Jozef Vanderoost

The correlation between the SOS in trabecular bone and stiffness and density studied by finite-element analysis

For the clinical assessment of osteoporosis (i.e., a degenerative bone disease associated with increased fracture risk), ultrasound has been proposed as an alternative or supplement to the dual-energy X-ray absorptiometry (DEXA) technique. However, the interaction of ultrasound waves with (trabecular) bone remains relatively poorly understood. The present study aimed to improve this understanding by simulating ultrasound wave propagation in 15 trabecular bone samples from the human lumbar spine, using microcomputed tomography-based finite-element modeling. The model included only the solid bone, without the bone marrow. Two structural parameters were calculated: the bone volume fraction (BV/TV) and the structural (apparent) elastic modulus (Es), and the ultrasound propagation parameter speed of sound (SOS). Relations between BV/TV and Es were similar to published experimental relations. At 1 MHz, correlations between SOS and the structural parameters BV/TV and Es were rather weak, but the results can be explained from the specific features of the trabecular structure and the intrinsic material elastic modulus Ei. In particular, the systematic differences between the three main directions provide information on the trabecular structure. In addition, at 1 MHz the correlation found between the simulated SOS values and those calculated from the simple bar equation was poor when the three directions are considered separately. Hence, under these conditions, the homogenization approach - including the bar equation - is not valid. However, at lower frequencies (50-300 kHz) this correlation significantly improved. It is concluded that detailed analysis of ultrasound wave propagation through the solid structure in various directions and with various frequencies, can yield much information on the structural and mechanical properties of trabecular bone.

Microstructural quality of vertebral trabecular bone can be assessed from ultrasonic wave propagation

Ultrasound is extensively studied as an alternative diagnostic “screening” tool for osteoporosis. However, only a few aspects about the interaction of ultrasonic waves with bone tissue are understood, primarily based on statistical correlations. Therefore, our long-term aim is to obtain a more mechanistic interpretation of ultrasonic wave propagation through bone microstructure. For this study our aim was to quantify the interplay between ultrasound frequency and bone microstructure in determining wave propagation. Three-dimensional (3D) numerical simulations were performed on 15 human trabecular bone samples from the lumbar spine (4×4×4 mm3). The 3D representation of trabecular bone architecture was obtained using microcomputed tomography at a resolution of 14 micrometer. The simulations were performed using commercial finite element (FE) software (MSC/Nastran), validated for this application. Three frequencies (1 MHz, 300 kHz and 50 kHz) were analyzed, and the velocity of wave propagation (Speed of Sound, SOS) was calculated. SOS showed no correlation with bone volume fraction (BV/TV) and a better correlation with the apparent elastic modulus. The variables were calculated in the three main directions of the bone sample. Our simulations at 50 kHz and 300 kHz frequency showed an excellent agreement between FE-calculated SOS and the SOS estimated with the bar velocity equation (R2 = 0.93 and R2 = 0.85 respectively). For 1 MHz, this correlation was significantly lower (R2 = 0.66), but could be substantially improved by including several morphometric parameters in a multiple regression (R2 = 0.79).

Microstructural simulation of ultrasonic wave propagation through vertebral bone samples

The use of ultrasound as an alternative diagnostic ldquoscreeningrdquo tool for osteoporosis has extensively been studied. One ultrasound parameter that has shown promise is the speed-of-sound (SOS) as it has been correlated experimentally to bone strength. Unfortunately, to date, a complete mechanical understanding of these findings is still missing. The aim of this study was therefore to look into the direction dependency of SOS, and the possibility to predict the microstructure starting from SOS. Fifteen human trabecular bone samples (4times4times4 mm3) from the lumbar spine were acquired; the samples had been scanned using micro-CT (resolution 14 micron) in order to obtain the 3D representation of their trabecular bone architecture. Three-dimensional numerical simulations were subsequently performed on all samples using a finite element (FE) approach (ANSYS, Inc) based on the general equations of motion. As such, SOS could be estimated. Additionally, the apparent elastic modulus ES was calculated directly from the FE model. All simulations were performed at a frequency of 1 MHz in the three main directions of the bone sample (resulting in 45 simulations): anterior-posterior (AP), medio-lateral (ML) and cranio-caudal (CC). Two groups can be distinguished when the relationship between ES and SOS is studied. The first group contains the measurements in the CC direction. They display high velocity values and a wide range of elastic moduli. The calculations in the transverse directions (AP and ML) are situated in the second group. This group is characterized by low values of the structural elastic moduli and a wide range of velocities. The direction dependency of these results could be understood by a simple model of trabecular bone. For the lumbar spine, this simple model has main trabeculae in the CC direction and smaller struts, arranged randomly connecting the main trabeculae, in the AP and ML direction. The simulated velocity is the velocity of the fastest wave through the bone sample, i.e., the wave that covers the shortest distance through the trabeculae. From these results can be concluded that ultrasonic wave propagation is direction dependent and this dependency can help in the characterization of the strength of the trabecular bone.

Simulation of ultrasound wave propagation through trabecular bone samples with and without bone marrow

For the clinical assessment of osteoporosis, ultrasound has been proposed as an alternative or supplement to the Dual‐Energy X‐ray Absorptiometry technique. However the interaction of ultrasound waves with (trabecular) bone remains relatively poorly understood. The aim of the present study was to improve the understanding of this interaction by simulating ultrasound wave propagation in fifteen trabecular bone samples from the human lumbar spine, using μCT based Finite Elements Modelling. The model included only the solid bone, without the bone marrow. Two structural parameters were calculated: the bone volume fraction (BV/TV) and the structural (apparent) elastic modulus (Es), and the ultrasound parameter Speed Of Sound (SOS). At 1 MHz, correlations between SOS and the parameters BV/TV and Es were rather weak but the results can be explained from the specific features of the trabecular structure and the intrinsic material elastic modulus Ei. The correlation found between the simulated SOS values and those...

THE CORRELATION BETWEEN SOS IN TRABECULAR BONE AND STIFFNESS AND DENSITY STUDIED BY FEM

For the clinical assessment of osteoporosis, i.e. a degenerative bone disease associated with increased fracture risk, ultrasound has been proposed as an alternative or supplement to the Dual-Energy X-ray Absorptiometry technique. However the interaction of ultrasound waves with (trabecular) bone remains relatively poorly understood. The aim of the present study was to improve the understanding of this interaction by simulating ultrasound wave propagation in human trabecular bone samples.