Abstract
The non-intrusiveness and low cost of ultrasonic interrogation is motivating the development of new means of detection of osteoporosis and other bone deficiencies. Bone is a porous media saturated with a viscous fluid and could thus be well characterized by the Biot model. The main purpose of this work is to present an in vitro methodology for the identification of the properties and structural parameters of the bone, adopting a statistical Bayesian inference technique using ultrasonic reflected signals at normal incidence. It is, in this respect, a companion paper to a previous work [J. Acoust. Soc. Am. 146, 3 (2019), pp. 1629-1640], where ultrasonic transmitted signals were considered. This approach allows the retrieval of some important parameters that characterize the bone structure and associated uncertainties. The method was applied to seven samples of bone extracted from femoral heads, immersed in water, and exposed to ultrasonic signals with a center frequency of ≈500 kHz. For all seven samples, signals at different sites were acquired to check the method robustness. The porosity, pore mean size and standard deviation, and the porous frame bulk modulus were all successfully identified using only ultrasonic reflected signals.
Highlights
Osteoporosis affects bone density and microstructure [1], reducing bone quality and increasing the risk of fractures
To avoid the invasive treatments that current radiographic or neutron activation technologies require for bone analysis, quantitative ultrasound assessments have been considered for more than 30 years [3,4,5,6,7,8,9,10,11,12,13,14,15,16]
The ill-posedness of the inverse problem was emphasized by the authors: if not enough prior information is available, different solutions to the inverse problems can be found
Summary
Osteoporosis affects bone density and microstructure [1], reducing bone quality and increasing the risk of fractures. It becomes possible to attempt an inverse problem, where the observation of a certain acoustic quantity (here an ultrasonic reflected signal) is used to infer the values of certain parameters of interest This was done previously with the Biot model, using impedance tube measurements [23], reflected and transmitted ultrasonic waves [24] and, in our previous work, using transmitted ultrasonic waves only [25]. Ultrasonic reflected waves are considered in this work at almost normal incidence on porous samples immersed in water The reason behind this choice of studying only the reflected waves is that in some cases, the observation of a transmitted wave is made difficult due to the high dissipation of waves within the bone samples.
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