Ultrasonic characterization of human cancellous bone using the Biot theory: Inverse problem

Abstract

This paper concerns the ultrasonic characterization of human cancellous bone samples by solving the inverse problem using experimental transmitted signals. The ultrasonic propagation in cancellous bone is modeled using the Biot theory modified by the Johnson et al. model for viscous exchange between fluid and structure. The sensitivity of the Young modulus and the Poisson ratio of the skeletal frame is studied showing their effect on the fast and slow wave forms. The inverse problem is solved numerically by the least squares method. Five parameters are inverted: the porosity, tortuosity, viscous characteristic length, Young modulus, and Poisson ratio of the skeletal frame. The minimization of the discrepancy between experiment and theory is made in the time domain. The inverse problem is shown to be well posed, and its solution to be unique. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.

Wave propagation in stereo-lithographical (STL) bone replicas at oblique incidence

“…It has been found that the predictions are particularly sensitive to the assumed values of viscous characteristic length. The 'best-fit' characteristic length values for the two replicas cited in Table 1 are about 13 times those found for real bone which lie between 5 and 10 lm [3,5]. This is consistent with the physical scaling of the replicas.…”

“…Cortical bone may generally be considered to be solid; cancellous bone consists of a complex open-celled porous network of rod-and plate-shaped elements termed trabeculae. In order to understand the dependence of ultrasound propagation, in particular, upon the material and structural properties of cancellous bone, Biot-based theories have been used extensively [1][2][3][4][5][6][7][8][9]. Biot theory predicts two compressional waves, often referred to as 'fast' and 'slow', when the waves propagating through the solid frame of bone and marrow are in-phase and out-of-phase respectively, and a shear wave.…”

Transient Acoustic Wave Propagation in Porous Media

“…It is diffusive at low frequencies and propagative at high frequencies. In this section, the direct and inverse scattering problems for the ultrasonic propagation in porous material having an elastic frame are solved [42][43][44][45][46]. An experimental application on human cancelous bone is discussed [42,43].…”

“…The sensitivity of E b and ν b has been examined in Ref. [43] As an application of this model, some numerical simulations are compared with experimental results. Experiments are performed in water using two broadband Panametrics A 303S plane piezoelectric transducers with a central frequency of 1 MHz in water, and diameter of 1cm.…”

Use of global sensitivity analysis to assess the soil poroelastic parameter influence

“…Obtaining structural images of a porous material, and estimating its physical properties, is a topic of considerable interest in many branches of activities in geophysics, underwater acoustics, civil engineering, and biomechanics [1][2][3][4][5][6][7][8].…”