RETRACTED: Experimental characterization of human cancellous bone via the first ultrasonic reflected wave – Application of Biot’s theory

Sadouki, Mustapha

doi:10.1016/j.apacoust.2020.107237

Cited by 3 publications

(9 citation statements)

References 48 publications

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“…Biot's equations are derived from linear elasticity equations governing the solid matrix, Navier-Stokes equations describing the behavior of the viscous fluid, and Darcy's law, which governs fluid flow within the porous matrix. The equations of motion for both the solid and fluid phases are expressed as follows [8,9,12]:…”

Section: Theoretical Modelmentioning

confidence: 99%

“…Here, α(ω) is a function of frequency called the dynamic tortuosity [10], which characterizes the viscous interactions between the fluid and the solid structure, significantly impacting acoustic wave damping in porous materials. At high frequencies, the expression for dynamic tortuosity α(ω) is given by the following [8,[10][11][12][13]: The theoretical framework we employ draws from the field of dynamic poroelasticity, originally formulated by Biot [9]. This theory provides a comprehensive and general description of the mechanical behavior of such porous media.…”

Section: Theoretical Modelmentioning

confidence: 99%

“…Ultrasonic wave propagation complexity in bones arises from factors such as saturating fluid properties [5], solid phase mechanical characteristics [6], anisotropy [7], and macroscopic structural parameters like porosity, tortuosity, and viscous characteristic length [7,8]. Developing a comprehensive theoretical model, such as Biot theory modified by Johnson, is crucial to address this complexity [9,10], aiding the solution of the inverse problem [4,[11][12][13] and enabling extraction of bone's physical and mechanical properties from ultrasonic measurements.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Modeling of a Transmission Coefficient for Ultrasonic Waves in Human Cancellous Bone

Sadouki,

Mahiou

2023

The 4th International Electronic Conference on Applied Sciences

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Section: Theoretical Modelmentioning

confidence: 99%

Section: Theoretical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical Modeling of a Transmission Coefficient for Ultrasonic Waves in Human Cancellous Bone

Sadouki,

Mahiou

2023

The 4th International Electronic Conference on Applied Sciences

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“…The porous material is a bi-phasic medium consisting of a solid part and a fluid part that saturates the pores. When the solid part is flexible, the two phases start moving simultaneously under excitation by an acoustic wave; in this case the dynamics of the movement is well described by Biot's theory [16][17][18]. In the case of a rigid material, the solid part remains immobile and the acoustic waves propagate only in the fluid.…”

Section: Acoustical Modelmentioning

confidence: 99%

“…( 17)) depends only on the flow resistivity σ and thickness L of the medium. Our objective is to find this two parameters simultaneously, supposedly unknown, by minimizing between the simulated reflected signal given by the expression (18) and the experimental reflected signal. The inverse problem then consists in finding the flow resistivity σ and thickness L of porous samples that minimize the function: [15] in the same position as the porous sample.…”

Section: Inverse Problemmentioning

confidence: 99%

Inverse Measurement of the Thickness and Flow Resistivity of Porous Materials via Reflected Low Frequency Waves-Frequency Approach

Sadouki¹

2021

Porous Fluids - Advances in Fluid Flow and Transport Phenomena in Porous Media

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A direct and inverse method is proposed for measuring the thickness and flow resistivity of a rigid air-saturated porous material using acoustic reflected waves at low frequency. The equivalent fluid model is considered. The interactions between the structure and the fluid are taken by the dynamic tortuosity of the medium introduced by Johnson et al. and the dynamic compressibility of the air introduced by Allard. A simplified expression of the reflection coefficient is obtained at very low frequencies domain (Darcy’s regime). This expression depends only on the thickness and flow resistivity of the porous medium. The simulated reflected signal of the direct problem is obtained by the product of the experimental incident signal and the theoretical reflection coefficient. The inverse problem is solved numerically by minimizing between simulated and experimental reflected signals. The tests are carried out using two samples of polyurethane plastic foam with different thicknesses and resistivity. The inverted values of thickness and flow resistivity are compared with those obtained by conventional methods giving good results.

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Experimental characterization of air-saturated porous material via low-frequencies ultrasonic transmitted waves

Sadouki

2021

Physics of Fluids

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An improved acoustic method is proposed for measuring the tortuosity and the viscous and thermal characteristic lengths of air-saturated porous materials via low-frequency ultrasonic transmitted waves (70 kHz–110 kHz). The equivalent fluid model is considered. The interaction between the saturated fluid and the structure is taken into account in two frequency response factors: the dynamic tortuosity of the medium and the dynamic compressibility of the air which are described by their high-frequency expansion in powers of the viscous and thermal skin depth, either limiting the expansion to the first two leading terms or the first three leading terms with the introduction of two new viscous and thermal shape factors. These two new factors play an important role in stabilizing and improving the inverted parameters of the tortuosity and the viscous and thermal characteristic lengths in the frequency band considered. The inverse problem is solved numerically in the frequency domain by minimizing the spectrum of simulated and experimental transmitted signals. Optimized parameters of tortuosity, viscous and thermal characteristic lengths, and viscous and thermal shape factors are obtained simultaneously. The tests are carried out with three samples of plastic foam. The results obtained by the two procedures are discussed and compared to those given in the literature.

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RETRACTED: Experimental characterization of human cancellous bone via the first ultrasonic reflected wave – Application of Biot’s theory

Cited by 3 publications

References 48 publications

Analytical Modeling of a Transmission Coefficient for Ultrasonic Waves in Human Cancellous Bone

Analytical Modeling of a Transmission Coefficient for Ultrasonic Waves in Human Cancellous Bone

Inverse Measurement of the Thickness and Flow Resistivity of Porous Materials via Reflected Low Frequency Waves-Frequency Approach

Experimental characterization of air-saturated porous material via low-frequencies ultrasonic transmitted waves

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