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.
