Soft Tissue Material Research Articles

Comparison of mechanical response of head structure with different brain material models under impact

Abstract Brian material models and mechanical properties are very important for pressure evolution experiments and numerical simulations in head structure under impact. A simplified head structure with core-shell finite element model was established, and the motion, skull stress, skull deformation, and brain stress were numerically simulated with different soft tissue material models. The equivalence of the material model in stress propagation simulation was discussed. In the present work, it showed that when the head with impact velocity of 1m/s, the head structure rebound with a velocity of 0.6 m/s ∼ 0.8m/s, and occurred between 600μs and 1000μs due to different material models, at this time, the stress wave oscillation propagated in the skull underwent 3-5 repeated loads. The positive pressure on the impact side of brain tissue could reach 400kPa ∼ 800kPa, the negative pressure on the opposite side was between −150 kPa to −385kPa, the skull strain was between −1.8 ‰ to −3.7 ‰, and the skull stress was between 25.3MPa ∼ 41.2MPa. In a larger range of impact velocities, material models with strain rate effect have more advantages in stress wave transmission and pressure changing within the core-shell structure. The strain rate effect characterized only by creep and relaxation has limited effects on impact simulation, and directly introducing different strain rate mechanical property interpolation for hyperelastic model simulation is more effective.

On the Relative Effects of Wall and Intraluminal Thrombus Constitutive Material Properties in Abdominal Aortic Aneurysm Wall Stress.

An abdominal aortic aneurysm (AAA) is a dilation localized in the infrarenal segment of the abdominal aorta that can expand continuously and rupture if left untreated. Computational methods such as finite element analysis (FEA) are widely used with in silico models to calculate biomechanical predictors of rupture risk while choosing constitutive material properties for the AAA wall and intraluminal thrombus (ILT). In the present work, we investigated the effect of different constitutive material properties for the wall and ILT on 21 idealized and 10 unruptured patient-specific AAA geometries. Three material properties were used to characterize the wall and two for the ILT, leading to six material model combinations for each AAA geometry subject to appropriate boundary conditions. The results of the FEA simulations indicate significant differences in the average peak wall stress (PWS), 99th percentile wall stress (99th WS), and spatially averaged wall stress (SAWS) for all AAA geometries subject to the choice of a material model combination. Specifically, using a material model combination with a compliant ILT yielded statistically higher wall stresses compared to using a stiff ILT, irrespective of the constitutive equation used to model the AAA wall. This work provides quantitative insight into the variability of the wall stress distributions ensuing from AAA FEA modeling due to its strong dependency on population-averaged soft tissue material characterizations. This dependency leads to uncertainty about the true biomechanical state of stress of an individual AAA and the subsequent assessment of its rupture risk.

Design and FEA verification of high dimensional and multi-field smart soft material

Abstract We designed a sophisticated smart soft tissue material that simulates the properties of biological soft tissue and detects three-dimensional force. Inspired by electronic skin, this material uses capacitive pressure sensors and multi-layer sensor packaging. Finite element analysis and multi-field simulation were employed for structural design and verification. The study evaluated the theory and practicality of a flexible capacitive 3D force sensor for detecting pressure and shear force. Mechanical and electrical properties were confirmed through force and electric field simulations. The 3D force detection method proved feasible, achieving sensitivity levels of 10−4 kPa −1 in the X and Y directions, and 10−3 kPa −1 in the Z direction, demonstrating the effectiveness of our design.

Soft tissue material properties based on human abdominal in vivo macro-indenter measurements

Simulations of human-technology interaction in the context of product development require comprehensive knowledge of biomechanical in vivo behavior. To obtain this knowledge for the abdomen, we measured the continuous mechanical responses of the abdominal soft tissue of ten healthy participants in different lying positions anteriorly, laterally, and posteriorly under local compression depths of up to 30 mm. An experimental setup consisting of a mechatronic indenter with hemispherical tip and two time-of-flight (ToF) sensors for optical 3D displacement measurement of the surface was developed for this purpose. To account for the impact of muscle tone, experiments were conducted with both controlled activation and relaxation of the trunk muscles. Surface electromyography (sEMG) was used to monitor muscle activation levels. The obtained data sets comprise the continuous force-displacement data of six abdominal measurement regions, each synchronized with the local surface displacements resulting from the macro-indentation, and the bipolar sEMG signals at three key trunk muscles. We used inverse finite element analysis (FEA), to derive sets of nonlinear material parameters that numerically approximate the experimentally determined soft tissue behaviors. The physiological standard values obtained for all participants after data processing served as reference data. The mean stiffness of the abdomen was significantly different when the trunk muscles were activated or relaxed. No significant differences were found between the anterior-lateral measurement regions, with exception of those centered on the linea alba and centered on the muscle belly of the rectus abdominis below the intertubercular plane. The shapes and areas of deformation of the skin depended on the region and muscle activity. Using the hyperelastic Ogden model, we identified unique material parameter sets for all regions. Our findings confirmed that, in addition to the indenter force-displacement data, knowledge about tissue deformation is necessary to reliably determine unique material parameter sets using inverse FEA. The presented results can be used for finite element (FE) models of the abdomen, for example, in the context of orthopedic or biomedical product developments.

Application of High-Frequency Ultrasound to Evaluate Forehead Filling Materials.

In recent years, soft tissue materials have been applied as forehead fillers. Some filling materials need to be removed or refilled in a timely manner in certain situations; therefore, it is important to develop a method to identify the location and type of filling materials. This study summarizes the imaging findings of different filling materials under high-frequency ultrasound, providing a reference for clinical treatment. We screened facial ultrasound images performed at the Plastic Surgery Hospital of the Chinese Academy of Medical Sciences from April 2015 to July 2023 and classified and summarized the types of frontal filling materials and their imaging results. This study included ultrasound imaging results from 114 patients, including 39 with hyaluronic acid (HA) filling, 45 with polyacrylamide hydrogel (PAG) filling, 14 who received autologous fat transplantation, 2 who received prosthesis implantation, 2 who received both HA and PAG filling, and 12 who received silicone oil filling. HA mainly manifests as an anechoic zone on ultrasonography, with images divisible into four types. PAG primarily presents as fine punctate echoes, divisible into five types. Fat transplantation presents as a low-echo area with uneven density, divisible into five types. Finally, the silicone oil-filling material appears as a cloud-like high echo on the forehead, visible throughout the entire skin layer, and unclear imaging in deep tissues. High-frequency ultrasound is a safe and reliable method to evaluate the type and position of forehead filling materials, which can be easily applied in clinical practice. This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .

Investigation on mussel periostracum, a viscoelastic-to-poro-gel graded material, as an interface between soft tissue and rigid materials

Mussel periostracum, a nonliving multifunctional gel that covers the rigid inorganic shells of mussels, provides protection against mechanical impacts, biofouling, and corrosion in harsh ocean environments. The inner part of the periostracum, which emerges from biological tissues, functions as a natural interface between tissue and inorganic materials. The periostracum shows significant potential for application in implantable devices that provide interfaces; however, this system remains unexplored. In this study, we revealed that the inner periostracum performs graded mechanical functions and efficiently dissipates energy to accommodate differences in stiffness and stress types on both sides. On the tissue end, the lightly pigmented periostracum exhibits extensibility and energy dissipation under repetitive tension. This process was facilitated by the slipping and reassembly of β-strands in the discovered major proteins, which we named periostracin proteins. On the shell end, the highly pigmented, mineralized, and porous segment of the periostracum provided stiffness and cushioned against compressive stresses exerted by the shell valves during closure. These findings offer a novel possibilities for the design of interfaces that bridge human tissue and devices.

Endo-Surgical Force Feedback System Design for Virtual Reality Applications in Medical Planning

Virtual reality (VR) applications for surgical planning and mentoring are currently becoming more widespread. Within these fields of applications, haptic systems are crucial to help the understanding of the feedback provided by the tissue during the interaction with the surgical tool. The accuracy of the VR scenario is related to many aspects, among them the ability of the haptic device to provide the force feedback and thus the adoption of proper characterization and modeling of the soft tissue behavior during deformation. This paper presents the current development concerning a VR environment to be equipped with a force feedback haptic device to simulate and experience clamping in colorectal surgery. The reaction at the clamp handle is provided starting from a FEA of the contact between the surgical tool and the tissue, coupled with the kinematic analysis of the mechanism. Connecting the virtual scenario to a microcontroller board, the reaction force is applied to the the haptic device, shaped as a clamping tool handle, so that the user may experience the tissue impedence during clamping. By simulations made through Simscape, a concept is evaluated according to some simulation paths that involve common scenarios of the virtual reality experience (such as collision, partial or total clamping operation). The novelty of the research regards the system design oriented to increase the accuracy of the soft tissue material behaviour through a preliminary off-line dedicated FEA investigation. Through Simulink simulations, the system design is verified so that the VR system set-up may be carried out. The results highlighted: (a) a good correspondence among the theoretical study of the reference kinematism that the haptic device must reproduce; (b) the implementation of a bilinear material model, derived off-line from FEA, is suitable to capture hyperelastic and geometric non-linearities of the soft tissue; (c) the feasibility of the open loop haptic control in accordance to the explored kinematism. The final goal of the research is to propose a system design approach able to tune the VR experince for teaching and mentoring through a in-house set-up easy to be tailored.

Finite element analysis of the cervical spine: dynamic characteristics and material property sensitivity study

The study aimed to investigate the dynamic characteristics of the cervical spine and determine the effect of the material properties of the cervical spinal components on it. A finite element model of the head-cervical spine was developed based on CT scan data, and the first six orders of modes (e.g. flexion-extension, lateral bending, and vertical, etc.) were verified by experimental and simulation studies. The material sensitivity study was conducted by varying elasticity modulus of cervical hard tissues (cortical bone, cancellous bone, endplates, and posterior elements) and soft tissues (intervertebral disc and ligaments). The results showed that increasing the elastic modulus of ligaments by 4 times increased the natural frequency by 77%, while increasing that of cancellous bone by 4 times only increased the natural frequency by 6%. In the axial mode, the cervical spine had not only axial deformation but also anterior-posterior deformation, with the largest deformation located at the intervertebral disc C6-C7. Decreasing the elastic modulus of a component in soft tissues by 80% increased modal displacement by up to 62%. The material properties of the intervertebral discs and ligaments had opposite effects on the modal displacement and deformation of the cervical spine. Low cervical discs were more susceptible to injury in a vertical vibration environment. Cervical spine dynamics were more sensitive to soft tissue material properties than to hard tissue material properties. Disc degeneration could reduce the range of vibratory motion of the cervical spine, thereby reducing the ability of the cervical spine to cushion head impacts.

Stable Isotope Analysis of Antipatharian Diets from the Northwestern Gulf of Mexico

Antipatharians, or black corals, form a key component of the benthic fauna found throughout the Gulf of Mexico (GOM). In the northwestern GOM, they are a common member of the communities found on the natural relic coral—algal banks known as the South Texas Banks as well as on artificial reefs. They are known to provide important habitat for many ecologically and economically important species in the area but are relatively understudied. Here we present a study on their trophic ecology using stable isotope analysis of carbon and nitrogen from 2 species, Antipathes atlantica and Stichopathes luetkeni from a mesophotic artificial reef in close proximity to the South Texas Banks. We observed that a large proportion of the 2 coral’s diets was composed of detrital matter, likely driven by the continuous disturbance of the benthos by high velocity benthic currents common to the region that support a persistent nepheloid layer below 30 m. Both species also show a reliance on different members of the planktonic community, with A. atlantica consuming more micro and mesozooplankton compared to S. luetkeni. Comparative analysis between soft tissue and skeletal material also indicates that A. atlantica may change its diet on a seasonal basis, while S. luetkeni appears to rely on detrital matter consistently. This study represents the first assessment of the diets of these organisms and provides valuable insight on the trophic ecology of 2 common antipatharian corals in the GOM on natural and artificial reef ecosystems.

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.

Experimental and analytical study on insertion force of composite-coated needle in soft tissue material.

Medical interventions require control over surgical needle insertion to minimize tissue damage and target inaccuracies during percutaneous procedures. The composite coating of the needle using Polydopamine (PDA), Polytetrafluoroethylene (PTFE), and Activated Carbon (C) has been used to reduce the damaging needle insertion force. This research aims to further understand the interfacial mechanics of coated needle insertion by studying the forces at the needle and tissue interface and developing an analytical insertion force model through a combined experimental and numerical method. The proposed analytical force model is divided into two components: (1) Friction force on the needle shaft, modeled using a modified Karnopp model that includes an elastic force component; (2) Cutting force on the needle tip, modeled using a constant cutting coefficient for a given tissue and insertion speed. In this work, the analytical model was established by incorporating experiments conducted at a reasonable 35 mm insertion depth in tissues. In a bovine kidney with a 35 mm insertion depth, the insertion force evaluated through experimentation and modeling differed by 6.5% for a bare needle and 17.1% for a coated needle. It is important to note that this difference in the analytical insertion force model is anticipated when dealing with real tissues with a highly complex structured tissue. Prediction of the insertion force could potentially be utilized in robotic needle systems for needle control to improve the success of percutaneous procedures.

Definition and evaluation of a finite element model of the human heel for diabetic foot ulcer prevention under shearing loads.

Diabetic foot ulcers are triggered by mechanical loadings applied to the surface of the plantar skin. Strain is considered to play a crucial role in relation to ulcer etiology and can be assessed by Finite Element (FE) modeling. A difficulty in the generation of these models is the choice of the soft tissue material properties. In the literature, many studies attempt to model the behavior of the heel soft tissues by implementing constitutive laws that can differ significantly in terms of mechanical response. Moreover, current FE models lack of proper evaluation techniques that could estimate their ability to simulate realistic strains. In this article, we propose and evaluate a FE model of the human heel for diabetic foot ulcer prevention. Soft tissue constitutive laws are defined through the fitting of experimental stretch-stress curves published in the literature. The model is then evaluated through Digital Volume Correlation (DVC) based on non-rigid 3D Magnetic Resonance Image Registration. The results from FE analysis and DVC show similar strain locations in the fat pad and strain intensities according to the type of applied loads. For additional comparisons, different sets of constitutive models published in the literature are applied into the proposed FE mesh and simulated with the same boundary conditions. In this case, the results in terms of strains show great diversity in locations and intensities, suggesting that more research should be developed to gain insight into the mechanical properties of these tissues.

Silicone phantoms fabricated with multi-material extrusion 3D printing technology mimicking imaging properties of soft tissues in CT

Recently, 3D printing has been widely used to fabricate medical imaging phantoms. So far, various rigid 3D printable materials have been investigated for their radiological properties and efficiency in imaging phantom fabrication. However, flexible, soft tissue materials are also needed for imaging phantoms for simulating several clinical scenarios where anatomical deformations is important. Recently, various additive manufacturing technologies have been used to produce anatomical models based on extrusion techniques that allow the fabrication of soft tissue materials. To date, there is no systematic study in the literature investigating the radiological properties of silicone rubber materials/fluids for imaging phantoms fabricated directly by extrusion using 3D printing techniques. The aim of this study was to investigate the radiological properties of 3D printed phantoms made of silicone in CT imaging. To achieve this goal, the radiodensity as described as Hounsfield Units (HUs) of several samples composed of three different silicone printing materials were evaluated by changing the infill density to adjust their radiological properties. A comparison of HU values with a Gammex Tissue Characterization Phantom was performed. In addition, a reproducibility analysis was performed by creating several replicas for specific infill densities. A scaled down anatomical model derived from an abdominal CT was also fabricated and the resulting HU values were evaluated. For the three different silicone materials, a spectrum ranging from −639 to +780 HU was obtained on CT at a scan setting of 120 kVp. In addition, using different infill densities, the printed materials were able to achieve a similar radiodensity range as obtained in different tissue-equivalent inserts in the Gammex phantom (238 HU to −673 HU). The reproducibility results showed good agreement between the HU values of the replicas compared to the original samples, confirming the reproducibility of the printed materials. A good agreement was observed between the HU target values in abdominal CT and the HU values of the 3D-printed anatomical phantom in all tissues.

PIPER adult comfort: an open-source full body human body model for seating comfort assessment and its validation under static loading conditions.

Introduction: In this paper we introduce an adult-sized FE full-body HBM for seating comfort assessments and present its validation in different static seating conditions in terms of pressure distribution and contact forces. Methods: We morphed the PIPER Child model into a male adult-sized model with the help of different target sources including his body surface scans, and spinal and pelvic bone surfaces and an open sourced full body skeleton. We also introduced soft tissue sliding under the ischial tuberosities (ITs). The initial model was adapted for seating applications with low modulus soft tissue material property and mesh refinements for buttock regions, etc. We compared the contact forces and pressure-related parameters simulated using the adult HBM with those obtained experimentally from the person whose data was used for the model development. Four seat configurations, with the seat pan angle varying from 0° to 15° and seat-to-back angle fixed at 100°, were tested. Results: The adult HBM could correctly simulate the contact forces on the backrest, seat pan, and foot support with an average error of less than 22.3N and 15.5N in the horizontal and vertical directions, which is small considering the body weight (785N). In terms of contact area, peak, and mean pressure, the simulation matched well with the experiment for the seat pan. With soft tissue sliding, higher soft tissue compression was obtained in agreement with the observations from recent MRI studies. Discussion: The present adult model could be used as a reference using a morphing tool as proposed in PIPER. The model will be published openly online as part of the PIPER open-source project (www.PIPER-project.org) to facilitate its reuse and improvement as well as its specific adaptation for different applications.

Spectral photon counting for panoramic dental imaging

Panoramic x-ray imaging is a versatile, low-dose imaging tool, which is routinely used for dental applications. In this work, we explore a further improvement of the concept by introducing recently developed spectral photon-counting detector technology into a conventional panoramic imaging unit. In addition we adapt spectral material decomposition algorithms to panoramic imaging needs. Finally, we provide first experimental results, demonstrating decomposition of an anthropomorphic head phantom into soft tissue and dentin basis material panoramic images, while keeping the noise level acceptable using regularization approaches. The obtained results reveal a potential benefit of spectral photon-counting technology also for dental imaging applications.

Identifiability of soft tissue constitutive parameters from in-vivo macro-indentation

Reliable identification of soft tissue material parameters is frequently required in a variety of applications, particularly for biomechanical simulations using finite element analysis (FEA). However, determining representative constitutive laws and material parameters is challenging and often comprises a bottleneck that hinders the successful implementation of FEA. Soft tissues exhibit a nonlinear response and are commonly modeled using hyperelastic constitutive laws. In-vivo material parameter identification, for which standard mechanical tests (e.g., uniaxial tension and compression) are inapplicable, is commonly achieved using finite macro-indentation test. Due to the lack of analytical solutions, the parameters are commonly identified using inverse FEA (iFEA), in which simulated results and experimental data are iteratively compared. However, determining what data must be collected to accurately identify a unique parameter set remains unclear. This work investigates the sensitivities of two types of measurements: indentation force-depth data (e.g., measured using an instrumented indenter) and full-field surface displacements (e.g., using digital image correlation). To eliminate model fidelity and measurement-related errors, we employed an axisymmetric indentation FE model to produce synthetic data for four 2-parameter hyperelastic constitutive laws: compressible Neo-Hookean, and nearly incompressible Mooney-Rivlin, Ogden, and Ogden-Moerman models. For each constitutive law, we computed the objective functions representing the discrepancies in the reaction force, the surface displacement, and their combination, and visualized them for hundreds of parameter sets, spanning a representative range as found in the literature for the bulk soft tissue complex in human lower limbs. Moreover, we quantified three identifiability metrics, which provided insights into the uniqueness (or lack thereof) and the sensitivities. This approach provides a clear and systematic evaluation of the parameter identifiability, which is independent of the selection of the optimization algorithm and initial guesses required in iFEA. Our analysis indicated that the indenter’s force-depth data, despite being commonly used for parameter identification, was insufficient for reliably and accurately identifying both parameters for all the investigated material models and that the surface displacement data improved the parameter identifiability in all cases, although the Mooney-Rivlin parameters remained poorly identifiable. Informed by the results, we then discuss several identification strategies for each constitutive model. Finally, we openly provide the codes used in this study, to allow others to further investigate the indentation problem according to their specifications (e.g., by modifying the geometries, dimensions, mesh, material models, boundary conditions, contact parameters, or objective functions).

Treatment verification in high dose rate brachytherapy using a realistic 3D printed head phantom and an imaging panel

Even though High Dose Rate (HDR) brachytherapy has good treatment outcomes in different treatment sites, treatment verification is far from widely implemented because of a lack of easily available solutions. Previously it has been shown that an imaging panel (IP) near the patient can be used to determine treatment parameters such as the dwell time and source positions in a single material pelvic phantom. In this study we will use a heterogeneous head phantom to test this IP approach, and simulate common treatment errors to assess the sensitivity and specificity of the error-detecting capabilities of the IP. A heterogeneous head-phantom consisting of soft tissue and bone equivalent materials was 3D-printed to simulate a base of tongue treatment. An High Dose Rate treatment plan with 3 different catheters was used to simulate a treatment delivery, using dwell times ranging from 0.3 s to 4 s and inter-dwell distances of 2 mm. The IP was used to measure dwell times, positions and detect simulated errors. Measured dwell times and positions were used to calculate the delivered dose. Dwell times could be determined within 0.1 s. Source positions were measured with submillimeter accuracy in the plane of the IP, and average distance accuracy of 1.7 mm in three dimensions. All simulated treatment errors (catheter swap, catheter shift, afterloader errors) were detected. Dose calculations show slightly different distributions with the measured dwell positions and dwell times (gamma pass rate for 1 mm/1% of 96.5%). Using an IP, it was possible to verify the treatment in a realistic heterogeneous phantom and detect certain treatment errors.

A Prediction Model for Skin Wound Suture Forces With Uncertain Material Parameters

To evaluate the forces required for the suture of skin wounds quickly and effectively, the nonlinear finite element method was used to calculate the suture forces for skin wounds with different sizes and material parameters. With the calculated results as samples, the prediction model for skin wound suture forces was constructed by means of the EBF neural network model. Given the uncertain skin material parameters influencing the reliability of numerical results, the Monte-Carlo method was used to analyze the uncertainty propagation of skin material parameters. Finally, the prediction analysis and measuring experiment of wound suture forces were carried out with pig skin specimens to verify the reliability of the method. The results showed that, the suture force increases first and then decreases according to the suture point sequence, and the peak force occurs before the center of the wound. For a 40 mm×10 mm wound, the peak suture force is about 1.7 N, and that for a 40 mm×14 mm wound is about 2.5 N. Influenced by the uncertainty of material parameters, the prediction results of suture forces fluctuate by as much as ±0.6 N. The proposed theoretical prediction model provides an effective solution to the problem of parameter uncertainty propagation for biological soft tissue materials such as skins, and makes an important mechanical reference for robotic surgical suture.

Statistical analysis of mechanical properties of biological soft tissue under quasi-static mechanical loading

The mechanical properties of biological soft tissues are inextricably linked to the field of health care, and their mechanical properties can be important indicators for diagnosing and detecting diseases; they can also be used to analyze the causes of organ diseases from a pathological point of view and thus guide the deployment of medical solutions. As an effective method to characterize the mechanical properties of materials, mechanical loading experiments have been successfully applied to the mechanical properties of materials, including tension, compression, pure shear, and so on. Under quasi-static loading, when the material is a biological soft tissue material between a solid and an ideal fluid, its viscoelastic properties strongly respond to the force stimulus, and the stress-strain-time in the elastic phase will have obvious disturbance characteristics. Therefore, the existing statistical methods are often difficult to quantitatively describe the mechanical properties of materials. Therefore, this study proposes an Interval Capture Point based on the principle of integration. The experimental data based on this method can characterize its nonlinear mechanical properties well, especially when the loading speed is extremely low and the soft materials show strong disturbance characteristics. The proposed method can still accurately characterize the hyperelastic and viscoelastic properties of the mechanical properties of biological soft tissues under quasi-static loading.

Neural Network Approaches for Soft Biological Tissue and Organ Simulations.

Given the functional complexities of soft tissues and organs, it is clear that computational simulations are critical in their understanding and for the rational basis for the development of therapies and replacements. A key aspect of such simulations is accounting for their complex, nonlinear, anisotropic mechanical behaviors. While soft tissue material models have developed to the point of high fidelity, in-silico implementation is typically done using the finite element (FE) method, which remains impractically slow for translational clinical time frames. As a potential path toward addressing the development of high fidelity simulations capable of performing in clinically relevant time frames, we review the use of neural networks (NN) for soft tissue and organ simulation using two approaches. In the first approach, we show how a NN can learn the responses for a detailed meso-structural soft tissue material model. 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. In the second approach, we go a step further with the use of a physics-based surrogate model to directly learn the displacement field solution without the need for raw training data or FE simulation datasets. In this approach we utilize a finite element mesh to define the domain and perform the necessary integrations, but not the finite element method (FEM) itself. We demonstrate with this approach, termed neural network finite element (NNFE), results in a trained NNFE model with excellent agreement with the corresponding "ground truth" FE solutions over the entire physiological deformation range on a cuboidal myocardium specimen. More importantly, the NNFE approach provided a significantly decreased computational time for a range of finite element mesh sizes. Specifically, as the FE mesh size increased from 2744 to 175,615 elements, the NNFE computational time increased from 0.1108 s to 0.1393 s, while the "ground truth" FE model increased from 4.541 s to 719.9 s, with the same effective accuracy. These results suggest that NNFE run times are significantly reduced compared with the traditional large-deformation-based finite element solution methods. We then show how a nonuniform rational B-splines (NURBS)-based approach can be directly integrated into the NNFE approach as a means to handle real organ geometries. While these and related approaches are in their early stages, they offer a method to perform complex organ-level simulations in clinically relevant time frames without compromising accuracy.