Showing 1–36 of 36 results for all: hyperelastic "soft tissue"

Fully differentiable framework for inverse identification of geometry and material parameters with application to determining stress-free configuration of soft tissues

Authors: Hyunoh Bae, Tianyi Hu, Adrian Buganza Tepole, Hector Gomez

Abstract: Medical images of soft… ▽ More Medical images of soft tissues typically depict loaded configurations rather than true unloaded (stress-free) states, which can bias biomechanical simulations and inverse material identification. A gradient-based inverse finite element framework is presented that jointly reconstructs an effective unloaded reference geometry and estimates hyperelastic material parameters from two or more observed deformed configurations. The formulation is fully differentiable and leverages exact end-to-end gradients to enable unified, simultaneous optimization of geometry and constitutive parameters. The objective function combines a nodal-position misfit with a deformation-gradient-based mismatch term, improving robustness under large deformations. Benchmark studies quantify the influence of loading diversity and observation count and demonstrate reduced sensitivity to poor material initialization. Finally, application to an MRI-derived breast model shows accurate recovery of the unloaded configuration and constitutive parameters from multiple gravity-loaded states. The framework provides a unified and scalable tool for inverse biomechanics with potential applications in personalized modeling, elastography, and surgical planning. △ Less

Submitted 29 September, 2026; v1 submitted 16 September, 2026; originally announced September 2026.

Generalizing Soft Tissue Deformation and Force Prediction Across Material Stiffness and Geometry

Authors: Madina Kojanazarova, Sidaty El Hadramy, Philippe C. Cattin

Abstract: Accurate soft… ▽ More Accurate soft tissue simulation is essential for surgical training, pre-operative planning, and haptic feedback systems. While learning-based surrogate models trained on data using the finite element method (FEM) offer a promising path to real-time inference, their reliability depends on well-calibrated constitutive models. Existing approaches neither provide systematic guidance on model selection across stiffness levels, nor generalize across different tissue stiffnesses or geometries. We perform a comprehensive calibration of hyperelastic constitutive models in the SOFA Framework using gravity-loaded silicone beams with different stiffnesses. Using calibrated simulations as training data, we use a softness conditioned equivariant graph neural network, enabling deformation and force prediction across multiple tissue types and unseen geometries. Our model achieves sub-millimeter mean deformation accuracy at 0.010s inference time, while showing that force prediction quality is directly tied to upstream calibration consistency. △ Less

Submitted 21 August, 2026; originally announced August 2026.

Intestinal peristalsis and wrinkling: A novel paradigm

Authors: René Thierry Djoumessi, Christopher Miller, Nipuni D. Nagahawatte, Marco Paggi, Leo K. Cheng, Alessio Gizzi

Abstract: …The framework reproduces for the first time physiological motility and overcoming large-displacements limitations (self-contact and volume locking) occurring in classical hyperelastic formulations of soft tissues. We introduce: i) layer-specific functions, segregating active cir… ▽ More A new computational framework for modeling the intestinal wall as a multi-layered fiber-reinforced continuum is presented. The framework reproduces for the first time physiological motility and overcoming large-displacements limitations (self-contact and volume locking) occurring in classical hyperelastic formulations of soft tissues. We introduce: i) layer-specific functions, segregating active circumferential and longitudinal muscle fibers while maintaining homogeneous passive reinforcement, and ii) a quasi-incompressible volumetric contribution, to handle large peristaltic contractions. Cell electrophysiology is further extended to reproduce both slow waves and spike bursting activities thus mimicking for the first time a localized neural excitation in a three-dimensional geometry of small intestine segment. We introduce a spatio-temporal modulation of contractility to accurately capture activation driven by both slow waves and spike bursts. The overall coupled nonlinear electromechanical boundary valued problem is modeled following the active strain approach. A robust augmented-Lagrangian contact algorithm is also embedded to avoid self-penetration and geometrical instabilities under large displacements. The 8-variables nonlinear governing equations are then discretized using in house P1-P2-P4 finite elements codes implemented within the GetFEM library. Numerical experiments demonstrate the ability of the proposed framework to reproduce physiological peristalsis, i.e., wall contraction greater than 80%, thus allowing full occlusion matching in vivo endoscopic images, and naturally generating wrinkling patterns consistent with experimental observations. We show that an active electromechanics anisotropic heterogeneous modeling strategy is critical for a numerically stable and physiologically accurate representation of gastrointestinal motility. △ Less

Submitted 31 July, 2026; originally announced July 2026.

Contact-based inverse analysis for nonlinear material identification in spatially heterogeneous solids

Authors: Bartłomiej Łazorczyk, Roger A. Sauer

Abstract: …Model Updating (FEMU) framework for identifying spatially varying constitutive parameters of nonlinear solids. The formulation considers large quasi-static deformations of hyperelastic 3D solids and thin shells due to mechanical contact. The proposed inverse approach utilizes full-field displacement measurements available at least on the free surface and, in… ▽ More This study presents a contact-based isogeometric Finite Element Model Updating (FEMU) framework for identifying spatially varying constitutive parameters of nonlinear solids. The formulation considers large quasi-static deformations of hyperelastic 3D solids and thin shells due to mechanical contact. The proposed inverse approach utilizes full-field displacement measurements available at least on the free surface and, in the case of pure Dirichlet boundary conditions, the resultant contact forces as well. The nonuniform material parameter fields are discretized using low-order Lagrange interpolation independent of the isogeometric analysis mesh, providing control over the inverse problem size and potential discontinuities in the material. The FEMU least-squares objective is minimized using a trust-region reflective algorithm - a local gradient-based optimization approach. Computational efficiency is enhanced through the analytical derivatives of the objective and a material continuation strategy. The proposed framework is evaluated through three numerical examples based on synthetically generated data: a Canham shell strip on a rigid foundation, indentation of a Koiter shell model of the human abdominal wall, and indentation of a Neo-Hookean block. The examples verify the ability of the proposed method to reconstruct inhomogeneous material via mechanical contact. Analytical derivatives improve the computational efficiency and facilitate conducting sensitivity and identifiability analyses of the material parameters. The presented approach is non-destructive and can be used for various inverse problems, such as in-vivo biomechanics of soft tissues and laboratory material characterization. △ Less

Submitted 20 July, 2026; originally announced July 2026.

Comments: 47 pages, 26 figures, 5 tables

An Octahedral Fibrous Constitutive Model for Heart Valve Mechanics and Function

Authors: Nishan Parvez, Prashant K. Purohit, Wensi Wu

Abstract: Fibrous soft… ▽ More Fibrous soft tissues derive their nonlinear mechanical response from networks of extracellular matrix fibers, whose organization gives rise to strain stiffening, the reverse Poynting effect, and anisotropic mechanical behavior. Motivated by these coupled features, we develop an anisotropic hyperelastic model for fibrous biological tissues that accounts for the contribution of the fiber network under both tensile and compressive deformation. We calibrate the model to experimental data for mitral valve leaflets using an inverse finite element approach that is coupled to automatic differentiation to facilitate efficient parameter calibration. Using the calibrated model, we investigate how anisotropy and fiber reorientation affect valve deformation under physiological loading. The results show that greater leaflet compliance in the radial direction yields proper valve closure, whereas localized fiber reorientation leads to stress concentrations that may promote progressive functional degradation. Fiber reorientation that makes the circumferential direction more compliant than the radial direction compromises valve closure and leads to mitral regurgitation. Chordal softening further amplifies the severity of this regurgitant response. These findings suggest that alterations in fiber architecture, especially when accompanied by chordal degradation, can contribute to the onset and progression of mitral valve incompetence. △ Less

Submitted 2 June, 2026; originally announced June 2026.

PINNOCHIO: Physics-Informed Neural Network for Coupled Hyperelastic Interface-Volume Simulation in Orthognathic Surgery

Authors: Jungwook Lee, Daeseung Kim, Kevin Gu, Zhangfeng Hu, Tianshu Kuang, Finn Hopeman, Michael A. K. Liebschner, Jaime Gateno, Pingkun Yan

Abstract: Predicting patient-specific facial soft-… ▽ More Predicting patient-specific facial soft-tissue deformation is critical for iterative orthognathic surgery planning. However, current computational methods face a strict accuracy-efficiency trade-off: high-fidelity Finite Element Methods (FEM) are computationally prohibitive, whereas pure deep learning models often produce biomechanically inconsistent results. While Physics-Informed Neural Networks (PINNs) offer a promising avenue, learning the complex heterogeneous mechanics of bone--soft-tissue interactions with only partial clinical supervision (i.e., outer facial surfaces) remains highly unstable. To overcome these challenges, we present PINNOCHIO, a novel physics-informed framework for facial soft-tissue simulation. PINNOCHIO introduces a hybrid sequential decomposition that explicitly decouples discontinuous bone--soft-tissue interface movements from continuous volumetric hyperelastic deformation. This structural separation enables stable training and facilitates a physics-enabled sim-to-real adaptation strategy, ensuring internal biomechanical consistency without requiring volumetric ground truth. Evaluated on a 40-patient clinical cohort, PINNOCHIO outperforms existing baselines in both surface accuracy and physical validity. Furthermore, it achieves a substantial speedup over FEM, successfully resolving the accuracy-efficiency trade-off to provide a highly reliable and practical tool for interactive surgical planning. △ Less

Submitted 31 May, 2026; originally announced June 2026.

Comments: This work has been submitted to MICCAI 2026

Exploring natural variation in tendon constitutive parameters via Bayesian data selection and mixed effects models

Authors: James Casey, Jessica Forsyth, Timothy Waite, Simon Cotter, Tom Shearer

Abstract: Combining microstructural mechanical models with experimental data enhances our understanding of the mechanics of soft… ▽ More Combining microstructural mechanical models with experimental data enhances our understanding of the mechanics of soft tissue, such as tendons. In previous work, a Bayesian framework was used to infer constitutive parameters from uniaxial stress-strain experiments on horse tendons, specifically the superficial digital flexor tendon (SDFT) and common digital extensor tendon (CDET), on a per-experiment basis. Here, we extend this analysis to investigate the natural variation of these parameters across a population of horses. Using a Bayesian mixed effects model, we infer population distributions of these parameters. Given that the chosen hyperelastic model does not account for tendon damage, careful data selection is necessary. Avoiding ad hoc methods, we introduce a hierarchical Bayesian data selection method. This two-stage approach selects data per experiment, and integrates data weightings into the Bayesian mixed effects model. Our results indicate that the CDET is stiffer than the SDFT, likely due to a higher collagen volume fraction. The modes of the parameter distributions yield estimates of the product of the collagen volume fraction and Young's modulus as 811.5 MPa for the SDFT and 1430.2 MPa for the CDET. This suggests that positional tendons have stiffer collagen fibrils and/or higher collagen volume density than energy-storing tendons. △ Less

Submitted 22 August, 2025; v1 submitted 17 December, 2024; originally announced December 2024.

Comments: 24 pages, 10 figures

Stabler Neo-Hookean Simulation: Absolute Eigenvalue Filtering for Projected Newton

Authors: Honglin Chen, Hsueh-Ti Derek Liu, David I. W. Levin, Changxi Zheng, Alec Jacobson

Abstract: Volume-preserving hyperelastic materials are widely used to model near-incompressible materials such as rubber and soft tissues. However, the numerical simulation of volume-preserving hyperelastic materials is notoriously challenging within… ▽ More Volume-preserving hyperelastic materials are widely used to model near-incompressible materials such as rubber and soft tissues. However, the numerical simulation of volume-preserving hyperelastic materials is notoriously challenging within this regime due to the non-convexity of the energy function. In this work, we identify the pitfalls of the popular eigenvalue clamping strategy for projecting Hessian matrices to positive semi-definiteness during Newton's method. We introduce a novel eigenvalue filtering strategy for projected Newton's method to stabilize the optimization of Neo-Hookean energy and other volume-preserving variants under high Poisson's ratio (near 0.5) and large initial volume change. Our method only requires a single line of code change in the existing projected Newton framework, while achieving significant improvement in both stability and convergence speed. We demonstrate the effectiveness and efficiency of our eigenvalue projection scheme on a variety of challenging examples and over different deformations on a large dataset. △ Less

Submitted 21 June, 2024; v1 submitted 9 June, 2024; originally announced June 2024.

Comments: SIGGRAPH 2024 (Conference track). Project page: https://www.cs.columbia.edu/cg/abs-psd/

Exponential time propagators for elastodynamics

Authors: Paavai Pari, Bikash Kanungo, Vikram Gavini

Abstract: …respectively. We demonstrate the accuracy and efficiency of the proposed method for one linear (linear cantilever beam) and three nonlinear (nonlinear cantilever beam, soft tissue elastomer, and hyperelastic rubber) benchmark systems. For a desired accuracy in energy, displaceme… ▽ More We propose a computationally efficient and systematically convergent approach for elastodynamics simulations. We recast the second-order dynamical equation of elastodynamics into an equivalent first-order system of coupled equations, so as to express the solution in the form of a Magnus expansion. With any spatial discretization, it entails computing the exponential of a matrix acting upon a vector. We employ an adaptive Krylov subspace approach to inexpensively and and accurately evaluate the action of the exponential matrix on a vector. In particular, we use an apriori error estimate to predict the optimal Kyrlov subspace size required for each time-step size. We show that the Magnus expansion truncated after its first term provides quadratic and superquadratic convergence in the time-step for nonlinear and linear elastodynamics, respectively. We demonstrate the accuracy and efficiency of the proposed method for one linear (linear cantilever beam) and three nonlinear (nonlinear cantilever beam, soft tissue elastomer, and hyperelastic rubber) benchmark systems. For a desired accuracy in energy, displacement, and velocity, our method allows for $10-100\times$ larger time-steps than conventional time-marching schemes such as Newmark-$β$ method. Computationally, it translates to a $\sim$$1000\times$ and $\sim$$10-100\times$ speed-up over conventional time-marching schemes for linear and nonlinear elastodynamics, respectively. △ Less

Submitted 8 May, 2024; originally announced May 2024.

An Anisotropic Constitutive Relationship by a Series of 8 Chain Models

Authors: Libin Yang, Teng Long, Lixiang Yang

Abstract: Hyperelastic models have been widely used to model polymers and… ▽ More Hyperelastic models have been widely used to model polymers and soft tissues. However, most hyperelastic models are phenomenological material models. Based on statistical mechanics and molecular chain configuration, 8 chain model or Arruda-Boyce model is a physical model which can be used to understand how microstructures of chains affect macroscopic mechanical properties of polymers and soft tissues. Mechanical properties of many polymers and soft tissues are directional dependent. Polymer matrix can be reinforced by fibers. For soft tissues, ligaments and tendons will lead to anisotropic properties. Since matrix and reinforcements are composed of similar microstructural molecular chains, they can be modeled by using the same mathematical model. In this paper, a series of 8 chain models is used to understand composite properties. That is, an isotropic 8 chain model will be used to model matrix and anisotropic 8 chain models will be used to model fibers. Replacing I_1 in isotropic 8 chain model with I_4 in anisotropic 8 chain model is physically corresponding to changing representative 8 chain cubic cell to 8 chain slender cell. This treatment not only simplifies exist anisotropic mathematical structures but also keeps microscopic physics of 8 chain model unchanged. △ Less

Submitted 22 March, 2024; originally announced March 2024.

Comments: 30 pages; 10 figures

Enhancing Biomechanical Simulations Based on A Posteriori Error Estimates: The Potential of Dual Weighted Residual-Driven Adaptive Mesh Refinement

Authors: Huu Phuoc Bui, Michel Duprez, Pierre-Yves Rohan, Arnaud Lejeune, Stephane P. A. Bordas, Marek Bucki, Franz Chouly

Abstract: …discretisation error that can be an be quantified with \emph{a posteriori} error estimates. The practical relevance of error estimates for biomechanics problems, especially for soft… ▽ More The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with a discretisation error that can be an be quantified with \emph{a posteriori} error estimates. The practical relevance of error estimates for biomechanics problems, especially for soft tissue where the response is governed by large strains, is rarely addressed. In this contribution, we propose an implementation of \emph{a posteriori} error estimates targeting a user-defined quantity of interest, using the Dual Weighted Residual (DWR) technique tailored to biomechanics. The proposed method considers a general setting that encompasses three-dimensional geometries and model non-linearities, which appear in hyperelastic soft tissues. We take advantage of the automatic differentiation capabilities embedded in modern finite element software, which allows the error estimates to be computed generically for a large class of models and constitutive laws. First we validate our methodology using experimental measurements from silicone samples, and then illustrate its applicability for patient-specific computations of pressure ulcers on a human heel. △ Less

Submitted 1 March, 2024; originally announced March 2024.

MSC Class: 65N30; 92C10; 74B20

Supersonic shear wave imaging in stretched soft strips: modeling for quantitative elastography

Authors: Alexandre Delory, Daniel A. Kiefer, Claire Prada, Fabrice Lemoult

Abstract: …We provide a theoretical model that accounts for the static deformation and allows the extraction of the mechanical parameters of the sample, including its rheology and hyperelastic behavior. Significance - To overcome some limitations of current elastography, we propose a method that would allow the simultaneous characterization of the viscoelastic and… ▽ More Objective - Shear wave elastography has enriched ultrasound medical imaging with quantitative measurements of tissue stiffness. However, this method still suffers from some limitations due to viscoelasticity, guiding geometry or static deformations. Approach - To explore these limitations, a nearly-incompressible soft elastomer strip is chosen to mimic the mechanical behavior of an elongated tissue. A supersonic shear wave scanner measures the propagation of shear waves within the strip. By repeating the experiment on the same sample for different orientations and static strains, the scanner estimates the shear wave velocity in a wide range from 2 to 6 m/s. Main results - The effect of waveguiding is highlighted and the spatio-temporal Fourier transform of the raw data provides dispersion diagrams. We provide a theoretical model that accounts for the static deformation and allows the extraction of the mechanical parameters of the sample, including its rheology and hyperelastic behavior. Significance - To overcome some limitations of current elastography, we propose a method that would allow the simultaneous characterization of the viscoelastic and hyperelastic properties of soft tissues, paving the way for robust quantitative elastography of elongated tissues. △ Less

Submitted 22 December, 2023; originally announced December 2023.

Current poisson's ratio values of finite element models are too low to consider soft tissues nearly-incompressible: illustration on the human heel region

Authors: Nolwenn Fougeron, Alessio Trebbi, Bethany Keenan, Yohan Payan, Gregory Chagnon

Abstract: Finite element analysis of soft… ▽ More Finite element analysis of soft tissues is a well-developed method that allows estimation of mechanical quantities (e.g. stresses, strains). A constitutive law has to be used to characterise the individual tissues. This is complex as biological tissues are generally visco-hyperelastic, anisotropic, and heterogenous. A specific characteristic, their nearly incompressibility, was well reported in the literature, but very little effort has been made to compare volume variations computed by the simulations with in vivo measurements. In the present study, volume changes of the fat pad during controlled indentations of the human heel region were estimated from segmented medical images using digital volume correlation. Indentations were repeated with high and mild intensity normal and shear loads. The experiment was reproduced using finite element modelling with several values of Poisson's ratio for the fat pad, extracted from literature values (from 0.4500 to 0.4999). Estimated fat pad volume changes were compared to the measured ones to assess the best value of Poisson's ratio in each indentation case. The impact of the Poisson's ratio on the Jacobian of the deformation gradient and the volumetric strains was also computed. A single value of Poisson's ratio could not fit all the indentation cases. Estimated volume changes were between 0.9 % - 11.7 % with a Poisson's ratio from 0.4500 to 0.4999. The best fit was obtained with a 0.4900 Poisson's ratio except for the high normal load where a value of 0.4999 resulted in less error. In conclusion, special care should be taken when setting the Poisson's ratio as the resulting estimated deformations may become unrealistic when the value is far from incompressible materials. △ Less

Submitted 7 December, 2023; originally announced December 2023.

Journal ref: Computer Methods in Biomechanics and Biomedical Engineering, 2023, pp.1 - 10

Generalized Finsler geometry and the anisotropic tearing of skin

Authors: John D. Clayton

Abstract: …for both direction (i.e., as in Finsler geometry) as well as magnitude. Equilibrium equations are derived using a variational method, extending concepts of finite-strain hyperelasticity coupled to phase-field mechanics to generalized Finsler space. For application to skin tearing, state vector components represent microscopic damage processes (e.g., fiber re… ▽ More A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections, geometrically characterizes evolving configurations of a deformable body with microstructure. An internal state vector is introduced on each configuration, describing subscale physics. A generalized Finsler metric depends on position and the state vector, where the latter dependence allows for both direction (i.e., as in Finsler geometry) as well as magnitude. Equilibrium equations are derived using a variational method, extending concepts of finite-strain hyperelasticity coupled to phase-field mechanics to generalized Finsler space. For application to skin tearing, state vector components represent microscopic damage processes (e.g., fiber rearrangements and ruptures) in different directions with respect to intrinsic orientations (e.g., parallel or perpendicular to Langer's lines). Nonlinear potentials, motivated from soft-tissue mechanics and phase-field fracture theories, are assigned with orthotropic material symmetry pertinent to properties of skin. Governing equations are derived for one- and two-dimensional base manifolds. Analytical solutions capture experimental force-stretch data, toughness, and observations on evolving microstructure, in a more geometrically and physically descriptive way than prior phenomenological models. △ Less

Submitted 8 August, 2024; v1 submitted 17 September, 2023; originally announced September 2023.

Comments: Updated version: minor typographical mistakes in original version now corrected

MSC Class: 53Z05 (Primary) 53B40; 74B20 (Secondary)

Journal ref: Symmetry, vol. 15, art. 1828, 2023

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

Authors: Ankush Aggarwal, Bjørn Sand Jensen, Sanjay Pant, Chung-Hao Lee

Abstract: …analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar, hyperelastic and incompressible… ▽ More 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. △ Less

Submitted 22 November, 2022; v1 submitted 28 September, 2022; originally announced October 2022.

An in silico-based review on anisotropic hyperelastic constitutive models for soft biological tissues

Authors: Hüsnü Dal, Alp Kağan Açan, Ciara Durcan, Mokarram Hossain

Abstract: We review nine invariant and dispersion-type anisotropic hyperelastic constitutive models for soft biological tissues based on their fitting performance to experimental data from three different human tissues. For this, we used a hybrid multi-objective optimization procedure. A genetic algorithm is devised to generate the initial guesses followed by a gradie… ▽ More We review nine invariant and dispersion-type anisotropic hyperelastic constitutive models for soft biological tissues based on their fitting performance to experimental data from three different human tissues. For this, we used a hybrid multi-objective optimization procedure. A genetic algorithm is devised to generate the initial guesses followed by a gradient-based search algorithm. The constitutive models are then fit to a set of uniaxial and biaxial tension experiments conducted on tissues with differing fiber orientations. For the in silico investigation, experiments conducted on aneurysmatic abdominal aorta, linea alba, and rectus sheath tissues are utilized. Accordingly, the models are ranked with respect to an objec tive normalized quality of fit metric. Finally, a detailed discussion is carried out on the fitting performance of each model. This work provides a valuable quantitative comparison of various anisotropic hyperelastic models, the findings of which can aid those modeling the behavior of soft tissues in selecting the best constitutive model for their particular application. △ Less

Submitted 28 July, 2022; originally announced July 2022.

Wrinkling as a mechanical instability in growing annular hyperelastic plates

Authors: Sumit Mehta, Gangadharan Raju, Prashant Saxena

Abstract: …in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in an incompressible annular hyperelastic plate. The governing differential equations for a two-dimensional plate system are derived using a variational principle with no apriori kinematic assumptions in the thickness dire… ▽ More Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in an incompressible annular hyperelastic plate. The governing differential equations for a two-dimensional plate system are derived using a variational principle with no apriori kinematic assumptions in the thickness direction. A linear bifurcation analysis is performed to investigate the stability behaviour of the growing hyperelastic annular plate by considering both axisymmetric and asymmetric perturbations. The resulting differential equations are then solved numerically using the compound matrix method to evaluate the critical growth factor that leads to wrinkling. The effect of boundary constraints, thickness, and radius ratio of the annular plate on the critical growth factor is studied. For most of the considered cases, an asymmetric bifurcation is the preferred mode of instability for an annular plate. Our results are useful to model the physics of wrinkling phenomena in growing planar soft tissues, swelling hydrogels, and pattern transition in two-dimensional films growing on an elastic substrate. △ Less

Submitted 26 June, 2022; v1 submitted 12 March, 2022; originally announced March 2022.

Comments: 23 pages, 7 figures

Bayesian inference on a microstructural, hyperelastic model of tendon deformation

Authors: James Haughton, Simon L. Cotter, William J. Parnell, Tom Shearer

Abstract: Microstructural models of soft… ▽ More Microstructural models of soft tissue deformation are important in applications including artificial tissue design and surgical planning. The basis of these models, and their advantage over their phenomenological counterparts, is that they incorporate parameters that are directly linked to the tissue's microscale structure and constitutive behaviour and can therefore be used to predict the effects of structural changes to the tissue. Although studies have attempted to determine such parameters using diverse, state-of-the-art, experimental techniques, values ranging over several orders of magnitude have been reported, leading to uncertainty in the true parameter values and creating a need for models that can handle such uncertainty. We derive a microstructural, hyperelastic model for transversely isotropic soft tissues and use it to model the mechanical behaviour of tendons. To account for parameter uncertainty, we employ a Bayesian approach and apply an adaptive Markov chain Monte Carlo algorithm to determine posterior probability distributions for the model parameters. The obtained posterior distributions are consistent with parameter measurements previously reported and enable us to quantify the uncertainty in their values for each tendon sample that was modelled. This approach could serve as a prototype for quantifying parameter uncertainty in other soft tissues. △ Less

Submitted 5 May, 2022; v1 submitted 13 January, 2022; originally announced January 2022.

Growth induced instabilities in a circular hyperelastic plate

Authors: Sumit Mehta, Gangadharan Raju, Prashant Saxena

Abstract: In this work, we have explored growth-induced mechanical instability in an isotropic circular hyperelastic plate. Consistent two-dimensional governing equations for a plate under a general finite strain are derived using a variational approach. The derived plate equations are solved using the compound matrix method for two cases of axisymmetric growth condit… ▽ More In this work, we have explored growth-induced mechanical instability in an isotropic circular hyperelastic plate. Consistent two-dimensional governing equations for a plate under a general finite strain are derived using a variational approach. The derived plate equations are solved using the compound matrix method for two cases of axisymmetric growth conditions - purely radial, and combined radial and circumferential growth. The effect of growth on the buckling behaviour of the plate (in particular, the critical growth factor and the associated buckling mode shapes) is investigated for different thickness values. These results are applicable to model growth induced deformation in planar soft tissues such as skin. △ Less

Submitted 11 March, 2021; originally announced March 2021.

MSC Class: 74K20; 74B15

Towards real-time finite-strain anisotropic thermo-visco-elastodynamic analysis of soft tissues for thermal ablative therapy

Authors: Jinao Zhang, Remi Jacob Lay, Stuart K. Roberts, Sunita Chauhan

Abstract: Accurate and efficient prediction of soft… ▽ More Accurate and efficient prediction of soft tissue temperatures is essential to computer-assisted treatment systems for thermal ablation. It can be used to predict tissue temperatures and ablation volumes for personalised treatment planning and image-guided intervention. Numerically, it requires full nonlinear modelling of the coupled computational bioheat transfer and biomechanics, and efficient solution procedures; however, existing studies considered the bioheat analysis alone or the coupled linear analysis, without the fully coupled nonlinear analysis. We present a coupled thermo-visco-hyperelastic finite element algorithm, based on finite-strain thermoelasticity and total Lagrangian explicit dynamics. It considers the coupled nonlinear analysis of (i) bioheat transfer under soft tissue deformations and (ii) soft tissue deformations due to thermal expansion/shrinkage. The presented method accounts for anisotropic, finite-strain, temperature-dependent, thermal, and viscoelastic behaviours of soft tissues, and it is implemented using GPU acceleration for real-time computation. We also demonstrate the translational benefits of the presented method for clinical applications using a simulation of thermal ablation in the liver. The key advantage of the presented method is that it enables full nonlinear modelling of the anisotropic, finite-strain, temperature-dependent, thermal, and viscoelastic behaviours of soft tissues, instead of linear elastic, linear viscoelastic, and thermal-only modelling in the existing methods. It also provides high computational speeds for computer-assisted treatment systems towards enabling the operator to simulate thermal ablation accurately and visualise tissue temperatures and ablation zones immediately. △ Less

Submitted 31 December, 2021; v1 submitted 22 September, 2020; originally announced September 2020.

Comments: Submitted to Computer Methods and Programs in Biomedicine

Journal ref: Computer Methods and Programs in Biomedicine, vol. 198, pp. 105789, 2021

A robust anisotropic hyperelastic formulation for the modelling of soft tissue

Authors: David R. Nolan, Artur L. Gower, Michel Destrade, Ray W. Ogden, Pat McGarry

Abstract: The Holzapfel-Gasser-Ogden (HGO) model for anisotropic hyperelastic behaviour of collagen fibre reinforced materials was initially developed to describe the elastic properties of arterial tissue, but is now used extensively for modelling a variety of soft biological tissues. Such materials can be regarded as incompressible, and when the incompressibility con… ▽ More The Holzapfel-Gasser-Ogden (HGO) model for anisotropic hyperelastic behaviour of collagen fibre reinforced materials was initially developed to describe the elastic properties of arterial tissue, but is now used extensively for modelling a variety of soft biological tissues. Such materials can be regarded as incompressible, and when the incompressibility condition is adopted the strain energy Ψof the HGO model is a function of one isotropic and two anisotropic deformation invariants. A compressible form (HGO-C model) is widely used in finite element simulations whereby the isotropic part of Ψis decoupled into volumetric and isochoric parts and the anisotropic part of Ψis expressed in terms of isochoric invariants. Here, by using three simple deformations (pure dilatation, pure shear and uniaxial stretch), we demonstrate that the compressible HGO-C formulation does not correctly model compressible anisotropic material behaviour, because the anisotropic component of the model is insensitive to volumetric deformation due to the use of isochoric anisotropic invariants. In order to correctly model compressible anisotropic behaviour we present a modified anisotropic (MA) model, whereby the full anisotropic invariants are used, so that a volumetric anisotropic contribution is represented. The MA model correctly predicts an anisotropic response to hydrostatic tensile loading, whereby a sphere deforms into an ellipsoid. It also computes the correct anisotropic stress state for pure shear and uniaxial deformation. To look at more practical applications, we developed a finite element user-defined material subroutine for the simulation of stent deployment in a slightly compressible artery. Significantly higher stress triaxiality and arterial compliance are computed when the full anisotropic invariants are used (MA model) instead of the isochoric form (HGO-C model). △ Less

Submitted 18 September, 2020; originally announced September 2020.

Journal ref: Journal of the Mechanical Behaviour of Biomedical Materials, 39 (2014) 48-60

Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging

Authors: Enrui Zhang, Minglang Yin, George Em Karniadakis

Abstract: …problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical properties of soft… ▽ More We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical properties of soft tissue based on the full-field displacement measurements under quasi-static loading. In our model, we apply two independent neural networks, one for approximating the solution of the corresponding forward problem, and the other for approximating the unknown material parameter field. As a proof of concept, we validate our model on a prototypical plane strain problem for incompressible hyperelastic tissue. The results show that the PINNs are effective in accurately recovering the unknown distribution of mechanical properties. By employing two neural networks in our model, we extend the capability of material identification of PINNs to include nonhomogeneous material parameter fields, which enables more flexibility of PINNs in representing complex material properties. △ Less

Submitted 2 September, 2020; originally announced September 2020.

Comments: 10 pages, 3 figures

Deficiencies in numerical models of anisotropic nonlinearly elastic materials

Authors: Aisling Ni Annaidh, Michel Destrade, Michael D. Gilchrist, Jerry G. Murphy

Abstract: Incompressible nonlinearly hyperelastic materials are rarely simulated in Finite Element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most commercial Finite Element packages therefore assume that the material is slightly compressible. It is then further assu… ▽ More Incompressible nonlinearly hyperelastic materials are rarely simulated in Finite Element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most commercial Finite Element packages therefore assume that the material is slightly compressible. It is then further assumed that the corresponding strain-energy function can be decomposed additively into volumetric and deviatoric parts. We show that this decomposition is not physically realistic, especially for anisotropic materials, which are of particular interest for simulating the mechanical response of biological soft tissue. The most striking illustration of the shortcoming is that with this decomposition, an anisotropic cube under hydrostatic tension deforms into another cube instead of a hexahedron with non-parallel faces. Furthermore, commercial numerical codes require the specification of a `compressibility parameter' (or `penalty factor'), which arises naturally from the flawed additive decomposition of the strain-energy function. This parameter is often linked to a `bulk modulus', although this notion makes no sense for anisotropic solids; we show that it is essentially an arbitrary parameter and that infinitesimal changes to it result in significant changes in the predicted stress response. This is illustrated with numerical simulations for biaxial tension experiments of arteries, where the magnitude of the stress response is found to change by several orders of magnitude when infinitesimal changes in `Poisson's ratio' close to the perfect incompressibility limit of 1/2 are made. △ Less

Submitted 4 September, 2020; originally announced September 2020.

Journal ref: Biomechanics and Modeling in Mechanobiology, 12 (2013) 781-791

Elastic Cherenkov effects in transversely isotropic soft materials-I: Theoretical analysis, simulations and inverse method

Authors: Guo-Yang Li, Yang Zheng, Yanlin Liu, Michel Destrade, Yanping Cao

Abstract: …media, by using both theoretical analysis and finite element (FE) simulations, and we apply the results to the non=invasive and non-destructive characterization of biological soft… ▽ More A body force concentrated at a point and moving at a high speed can induce shear-wave Mach cones in dusty-plasma crystals or soft materials, as observed experimentally and named the elastic Cherenkov effect (ECE). The ECE in soft materials forms the basis of the supersonic shear imaging (SSI) technique, an ultrasound-based dynamic elastography method applied in clinics in recent years. Previous studies on the ECE in soft materials have focused on isotropic material models. In this paper, we investigate the existence and key features of the ECE in anisotropic soft media, by using both theoretical analysis and finite element (FE) simulations, and we apply the results to the non=invasive and non-destructive characterization of biological soft tissues. We also theoretically study the characteristics of the shear waves induced in a deformed hyperelastic anisotropic soft material by a source moving with high speed, considering that contact between the ultrasound probe and the soft tissue may lead to finite deformation. On the basis of our theoretical analysis and numerical simulations, we propose an inverse approach to infer both the anisotropic and hyperelastic parameters of incompressible transversely isotropic (TI) soft materials. Finally, we investigate the properties of the solutions to the inverse problem by deriving the condition numbers in analytical form and performing numerical experiments. In Part II of the paper, both ex vivo and in vivo experiments are conducted to demonstrate the applicability of the inverse method in practical use. △ Less

Submitted 31 August, 2020; originally announced September 2020.

Journal ref: Journal of the Mechanics and Physics of Solids, 96 (2016) 388-410

Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis

Authors: Yi Jiang, Guoyang Li, Lin-Xue Qian, Si Liang, Michel Destrade, Yanping Cao

Abstract: …vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft… ▽ More We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus mu0 varies from 1.8 to 3.2 kPa, the stiffening parameter b of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- (A) and fourth-order (D) constants of weakly nonlinear elasticity from -1.3 to -20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired t-test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery. △ Less

Submitted 31 August, 2020; originally announced September 2020.

Journal ref: Biomechanics and Modeling in Mechanobiology, volume 14, pages 1119=1128(2015)

Towards Fast Biomechanical Modeling of Soft Tissue Using Neural Networks

Authors: Felix Meister, Tiziano Passerini, Viorel Mihalef, Ahmet Tuysuzoglu, Andreas Maier, Tommaso Mansi

Abstract: …time integration. Towards this goal, we explore in this paper for the first time the use of neural networks to directly learn the underlying biomechanics. Given a 3D mesh of a soft… ▽ More To date, the simulation of organ deformations for applications like therapy planning or image-guided interventions is calculated by solving the elastodynamics equations. While efficient solvers have been proposed for fast simulations, methods that are both real-time and accurate are still an open challenge. An ideal, interactive solver would be able to provide physically and numerically accurate results at high frame rate, which requires efficient force computation and time integration. Towards this goal, we explore in this paper for the first time the use of neural networks to directly learn the underlying biomechanics. Given a 3D mesh of a soft tissue segmented from medical images, we train a neural network to predict vertex-wise accelerations for a large time step based on the current state of the system. The model is trained using the deformation of a bar under torsion, and evaluated on different motions, geometries, and hyperelastic material models. For predictions of ten times the original time step we observed a mean error of 0.017mm $\pm$ 0.014 (0.032) at a mesh size of 50mm x 50mm x 100mm. Predictions at 20dt yield an error of 2.10mm $\pm$ 1.73 (4.37) and by further increasing the prediction time step the maximum error rises to 38.3mm due to an artificial stiffening. In all experiments our proposed method stayed stable, while the reference solver fails to converge. Our experiments suggest that it is possible to directly learn the mechanical simulation and open further investigations for the direct application of machine learning to speed-up biophysics solvers. △ Less

Submitted 13 December, 2018; originally announced December 2018.

Comments: Accepted in Medical Imaging meets NeurIPS Workshop, NeurIPS 2018

A New Continuum-Based Thick Shell Finite Element for Soft Biological Tissues in Dynamics: Part 1 - Preliminary Benchmarking Using Classic Verification Experiments

Authors: Bahareh Momenan, Michel R. Labrosse

Abstract: …the whole tissue thickness at once, and feature larger critical time steps. However, the capabilities of existing shell elements to account for irregular geometries, and hyperelastic, anisotropic 3D deformations characteristic of… ▽ More For the finite element simulation of thin soft biological tissues in dynamics, shell elements, compared to volume elements, can capture the whole tissue thickness at once, and feature larger critical time steps. However, the capabilities of existing shell elements to account for irregular geometries, and hyperelastic, anisotropic 3D deformations characteristic of soft tissues are still limited. As improvement, we developed a new general nonlinear thick continuum-based (CB) shell finite element (FE) based on the Mindlin-Reissner shell theory, with large bending, large distortion and large strain capabilities, embedded in the updated Lagrangian formulation and explicit time integration. We performed numerical benchmark experiments available from the literature that focus on engineering linear elastic materials, which, verified and proved the new thick CB shell FE to: 1) be accurate an efficient 2) be powerful in handling large 3D deformations, curved geometries, 3) accommodate coarse distorted meshes, and 4) achieve comparatively fast computational times. The new element was also insensitive to three types of locking (shear, membrane and volumetric), and warping effects. The capabilities of the present thick CB shell FE in the biomedical realm are illustrated in a companion article (Part 2), in which anisotropic incompressible hyperelastic constitutive relations are implemented and verified. △ Less

Submitted 11 January, 2018; originally announced January 2018.

Comments: 20 pages, 20 figures

MSC Class: 74S05 (Primary); 74G05; 74A05 (Secondary)

Micropipette aspiration method for characterizing biological materials with surface energy

Authors: Y. Ding, G. F. Wang, X. Q. Feng, S. W. Yu

Abstract: …mechanical properties have neglected the effects of surface stress. In this work, we investigate the micropipette aspiration to measure the mechanical properties of cells and soft… ▽ More Many soft biological tissues possess a considerable surface stress, which plays a significant role in their biophysical functions, but most previous methods for characterizing their mechanical properties have neglected the effects of surface stress. In this work, we investigate the micropipette aspiration to measure the mechanical properties of cells and soft tissues with surface effects. The neo-Hookean constitutive model is adopted to describe the hyperelasticity of the measured biological material, and the surface effect is considered through the finite element method. It is found that when the pipette radius or aspiration length is comparable to the elastocapillary length, surface energy may distinctly alter the aspiration response. Generally, both the aspiration length and the bulk normal stress decreases as surface energy increases, and thus neglecting the surface energy will lead to an overestimation of elastic modulus. Through dimensional analysis and numerical simulations, we provide an explicit relation between the imposed pressure and the aspiration length. This method can be applied to accurately determine the mechanical properties of soft biological tissues and organs, e.g., tumors and embryos. △ Less

Submitted 11 January, 2018; originally announced January 2018.

Comments: 19 pages and 6 figures

Journal ref: Journal of Biomechanics 2018, 80, 32-36

Multi-Material 3-D Viscoelastic Model of a Transtibial Residuum from In-vivo Indentation and MRI Data

Authors: David Moinina Sengeh, Kevin Mattheus Moerman, Arthur Petron, Hugh Herr

Abstract: …residuum. This study presents the evaluation of such a model using a combined experimental-numerical approach. The model geometry and tissue boundaries are derived from MRI. The soft… ▽ More Although the socket is critical in a prosthetic system for a person with limb amputation, the methods of its design are largely artisanal. A roadblock for a repeatable and quantitative socket design process is the lack of predictive and patient specific biomechanical models of the residuum. This study presents the evaluation of such a model using a combined experimental-numerical approach. The model geometry and tissue boundaries are derived from MRI. The soft tissue non-linear elastic and viscoelastic mechanical behavior was evaluated using inverse finite element analysis (FEA) of in-vivo indentation experiments. A custom designed robotic in-vivo indentation system was used to provide a rich experimental data set of force versus time at 18 sites across a limb. During FEA, the tissues were represented by two layers, namely the skin-adipose layer and an underlying muscle-soft tissue complex. The non-linear elastic behavior was modeled using 2nd order Ogden hyperelastic formulations, and viscoelasticity was modeled using the quasi-linear theory of viscoelasticity. To determine the material parameters for each tissue, an inverse FEA based optimization routine was used that minimizes the combined mean of the squared force differences between the numerical and experimental force-time curves for indentations at 4 distinct anatomical regions on the residuum. The optimization provided the following material parameters for the skin-adipose layer: c=5.22 kPa, m=4.79, gamma=3.57 MPa, tau=0.32 s and for the muscle-soft tissue complex: c=5.20 kPa, m=4.78, gamma=3.47 MPa, tau=0.34 s. These parameters were evaluated to predict the force-time curves for the remaining 14 anatomical locations. The mean percentage error (mean absolute error/ maximum experimental force) for these predictions was 7 +/- 3%. The mean percentage error at the 4 sites used for the optimization was 4%. △ Less

Submitted 29 February, 2016; originally announced February 2016.

Journal ref: Journal of the Mechanical Behavior of Biomedical Materials, 2016

Control of Tension-Compression Asymmetry in Ogden Hyperelasticity with Application to Soft Tissue Modelling

Authors: Kevin M. Moerman, Ciaran K. Simms, Thomas Nagel

Abstract: This paper discusses tension-compression asymmetry properties of Ogden hyperelastic formulations. It is shown that if all negative or all positive Ogden coefficients are used, tension-compression asymmetry occurs the degree of which cannot be separately controlled from the degree of non-linearity. A simple hybrid form is therefore proposed providing separate… ▽ More This paper discusses tension-compression asymmetry properties of Ogden hyperelastic formulations. It is shown that if all negative or all positive Ogden coefficients are used, tension-compression asymmetry occurs the degree of which cannot be separately controlled from the degree of non-linearity. A simple hybrid form is therefore proposed providing separate control over the tension-compression asymmetry. It is demonstrated how this form relates to a newly introduced generalised strain tensor class which encompasses both the tension-compression asymmetric Seth-Hill strain class and the tension-compression symmetric Bažant strain class. If the control parameter is set to q=0.5 a tension-compression symmetric form involving Bažant strains is obtained with the property Ψ(λ_1,λ_2,λ_3 )=Ψ(1/λ_1 ,1/λ_2 ,1/λ_3 ). The symmetric form may be desirable for the definition of ground matrix contributions in soft tissue modelling allowing all deviation from the symmetry to stem solely from fibrous reinforcement. Such an application is also presented demonstrating the use of the proposed formulation in the modelling of the non-linear elastic and transversely isotropic behaviour of skeletal muscle tissue in compression (the model implementation and fitting procedure have been made freely available). The presented hyperelastic formulations may aid researchers in independently controlling the degree of tension-compression asymmetry from the degree of non-linearity, and in the case of anisotropic materials may assist in determining the role played by, either the ground matrix, or the fibrous reinforcing structures, in generating asymmetry. △ Less

Submitted 11 December, 2015; originally announced December 2015.

Comments: 20 pages

A Galerkin least-square stabilisation technique for hyperelastic biphasic soft tissue

Authors: Julien Vignollet, Chris J. Pearce, Lukasz Kaczmarczyk

Abstract: An hyperelastic biphasic model is presented. For slow-draining problems (permeability less than 1\times10-2 mm4 N-1 s-1), numerical instabilities in the form of non-physical oscillations in the pressure field are observed in 3D problems using tetrahedral Taylor-Hood finite elements. As an alternative to considerable mesh refinement, a Galerkin least-square s… ▽ More An hyperelastic biphasic model is presented. For slow-draining problems (permeability less than 1\times10-2 mm4 N-1 s-1), numerical instabilities in the form of non-physical oscillations in the pressure field are observed in 3D problems using tetrahedral Taylor-Hood finite elements. As an alternative to considerable mesh refinement, a Galerkin least-square stabilization framework is proposed. This technique drastically reduces the pressure discrepancies and prevents these oscillations from propagating towards the centre of the medium. The performance and robustness of this technique are demonstrated on a 3D numerical example. △ Less

Submitted 31 October, 2011; originally announced October 2011.

Morphogenesis of growing soft tissues

Authors: Julien Dervaux, Martine Ben Amar

Abstract: Recently, much attention has been given to a noteworthy property of some soft… ▽ More Recently, much attention has been given to a noteworthy property of some soft tissues: their ability to grow. Many attempts have been made to model this behaviour in biology, chemistry and physics. Using the theory of finite elasticity, Rodriguez has postulated a multiplicative decomposition of the geometric deformation gradient into a growth-induced part and an elastic one needed to ensure compatibility of the body. In order to fully explore the consequences of this hypothesis, the equations describing thin elastic objects under finite growth are derived. Under appropriate scaling assumptions for the growth rates, the proposed model is of the Foppl-von Karman type. As an illustration, the circumferential growth of a free hyperelastic disk is studied. △ Less

Submitted 12 December, 2007; originally announced December 2007.

Comments: 4 pages, 3 figures

Instabilities in elastomers and soft tissues

Authors: Alain Goriely, Michel Destrade, Martine Ben Amar

Abstract: Biological soft… ▽ More Biological soft tissues exhibit elastic properties which can be dramatically different from rubber-type materials (elastomers). To gain a better understanding of the role of constitutive relationships in determining material responses under loads we compare three different types of instabilities (two in compression, one in extension) in hyperelasticity for various forms of strain energy functions typically used for elastomers and for soft tissues. Surprisingly, we find that the strain-hardening property of soft tissues does not always stabilize the material. In particular we show that the stability analyses for a compressed half-space and for a compressed spherical thick shell can lead to opposite conclusions: a soft tissue material is more stable than an elastomer in the former case and less stable in the latter case. △ Less

Submitted 29 November, 2007; originally announced November 2007.

Comments: 16 pages

Journal ref: The Quarterly Journal of Mechanics and Applied Mathematics 59 (2006) 615-630

In-vivo measurement of the human soft tissues constitutive laws. Applications to Computer Aided Surgery

Authors: Patrick Schiavone, T. Boudou, J. Ohayon, Y. Payan

Abstract: …Aided Surgery applications since orthopaedic surgeons were looking for numerical tools able to predict risks of fractures. More recently, biomechanicians started to address soft… ▽ More In the 80's, biomechanicians were asked to work on Computer Aided Surgery applications since orthopaedic surgeons were looking for numerical tools able to predict risks of fractures. More recently, biomechanicians started to address soft tissues arguing that most of the human body is made of such tissues that can move as well as deform during surgical gestures [1]. An intra-operative use of a continuous Finite Element (FE) Model of a given tissue mainly faces two problems: (1) the numerical simulations have to be "interactive", i.e. sufficiently fast to provide results during surgery (which can be a strong issue in the context of hyperelastic models for example) and (2) during the intervention, the surgeon needs a device that can be used to provide to the model an estimation of the patient-specific constitutive behaviour of the soft tissues. This work proposes an answer to the second point, with the design of a new aspiration device aiming at characterizing the in vivo constitutive laws of human soft tissues. The device was defined in order to permit sterilization as well an easy intra-operative use. △ Less

Submitted 30 August, 2007; originally announced August 2007.

Journal ref: Dans Computer Methods in Biomechanics ans Biomechanical Engineering - XXXII Congress of the Société de Biomécanique, Lyon : France (2007)

A Robust Solution Procedure for Hyperelastic Solids with Large Boundary Deformation

Authors: Suzanne M. Shontz, Stephen A. Vavasis

Abstract: Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of… ▽ More Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a solution procedure for Lagrangian finite element discretization of a static nonlinear compressible Mooney-Rivlin hyperelastic solid. We consider the case in which the boundary condition is a large prescribed deformation, so that mesh tangling becomes an obstacle for straightforward algorithms. Our solution procedure involves a largely geometric procedure to untangle the mesh: solution of a sequence of linear systems to obtain initial guesses for interior nodal positions for which no element is inverted. After the mesh is untangled, we take Newton iterations to converge to a mechanical equilibrium. The Newton iterations are safeguarded by a line search similar to one used in optimization. Our computational results indicate that the algorithm is up to 70 times faster than a straightforward Newton continuation procedure and is also more robust (i.e., able to tolerate much larger deformations). For a few extremely large deformations, the deformed mesh could only be computed through the use of an expensive Newton continuation method while using a tight convergence tolerance and taking very small steps. △ Less

Submitted 14 June, 2011; v1 submitted 31 August, 2006; originally announced September 2006.

Comments: Revision of earlier version of paper. Submitted for publication in Engineering with Computers on 9 September 2010. Accepted for publication on 20 May 2011. Published online 11 June 2011. The final publication is available at http://www.springerlink.com

ACM Class: G.1.0; G.1.5; G.1.8; J.2

Comparison of linear and non-linear soft tissue models with post-operative CT scan in maxillofacial surgery

Authors: Matthieu Chabanas, Yohan Payan, Christophe Marecaux, Pascal Swider, Franck Boutault

Abstract: A Finite Element model of the face soft tissue is proposed to simulate the morphological outcomes of maxillofacial surgery. Three modelling options are implemented: a linear elastic model with small and large deformation hypothesis, and an hyperelastic Mooney-Rivlin model. An eva… ▽ More A Finite Element model of the face soft tissue is proposed to simulate the morphological outcomes of maxillofacial surgery. Three modelling options are implemented: a linear elastic model with small and large deformation hypothesis, and an hyperelastic Mooney-Rivlin model. An evaluation procedure based on a qualitative and quantitative comparison of the simulations with a post-operative CT scan is detailed. It is then applied to one clinical case to evaluate the differences between the three models, and with the actual patient morphology. First results shows in particular that for a "simple" clinical procedure where stress is less than 20%, a linear model seams sufficient for a correct modelling. △ Less

Submitted 26 June, 2006; originally announced June 2006.

Journal ref: Lecture notes in computer science (LNCS) 3078 (2004) 19-27