Estimating material parameters of human skin in vivo

An accurate mathematical representation of the mechanical behaviour of human skin is essential when simulating deformations occurring in the skin during body movements or clinical procedures. In this study constitutive stress–strain relationships based on experimental data from human skin in vivo were obtained. A series of multiaxial loading experiments were performed on the forearms of four age- and gender matched subjects. The tissue geometry, together with recorded displacements and boundary forces, were combined in an analysis using finite element modelling. A non-linear optimization technique was developed to estimate values for the material parameters of a previously published constitutive law, describing the stress–strain relationship as a non-linear anisotropic membrane. Ten sets of material parameters where estimated from the experiments, showing considerable differences in mechanical behaviour both between individual subjects as well as mirrored body locations on a single subject. The accuracy of applications that simulate large deformations of human skin could be improved by using the parameters found from the in vivo experiments as described in this study.     

The mechanical behaviour of brain tissue: large strain response and constitutive modelling

The non-linear mechanical behaviour of porcine brain tissue in large shear deformations is determined. An improved method for rotational shear experiments is used, producing an approximately homogeneous strain field and leading to an enhanced accuracy. Results from oscillatory shear experiments with a strain amplitude of 0.01 and frequencies ranging from 0.04 to 16 Hz are given. The immediate loss of structural integrity, due to large deformations, influencing the mechanical behaviour of brain tissue, at the time scale of loading, is investigated. No significant immediate mechanical damage is observed for these shear deformations up to strains of 0.45. Moreover, the material behaviour during complex loading histories (loading-unloading) is investigated. Stress relaxation experiments for strains up to 0.2 and constant strain rate experiments for shear rates from 0.01 to 1 s(-1) and strains up to 0.15 are presented. A new differential viscoelastic model is used to describe the mechanical response of brain tissue. The model is formulated in terms of a large strain viscoelastic framework and considers non-linear viscous deformations in combination with non-linear elastic behaviour. This constitutive model is readily applicable in three-dimensional head models in order to predict the mechanical response of the intra-cranial contents due to an impact.     

Torsion and bending imposed on a new anterior cruciate ligament prosthesis during knee flexion: an evaluation method

A new composite prosthesis was recently proposed for the anterior cruciate ligament. It is implanted in the femur and the tibia through two anchoring channels. Its intra-articular portion, composed of a fiber mesh sheath wrapped around a silicone rubber cylindrical core, reproduces satisfactorily the ligament response in tension. However, the prosthesis does not only undergo elongation. In addition, it is submitted to torsion in its intra-articular portion and bending at its ends. This paper presents a new method to evaluate these two types of deformations throughout a knee flexion by means of a geometric model of the implanted prosthesis. Input data originate from two sources: (i) a three-dimensional anatomic topology of the knee joint in full extension, providing the localization of the prosthesis anchoring channels, and ii) a kinematic model of the knee describing the motion of these anchoring channels during a physiological flexion of the knee joint. The evaluation method is independent of the way input data are obtained. This method, applied to a right cadaveric knee, shows that the orientation of the anchoring channels has a large effect on the extent of torsion and bending applied to the implanted prosthesis throughout a knee flexion, especially on the femoral side. The study suggests also the best choice for the anchoring channel axes orientation.     

Detailed finite element modelling of deep needle insertions into a soft tissue phantom using a cohesive approach

Detailed finite element modelling of needle insertions into soft tissue phantoms encounters difficulties of large deformations, high friction, contact loading and material failure. This paper demonstrates the use of cohesive elements in high-resolution finite element models to overcome some of the issues associated with these factors. Experiments are presented enabling extraction of the strain energy release rate during crack formation. Using data from these experiments, cohesive elements are calibrated and then implemented in models for validation of the needle insertion process. Successful modelling enables direct comparison of finite element and experimental force–displacement plots and energy distributions. Regions of crack creation, relaxation, cutting and full penetration are identified. By closing the loop between experiments and detailed finite element modelling, a methodology is established which will enable design modifications of a soft tissue probe that steers through complex mechanical interactions with the surrounding material.     

C4–C5 segment finite element model development,validation, and load-sharing investigation

Detailed cervical spine models are necessary to better understand cervical spine response to loading, improve our understanding of injury mechanisms, and specifically for predicting occupant response and injury in auto crash scenarios. The focus of this study was to develop a C4–C5 finite element model with accurate representations of each tissue within the segment. This model incorporates more than double the number of elements of existing models, required for accurate prediction of response. The most advanced material data available were then incorporated using appropriate nonlinear constitutive models to provide accurate predictions of response at physiological levels of loading. This tissue-scale segment model was validated against a wide variety of experimental data including different modes of loading (axial rotation, flexion, extension, lateral bending, and translation), and different load levels. In general, the predicted response of the model was within the single standard deviation response corridors for both low and high load levels. Importantly, this model demonstrates that appropriate refinement of the finite element mesh, representation at the tissue level, and sufficiently detailed material properties and constitutive models provide excellent response predictions without calibration of the model to experimental data. Load sharing between the disc, ligaments, and facet joints was investigated for various modes of loading, and the dominant load-bearing structure was found to correlate with typical anatomical injury sites for these modes of loading. The C4–C5 model forms the basis for the development of a full cervical spine model. Future studies will focus on tissue-level injury prediction and dynamic response.     

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time; Application to non-rigid neuroimage registration

Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer.     

Does subcutaneous adipose tissue behave as an (anti-)thixotropic material?

Although subcutaneous adipose tissue undergoes large deformations on a daily basis, there is no adequate mechanical model to describe the transfer of mechanical load from the skin throughout the tissue to deeper layers. In order to develop such a non-linear model, a set of experimental data is required. Accordingly, this study examines the long term behavior of adipose tissue under small strain and its response to various large strain profiles. The results show that the shear modulus dramatically increases to about an order of magnitude after a loading period between 250 and 1250 s, but returns to its initial value within 3 h of recovery from loading. In addition, it was observed that the stress–strain responses for various large strain history sequences are reproducible up to a strain of 0.15. For increasing strains, the stress decreases for subsequent loading cycles and, above 0.3 strain, tissue structure changes such that the stress becomes independent of the applied strain. From the results, it can be concluded that adipose tissue likely behaves as an (anti-) thixotropic material and that a Mooney–Rivlin model might be appropriate to simulate behavior at physiologically relevant high strains. However, before the model is developed more fully, further experimental research is needed to ratify that the material is (anti-)thixotropic.     

Subject-specific non-linear biomechanical model of needle insertion into brain

The previous models for predicting the forces acting on a needle during insertion into very soft organs (such as, e.g. brain) relied on oversimplifying assumptions of linear elasticity and specific experimentally derived functions for determining needle-tissue interactions. In this contribution, we propose a more general approach in which the needle forces are determined directly from the equations of continuum mechanics using fully non-linear finite element procedures that account for large deformations (geometric non-linearity) and non-linear stress-strain relationship (material non-linearity) of soft tissues. We applied these procedures to model needle insertion into a swine brain using the constitutive properties determined from the experiments on tissue samples obtained from the same brain (i.e. the subject-specific constitutive properties were used). We focused on the insertion phase preceding puncture of the brain meninges and obtained a very accurate prediction of the needle force. This demonstrates the utility of non-linear finite element procedures in patient-specific modelling of needle insertion into soft organs such as, e.g. brain.     

A new method to investigate in vivo knee behavior using a finite element model of the lower limb

Several finite element models have been developed for estimating the mechanical response of joint internal structures, where direct or indirect in vivo measurement is difficult or impossible. The quality of the predictions made by those models is largely dependent on the quality of the experimental data (e.g. load/displacement) used to drive them. Also numerical problems have been described in the literature when using implicit finite element techniques to simulate problems that involve contacts and large displacements. In this study, a unique strategy was developed combining high accuracy in vivo three-dimensional kinematics and a lower limb finite element model based on explicit finite element techniques. The method presents an analytical technique applied to a dynamic loading condition (impact during hopping on one leg). The validation of the lower limb model focused on the response of the whole model and the knee joint in particular to the imposed 3D femoral in vivo kinematics and ground reaction forces. The approach outlined in this study introduces a generic tool for the study of in vivo knee joint behavior.     

Finite element modelling of glenohumeral kinematics following total shoulder arthroplasty

Due to the shallowness of the glenohumeral joint, a challenging but essential requirement of a glenohumeral prosthesis is the prevention of joint dislocation. Weak glenoid bone stock and frequent dysfunction of the rotator cuff, both of which are common with rheumatoid arthritis, make it particularly difficult to achieve this design goal. Although a variety of prosthetic designs are commercially available only a few experimental studies have investigated the kinematics and dislocation characteristics of design variations. Analytical or numerical methods, which are predictive and more cost-effective, are, apart from simple rigid-body analyses, non-existent. The current investigation presents the results of a finite element analysis of the kinematics of a total shoulder joint validated using recently published experimental data for the same prostheses. The finite element model determined the loading required to dislocate the humeral head, and the corresponding translations, to within 4% of the experimental data. The finite element method compared dramatically better to the experimental data (mean difference=2.9%) than did rigid-body predictions (mean difference=37%). The goal of this study was to develop an accurate method that in future studies can be used for further investigations of the effect of design parameters on dislocation, particularly in the case of a dysfunctional rotator cuff. Inherently, the method also evaluates the glenoid fixation stresses in the relatively weak glenoid bone stock. Hence, design characteristics can be simultaneously optimised against dislocation as well as glenoid loosening.     

A three-dimensional inverse finite element analysis of the heel pad

Quantification of plantar tissue behavior of the heel pad is essential in developing computational models for predictive analysis of preventive treatment options such as footwear for patients with diabetes. Simulation based studies in the past have generally adopted heel pad properties from the literature, in return using heel-specific geometry with material properties of a different heel. In exceptional cases, patient-specific material characterization was performed with simplified two-dimensional models, without further evaluation of a heel-specific response under different loading conditions. The aim of this study was to conduct an inverse finite element analysis of the heel in order to calculate heel-specific material properties in situ. Multidimensional experimental data available from a previous cadaver study by Erdemir et al. ("An Elaborate Data Set Characterizing the Mechanical Response of the Foot," ASME J. Biomech. Eng., 131(9), pp. 094502) was used for model development, optimization, and evaluation of material properties. A specimen-specific three-dimensional finite element representation was developed. Heel pad material properties were determined using inverse finite element analysis by fitting the model behavior to the experimental data. Compression dominant loading, applied using a spherical indenter, was used for optimization of the material properties. The optimized material properties were evaluated through simulations representative of a combined loading scenario (compression and anterior-posterior shear) with a spherical indenter and also of a compression dominant loading applied using an elevated platform. Optimized heel pad material coefficients were 0.001084 MPa (μ), 9.780 (α) (with an effective Poisson's ratio (ν) of 0.475), for a first-order nearly incompressible Ogden material model. The model predicted structural response of the heel pad was in good agreement for both the optimization (<1.05% maximum tool force, 0.9% maximum tool displacement) and validation cases (6.5% maximum tool force, 15% maximum tool displacement). The inverse analysis successfully predicted the material properties for the given specimen-specific heel pad using the experimental data for the specimen. The modeling framework and results can be used for accurate predictions of the three-dimensional interaction of the heel pad with its surroundings.     

Developing simulations to reproduce in vivo fluoroscopy kinematics in total knee replacement patients

For clinically predictive testing and design-phase evaluation of prospective total knee replacement (TKR) implants, devices should ideally be evaluated under physiological loading conditions which incorporate population-level variability. A challenge exists for experimental and computational researchers in determining appropriate loading conditions for wear and kinematic knee simulators which reflect in vivo joint loading conditions. There is a great deal of kinematic data available from fluoroscopy studies. The purpose of this work was to develop computational methods to derive anterior–posterior (A–P) and internal–external (I–E) tibiofemoral (TF) joint loading conditions from in vivo kinematic data. Two computational models were developed, a simple TF model, and a more complex lower limb model. These models were driven through external loads applied to the tibia and femur in the TF model, and applied to the hip, ankle and muscles in the lower limb model. A custom feedback controller was integrated with the finite element environment and used to determine the external loads required to reproduce target kinematics at the TF joint. The computational platform was evaluated using in vivo kinematic data from four fluoroscopy patients, and reproduced in vivo A–P and I–E motions and compressive force with a root-mean-square (RMS) accuracy of less than 1 mm, 0.1°, and 40 N in the TF model and in vivo A–P and I–E motions, TF flexion, and compressive loads with a RMS accuracy of less than 1 mm, 0.1°, 1.4°, and 48 N in the lower limb model. The external loading conditions derived from these models can ultimately be used to establish population variability in loading conditions, for eventual use in computational as well as experimental activity simulations.     

The effect of connective tissue material uncertainties on knee joint mechanics under isolated loading conditions

Although variability in connective tissue parameters is widely reported and recognized, systematic examination of the effect of such parametric uncertainties on predictions derived from a full anatomical joint model is lacking. As such, a sensitivity analysis was performed to consider the behavior of a three-dimensional, non-linear, finite element knee model with connective tissue material parameters that varied within a given interval. The model included the coupled mechanics of the tibio-femoral and patello-femoral degrees of freedom. Seven primary connective tissues modeled as non-linear continua, articular cartilages described by a linear elastic model, and menisci modeled as transverse isotropic elastic materials were included. In this study, a multi-factorial global sensitivity analysis is proposed, which can detect the contribution of influential material parameters while maintaining the potential effect of parametric interactions. To illustrate the effect of material uncertainties on model predictions, exemplar loading conditions reported in a number of isolated experimental paradigms were used. Our findings illustrated that the inclusion of material uncertainties in a coupled tibio-femoral and patello-femoral model reveals biomechanical interactions that otherwise would remain unknown. For example, our analysis revealed that the effect of anterior cruciate ligament parameter variations on the patello-femoral kinematic and kinetic response sensitivities was significantly larger, over a range of flexion angles, when compared to variations associated with material parameters of tissues intrinsic to the patello-femoral joint. We argue that the systematic sensitivity framework presented herein will help identify key material uncertainties that merit further research and provide insight on those uncertainties that may not be as relative to a given response.     

An approach to the mechanical constitutive modelling of arterial tissue based on homogenization and optimization

This paper is concerned with characterizing the quasistatic mechanical behaviour of arterial tissue undergoing finite deformation through hyperelastic constitutive functions. Commonly the parameters of constitutive functions are established by a process of optimization based on experimental data. Instead we construct a finite element model of a representative volume element of the material and compute its homogenized response to a range of deformations. These data are then used to provide objective functions for optimizing the parameters of two analytical models from the literature.