Ultrasonically determined thickness of long cortical bones: Three-dimensional simulations of in vitro experiments.
It was reported in a previous study that simulated guided wave axial transmission velocities on two-dimensional (2D) numerically reproduced geometry of long bones predicted moderately real in vitro ultrasound data on the same bone samples. It was also shown that fitting of ultrasound velocity with simple analytical model yielded a precise estimate (UTh) for true cortical bone thickness. This current study expands the 2D bone model into three dimensions (3D). To this end, wave velocities and UTh were determined from experiments and from time-domain finite-difference simulations of wave propagation, both performed on a collection of 10 human radii (29 measurement sites). A 3D numerical bone model was developed with tuneable fixed material properties and individualized geometry based on X-ray computed tomography reconstructions of real bones. Simulated UTh data were in good accordance (root-mean-square error was 0.40 mm; r(2)=0.79, p<0.001) with true cortical thickness, and hence the measured phase velocity can be well estimated by using a simple analytical inversion model also in 3D. Prediction of in vitro data was improved significantly (by 10% units) and the upgraded bone model thus explained most of the variability (up to 95% when sites were carefully matched) observed in in vitro ultrasound data.
Moilanen
Petro
P
Université Pierre et Marie Curie - Paris 6, Laboratoire d'Imagerie Paramétrique, UMR7623, Paris, F-75005, France. pemoilan@cc.jyu.fi
Talmant
Maryline
M
Nicholson
Patrick H F
PH
Cheng
Sulin
S
Timonen
Jussi
J
Laugier
Pascal
P
D001842:Bone and Bones / Q000000981:diagnostic imaging*; D003198:Computer Simulation; D020342:Finite Element Analysis; D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D066298:In Vitro Techniques; D009716:Numerical Analysis, Computer-Assisted; D012680:Sensitivity and Specificity; D012984:Software; D014057:Tomography, X-Ray Computed; D014463:Ultrasonography / Q000379:methods*