Mohamed Fellah

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

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.

Application of the Biot model to ultrasound in bone: Inverse problem

This paper concerns the ultrasonic characterization of human cancellous bone samples by solving the inverse problem using experimentally measured signals. The inverse problem is solved numerically by the least squares method. Five parameters are inverted: 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 ultrasonic propagation in cancellous bone is modelled using the Biot theory modified by the Johnson-Koplik-Dashen 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 waveforms. 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.

Direct and inverse scattering of transient acoustic waves by a slab of rigid porous material

This paper provides a temporal model of the direct and inverse scattering problem for the propagation of transient ultrasonic waves in a homogeneous isotropic slab of porous material having a rigid frame. This new time domain model of wave propagation takes into account the viscous and thermal losses of the medium as described by the model of Johnson et al. [D. L. Johnson, J. Koplik, and R. Dashen, J. Fluid. Mech. 176, 379 (1987)] and Allard [J. F. Allard (Chapman and Hall, London, 1993)] modified by a fractional calculus based method applied in the time domain. This paper is devoted to the analytical calculus of acoustic field in a slab of porous material. The main result is the derivation of the expression of the scattering operators (reflection and transmission) which are the responses of the medium to an incident acoustic pulse. In this model the reflection operator is the sum of two contributions: the first interface and the bulk of the medium. Experimental and numerical results are given as a validation of our model.

Measuring flow resistivity of porous materials at low frequencies range via acoustic transmitted waves

An acoustic transmissivity method is proposed for measuring flow resistivity of porous materials having rigid frame. Flow resistivity of porous material is defined as the ratio between the pressure difference across a sample and the velocity of flow of air through that sample per unit cube. The proposed method is based on a temporal model of the direct and inverse scattering problem for the diffusion of transient low-frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. The transmission scattering operator for a slab of porous material is derived from the response of the medium to an incident acoustic pulse. The flow resistivity is determined from the solution of the inverse problem. The minimization between experiment and theory is made in the time domain. Tests are performed using industrial plastic foams. Experimental and numerical results, and prospects are discussed.

Measuring the porosity of porous materials having a rigid frame via reflected waves: A time domain analysis with fractional derivatives

An ultrasonic reflectivity method is proposed for measuring porosity of porous materials having a rigid frame. Porosity is the relative fraction by volume of the air contained within a material. It is important as one of the several parameters required by acoustical theory to characterize porous materials like plastic foams and fibrous or granular materials. The proposed method is based on a temporal model of the direct and inverse scattering problem for the propagation of transient ultrasonic waves in a homogeneous isotropic slab of porous material having a rigid frame. This time domain model of wave propagation was initially introduced by the authors [Z. E. A. Fellah and C. Depollier, J. Acoust. Soc. Am. 107, 683 (2000)]. The viscous and thermal losses of the medium are described by the model devised by Johnson et al. [D. L. Johnson, J. Koplik, and R. Dashen, J. Fluid. Mech, 176, 379 (1987)] and Allard [J. F. Allard, Chapman and Hall, London, (1993)] modified by a fractional calculus-based method applie...

Measuring flow resistivity of porous material via acoustic reflected waves

An acoustic reflectivity method is proposed for measuring flow resistivity of porous materials having rigid frame. The flow resistivity of porous material is defined as the ratio between the pressure difference across a sample and the velocity of flow of air through that sample per unit cube. It is important as one of the several parameters required by acoustical theory to characterize porous materials like plastic foams and fibrous or granular materials. The proposed method is based on a temporal model of the direct and inverse scattering problem for the diffusion of transient low-frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. This time domain model of wave propagation was initially introduced by the authors [Z.E.A. Fellah and C. Depollier, J. Acoust. Soc. Am. 107, 683 (2000)]. The viscous losses of the medium are described by the model devised by Johnson et al. [D. L. Johnson, J. Koplik, and R. Dashen, J. Fluid. Mech. 176, 379 (1987)]. Reflection and transmissio...

Solution in time domain of ultrasonic propagation equation in a porous material

This paper provides an analytical solution in the time domain for the propagation of transient ultrasonic waves in a homogeneous isotropic porous material having a rigid frame. The coefficients of the propagation equation are constant and depend only on the acoustical parameters of the porous material. The propagation equation contains fractional derivative terms that describe viscous and thermal interactions between the solid and the fluid. The dynamic response of the material is obtained using the Laplace transform method. An experimental application to porous plastic foams is given to validate the solution of the propagation equation.

Transient ultrasound propagation in porous media using Biot theory and fractional calculus: application to human cancellous bone.

A temporal model based on the Biot theory is developed to describe the transient ultrasonic propagation in porous media with elastic structure, in which the viscous exchange between fluid and structure are described by fractional derivatives. The fast and slow waves obey a fractional wave equation in the time domain. The solution of Biots equations in time depends on the Green functions of each of the waves (fast and slow), and their fractional derivatives. The reflection and transmission operators for a slab of porous materials are derived in the time domain, using calculations in the Laplace domain. Their analytical expressions, depend on Greens function of fast and slow waves. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.

Measuring permeability of porous materials at low frequency range via acoustic transmitted waves

An acoustical transmission method is proposed for measuring permeability of porous materials having rigid frame. Permeability is one of the several parameters required by acoustical theory to characterize porous materials such as plastic foams and fibrous or granular materials. The proposed method is based on a temporal model of the direct and inverse scattering problem for the diffusion of transient low frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. This time domain model of wave propagation was initially introduced by the authors [Z.E.A Fellah and C. Depollier, J. Acoust. Soc. Am. 107, 683 (2000)]. The viscous losses of the medium are described by the model devised by Johnson et al. [J. Fluid. Mech. 176, 379 (1987)]. Reflection and transmission scattering operators for a slab of porous material are derived from the responses of the medium to an incident acoustic pulse. The permeability is determined from the expressions of these operators. Experimental and numerical validation results of this method are presented. This method has the advantage of being simple, rapid, and efficient.

Measuring static thermal permeability and inertial factor of rigid porous materials (L)

An acoustic method based on sound transmission is proposed for deducing the static thermal permeability and the inertial factor of porous materials having a rigid frame at low frequencies. The static thermal permeability of porous material is a geometrical parameter equal to the inverse trapping constant of the solid frame [Lafarge et al., J. Acoust. Soc. Am. 102, 1995 (1997)] and is an important characteristic of the porous material. The inertial factor [Norris., J. Wave Mat. Interact. 1, 365 (1986)] describes the fluid structure interactions in the low frequency range (1-3 kHz). The proposed method is based on a temporal model of the direct and inverse scattering problems for the propagation of transient audible frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. The static thermal permeability and the inertial factor are determined from the solution of the inverse problem. The minimization between experiment and theory is made in the time domain. Tests are performed using industrial plastic foams. Experimental and theoretical data are in good agreement. Furthermore, the prospects are discussed. This method has the advantage of being simple, rapid, and efficient.