A Biot model for the determination of material parameters of cancellous bone from acoustic measurements

2018 ◽  
Vol 34 (8) ◽  
pp. 085009 ◽  
Author(s):  
Hua Chen ◽  
Robert P Gilbert ◽  
Philippe Guyenne
Keyword(s):  
Cancellous Bone ◽  
Acoustic Measurements ◽  
Biot Model ◽  
Material Parameters

scholarly journals DETERMINATION OF THE PARAMETERS OF CANCELLOUS BONE USING HIGH FREQUENCY ACOUSTIC MEASUREMENTS II: INVERSE PROBLEMS

2007 ◽  
Vol 15 (02) ◽  
pp. 199-220 ◽  
Author(s):  
JAMES L. BUCHANAN ◽  
ROBERT P. GILBERT
Keyword(s):  
Cancellous Bone ◽  
High Frequency ◽  
Acoustic Pressure ◽  
Measured Data ◽  
Acoustic Measurements ◽  
Biot Model ◽  
Parameter Recovery ◽  
Recovery Algorithm ◽  
Poroelastic Media

In a precursor to this article the Biot model was used to model poroelastic media. The question this article addresses is whether the sort of experiments described by McKelvie and Palmer, Williams, and Hosokawa and Otani can be used to determine the parameters of the Biot model. A method of computing acoustic pressure in the low 100 kHz range was developed in Buchanan and Gilbert, "Determination of the parameters of cancellous bone using high frequency acoustic measurements," which appeared in Math. Comput. Modelling. In the present work a parameter recovery algorithm which uses parallel processing is developed and tested. It is found that when it is assumed that the agreement between calculated and measured data is about two digits, porosity can be determined to within about 1–2% and permeability, pore size and the bulk moduli to within about 40%, but in most cases less than 20%.

DETERMINATION OF THE PARAMETERS OF CANCELLOUS BONE USING LOW FREQUENCY ACOUSTIC MEASUREMENTS

2004 ◽  
Vol 12 (02) ◽  
pp. 99-126 ◽  
Author(s):  
JAMES L. BUCHANAN ◽  
ROBERT P. GILBERT ◽  
KHALDOUN KHASHANAH
Keyword(s):  
Cancellous Bone ◽  
Low Frequency ◽  
Acoustic Measurements ◽  
Biot Model ◽  
Poroelastic Media ◽  
High Degree

The Biot model is widely used to model poroelastic media. Several authors have studied its applicability to cancellous bone. In this article the feasibility of determining the Biot parameters of cancellous bone by acoustic interrogation using frequencies in the 5–15 kHz range is studied. It is found that the porosity of the specimen can be determined with a high degree of accuracy. The degree to which other parameters can be determined accurately depends upon porosity.

Determination of cancellous bone density using low frequency acoustic measurements

2008 ◽  
Vol 87 (10-11) ◽  
pp. 1213-1225 ◽  
Author(s):  
Robert P. Gilbert ◽  
Philippe Guyenne ◽  
George C. Hsiao
Keyword(s):  
Bone Density ◽  
Cancellous Bone ◽  
Low Frequency ◽  
Acoustic Measurements

scholarly journals Determination of anisotropic elastic parameters from morphological parameters of cancellous bone for osteoporotic lumbar spine

2021 ◽  
Author(s):  
Christoph Oefner ◽  
Elena Riemer ◽  
Kerstin Funke ◽  
Michael Werner ◽  
Christoph-Eckhard Heyde ◽  
...  
Keyword(s):  
Finite Element ◽  
Lumbar Spine ◽  
Cancellous Bone ◽  
Elastic Constants ◽  
Bone Volume ◽  
Human Bone ◽  
Homogenization Theory ◽  
Elastic Parameters ◽  
Anisotropic Elastic

AbstractIn biomechanics, large finite element models with macroscopic representation of several bones or joints are necessary to analyze implant failure mechanisms. In order to handle large simulation models of human bone, it is crucial to homogenize the trabecular structure regarding the mechanical behavior without losing information about the realistic material properties. Accordingly, morphology and fabric measurements of 60 vertebral cancellous bone samples from three osteoporotic lumbar spines were performed on the basis of X-ray microtomography (μCT) images to determine anisotropic elastic parameters as a function of bone density in the area of pedicle screw anchorage. The fabric tensor was mapped in cubic bone volumes by a 3D mean-intercept-length method. Fabric measurements resulted in a high degree of anisotropy (DA = 0.554). For the Young’s and shear moduli as a function of bone volume fraction (BV/TV, bone volume/total volume), an individually fit function was determined and high correlations were found (97.3 ≤ R2 ≤ 99.1,p < 0.005). The results suggest that the mathematical formulation for the relationship between anisotropic elastic constants and BV/TV is applicable to current μCT data of cancellous bone in the osteoporotic lumbar spine. In combination with the obtained results and findings, the developed routine allows determination of elastic constants of osteoporotic lumbar spine. Based on this, the elastic constants determined using homogenization theory can enable efficient investigation of human bone using finite element analysis (FEA).

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