Finite element modeling of acoustic wave propagation and energy deposition in bone during extracorporeal shock wave treatment

Abstract

It is well known that extracorporeal shock wave treatment is capable of providing a non-surgical and relatively pain free alternative treatment modality for patients suffering from musculoskeletal disorders but do not respond well to conservative treatments. The major objective of current work is to investigate how the shock wave (SW) field would change if a bony structure exists in the path of the acoustic wave. Here, a model of finite element method (FEM) was developed based on linear elasticity and acoustic propagation equations to examine SW propagation and deflection near a mimic musculoskeletal bone. High-speed photography experiments were performed to record cavitation bubbles generated in SW field with the presence of mimic bone. By comparing experimental and simulated results, the effectiveness of FEM model could be verified and strain energy distributions in the bone were also predicted according to numerical simulations. The results show that (1) the SW field will be deflected with the presence of bony structure and varying deflection angles can be observed as the bone shifted up in the z-direction relative to SW geometric focus (F2 focus); (2) SW deflection angels predicted by the FEM model agree well with experimental results obtained from high-speed photographs; and (3) temporal evolutions of strain energy distribution in the bone can also be evaluated based on FEM model, with varied vertical distance between F2 focus and intended target point on the bone surface. The present studies indicate that, by combining MRI/CT scans and FEM modeling work, it is possible to better understand SW propagation characteristics and energy deposition in musculoskeletal structure during extracorporeal shock wave treatment, which is important for standardizing the treatment dosage, optimizing treatment protocols, and even providing patient-specific treatment guidance in clinic.

Safe and Effective Treatment of Compromised Clavicle Fracture of the Medial and Lateral Third Using Focused Shockwaves

“…We see peak negative pressures in the close vicinity of the clavicle, which rapidly falls off with distance. A similar deflection to the peak positive pressures about the bone interface can be observed for the negative pressures [ 55 ]. Taking a closer look at the waveform recorded at the surface of the lung tissue, corresponding to the most considerable observed tensile pressure pmin = −0.68 MPa ( Figure 4 E), we see the expected enhanced negative pressure due to the reflection at the tissue/air interface.…”

Three-dimensional numerical analysis of wall stress induced by asymmetric oscillation of microbubble trains inside micro-vessels

“…In FEM simulations, it is normally recommended that the mesh size should be smaller than 1/6 of the wavelength. 23,38 Considering that the speed of sound in the blood and tissue is close to 1500 m/s, 39 the criterion for choosing the mesh size is that the grid should be less than 50 lm when ultrasound of frequency in the range of 1-5 MHz is applied. The mesh sizes we used are much smaller than 50 lm (i.e., 1/6 of wavelength, for a frequency of 5 MHz), thus more than adequately satisfying the conditions for utilizing FEM.…”

Toward a Unified Multiscale Computational Model of the Human Body's Immediate Responses to Blast-Related Trauma: A Review of the Scientific Literature

“…The methods provide accurate simulations of both the blast wave propagation and its interaction with the human head (Lockhart, 2010). FEMs were applied to both in vivo and in vitro blast-induced neurotrauma models (Panzer, Matthews, et al, 2012) in extracorporeal shock wave treatment of musculoskeletal disorders (Wang, Matula, et al, 2013), as well as many more applications.…”