Digital image correlation and finite element modelling as a method to determine mechanical properties of human soft tissue in vivo

The mechanical properties of human soft tissue are crucial for impact biomechanics, rehabilitation engineering, and surgical simulation. Validation of these constitutive models using human data remains challenging and often requires the use of non-invasive imaging and inverse finite element (FE) analysis. Post-processing data from imaging methods such as tagged magnetic resonance imaging (MRI) can be challenging. Digital image correlation (DIC), however, is a relatively straightforward imaging method. DIC has been used in the past to study the planar and superficial properties of soft tissue and excised soft tissue layers. However, DIC has not been used to non-invasive study of the bulk properties of human soft tissue in vivo. Thus, the goal of this study was to assess the use of DIC in combination with FE modelling to determine the bulk material properties of human soft tissue. Indentation experiments were performed on a silicone gel soft tissue phantom. A two camera DIC setup was then used to record the 3D surface deformation. The experiment was then simulated using a FE model. The gel was modelled as Neo-Hookean hyperelastic, and the material parameters were determined by minimising the error between the experimental and FE data. The iterative FE analysis determined material parameters (μ=1.80 kPa, K=2999 kPa) that were in close agreement with parameters derived independently from regression to uniaxial compression tests (μ=1.71 kPa, K=2857 kPa). Furthermore the FE model was capable of reproducing the experimental indentor force as well as the surface deformation found (R²=0.81). It was therefore concluded that a two camera DIC configuration combined with FE modelling can be used to determine the bulk mechanical properties of materials that can be represented using hyperelastic Neo-Hookean constitutive laws.     

Dynamic finite element modeling of poroviscoelastic soft tissue

Clinical evidences relative to biomechanical factors have demonstrated their important contribution to the behaviour of soft tissues. Finite element (FE) analysis is used to study the mechanical behaviour of soft tissue because it can provide numerical solutions to problems that are intractable to analytic solutions. This study focuses on the development of a FE model of a poroelastic biological tissue, which incorporates the viscoelastic material behaviour, finite deformation and inertial effect. The FE formulation is based on the weak form derived from the governing equation, and Newmark-beta method as well as Newton's method is incorporated into the implicit non-linear solutions. One-dimensional analytical solutions were used to verify the theoretical formulation and the numerical implementation of the proposed model. This study was further extended to analyze two-dimensional biomechanical models and the results clearly demonstrate the importance of including finite deformation, viscoelasticity and inertial effects.     

A real time finite element based tissue simulation method incorporating nonlinear elastic behavior

This paper presents a new finite element simulation approach for surgical simulators. Based on the solution of the algebraic equations derived from a nonlinear elastic model, we propose a real time simulation rule based on the implicit relation between the displacements of contacted and free nodes. This rule is an analytic expression in the linear case, and an approximation of the implicit relation in the non-linear case. We also remove some of the restrictions on flexibility exhibited by previous linear and nonlinear approaches. In the linear case, real time reconfiguration of the contacted nodes and the boundary constraints is realized using the simulation rule, while in the nonlinear case, a similar result is obtained by employing affine mapping. These methods allow nonlinear material properties to be applied to real time tissue simulation, with an efficiency comparable to that of the tensor matrix method for linear elastic models.     

Biphasic finite element modeling of hydrated soft tissue contact using an augmented Lagrangian method

A study of biphasic soft tissues contact is fundamental to understanding the biomechanical behavior of human diarthrodial joints. To date, biphasic-biphasic contact has been developed for idealized geometries and not been accessible for more general geometries. In this paper a finite element formulation is developed for contact of biphasic tissues. The augmented Lagrangian method is used to enforce the continuity of contact traction and fluid pressure across the contact interface, and the resulting method is implemented in the commercial software COMSOL Multiphysics. The accuracy of the implementation is verified using 2D axisymmetric problems, including indentation with a flat-ended indenter, indentation with spherical-ended indenter, and contact of glenohumeral cartilage layers. The biphasic finite element contact formulation and its implementation are shown to be robust and able to handle physiologically relevant problems.     

Statistical finite element method for real-time tissue mechanics analysis

The finite element (FE) method can accurately calculate tissue deformation. However, its low speed renders it ineffective for many biomedical applications involving real-time data processing. To accelerate FE analysis, we introduce a novel tissue mechanics simulation technique. This technique is suitable for real-time estimation of tissue deformation of specific organs, which is required in computer-aided diagnostic or therapeutic procedures. In this method, principal component analysis is used to describe each organ shape and its corresponding FE field for a pool of patients by a small number of weight factors. A mapping function is developed to relate the parameters of organ shape to their FE field counterpart. We show that irrespective of the complexity of the tissue's constitutive law or its loading conditions, the proposed technique is highly accurate and fast in estimating the FE field. Average deformation errors of less than 2% demonstrate the accuracy of the proposed technique.     

A practical method to determine the amount of tissue to analyze using laser scanning cytometry.

BACKGROUND: Laser scanning cytometry (LSC) is a new technology similar to flow cytometry but generates data from analysis of successive microscopic fields. Unlike its use in other applications, LSC-generated data are not random when used for tissue sections, but are dependent on the microanatomy of the tissue and the distribution and expression of the protein under investigation. For valid LSC analysis, the data generated requires the evaluation of a sufficient tissue area to ensure an accurate representation of expression within the tissue of interest. METHODS: In this report, we describe a simple and common sense method for determining the area of tissue required for sound LSC analysis by tracking the variation in the measure of target expression with increasing number of fields until it approaches zero. RESULTS: This approach was used to evaluate the expression of immunohistochemical markers with differing tissue distributions in liver (PMP70, CYP1A2, and Ki67 positive macrophages) and a colorectal adenocarcinoma (activated caspase-3 positive cells), which exhibited diffuse, regional (centrilobular), random, and irregular distribution patterns respectively. CONCLUSIONS: Analyses of these markers demonstrated that the amount of tissue area required to reach a steady measure of a parameter increased with increasing variability of the tissue distribution.     

Quantification of soft tissue balance in total knee arthroplasty using finite element analysis

Unbalanced contact force on the tibial component has been considered a factor leading to loosening of the implant and increased wear of the bearing surface in total knee arthroplasty. Because it has been reported that good alignment cannot guarantee successful clinical outcomes, the soft tissue balance should be checked together with the alignment. Finite element models of patients' lower extremities were developed to analyse the medial and lateral contact force distribution on the tibial insert. The distributions for four out of five patients were not balanced equally, even though the alignment angles were within a clinically acceptable range. Moreover, the distribution was improved by changing soft tissue release and ligament tightening for the specific case. Integration of the biomechanical modelling, image matching and finite element analysis techniques with the patient-specific properties and various dynamic loading would suggest a clinically relevant pre-operative planning for soft tissue balancing.     

3-D finite element modelling of facial soft tissue and preliminary application in orthodontics

Prediction of soft tissue aesthetics is important for achieving an optimal outcome in orthodontic treatment planning. Previously, applicable procedures were mainly restricted to 2-D profile prediction. In this study, a generic 3-D finite element (FE) model of the craniofacial soft and hard tissue was constructed, and individualisation of the generic model based on cone beam CT data and mathematical transformation was investigated. The result indicated that patient-specific 3-D facial FE model including different layers of soft tissue could be obtained through mathematical model transformation. Average deviation between the transformed model and the real reconstructed one was 0.47 ± 0.77 mm and 0.75 ± 0.84 mm in soft and hard tissue, respectively. With boundary condition defined according to treatment plan, such FE model could be used to predict the result of orthodontic treatment on facial soft tissue.     

3-D finite element modelling of facial soft tissue and preliminary application in orthodontics

Prediction of soft tissue aesthetics is important for achieving an optimal outcome in orthodontic treatment planning. Previously, applicable procedures were mainly restricted to 2-D profile prediction. In this study, a generic 3-D finite element (FE) model of the craniofacial soft and hard tissue was constructed, and individualisation of the generic model based on cone beam CT data and mathematical transformation was investigated. The result indicated that patient-specific 3-D facial FE model including different layers of soft tissue could be obtained through mathematical model transformation. Average deviation between the transformed model and the real reconstructed one was 0.47?±?0.77?mm and 0.75?±?0.84?mm in soft and hard tissue, respectively. With boundary condition defined according to treatment plan, such FE model could be used to predict the result of orthodontic treatment on facial soft tissue.     

Methodology to determine failure characteristics of planar soft tissues using a dynamic tensile test

Predicting the injury risk in automotive collisions requires accurate knowledge of human tissues, more particularly their mechanical properties under dynamic loadings. The present methodology aims to determine the failure characteristics of planar soft tissues such as skin, hollow organs and large vessel walls. This consists of a dynamic tensile test, which implies high-testing velocities close to those in automotive collisions. To proceed, I-shaped tissue samples are subjected to dynamic tensile tests using a customized tensile device based on the drop test principle. Data acquisition has especially been adapted to heterogeneous and soft biological tissues given that standard measurement systems (considered to be global) have been completed with a non-contact and full-field strain measurement (considered to be local). This local measurement technique, called the Image Correlation Method (ICM) provides an accurate strain analysis by revealing strain concentrations and avoids damaging the tissue. The methodology has first been applied to human forehead skin and can be further expanded to other planar soft tissues. The failure characteristics for the skin in terms of ultimate stress are 3 MPa +/- 1.5 MPa. The ultimate global longitudinal strains are equal to 9.5%+/-1.9% (Green-Lagrange strain), which contrasts with the ultimate local longitudinal strain values of 24.0%+/-5.3% (Green-Lagrange strain). This difference is a consequence of the tissue heterogeneity, clearly illustrated by the heterogeneous distribution of the local strain field. All data will assist in developing the tissue constitutive law that will be implemented in finite element models.     

An inverse finite element method for determining the anisotropic properties of the cornea

An inverse finite element method was developed to determine the anisotropic properties of bovine cornea from an in vitro inflation experiment. The experiment used digital image correlation (DIC) to measure the three-dimensional surface geometry and displacement field of the cornea at multiple pressures. A finite element model of a bovine cornea was developed using the DIC measured surface geometry of the undeformed specimen. The model was applied to determine five parameters of an anisotropic hyperelastic model that minimized the error between the measured and computed surface displacement field and to investigate the sensitivity of the measured bovine inflation response to variations in the anisotropic properties of the cornea. The results of the parameter optimization revealed that the collagen structure of bovine cornea exhibited a high degree of anisotropy in the limbus region, which agreed with recent histological findings, and a transversely isotropic central region. The parameter study showed that the bovine corneal response to the inflation experiment was sensitive to the shear modulus of the matrix at pressures below the intraocular pressure, the properties of the collagen lamella at higher pressures, and the degree of anisotropy in the limbus region. It was not sensitive to a weak collagen anisotropy in the central region.     

Application of the u-p finite element method to the study of articular cartilage.

The finite element method using the principle of virtual work was applied to the biphasic theory to establish a numerical routine for analyses of articular cartilage behavior. The matrix equations that resulted contained displacements of the solid matrix (mu) and true fluid pressure (p) as the unknown variables at the element nodes. Both small and large strain conditions were considered. The algorithms and computer code for the analysis of two-dimensional plane strain, plane stress, and axially symmetric cases were developed. The u-p finite element numerical procedure demonstrated excellent agreement with available closed-form and numerical solutions for the configurations of confined compression and unconfined compression under small strains, and for confined compression under large strains. The model was also used to examine the behavior of a repaired articular surface. The differences in material properties between the repair tissue and normal cartilage resulted in significant deformation gradients across the repair interface as well as increased fluid efflux from the tissue.     

A method to determine the end point of decalcification of hard tissue and bone

A method for decalcification end point determination of mineralized tissue is described. The calcium content of the decalcification solution was determined colorimetrically with a "continuous automatic analyzer" with a high degree of accuracy. The end point method used has been tested on two decalcification methods, 5% nitric acid with or without ultrasonic treatment. The results suggest it is possible to quantitate the decalcification process.     

Analysis of the main soft tissue stress associated with flexible flatfoot deformity: a finite element study

Biomechanics and Modeling in Mechanobiology - A better understanding of soft tissue stress and its role in supporting the medial longitudinal arch in flexible flatfoot could help to guide the...     

A finite element model technique to determine the mechanical response of a lumbar spine segment under complex loads

This study presents a CT-based finite element model of the lumbar spine taking into account all function-related boundary conditions, such as anisotropy of mechanical properties, ligaments, contact elements, mesh size, etc. Through advanced mesh generation and employment of compound elements, the developed model is capable of assessing the mechanical response of the examined spine segment for complex loading conditions, thus providing valuable insight on stress development within the model and allowing the prediction of critical loading scenarios. The model was validated through a comparison of the calculated force-induced inclination/deformation and a correlation of these data to experimental values. The mechanical response of the examined functional spine segment was evaluated, and the effect of the loading scenario determined for both vertebral bodies as well as the connecting intervertebral disc.     

Probabilistic fatigue analysis of all-ceramic crowns based on the finite element method

The reliability evaluation and lifetime prediction of oral restorations for dentists have always been the major concern in the field of prosthodontics. This study introduced a new methodology for dealing with stress–strength interference and an analysis to quantify the reliability of all-ceramic crowns. The response stress was based on finite element models of all-ceramic crowns, which were constructed by reverse techniques. The method utilized in this study was a probabilistic analysis that considered the all-ceramic crown as a structural component associated with multiple factors involved in the all-ceramic system including occlusal loads and mechanical properties of porcelain. The results suggested the survival probability of all-ceramic crowns after 1, 5, 10, 15, and 20 years could be computed to be 98.89%, 98.03%, 97.50%, 97.13%, and 96.93%, respectively. Probabilistic analysis methods offer a systematic technique to incorporate and account for the nature of uncertainty in ceramic restorations and allow prediction of the reliability of all-ceramic crowns under cyclic occlusal loads with accuracy.     

Cell-level finite element studies of viscous cells in planar aggregates

A new cell-level finite element formulation is presented and used to investigate how epithelia and other planar collections of viscous cells might deform during events such as embryo morphogenesis and wound healing. Forces arising from cytoskeletal components, cytoplasm viscosity, and cell-cell adhesions are included. Individual cells are modeled using multiple finite elements, and cell rearrangements can occur. Simulations of cell-sheet stretching indicate that the initial stages of sheet stretching are characterized by changes in cell shape, while subsequent stages are governed by cell rearrangement. Inferences can be made from the simulations about the forces that act in real cell sheets when suitable experimental data are available.     

A quasi-incompressible and quasi-inextensible finite element analysis of fibrous soft biological tissues

Biomechanics and Modeling in Mechanobiology - The contribution presents an extension and application of a recently proposed finite element formulation for quasi-inextensible and...     

A sub-domain inverse finite element characterization of hyperelastic membranes including soft tissues

Quantification of the mechanical behavior of hyperelastic membranes in their service configuration, particularly biological tissues, is often challenging because of the complicated geometry, material heterogeneity, and nonlinear behavior under finite strains. Parameter estimation thus requires sophisticated techniques like the inverse finite element method. These techniques can also become difficult to apply, however, if the domain and boundary conditions are complex (e.g. a non-axisymmetric aneurysm). Quantification can alternatively be achieved by applying the inverse finite element method over sub-domains rather than the entire domain. The advantage of this technique, which is consistent with standard experimental practice, is that one can assume homogeneity of the material behavior as well as of the local stress and strain fields. In this paper, we develop a sub-domain inverse finite element method for characterizing the material properties of inflated hyperelastic membranes, including soft tissues. We illustrate the performance of this method for three different classes of materials: neo-Hookean, Mooney Rivlin, and Fung-exponential.