James M. Drake | Searcharxiv

arXiv2018

A Bayesian approach for energy-based estimation of acoustic aberrations in high intensity focused ultrasound treatment

High intensity focused ultrasound is a non-invasive method for treatment of diseased tissue that uses a beam of ultrasound to generate heat within a small volume. A common challenge in application of this technique is that heterogeneity of the biological medium can defocus the ultrasound beam. Here we reduce the problem of refocusing the beam to the inverse problem of estimating the acoustic aberration due to the biological tissue from acoustic radiative force imaging data. We solve this inverse problem using a Bayesian framework with a hierarchical prior and solve the inverse problem using a Metropolis-within-Gibbs algorithm. The framework is tested using both synthetic and experimental datasets. We demonstrate that our approach has the ability to estimate the aberrations using small datasets, as little as 32 sonication tests, which can lead to significant speedup in the treatment process. Furthermore, our approach is compatible with a wide range of sonication tests and can be applied to other energy-based measurement techniques.

physics.med-ph↗

arXiv1996

Mathematical pressure volume models of the cerebrospinal fluid

Numerous mathematical models have emerged in the medical literature over the past two decades attempting to characterize the pressure and volume dynamics the central nervous system compartment. These models have been used to study he behavior of this compartment under such pathological clinical conditions s hydrocephalus, head injury and brain edema. The number of different pproaches has led to considerable confusion regarding the validity, accuracy or appropriateness of the various models. In this paper we review the mathematical basis for these models in a mplified fashion, leaving the mathematical details to appendices. We show at most previous models are in fact particular cases of a single basic differential equation describing the evolution in time of the cerebrospinal fluid pressure (CFS). Central to this approach is the hypothsis that the rate change of CSF volume with respect to pressure is a measure of the compliance of the brain tissue which as a consequence leads to particular models epending on the form of the compliance funtion. All such models in fact give essentially no information on the behavior of the brain itself. More recent models (solved numerically using the Finite Element Method) have begun to address this issue but have difficulties due to the lack of information about the mechanical properties of the brain. Suggestions are made on how development of models which account for these chanical properties might be developed.

math.NA↗