A numerical study about the determination of parameters in an incompressible and linearly elastic solid / Estudo numérico sobre a determinação de parâmetros em um sólido elástico-linear e incompressível

AUTOR(ES)
DATA DE PUBLICAÇÃO

2008

RESUMO

The theory of classical linear elasticity is used to model of problems in medical physics that are related to the determination of elastic parameters of biological tissues from the measurement in vivo, or, in vitro of either displacements or strains. Based on experimental observations, which indicate that the abnormal biological tissues have different mechanical behavior from normal biological tissues, researchers have modeled these tissues as an incompressible, heterogeneous, and isotropic linear elastic solid. In this work a class of plane problems related to the determination of the shear elastic modulus µ of biological tissues is examined. A non-iterative numerical procedure to obtain an approximate solution to these problems from known displacement fields is proposed. The displacement fields are obtained from experiments that are possible to reproduce in laboratory. The experiments are quasi-static and are simulated numerically using the finite element method. Results for the distribution of µ in long, straight cylinders of rectangular cross-sections, containing either centered or eccentric circular inclusions that are more, or, less stiff than the surrounding elastic medium, are presented. Additionally, the results obtained in this study are compared with results of other researchers who use dynamical experiments. In this sense, two cases of centered circular inclusions are solved by using an adaptation of the dynamical case to the static case. Finally, the case of an inclusion with a complex geometry that is six times more rigid than the surrounding medium is solved. In all cases analyzed, the results are satisfactory, despite the fact that they were obtained with a reduced number of finite elements. It should be noted that no method of regularization has been used to treat the displacement data obtained from the simulated experiments. This work is of great interest in the detection of cancerous tumours, such as those in the breasts and in the prostate, and in the differential diagnosis of biological tissues.

ASSUNTO(S)

elastografia elasticidade linear clássica classical linear elasticity problema inverso inverse problem finite element method biological tissues método dos elementos finitos tecidos biológicos elastography

ACESSO AO ARTIGO

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