Background Information
Extracorporeal Shock Wave Therapy (ESWT) is a noninvasive technique for the treatment of a variety of musculoskeletal conditions such as delayed union of fractures, plantar fasciitis and calcified tendonitis of the shoulder. Shock waves were first used medically as lithotripsy (ESWL) to pulverize hardened calcified deposits such as kidney stones. This technique was first use beyond lithotripsy to treat calcifications in the shoulder as these deposits are similar to renal calculi. Later it was shown to improve bone regeneration in the treatment of non-unions, which are bone fractures that fail to heal over time. In lithotripsy, a shock wave is generated in a liquid bath, focused through the use of an ellipsoid reflector and it then propagates into the body where it strikes the area of interest. Current numerical models are limited to simplified situations because the structure of the wave is highly nonlinear and therefore difficult to model with traditional finite difference and finite element techniques. I would like to use high-resolution finite volume methods to capture this nonlinear behavior and model the shock wave propagation in bone and tissue. This approach has been successfully applied to many problems in acoustic or elastic wave propagation in heterogeneous media.
UW ESWT Research Group
At the University of Washington we have an interdisciplinary group that is interested in better understanding ESWT. The following are some of the ways we are investigating this problem.Lithotripter Experiments
Dr. Tom Matula and Dr. Mike Bailey at the Applied Physics Lab (APL) have performed many experiments using Dornier HM3 lithotripsy device. The following series of images shows the interaction of the shockwave with an acrylic cylinder. This experiment was performed by Brian Maconoghy.Dr. Michael Chang is an orthopedic surgeon at the University of Washington Medical Center and will be using the Storz devices to perform various experiments.
Dr. Randy Ching is the head of the Applied Biomechanics Lab and is part of a group that is able to rapidly prototype 3D bone models. They reconstruct a 3D image from CT scan data and use this to create plastic bones. We have been able to use both the plastic and digital version of the bone data in our experiments. The plastic bone has been used by Tom Matula's group for cavitation path experiments. I have performed numerical experiments for comparison with the laboratory work using the digital version of the same 3D bone.
Numerical Experiments
We are currently modeling shock wave propagation and reflection using the Euler equations of gas dynamics with a modified equation of state and the linear elasticity equations. These sets of equations can be written in conservation law form and are therefore well suited to numerical approximation by finite volume methods. My work to this point has involved the use of a Godunov-type method, which utilizes Riemann solvers in the wave propagation algorithm to model the physical system. I have been able to obtain results for some model two- and three- dimensional problems by using the CLAWPACK software package developed by Randy LeVeque at the University of Washington.
ResultsESWT pulse propagating into a foot (2d test):
CT Scan Image and regions identified as bone:
Computational domain with four materials: brass, water/tissue, air, bone
animation of computational results
zoomed in animation of Schlieren plots
Computation of Compression, Tension and Shear in a foot (2D test):
These calculations will be useful in determining where energy is deposited or where tissue damage occurs as a result of ESWT treatment.
3D computation of maximum tension with comparison to laboratory experiment.
Additional information can be found here.
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