RESUMEN
Closed-form solutions for the effective rheological properties of a 2D viscoelastic drained porous medium made of a Generalized Maxwell viscoelastic matrix and pore inclusions are developed and applied for cortical bone. The in-plane (transverse) effective viscoelastic bulk and shear moduli of the Generalized Maxwell rheology of the homogenized medium are expressed as functions of the porosity and the viscoelastic properties of the solid phase. When deriving these functions, the classical inverse Laplace-Carson transformation technique is avoided, due to its complexity, by considering the short and long term approximations. The approximated results are validated against exact solutions obtained from the inverse Laplace-Carson transform for a simple configuration when the later is available. An application for cortical bone with assumption of circular pore in the transverse plane shows that the proposed approximation fit very well with experimental data.
Asunto(s)
Hueso Cortical , Elasticidad , Hueso Cortical/metabolismo , Porosidad , Reología , Viscosidad , Agua/metabolismoRESUMEN
The aim of this work is to evaluate the effects of the heterogeneity and anisotropy of material properties of cortical bone on its ultrasonic response obtained by using axial transmission method. The heterogeneity and anisotropy of material properties are introduced by using a parametric probabilistic model. The geometrical configuration of the tested sample is described by a tri-layer medium composed of a heterogeneous and anisotropic solid layer sandwiched between two acoustic fluid layers of which one of these layers is excited by an acoustic linear source. The numerical results focus on studying of an interest quantity, called velocity of the first arriving signal, showing that it strongly depends on the dispersion induced by statistical fluctuations of stochastic elasticity field.
Asunto(s)
Huesos/diagnóstico por imagen , Ultrasonido/métodos , Animales , Anisotropía , Simulación por Computador , Elasticidad , Humanos , Modelos Estadísticos , Movimiento (Física) , Análisis Numérico Asistido por Computador , Sonido , Procesos Estocásticos , Factores de Tiempo , UltrasonografíaRESUMEN
Cortical bone and the surrounding soft tissues are attenuating and heterogeneous media, which might affect the signals measured with axial transmission devices. This work aims at evaluating the effect of the heterogeneous acoustic absorption in bone and in soft tissues on the bone ultrasonic response. Therefore, a two-dimensional finite element time-domain method is derived to model transient wave propagation in a three-layer medium composed of an inhomogeneous transverse isotropic viscoelastic solid layer, sandwiched between two viscous fluid layers. The model couples viscous acoustic propagation in both fluid media with the anisotropic viscoelastic response of the solid. A constant spatial gradient of material properties is considered for two values of bone thicknesses (0.6 and 4 mm). In the studied configuration, absorption in the surrounding fluid tissues does not affect the results, whereas bone viscoelastic properties have a significant effect on the first arriving signal (FAS) velocity. For a thin bone, the FAS velocity is governed by the spatially averaged bone properties. For a thick bone, the FAS velocity may be predicted using a one-dimensional model.