Arturo N. Natali

Viscoelastic Response of the Periodontal Ligament : An Experimental-Numerical Analysis

A viscoelastic constitutive model for the periodontal ligament (PDL) capable of accounting for large strains, anisotropy, and inelastic time-dependent effects was developed. Anisotropy characteristics are determined by the composite nature of the tissue and, in particular, by the distribution of collagen fibres. Time-dependent viscous phenomena are due to microstructural modifications during loading, such as fluid fluxes moving through the solid matrix and the internal rearrangement of fibers and constitutive adaptation. The viscoelastic model presented here was implemented in a general purpose finite element code. In vitro experimental tests were carried out on the PDL specimens of adult pigs to obtain stress-relaxation and cyclic stress-strain curves. The comparison of experimental and numerical results revealed good correspondence and confirmed the capability of the formulation assumed to properly interpret the viscoelastic behavior of the PDL.

Ultrasound velocity and attenuation in cancellous bone samples from lumbar vertebra and calcaneus.

Abstract: We report a study of ultrasound velocity and broadband ultrasound attenuation (BUA) in human cancellous bone samples. The influence of density and microarchitecture on ultrasound propagation in cancellous bone was examined. A total of 20 samples from vertebra L1 and 21 from calcanei were studied. The direction of ultrasound propagation was anteroposterior in the vertebra and lateromedial in the calcaneus. The relationships between ultrasonic parameters and density of bone samples, apparent ash density, trabecular bone volume (BV/TV) and trabecular thickness (Tb.Th) were analyzed using a simple linear model and a multiple regression model. Velocity of ultrasound and BUA were positively correlated with density and morphometric parameters, in both vertebra and calcaneus. The best correlation was found between velocity and bone sample density in vertebra (r= 0.961, p < 0.0001) and the worst between velocity and trabecular thickness in calcaneus (r= 0.632, p= 0.002). The best correlation for BUA was with BV/TV in vertebra (r= 0.960, p < 0.0001). Using the stepwise regression procedure, BV/TV only was selected as significant for BUA and apparent ash density with Tb.Th for velocity, in both vertebra and in calcaneus. The possible influence of trabecular configuration on ultrasonic parameters is discussed, emphasizing the different slopes of regression lines obtained for vertebra and calcaneus, sites with different architecture of trabecular bone.

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 analysis of heel pad tissues mechanics

This paper presents a visco-hyperelastic constitutive model developed to describe the biomechanical response of heel pad tissues. The model takes into account the typical features of the mechanical response such as large displacement, strain phenomena, and non-linear elasticity together with time-dependent effects. The constitutive model was formulated, starting from the analysis of the complex structural and micro-structural configuration of the tissues, to evaluate the relationship between tissue histology and mechanical properties. To define the constitutive model, experimental data from mechanical tests were analyzed. To obtain information about the mechanical response of the tissue so that the constitutive parameters could be established, data from both in vitro and in vivo tests were investigated. Specifically, the first evaluation of the constitutive parameters was performed by a coupled deterministic and stochastic optimization method, accounting for data from in vitro tests. The comparison of constitutive model results and experimental data confirmed the models capability to describe the compression behaviour of the heel pad tissues, regarding both constant strain rate and stress relaxation tests. Based on the data from additional experimental tests, some of the constitutive parameters were modified in order to interpret the in vivo mechanical response of the heel pad tissues. This approach made it possible to interpret the actual mechanical function of the tissues.

Constitutive modelling of inelastic behaviour of cortical bone.

A visco-elasto-plastic constitutive model is formulated for investigating the mechanics of cortical bone tissue, accounting for an anisotropic configuration and post-elastic and time-dependent phenomena. The constitutive model is developed with reference to experimental data obtained from literature on the behaviour of cortical bone taken from multiple samples. Regarding the constitutive model, a specific procedure based on a coupled deterministic and stochastic method is applied in order to determine the values of the constitutive parameters with regard to human samples. The procedure entails processing of data deduced from mechanical tests to achieve relationships between permanent and total strain, elastic modulus and strain rate, and creep elastic modulus and time. Numerical results obtained by using a finite element model are compared with tensile experimental data on cortical bone including the post-elastic range and creep phenomena. The model shows an excellent capability to describe the tensile behaviour of the cortical bone for the specific mechanical condition analysed.

A Transversally Isotropic Elasto-damage Constitutive Model for the Periodontal Ligament

A numerical formulation of an elasto-damage constitutive model was developed and implemented in a finite element software to investigate the biomechanical response of the periodontal ligament (PDL). The mathematical framework accounts for the description of large strains, anisotropy and inelastic phenomena. The anisotropic mechanical response is caused by the spatial orientation of the sub-structures of the tissue, such as collagen fibres. Inelastic behaviour, induced by high level strains, is modelled by means of damage models. In vitro experimental testing on PDL samples from pigs was performed to obtain tensile stress-strain curves. A finite element analysis is presented in order to define a general numerical approach. A comparison of numerical and experimental data is provided in order to show the reliability and effectiveness of the formulation assumed.

Investigation on the load-displacement curves of a human healthy heel pad: In vivo compression data compared to numerical results

The aims of the present work were to build a 3D subject-specific heel pad model based on the anatomy revealed by MR imaging of a subjects heel pad, and to compare the load-displacement responses obtained from this model with those obtained from a compression device used on the subjects heel pad. A 30 year-old European healthy female (mass=54kg, height=165cm) was enrolled in this study. Her left foot underwent both MRI and compression tests. A numerical model of the heel region was developed based on a 3D CAD solid model obtained by MR images. The calcaneal fat pad tissue was described with a visco-hyperelastic model, while a fiber-reinforced hyperelastic model was formulated for the skin. Numerical analyses were performed to interpret the mechanical response of heel tissues. Different loading conditions were assumed according to experimental tests. The heel tissues showed a non-linear visco-elastic behavior and the load-displacement curves followed a characteristic hysteresis form. The energy dissipation ratios measured by experimental tests (0.25±0.02 at low strain rate and 0.26±0.03 at high strain rate) were comparable with those evaluated by finite element analyses (0.23±0.01 at low strain rate and 0.25±0.01 at high strain rate). The validity and efficacy of the investigation performed was confirmed by the interpretation of the mechanical response of the heel tissues under different strain rates. The mean absolute percentage error between experimental data and model results was 0.39% at low strain rate and 0.28% at high strain rate.

Decellularized human skeletal muscle as biologic scaffold for reconstructive surgery

Engineered skeletal muscle tissues have been proposed as potential solutions for volumetric muscle losses, and biologic scaffolds have been obtained by decellularization of animal skeletal muscles. The aim of the present work was to analyse the characteristics of a biologic scaffold obtained by decellularization of human skeletal muscles (also through comparison with rats and rabbits) and to evaluate its integration capability in a rabbit model with an abdominal wall defect. Rat, rabbit and human muscle samples were alternatively decellularized with two protocols: n.1, involving sodium deoxycholate and DNase I; n.2, trypsin-EDTA and Triton X-NH4OH. Protocol 2 proved more effective, removing all cellular material and maintaining the three-dimensional networks of collagen and elastic fibers. Ultrastructural analyses with transmission and scanning electron microscopy confirmed the preservation of collagen, elastic fibres, glycosaminoglycans and proteoglycans. Implantation of human scaffolds in rabbits gave good results in terms of integration, although recellularization by muscle cells was not completely achieved. In conclusion, human skeletal muscles may be effectively decellularized to obtain scaffolds preserving the architecture of the extracellular matrix and showing mechanical properties suitable for implantation/integration. Further analyses will be necessary to verify the suitability of these scaffolds for in vitro recolonization by autologous cells before in vivo implantation.

A numerical model for investigating the mechanics of calcaneal fat pad region.

The present paper pertains to the definition of a numerical model of the calcaneal fat pad region, considering a structure composed of adipose and connective tissues organized in fibrous septae and adipose chambers. The mechanical response is strongly influenced by the structural conformation, as the dimension of adipose chambers, the thickness of connective septae walls and the mechanical properties of the different soft tissues. In order to define the constitutive formulation of adipose tissues, experimental data from pig specimens are considered, according to the functional similarity, while the mechanical response of connective tissue septae is assumed with regard to the mechanical behaviour that characterize ligaments. Different numerical models are provided accounting for the variation of chambers dimensions, septae wall thickness and tissues characteristics. The spiral angles of collagen fibres within the septae influence the capability of the structure to withstand the bulging of chambers. The analysis considers different orientation of the fibres. The response of calcaneal fat pad region is evaluated in comparison with experimental data from unconfined compression tests. The present work provides a preliminary approach to enhance the correlation between the structural conformation and tissues mechanical properties towards the biomechanical response of overall heel pad region.

Investigation of bone inelastic response in interaction phenomena with dental implants

OBJECTIVES The aim of the paper is to analyze the effects of misfits in multi-implant oral prostheses caused by defects in manufacturing of bar connecting implants. The consequent stress-strain state on peri-implant bone tissue must be carefully considered because of the significant effects induced. MATERIALS AND METHODS The case of a two-implant prosthesis connected by a titanium cast bar in the pre-molar mandible region is investigated. The complex geometry requires the use of refined finite element model. In consideration of the action induced on the bone tissue, a specific constitutive model that includes inelastic behavior is implemented. The linear misfits considered, estimated with reference to experimental works already present in the literature, induce relevant strains in the peri-implant bone tissue up to a post-elastic phase. Relaxation phenomena are also evaluated. The interaction between the bone and implant is modeled by using contact elements to represent possible detachments at the bone-implant interface. RESULTS The response of the bone material is reported with regard to the stress/strain field induced, evaluating the inelastic behavior in terms of plastic and relaxation responses. The effects on the peri-implant bone tissue at the interface are evaluated. SIGNIFICANCE The analysis confirms that the interaction phenomena between the multi-implant oral prostheses and bone induced by the misfit defects of normal intensity induce significant strain in the bone tissue and inelastic phenomena must be taken into account. Local permanent strains of bone tissue and relaxation phenomena represent short-term tissue response for a correct interpretation of the real biomechanical behavior of multiple implant frames.