Deep Wave Probing and Imaging of Heavy Tailed Fabric

高分辨率生物医学成像对于癌症早期检测、药物效率监测、计算机辅助手术以及总体上评估组织、器官和骨骼的健康状况至关重要。新的生物医学成像技术也可应用于成像和监测的其他领域，如大气遥感和反射地震学。该项目将支持生物医学成像新技术的开发和分析，整合应用数学、物理和生物医学工程方面的专家以及生物医学成像公司的从业人员的工作。建立和分析剪切波弹性成像模型，为早期疾病定性和治疗随访提供新的、有针对性的、非侵入性的生物标志物。这项技术还使人们能够破译哪些结构成分对全球机械组织行为有贡献，这一全新的理解打开了通过临床可用的成像方法在10-100μm尺度上量化组织血管组织的大门。血管结构异常是肿瘤治疗中的一个关键预后因素，它的量化对于患者分层和治疗反应具有重要的潜力。该项目为研究生提供研究培训机会。该项目的一个主要目标是深化描述波场在复杂介质中传播的统计结构的理论，并将该理论用于随机介质中波的经典和新应用。重点在于理解短程和长程随机介质中的波以及分数控制方程，这在一定程度上是因为它与组织建模的相关性。这种介质有一种统计结构，只有关联的幂衰减，这种结构被称为重尾介质组构。该分析还利用了尺度分离，并涉及随机微分方程的尺度限制。将开发新的技术来区分散射效应和衰减，这是波传播的一个经典挑战，同时也有直接的应用。在生物医学成像的背景下，这种区分对于正确的组织分类是重要的。还将发展新的理论来模拟具有复杂非线性对比度的波。对于随机介质中的波，将更好地理解沿边界的传播和模式耦合，以及通过粗糙边界的传输和反射。在这个项目中开发的随机波建模的新方法也将在随机分析中引起普遍的兴趣。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.