meso-structural model for exogenously cross-linked planar soft tissues. The NN material model not only reproduced the full anisotropic mechanical responses but also demonstrated a considerable efficiency improvement, as it was trained over a range of realizable fibrous structures. Results of parametric simulations were then performed, as well as population-based bicuspid AV fiber structure, that demonstrated the efficiency and robustness of the present approach. In summary, the present approach that integrates HOST and NN material model provides an efficient computational analysis framework with increased physical and functional realism for the simulation of native and replacement tri-leaflet heart valves.