Bone cortical thickness and porosity assessment using ultrasound guided waves: An ex vivo validation study

Abstract

Several studies showed the ability of the cortex of long bones such as the radius and tibia to guide mechanical waves. Such experimental evidence has given rise to the emergence of a category of quantitative ultrasound techniques, referred to as the axial transmission, specifically developed to measure the propagation of ultrasound guided waves in the cortical shell along the axis of long bones. An ultrasound axial transmission technique, with an automated approach to quantify cortical thickness and porosity is described. The guided modes propagating in the cortex are recorded with a 1-MHz custom made linear transducer array. Measurement of the dispersion curves is achieved using a two-dimensional spatio-temporal Fourier transform combined with singular value decomposition. Automatic parameters identification is obtained through the solution of an inverse problem in which the dispersion curves are predicted with a two-dimensional transverse isotropic free plate model. Thirty-one radii and fifteen tibiae harvested from human cadavers underwent axial transmission measurements. Estimates of cortical thickness and porosity were obtained on 40 samples out of 46. The reproducibility, given by the root mean square error of the standard deviation of estimates, was 0.11 mm for thickness and 1.9% for porosity. To assess accuracy, site-matched micro-computed tomography images of the bone specimens imaged at 9 μm voxel size served as the gold standard. Agreement between micro-computed tomography and axial transmission for quantification of thickness and porosity at the radius and tibia ranged from R=0.63 for porosity (root mean square error RMSE=1.8%) to 0.89 for thickness (RMSE=0.3 mm). Despite an overall good agreement for porosity, the method performs less well for porosities lower than 10%. The heterogeneity and general complexity of cortical bone structure, which are not fully accounted for by our model, are suspected to weaken the model approximation. This study presents the first validation study for assessing cortical thickness and porosity using the axial transmission technique. The automatic signal processing minimizes operator-dependent errors for parameters determination. Recovering the waveguide characteristics, that is to say cortical thickness and porosity, could provide reliable information about skeletal status and future fracture risk.

Ultrasound-Based Estimates of Cortical Bone Thickness and Porosity Are Associated With Nontraumatic Fractures in Postmenopausal Women: A Pilot Study

“…Fixed matrix properties did not take into account the inevitable interindividual variability of bone tissue properties . However, such a hypothesis has been found to yield reasonably accurate ex vivo identification of Ct.Th and Ct.Po of human radius and tibia specimens . This model simplification can be avoided using a model parametrized in terms of thickness and stiffness (ie., including four independent stiffness coefficients to account for the generally accepted transverse isotropy of cortical long bones measured axially).…”

“…(74) However, such a hypothesis has been found to yield reasonably accurate ex vivo identification of Ct.Th and Ct.Po of human radius and tibia specimens. (40) This model simplification can be avoided using a model parametrized in terms of thickness and stiffness (ie., including four independent stiffness coefficients to account for the generally accepted transverse isotropy of cortical long bones measured axially). Our group achieved concurrent estimates of both thickness and bulk wave velocities (directly reflecting the elastic properties) of cortical bone using such a transverse isotropic plate model.…”

“…Second, in the case of waveguide parameters estimation, instead of spanning all measurable waves, the testing vectors are limited to the guided modes of a dedicated cortical bone waveguide model . The waveguide model is a 2D transverse isotropic free plate, parametrized in terms of thickness and elasticity .…”

“…(29) Second, in the case of waveguide parameters estimation, instead of spanning all measurable waves, the testing vectors are limited to the guided modes of a dedicated cortical bone waveguide model. (40) The waveguide model is a 2D transverse isotropic free plate, parametrized in terms of thickness and elasticity. (37) Subsequently, we use an asymptotic homogenization approach to predict the mesoscopic stiffness coefficients from the microstructure, so that the elasticity of our model is parametrized in terms of porosity, assuming that the bone matrix is spatially homogeneous and uniform among individuals.…”

“…(39) We recently showed that BDAT combined with an appropriate waveguide model allows the concurrent identification of Ct.Th and Ct.Po of ex vivo human specimens. (40) In a pilot in vivo study, BDAT could identify Ct.Th nearly as accurately as conventional HRpQCT. (41) The assessment of Ct.Th and Ct.Po by BDAT may improve the identification of patients at high risk of fracture.…”