Fabric dependence of quasi-waves in anisotropic porous media

Cardoso, Luís; Cowin, Stephen C.

doi:10.1121/1.3557032

Cited by 29 publications

(28 citation statements)

References 94 publications

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“…The governing equations for anisotropic poroelasticity were developed and extended to include the dependence of the constitutive relations upon pore structure fabric (Cowin [35,36]). Dynamic poroelasticity was extended by Cardoso and Cowin [37] and Cowin and Cardoso [38] to include the pore structure fabric tensor as a variable. The pore structure of the RVE is assumed to be characterized by porosity and a pore structure fabric tensor F; thus, both J and T C ¼ M are functions of F and /.…”

Section: Fabric Dependence Of Microvelocity Averagingmentioning

confidence: 99%

Tortuosity and the Averaging of Microvelocity Fields in Poroelasticity

Souzanchi¹,

Cardoso²,

Cowin

2013

Journal of Applied Mechanics

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The relationship between the macro-and microvelocity fields in a poroelastic representative volume element (RVE) has not being fully investigated. This relationship is considered to be a function of the tortuosity: a quantitative measure of the effect of the deviation of the pore fluid streamlines from straight (not tortuous) paths in fluid-saturated porous media. There are different expressions for tortuosity based on the deviation from straight pores, harmonic wave excitation, or from a kinetic energy loss analysis. The objective of the work presented is to determine the best expression for tortuosity of a multiply interconnected open pore architecture in an anisotropic porous media. The procedures for averaging the pore microvelocity over the RVE of poroelastic media by Coussy and by Biot were reviewed as part of this study, and the significant connection between these two procedures was established. Success was achieved in identifying the Coussy kinetic energy loss in the pore fluid approach as the most attractive expression for the tortuosity of porous media based on pore fluid viscosity, porosity, and the pore architecture. The fabric tensor, a 3D measure of the architecture of pore structure, was introduced in the expression of the tortuosity tensor for anisotropic porous media. Practical considerations for the measurement of the key parameters in the models of Coussy and Biot are discussed. In this study, we used cancellous bone as an example of interconnected pores and as a motivator for this study, but the results achieved are much more general and have a far broader application than just to cancellous bone.

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Section: Fabric Dependence Of Microvelocity Averagingmentioning

confidence: 99%

Tortuosity and the Averaging of Microvelocity Fields in Poroelasticity

Souzanchi¹,

Cardoso²,

Cowin

2013

Journal of Applied Mechanics

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“…Analytical expressions were given in Cowin and Cardoso [26] for the velocity and attenu ation of each wave mode for the case in which the direction of wave propagation coincides with the normal to a plane of symme try of the anisotropic medium. Later, that study was extended to the propagation of waves along an arbitrary direction in orthotropic porous media [23]. Global changes in velocity of wave propagation depend on the porosity and material properties of the solid and fluid constituents (i.e., density and EC of tissue matrix and marrow), while directional changes of ultrasound wave veloc ity are a function of the porous media microarchitecture as quanti fied by the fabric tensor.…”

Section: Directionalmentioning

confidence: 99%

“…Global changes in velocity of wave propagation depend on the porosity and material properties of the solid and fluid constituents (i.e., density and EC of tissue matrix and marrow), while directional changes of ultrasound wave veloc ity are a function of the porous media microarchitecture as quanti fied by the fabric tensor. For the present study, the longitudinal fast wave velocity was computed using equations in Cardoso and Cowin [23] along three anatomical directions ML, SI, and AP, using the measurements of porosity and fabric from each trabecu lar bone sample. TMD from pCT was used to calculate the tissue modulus for each sample [30,33] and the apparent density of the solid constituent.…”

Section: Directionalmentioning

confidence: 99%

“…The role of anisotropic architecture on the mechanical properties o f trabecular bone was introduced by Cowin [17] using a fabric tensor F. The fabric tensor F is a quantitative stereological measure of the degree o f structural ani sotropy and the mechanical principal orientations o f cancellous bone. More recently, Cowin and Cardoso [23][24][25][26] introduced the fabric tensor in the wave propagation equations to calculate the velocity of longitudinal and shear waves in anisotropic porous m edia and along any direction within the porous m edia [23][24][25][26][27]. This approach provides the potential to use ultrasound mea surements in bone to examine tissue architecture in addition to bone mass.…”

Section: Introductionmentioning

confidence: 99%

“…However, the structure-function relationship between microarchitecture, acoustic, and mechanical properties in cancellous bone is highly complex. To better understand the relationship between microarchitecture, acoustic, and mechanical prop erties in trabecular bone, we recently developed an architecturedensity based approach for acoustic wave propagation in aniso tropic poroelastic media [23][24][25][26]. The role of anisotropic architecture on the mechanical properties o f trabecular bone was introduced by Cowin [17] using a fabric tensor F. The fabric tensor F is a quantitative stereological measure of the degree o f structural ani sotropy and the mechanical principal orientations o f cancellous bone.…”

Section: Introductionmentioning

confidence: 99%

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Changes of Elastic Constants and Anisotropy Patterns in Trabecular Bone During Disuse-Induced Bone Loss Assessed by Poroelastic Ultrasound

Cardoso

Schaffler

2015

Journal of Biomechanical Engineering

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Currently, the approach most widely used to examine bone loss is the measurement of bone mineral density (BMD) using dual X-ray absorptiometry (DXA). However, bone loss due to immobilization creates changes in bone microarchitecture, which in turn are related to changes in bone mechanical function and competence to resist fracture.Unfortunately, the relationship between microarchitecture and mechanical function within the framework of immobilization and antiresorptive therapy has not being fully investigated. The goal of the present study was to investigate the structure–function relationship in trabecular bone in the real-world situations of a rapidly evolving osteoporosis(disuse), both with and without antiresorptive treatment. We evaluated the structure–function relationship in trabecular bone after bone loss (disuse-induced osteoporosis)and bisphosphonate treatment (antiresorptive therapy using risedronate) in canine trabecular bone using lCT and ultrasound wave propagation. Microstructure values determined from lCT images were used into the anisotropic poroelastic model of wave propagation in order to compute the apparent elastic constants (EC) and elastic anisotropy pattern of bone. Immobilization resulted in a significant reduction in trabecular thickness (Tb.Th) and bone volume fraction (BV/TV), while risedronate treatment combined with immobilization exhibited a lesser reduction in Tb.Th and BV/TV, suggesting that risedronate treatment decelerates bone loss, but it was unable to fully stop it. Risedronate treatment also increased the tissue mineral density (TMD), which when combined with the decrease in Tb.Th and BV/TV may explain the lack of significant differences invBMD in both immobilization and risedronate treated groups. Interestingly, changes inapparent EC were much stronger in the superior–inferior (SI) direction than in the medial–lateral (ML) and anterior–posterior (AP) anatomical directions, producing changes in elastic anisotropy patterns. When data were pooled together, vBMD was able to explain 58% of ultrasound measurements variability, a poroelastic wave propagation analytical model (i.e., BMD modulated by fabric directionality) was able to predict 81%of experimental wave velocity variability, and also explained 91% of apparent EC and changes in elastic anisotropy patterns. Overall, measurements of vBMD were unable to distinguish changes in apparent EC due to immobilization or risedronate treatment.However, anisotropic poroelastic ultrasound (PEUS) wave propagation was able to distinguish functional changes in apparent EC and elastic anisotropy patterns due to immobilization and antiresorptive therapy, providing an enhanced discrimination of anisotropic bone loss and the structure–function relationship in immobilized and risedronate-treated bone, beyond vBMD.

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Microarchitecture and bone quality in the human calcaneus: Local variations of fabric anisotropy

Souzanchi¹,

Palacio-Mancheno²,

Borisov³

et al. 2012

Journal of Bone and Mineral Research

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The local variability of microarchitecture of human trabecular calcaneus bone is investigated using high resolution microCT scanning. The fabric tensor is employed as the measure of the microarchitecture of the pore structure of a porous medium. It is hypothesized that a fabric tensor-dependent poroelastic ultrasound approach will more effectively predict the data variance than will porosity alone. The specific aims of the present study are i) to quantify the morphology and local anisotropy of the calcaneus microarchitecture with respect to anatomical directions, ii) to determine the interdependence, or lack thereof, of microarchitecture parameters, fabric, and volumetric bone mineral density (vBMD), and iii) to determine the relative ability of vBMD and fabric measurements in evaluating the variance in ultrasound wave velocity measurements along orthogonal directions in the human calcaneus. Our results show that the microarchitecture in the analyzed regions of human calcanei is anisotropic, with a preferred alignment along the posterior-anterior direction. Strong correlation was found between most scalar architectural parameters and vBMD. However, no statistical correlation was found between vBMD and the fabric components, the measures of the pore microstructure orientation. Therefore, among the parameters usually considered for cancellous bone (i.e., classic histomorphometric parameters such as porosity, trabecular thickness, number and separation), only fabric components explain the data variance that cannot be explained by vBMD, a global mass measurement, which lacks the sensitivity and selectivity to distinguish osteoporotic from healthy subjects because it is insensitive to directional changes in bone architecture. This study demonstrates that a multi-directional, fabric-dependent poroelastic ultrasound approach has the capability of characterizing anisotropic bone properties (bone quality) beyond bone mass, and could help to better understand anisotropic changes in bone architecture using ultrasound.

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Fabric dependence of quasi-waves in anisotropic porous media

Cited by 29 publications

References 94 publications

Tortuosity and the Averaging of Microvelocity Fields in Poroelasticity

Tortuosity and the Averaging of Microvelocity Fields in Poroelasticity

Changes of Elastic Constants and Anisotropy Patterns in Trabecular Bone During Disuse-Induced Bone Loss Assessed by Poroelastic Ultrasound

Microarchitecture and bone quality in the human calcaneus: Local variations of fabric anisotropy

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