Ultrasonic wave propagation in human cancellous bone: Application of Biot theory

Abstract

Ultrasonic wave propagation in human cancellous bone is considered. Reflection and transmission coefficients are derived for a slab of cancellous bone having an elastic frame using Biot's theory modified by the model of Johnson et al. [J. Fluid Mech. 176, 379-402 (1987)] for viscous exchange between fluid and structure. Numerical simulations of transmitted waves in the time domain are worked out by varying the modified Biot parameters. The variation is applied to the governing parameters and is about 20%. From this study, we can gain an insight into the sensitivity of each physical parameter used in this theory. Some parameters play an important role in slow-wave wave form, such as the viscous characteristic length lambda and pore fluid bulk modulus Kf. However, other parameters play an important role in the fast-wave wave form, such as solid density rhos and shear modulus N. We also note from these simulations that some parameters such as porosity phi, tortuosity alpha(infinty), thickness, solid bulk modulus Ks, and skeletal compressibility frame Kb, play an important role simultaneously in both fast and slow wave forms compared to other parameters which act on the wave form of just one of the two waves. The sensitivity of the modified Biot parameters with respect to the transmitted wave depends strongly on the coupling between the solid and fluid phases of the cancellous bone. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.

A Review of the State of Art in Applying Biot Theory to Acoustic Propagation through the Bone

“…Of these, the various forms of Biot theory have shown some promise. That by Fellah et al [26], has been found to give excellent agreement with data obtained from transmitting ultrasonic pulses through water-filled samples of human cancellous bone. Using another version of Biot theory, Lee et al [36] have observed that the phase velocity is approximately non-dispersive and the attenuation coefficient linearly increases with frequency.…”

“…Fellah et al [26] have presented an analytical model of the reflection and transmission coefficient of a slab of cancellous bone with an elastic frame based on the Biot theory modified by Johnson et al [42] to describe the viscous interaction between fluid and structure. By comparing predictions with laboratory data on ultrasonic pulse transmission through water-filled samples of human cancellous bone, Fellah et al [26] have concluded that the modified Biot theory using Johnson et al [42] model is suitable for describing the propagation of ultrasonic wave in cancellous bone. A significant attraction of the Biot theory is that it includes structurally dependent parameters including permeability and tortuosity as well as the elastic constants of the porous frame and frame material (Allard [44]).…”

Influence of cancellous bone microstructure on two ultrasonic wave propagations in bovine femur: An in vitro study

“…Its inhomogeneity makes its interaction with ultrasound complex. However, the porous structure of cancellous bone causes an interesting phenomenon in which two longitudinal waves appear ͑Biot, 1956a͑Biot, , 1956bHosokawa and Otani, 1997;Hosokawa and Otani, 1998;Hoffmeister et al, 2000;Kaczmarek et al, 2002;Cardoso et al, 2003;Fellah et al, 2004;Hughes et al, 1999. The cited studies have reported that the fast wave is mainly associated with the porous network structure of trabeculae ͑solid part͒ and that the slow wave is associated with the soft tissue ͑bone marrow͒ that fills the pore space of the trabeculae.…”

A generalized recursive convolution method for time-domain propagation in porous media

“…Propagation of transient signals in porous media has important practical applications, for instance, in bioacoustics to characterize bone properties (Cardoso et al, 2003;Fellah et al, 2004;Ha€ ıat et al, 2008), in building acoustics to determine acoustic absorption of materials (Fellah et al, 2003) or in outdoor sound propagation to account for the reflection of waves from the ground. For this type of signal, time-domain methods are advantageous over frequencydomain methods.…”