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.