TRANSCOSTAL PHASED-ARRAY REFOCUSING USING ITERATIVE SPARSE OPTIMIZATION AND THE SEMIDEFINITE RELAXATION METHOD

Open Access
Author:
Mcmahon, Daniel F
Area of Honors:
Electrical Engineering
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Mohamed Khaled Almekkawy, Thesis Supervisor
  • Julio Urbina, Honors Advisor
Keywords:
  • Ultrasound
  • HIFU
  • Optimization
  • Transcostal
  • Noninvasive
  • Cancer Therapy
Abstract:
Administration of High Intensity Focused Ultrasound (HIFU) treat to tumors in organs shadowed by the ribs is challenging because the ribs absorb ultrasound beams’ energy causing the temperature of the ribs to rise, while also distorting the beams, and limiting the focal heat deposition. As a result, the ribs necessitate the continued development of novel focusing algorithms that seek to address the difficulties that they present. In this paper, a new approach that iteratively removes transducer elements is introduced. The method builds on the Limited Power Deposition (LPD) method, which utilized Semidefinite Relaxation (SDR) as a means of relaxing otherwise nonconvex constraints into convex form. The method discussed in this paper iteratively induces sparsity using the one-norm squared as a convex surrogate for the zero-norm. A 1-MHz spherical phased-array is focused onto a target in an inhomogeneous medium in simulations to test the algorithms efficacy. The results of focusing the array with the suggested algorithm are compared to the ray tracing (shadowing) approach. The movement of the waves as they traveled from the array towards the target was modeled using a finite difference time domain propagation model. Temperature simulations that utilized the inhomogeneous Bioheat Transfer Equation (BHTE) were used to determine the temperature rise profile within the Region of Interest (ROI). These simulation results illustrate the benefits of the optimization based approach proposed in this paper over other sparse methods, such as the shadowing method. Accordingly, it is possible to retain the advantages that accompany sparse algorithms, like the shadowing method, without having as large of an impact on focal power deposition. For example, the shutoff transducers could be used for other purposes, such as motion tracking and subsequent refocusing. Due to the ribs’ influence on the ultrasound beam, the focal power deposition is lessened, and as a result, treatment times are increased. Due to the increased duration of treatment, considering the ROI to be static may lessen treatment efficacy. Thus, motion tracking would allow treatments of organs, such as the liver, that are both obscured by the ribs and constantly moving to be more effective. Alternatively, in situations where power conservation is essential, like field treatment administration, then elimination of transducers can act as a means of eliminating unnecessary power consumption.