Experimental-numerical analysis of minipig's multi-rooted teeth

The paper pertains to the analysis of the biomechanical behaviour of the periodontal ligament (PDL) by using a combined experimental and numerical approach. Experimental analysis provides information about a two-rooted pig premolar tooth in its socket with regard to morphological configuration and deformational response. The numerical analysis developed for the present investigation adopts a specific anisotropic hyperelastic formulation, accounting for tissue structural arrangement. The parameters to be adopted for the PDL constitutive model are evaluated with reference to data deducted from experimental in vitro tests on different specimens taken from literature. According to morphometric data relieved, solid models are provided as basis for the development of numerical models that adopt the constitutive formulation proposed. A reciprocal validation of experimental and numerical data allows for the evaluation of reliability of results obtained. The work is intended as preliminary investigation to study the correlation between mechanical status of PDL and induction to cellular activity in orthodontic treatments.     

Constitutive formulation and numerical analysis of the heel pad region

The aim of this work is to provide a numerical approach for the investigation of the mechanical behaviour of the heel pad region. A visco-hyperelastic model is formulated with regard to fat pad tissue, while a fibre-reinforced hyperelastic model is considered for the heel skin tissue. Bone components are defined by means of an orthotropic linear elastic model. Particular attention is paid to the evaluation of constitutive parameters within different models adopted in consideration of experimental tests data. Preliminarily, indentation tests on a skinless cadaveric foot are considered with regard to fat pad tissue. Indentation tests on an intact heel pad of a cadaveric foot are subsequently adopted for the final identification of constitutive parameters of fat pad and skin tissues. A numerical model of the rear foot is defined and different loading conditions are assumed according to experimental data. A comparison between experimental and numerical data leads to the evaluation of the real capability of the procedure to interpret the actual response of the rear foot.     

Subject-specific models of the hindfoot reveal a relationship between morphology and passive mechanical properties

The morphology of the bones, articular surfaces and ligaments and the passive mechanical characteristics of the ankle complex were reported to vary greatly among individuals. The goal of this study was to test the hypothesis that the variations observed in the passive mechanical properties of the healthy ankle complex are strongly influenced by morphological variations. To evaluate this hypothesis six numerical models of the ankle joint complex were developed from morphological data obtained from MRI of six cadaveric lower limbs, and from average reported data on the mechanical properties of ligaments and articular cartilage. The passive mechanical behavior of each model, under a variety of loading conditions, was found to closely match the experimental data obtained from each corresponding specimen. Since all models used identical material properties and were subjected to identical loads and boundary conditions, it was concluded that the observed variations in passive mechanical characteristics were due to variations in morphology, thus confirming the hypothesis. In addition, the average and large variations in passive mechanical behavior observed between the models were similar to those observed experimentally between cadaveric specimens. The results suggest that individualized subject-specific treatment procedures for ankle complex disorders are potentially superior to a one-size-fits-all approach.     

A visco-hyperelastic-damage constitutive model for the analysis of the biomechanical response of the periodontal ligament

The periodontal ligament (PDL), as other soft biological tissues, shows a strongly non-linear and time-dependent mechanical response and can undergo large strains under physiological loads. Therefore, the characterization of the mechanical behavior of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non-linearity. The microstructural arrangement determines specific anisotropic properties. A hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for the PDL and properly arranged for investigating the viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. These phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic-damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. The accuracy of the formulation is evaluated by using results of experimental tests performed on animal model, accounting for different strain rates and for strain states capable of inducing damage phenomena. The comparison shows a good agreement between numerical results and experimental data.     

Constitutive formulation and numerical analysis of the heel pad region

The aim of this work is to provide a numerical approach for the investigation of the mechanical behaviour of the heel pad region. A visco-hyperelastic model is formulated with regard to fat pad tissue, while a fibre-reinforced hyperelastic model is considered for the heel skin tissue. Bone components are defined by means of an orthotropic linear elastic model. Particular attention is paid to the evaluation of constitutive parameters within different models adopted in consideration of experimental tests data. Preliminarily, indentation tests on a skinless cadaveric foot are considered with regard to fat pad tissue. Indentation tests on an intact heel pad of a cadaveric foot are subsequently adopted for the final identification of constitutive parameters of fat pad and skin tissues. A numerical model of the rear foot is defined and different loading conditions are assumed according to experimental data. A comparison between experimental and numerical data leads to the evaluation of the real capability of the procedure to interpret the actual response of the rear foot.     

Measurement of the circumferential mechanical properties of the umbilical vein: experimental and numerical analyses

Coronary artery disease is responsible for almost 30% of all deaths worldwide. The saphenous vein and umbilical vein (UV) are the most common veins using for treatment as a coronary artery bypass graft (CABG). The mechanical properties of UV belonging to its long-term patency for CABG are very important. However, there is a lack of knowledge on the linear elastic and nonlinear hyperelastic mechanical properties of the UV. In this study, three stress definitions (second Piola–Kichhoff stress, engineering stress and true stress) and four strain definitions (Almansi–Hamel strain, Green–St Venant strain, engineering strain and true strain) are used to determine the elastic modulus, maximum stress and strain of eight human UVs under circumferential loading. The nonlinear mechanical behaviour of the UV is computationally investigated using Mooney–Rivlin hyperelastic model. A numerical finite element analysis is also carried out to simulate the constitutive modelling versus its numerical results. The results show that the Almansi–Hamel strain definition overestimates the elastic modulus while Green–St Venant strain definition underestimates the elastic modulus at different stress definitions. The true stress–true strain definition, which gives more accurate measurements of the tissue's response using the instantaneous values, reveals the Young's modulus and maximum stress of 2.18 and 6.01 MPa, respectively. The Mooney–Rivlin material model is well represented by the nonlinear mechanical behaviour of the UV. The findings of this study could have implications not only for understanding the extension and rupture mechanism of UV but also for interventions and surgeries, including balloon angioplasty, bypass and stenting.     

Mechanical analysis of the ring opening test applied to human ascending aortas

This work presents experiments, modelling and numerical simulation aimed at describing the mechanical response of human ascending aortas in the ring opening test. The objective is to quantify, from the opening angles measured in the test, the residual stress distribution along the artery wall and, afterwards, how this stress pattern changes when the artery is subjected to standard physiological pressures. The cases studied correspond to four groups including both healthy and pathological arteries. The tissues are characterized via tensile test measurements that enable to derive the material parameters of two constitutive models adopted in the present analysis. Overall, the numerical results obtained for all groups were found to be a useful data that allow to estimate the residual stress and their influence on the vessels under normal and hypertension physiological conditions.     

Orthotropic properties of cancellous bone modelled as parameterized cellular material

Analysis of stresses and strains in bone tissues and simulation of their adaptive remodelling require exhaustive information about distribution of constitutive properties of cancellous bone and their relationships to microstructural parameters. Homogenization of “equivalent” trabecular microstructures appears to be an advantageous tool for this task. In this study, parameterized orthotropic constitutive models of cancellous bone are derived from finite element analysis of repeatable microstructure cells. The models, based on a space-filling dodecahedron, are fully three-dimensional and are parameterized with four shape parameters. Variation of the parameters allows to imitate most of typical microstructure patterns observed in real bones, along with a variety of intermediate geometries. Finite element models of cells are generated by a special-purpose structured mesh generator for any arbitrary set of shape parameter values. Static numerical tests are performed for an exhaustive number of parameter value sets (microstructure instances). Coefficients of elastic orthotropic stiffness matrix are determined as tabularized functions of elastic constants versus the shape parameters. Additionally, they are correlated to apparent density and principal fabric tensor values. Comparison of the results with micro-FE data obtained for a large set of cancellous bone specimens proves a good agreement.     

Orthotropic properties of cancellous bone modelled as parameterized cellular material

Analysis of stresses and strains in bone tissues and simulation of their adaptive remodelling require exhaustive information about distribution of constitutive properties of cancellous bone and their relationships to microstructural parameters. Homogenization of "equivalent" trabecular microstructures appears to be an advantageous tool for this task. In this study, parameterized orthotropic constitutive models of cancellous bone are derived from finite element analysis of repeatable microstructure cells. The models, based on a space-filling dodecahedron, are fully three-dimensional and are parameterized with four shape parameters. Variation of the parameters allows to imitate most of typical microstructure patterns observed in real bones, along with a variety of intermediate geometries. Finite element models of cells are generated by a special-purpose structured mesh generator for any arbitrary set of shape parameter values. Static numerical tests are performed for an exhaustive number of parameter value sets (microstructure instances). Coefficients of elastic orthotropic stiffness matrix are determined as tabularized functions of elastic constants versus the shape parameters. Additionally, they are correlated to apparent density and principal fabric tensor values. Comparison of the results with micro-FE data obtained for a large set of cancellous bone specimens proves a good agreement.     

Elastic properties of cancellous bone derived from finite element models of parameterized microstructure cells

Evaluation of constitutive properties of cancellous bone and their relationships to microstructural parameters is a crucial issue in analysis of stresses and strains in bone tissues and simulation of their remodelling. Known limitations of experimental methods as well as of the micro-FE techniques make the analysis and homogenization of 'equivalent' trabecular microstructures an advantageous tool for this task. In this study, parameterized orthotropic constitutive models of cancellous bone are derived from finite element analysis of repeatable microstructure cells. Two cell types are analysed: cube- and prism-based. The models are fully three-dimensional, have realistic curvilinear shapes and are parameterized with three shape parameters. Variation of the parameters allows to imitate most of the typical microstructure patterns observed in real bones, along with variety of intermediate geometries. Finite element models of cells are generated by a special-purpose structured mesh generator for any arbitrary set of shape parameter values. Six static numerical tests are performed for an exhaustive number of parameter value sets (microstructure instances). Multi-point boundary conditions imposed on the models ensure mutual fitting of deformed neighbouring cells. Values of computed stresses allow to determine all coefficients of elastic orthotropic stiffness matrix. Results have a form of tabularized functions of elastic constants versus the shape parameters. Comparison of the results with micro-FE data obtained for a large set of cancellous bone specimens proves a good agreement, though evidently better in the case of the prism-based cell model.     

The effect of damage to the lateral collateral ligaments on the mechanical characteristics of the ankle joint--an in-vitro study

Injuries to the lateral collateral ligaments of the ankle joint are among the most frequently occurring injuries at the lower limb. The present study was conducted for the purpose of establishing the basis for the development of a quantitative diagnostic procedure for such injuries. To achieve this goal, the effect of four types of ligament injuries on the three-dimensional mechanical characteristics of the ankle were investigated. These types of injuries consisted of: 1) isolated tear of the anterior talofibular ligament; 2) isolated tear of the calcaneofibular ligament; 3) isolated tear of the posterior talofibular ligament; and 4) combined tear of both the anterior talofibular ligament and the calcaneofibular ligament. The experiments were conducted on 31 amputated lower limbs and consisted of comparing the three-dimensional load-displacement and flexibility characteristics of the ankle joint prior to and following sectioning of selected ligaments. The experimental and analytical procedures used to derive these characteristics was developed previously by the authors. From the results of this study it was concluded that the three-dimensional flexibility characteristics of the ankle joint are strongly influenced by damage to the lateral collateral ligaments. Furthermore, it was found that each type of ligament injury produced unique and identifiably changes in the flexibility characteristics of the ankle. These unique changes, which are described in detail in this paper, can be used to discriminate between the different types of ligament injuries. Consequently, it was concluded that it is feasible to develop a quantitative diagnostic procedure for ankle ligament injuries based on the effect of the injury on the flexibility characteristics of the ankle.     

Modeling the effect of collagen fibril alignment on ligament mechanical behavior

Ligament mechanical behavior is primarily regulated by fibrous networks of type I collagen. Although these fibrous networks are typically highly aligned, healthy and injured ligament can also exhibit disorganized collagen architecture. The objective of this study was to determine whether variations in the collagen fibril network between neighboring ligaments can predict observed differences in mechanical behavior. Ligament specimens from two regions of bovine fetlock joints, which either exhibited highly aligned or disorganized collagen fibril networks, were mechanically tested in uniaxial tension. Confocal microscopy and FiberFit software were used to quantify the collagen fibril dispersion and mean fibril orientation in the mechanically tested specimens. These two structural parameters served as inputs into an established hyperelastic constitutive model that accounts for a continuous distribution of planar fibril orientations. The ability of the model to predict differences in the mechanical behavior between neighboring ligaments was tested by (1) curve fitting the model parameters to the stress response of the ligament with highly aligned fibrils and then (2) using this model to predict the stress response of the ligament with disorganized fibrils by only changing the parameter values for fibril dispersion and mean fibril orientation. This study found that when using parameter values for fibril dispersion and mean fibril orientation based on confocal imaging data, the model strongly predicted the average stress response of ligaments with disorganized fibrils (\(R^{2}=0.97\)); however, the model only successfully predicted the individual stress response of ligaments with disorganized fibrils in half the specimens tested. Model predictions became worse when parameters for fibril dispersion and mean fibril orientation were not based on confocal imaging data. These findings emphasize the importance of collagen fibril alignment in ligament mechanics and help advance a mechanistic understanding of fibrillar networks in healthy and injured ligament.     

A constituent-based model for the nonlinear viscoelastic behavior of ligaments

This paper presents a constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues and in particular of ligaments. The constitutive law is a generalization of the well-known quasi-linear viscoelastic theory (QLV) in which the elastic response of the tissue and the time-dependent properties are independently modeled and combined into a convolution time integral. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the time-dependent regime by means of a suitably developed time discretization scheme. The time-dependent constitutive law is based on the postulate that a constituent-based relaxation behavior may be defined through two different stress relaxation functions: one for the isotropic matrix and one for the reinforcing (collagen) fibers. The constitutive parameters of the viscoelastic model have been estimated by curve fitting the stress relaxation experiments conducted on medial collateral ligaments (MCLs) taken from the literature, whereas the predictive capability of the model was assessed by simulating experimental tests different from those used for the parameter estimation. In particular, creep tests at different maximum stresses have been successfully simulated. The proposed nonlinear viscoelastic model is able to predict the time-dependent response of ligaments described in experimental works (Bonifasi-Lista et al., 2005, J. Orthopaed. Res., 23, pp. 67-76; Hingorani et al., 2004, Ann. Biomed. Eng., 32, pp. 306-312; Provenzano et al., 2001, Ann. Biomed. Eng., 29, pp. 908-214; Weiss et al., 2002, J. Biomech., 35, pp. 943-950). In particular, the nonlinear viscoelastic response which implies different relaxation rates for different applied strains, as well as different creep rates for different applied stresses and direction-dependent relaxation behavior, can be described.