Deep Wave Probing and Imaging of Heavy Tailed Fabric

University Of California-Irvine, Irvine CA

Investigators

Abstract

High resolution biomedical imaging is fundamentally important for early cancer detection, monitoring of drug efficiency, computer assisted surgery, and evaluating the health of tissue, organs and bones in general. New biomedical imaging techniques can also be applied in other areas of imaging and monitoring, such as remote sensing through the atmosphere and reflection seismology. This project will support the development and analysis of new techniques for biomedical imaging, integrating the work of specialists in applied mathematics, physics and biomedical engineering, as well as practitioners in biomedical imaging companies. Models for shear wave elasticity imaging will be developed and analyzed, which provides novel, pertinent, non-invasive biomarkers for early disease characterization and therapy follow-up. This technique also enables one to decipher which structural component contributes to the global mechanical tissue behavior, and this fundamental new understanding opens the gateway to quantify the vascular organization of tissue at the 10-100μm-scale via clinically available imaging methods. Abnormal vascular fabric is a key prognostic factor in cancer therapy, and its quantification for patient stratification and response to therapy has significant potential. The project provides research training opportunities for graduate students. A main objective of the project is to further the theory that describes the statistical structure of wave fields propagating through complex media, as well as use the theory in the context of classical and new applications for waves in random media. There is a focus on understanding waves in short- and long-range random media as well as with fractional governing equations, which is in part motivated by its relevance in tissue modeling. This media has a statistical structure with only power law decay of correlations, with such structure referred to as heavy tailed medium fabric. The analysis also exploits scale separations and involves scaling limits for stochastic differential equations. Novel techniques will be developed for differentiating between scattering effects and attenuation, which is a classical challenge for wave propagation while also having direct applications. In the context of biomedical imaging, such differentiation is important for proper tissue classification. New theory will also be developed for modeling waves with complex nonlinear contrast. A better understanding of propagation and mode coupling along boundaries as well as the transmission through and reflection from rough boundaries will be established for waves in random media. The novel approaches for random waves modeling developed in this project will also be of general interest in stochastic analysis. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.