Many important developments in medical ultrasound are enabled by large-scale ultrasound simulations, which are essential for the design, evaluation, and optimization of new devices and applications. Despite the pervasiveness of computer simulations in medical ultrasound, numerous problems in diagnostic and therapeutic ultrasound remain unsolved, where better numerical models are expected to play a crucial role in the solution to these problems. In particular, signi?cant improvements are needed in the available software for simulations of shock waves produced by histotripsy transducers to facilitate effective noninvasive treatments of liver, prostate, and brain tumors. Better, more effective simulation software is required to enable improvements in shear wave imaging of liver ?brosis, thyroid tumors, and breast tumors, and enhanced software tools are needed for simulations of ultrafast imaging and of other dynamic ultrasound imaging sequences. Improved models and methods are also needed for the attenuation of transient compressional and shear waves in soft tissues, which is signi?cant for shear wave imaging, ultrasound microscopy, quantitative ultrasound, and ultrasound tomography. The main goal of this proposal is to create valuable new software resources that will enable new solutions of fundamental problems in medical ultrasound through the completion of three speci?c aims.
In Aim 1, we propose to create new transient nonlinear full-wave ultrasound simulations for histotripsy using the discontinuous Galerkin (DG) method. Unlike ?nite difference, ?nite element, pseudo-spectral, and k-space methods, the discontinuous Galerkin method is ideal for full-wave models of shock waves evaluated on high performance computing systems. This is important because all of the existing nonlinear full-wave modeling tools for medical ultrasound that are based on these other methods encounter signi?cant dif?culties when attempting to model highly nonlinear pressure ?elds for histotripsy.
In Aim 2, we propose to create transient full-wave simulations of shear waves with the discontinuous Galerkin method, which has similar advantages when applied to simulations of shear waves. We will also address another limitation of present shear wave simulations by augmenting the proposed shear wave simulations with a fractional calculus model that describes the attenuation and dispersion of shear waves in soft tissue.
In Aim 3, we propose to create new programs for graphics processing units and compute clusters that further accelerate all of the existing programs in FOCUS, the `Fast Object-oriented C++ Ultrasound Simulator,' in order to facilitate effective numerical modeling of ultrafast imaging and other ultrasound imaging sequences.
Aim 3 will also integrate a new numerical technique into FOCUS that models the power law attenuation and dispersion described by several different time-fractional and space-fractional models developed for medical ultrasound. Overall, we anticipate that the simulation software produced by the proposed effort has great potential to achieve both immediate and long-term impact across the entire ?eld of medical ultrasound, particularly for applications of histotripsy, shear wave elasticity imaging, and other therapeutic and diagnostic ultrasound applications.
Many important research developments in diagnostic and therapeutic ultrasound are enabled by large-scale ultrasound simulations, which are essential tools that are routinely employed in the design, evaluation, and optimization of ultrasound devices and applications. However, the existing software tools for simulating histotripsy, shear wave elasticity imaging, ultrafast imaging, and related methods in medical ultrasound have several funda- mental weaknesses that are presently hindering progress in these emerging areas. To address these de?ciencies, we propose to develop new high performance computing-based solutions to these and other important problems in therapeutic and diagnostic ultrasound.
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| Meerschaert, Mark M; Magin, Richard L; Ye, Allen Q (2016) Anisotropic fractional diffusion tensor imaging. J Vib Control 22:2211-2221 |
| Zhao, Xiaofeng; McGough, Robert J (2016) Time-domain comparisons of power law attenuation in causal and noncausal time-fractional wave equations. J Acoust Soc Am 139:3021 |
| Meerschaert, Mark M; Sabzikar, Farzad; Chen, Jinghua (2015) TEMPERED FRACTIONAL CALCULUS. J Comput Phys 293:14-28 |
| Meerschaert, Mark M; Schilling, René L; Sikorskii, Alla (2015) STOCHASTIC SOLUTIONS FOR FRACTIONAL WAVE EQUATIONS. Nonlinear Dyn 80:1685-1695 |
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| Meerschaert, Mark M; Sabzikar, Farzad (2014) STOCHASTIC INTEGRATION FOR TEMPERED FRACTIONAL BROWNIAN MOTION. Stoch Process Their Appl 124:2363-2387 |
| Anderson, Paul L; Meerschaert, Mark M; Zhang, Kai (2013) FORECASTING WITH PREDICTION INTERVALS FOR PERIODIC ARMA MODELS. J Time Ser Anal 34:187-193 |
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