José Antonio Bea

Nonlinear mechanical property of tracheal cartilage: A theoretical and experimental study

BACKGROUND Despite being the stiffest airway of the bronchial tree, the trachea undergoes significant deformation due to intrathoracic pressure during breathing. The mechanical properties of the trachea affect the flow in the airway and may contribute to the biological function of the lung. METHOD A Fung-type strain energy density function was used to investigate the nonlinear mechanical behavior of tracheal cartilage. A bending test on pig tracheal cartilage was performed and a mathematical model for analyzing the deformation of tracheal cartilage was developed. The constants included in the strain energy density function were determined by fitting the experimental data. RESULT The experimental data show that tracheal cartilage is a nonlinear material displaying higher strength in compression than in tension. When the compression forces varied from -0.02 to -0.03N and from -0.03 to -0.04N, the deformation ratios were 11.03+/-2.18% and 7.27+/-1.59%, respectively. Both were much smaller than the deformation ratios (20.01+/-4.49%) under tension forces of 0.02 to 0.01N. The Fung-type strain energy density function can capture this nonlinear behavior very well, whilst the linear stress-strain relation cannot. It underestimates the stability of trachea by exaggerating the displacement in compression. This study may improve our understanding of the nonlinear behavior of tracheal cartilage and it may be useful for the future study on tracheal collapse behavior under physiological and pathological conditions.

Stress transfer properties of different commercial dental implants: a finite element study

Dental implantology has high success rates, and a suitable estimation of how stresses are transferred to the surrounding bone sheds insight into the correct design of implant features. In this study, we estimate stress transfer properties of four commercial implants (GMI, Lifecore, Intri and Avinent) that differ significantly in macroscopic geometry. Detailed three-dimensional finite element models were adopted to analyse the behaviour of the bone-implant system depending on the geometry of the implant (two different diameters) and the bone–implant interface condition. Occlusal static forces were applied and their effects on the bone, implant and bone–implant interface were evaluated. Large diameters avoided overload-induced bone resorption. Higher stresses were obtained with a debonded bone–implant interface. Relative micromotions at the bone–implant interface were within the limits required to achieve a good osseointegration. We anticipate that the methodology proposed may be a useful tool for a quantitative and qualitative comparison between different commercial dental implants.

EVALUATION OF THE PROBABILITY DISTRIBUTION OF CRACK PROPAGATION LIFE IN METAL FATIGUE BY MEANS OF PROBABILISTIC FINITE ELEMENT METHOD AND B-MODELS

Abstract In this paper, a new model for the prediction of the cumulative distribution function of fatigue life of structural elements during the crack propagation stage is established. This problem is considered as a cumulative damage process following the probabilistic approach of Bogdanoff and Kozin (B-models). The initial and final crack lengths, the crack propagation angle, the material fracture and elastic parameters and the external loads have been the random variables considered here. The theoretical bases of the model and the procedure to construct it are described in the forthcoming paragraphs such as several examples for mode I problems including the comparison with experimental results.

Engineered arterial models to correlate blood flow to tissue biological response

This paper reviews how biomedical engineers, in collaboration with physicians, biologists, chemists, physicists, and mathematicians, have developed models to explain how the impact of vascular interventions on blood flow predicts subsequent vascular repair. These models have become increasingly sophisticated and precise, propelling us toward optimization of cardiovascular therapeutics in general and personalizing treatments for patients with cardiovascular disease.

Corrections to B-models for fatigue life prediction of metals during crack propagation

In this paper a new model for the prediction of the Cumulative Distribution Function (CDF) of fatigue life of structural elements during the crack propagation stage is described. This problem is considered as a cumulative damage process following the probabilistic approach of Bogdanoff and Kozin [1] (B-models). The initial and final crack lengths, the crack propagation angle, the material fracture and elastic parameters and the external loads may be considered as random variables. In this initial approach, a linear approximation of the random variable ‘fatigue life’ and a truncated uniform distribution for the crack length variable are considered. Two corrections to this model are discussed: a second-order approximation of the fatigue life to compute its variance, and a modification of the Probability Density Distribution (PDD) of the crack length, which is now derived from the truncated uniform distributions of the initial and final crack lengths. Some examples for mode I are compared to the ones obtained using a Monte Carlo scheme with 400 000 samples, showing a good agreement and a much better performance of the corrected version of the model, specially for big standard deviations. Copyright

A random fatigue of mechanize titanium abutment studied with Markoff chain and stochastic finite element formulation

Abstract To measure fatigue in dental implants and in its components, it is necessary to use a probabilistic analysis since the randomness in the output depends on a number of parameters (such as fatigue properties of titanium and applied loads, unknown beforehand as they depend on mastication habits). The purpose is to apply a probabilistic approximation in order to predict fatigue life, taking into account the randomness of variables. More accuracy on the results has been obtained by taking into account different load blocks with different amplitudes, as happens with bite forces during the day and allowing us to know how effects have different type of bruxism on the piece analysed.

Theoretical and experimental studies on the nonlinear mechanical property of tracheal cartilage

The mechanical property of the trachea affects the flow in the airway and may contribute to the biological function of the lung. Like many other biological tissues, the tracheal cartilage is likely to be a nonlinear material. To investigate the nonlinearity of tracheal cartilage, Fung-type strain energy density function was used. A mathematical model for analyzing the deformation of tracheal cartilage was developed and a bending test on pig trachea was performed. By fitting the experimental data, the constants included in the strain energy density function were therefore determined. The experimental data shows that tracheal cartilage displays higher strength in compression than in extension. Fung-type strain energy density function can capture this nonlinear behavior very well, whilst the linear stress-strain relation cannot. This study contributes to a better understanding of the material of tracheal cartilage and further benefits to its mechanical behavior under physiological and pathological conditions.

A New Model to Study Fatigue in Dental Implants Based on Probabilistic Finite Elements and Cumulative Damage Model

The aim of this study was to predict the fatigue life of two different connections of a dental implant as in load transfer to bone. Two three-dimensional models were created and assembled. All models were subjected to a natural masticatory force of 118 N in the angle of 75° to the occlusal plane. All degrees of freedom in the inferior border of the cortical bone were restrained, and the mesial and distal borders of the end of the bone section were constrained. Fatigue material data and loads were assumed as random variables. Maximum principal stresses on bone were evaluated. Then, the probability of failure was obtained by the probabilistic approach. The maximum principal stress distribution predicted in the cortical and trabecular bone is 32 MPa for external connection and 39 MPa for internal connection. A mean life of 103 and 210 million cycles were obtained for external and internal connection, respectively. Probability cumulative function was also evaluated for both connection types. This stochastic model employs a cumulative damage model and probabilistic finite element method. This methodology allows the possibility of measured uncertainties and has a good precision on the results.

Long-Term Fatigue and Its Probability of Failure Applied to Dental Implants

It is well known that dental implants have a high success rate but even so, there are a lot of factors that can cause dental implants failure. Fatigue is very sensitive to many variables involved in this phenomenon. This paper takes a close look at fatigue analysis and explains a new method to study fatigue from a probabilistic point of view, based on a cumulative damage model and probabilistic finite elements, with the goal of obtaining the expected life and the probability of failure. Two different dental implants were analysed. The model simulated a load of 178 N applied with an angle of 0°, 15°, and 20° and a force of 489 N with the same angles. Von Mises stress distribution was evaluated and once the methodology proposed here was used, the statistic of the fatigue life and the probability cumulative function were obtained. This function allows us to relate each cycle life with its probability of failure. Cylindrical implant has a worst behaviour under the same loading force compared to the conical implant analysed here. Methodology employed in the present study provides very accuracy results because all possible uncertainties have been taken in mind from the beginning.

A Probabilistic Extended Finite Element Approach: Application to the Prediction of Bone Crack Propagation

The Extended Finite Element Method (XFEM), has become a well-known tool to simulate crack propagation problems using non-structured meshes avoiding the remeshing process usually needed in this type of problems and allowing the inclusion of appropriate shape functions that reflect the asymptotic displacement field, near the crack tip, via a partition of unity fracture approach. However, in this kind of numerical applications, all the variables involved have been considered as deterministic (defined by a single given value), despite the well-known uncertainty associated to many of them (external loads, geometry and material properties, among others). The combination of the XFEM and probabilistic techniques is here proposed and formulated allowing treating fracture mechanics problems from a probabilistic point of view. We present the implementation of this probabilistic extended finite element method and apply it to the prediction of the appearance and propagation of a femur’s neck fracture under probabilistic loads.