Novel pseudo-differential methods to drastically increase computational speed and accuracy for biomedical ultrasound imaging and focusing

Project Summary / Abstract The practical contribution of computational mathematics to ultrasound-based biomedical applications hinges on the efficiency and accuracy of algorithms to simulate the propagation of waves in models of biological media. Such algorithms lie at two extremes: oversimplified closed-form methods and overdone full-waveform

computational simulations based on differential equations. The former methods (such as constant-speed wave migration) are very fast, but their stringent assumptions are inaccurate for realistic biological media. The latter methods (such as finite differences/elements) are accurate but unnecessarily complex, requiring super-

computing resources to run. We propose a novel implementation of pseudo-differential algorithms to bridge these two extremes. This approach strikes a valuable balance between accuracy and complexity, thus resolving the bottleneck caused by the inefficiency of full-waveform simulations. Upon implementation of the proposed methods, the optimization of the insonation profile and/or inversion of

measurements could be fully automated, be deployed in real-time, and fit into the clinical/surgical workflow. Such a development would drastically expand the use of ultrasound in the clinical arena where there is a great need to monitor perfusion of organs to avoid ischemic injury and real-time assessment of therapeutic procedures.

Overall, our goal is to implement a novel, unexploited set of mathematical and computational tools to improve the speed and automation of ultrasound simulations to enhance ultrasound-based technologies in clinical environments with limited computational resources. Under the mentorship of the PIs, teams of undergraduate students at University of Texas at Tyler will participate

in the research study. This project provides an effective training ground for them to apply their education, and to experience what it is like to be a professional engineer working in an interdisciplinary team. The students will be exposed to state-of-the-art research on computational mathematics for biomedical imaging (integral geometry,

differential equations, signal processing, and computer programming). In addition to part-time employment during 21 weeks of school semesters at University of Texas at Tyler, the students will work as summer interns at the Predictive Analytics Laboratory of Baylor College of Medicine and Texas Children’s Hospital. This

internship program offers nine paid weeks focused on the proposed research project, attendance in research and professional development seminars designed for undergraduates, career development workshops, and designated housing near the workplace. These integrated practical activities will empower the students and offer

them opportunities to understand the impact of engineering on healthcare technologies.