Institute of Fundamental Technological Research

The paper presents a method that allows the thickness of a compact bone layer and longitudinal wave velocity in the bone to be determined simultaneously with the use of reflected waves, with particular emphasis on the case of layers when the propagation time through the layer is shorter than the time duration of the interrogating pulse.

The proposed method estimates simultaneously the thickness of the cortical bone layer and acoustic wave velocity by fitting the temporal spectrum of the simulated reflected wave to the spectrum of the reflected wave measured experimentally. For the purpose of echo-simulations the model of “soft tissue – compact bone layer – cancellous bone” was developed. Next, the cost function was defined as the least square error between the measured and simulated temporal spectra. Minimization of the cost function allowed us to determine the values of the parameters of the cortical bone layer which best fitted the measurements. To solve the optimization problem a simulated annealing algorithm was used.

The method was tested using acoustic data obtained at the frequency of 0.6 MHz and 1 MHz respectively for a custom designed bone mimicking phantom and a calf femur. For the cortical shell of the calf femur whose thickness varies from 2.1 mm to 2.4 mm and velocity of 2910 m/s, the relative errors of the thickness estimation ranged from 0.4% to 5.5%. The corresponding error of the acoustic wave velocity estimation in the layer was 3.1%. In the case of artificial bone the thickness of the cortical layer was equal to 1.05 and 1.2 mm and acoustic wave velocity was 2900 m/s. These parameters were determined with the errors ranging from 1.9% to 10.8% and from 3.9% to 4.5% respectively.

Bone quantitative ultrasound, Human cortical bone, Human cancellous bone, Ultrasound attenuation, Layered media

The aim of this work is to present preliminary results of the layer thickness assessment method based on optimization approach. The developed method is based on a multilayer model structure. The measured acoustic signal reflected from the layer is compared with a simulated signal on the basis of a multilayer model. The cost function is defined as the difference between the reflected signal measured using pulse echo approach and the simulated signal. The thickness of the solid layer is the parameter which minimizes the cost function yielding desired solution. Minimization of the cost function is performed with the simulated annealing algorithm. The results obtained with the developed method using measurement data of a custom design model are compared with the reference value and the accuracy of the method is checked. The relative error of the thickness estimation is 1.44 %.

Bone quantitative ultrasound, Human cortical bone, Human cancellous bone, Ultrasound attenuation, Layered media

Estimation of the thickness and sound velocity of cortical bone is important per se as well as for correcting measurements of cancellous bone properties. We propose a method that allows the thickness of a compact bone layer and longitudinal wave velocity in the bone to be determined simultaneously with the use of the reflected waves, with particular emphasis on the 1mm - 3mm thick bone layers corresponding to the thickness of the cortex of the human femur. The method was tested using ultrasonic data obtained from cortical bone phantoms and a fresh calf bone specimen. The results show that the method seems to be well suited to be employed for the determination of the thickness and acoustic wave velocity of the cortical bone layer.

Cortical bone, trabecular bone, thickness and velocities of cortical shell, reflected waves, BUA