Adaptive Information Refinement Modeling of Nonlinear Shear Wave Propagation in Biological Tissue

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This project will combine high-resolution experiments with recent advances in mathematical information theory to describe the propagation of shear waves in human tissue and simulants, laying the foundation for development of novel medical diagnostic equipment and a better understanding of injuries such as concussion. Wave propagation through biological tissue is a fundamental physical process upon which numerous diagnostic and therapeutic techniques are based. Well-established diagnostic techniques include ultrasound imaging based upon high-frequency sound waves or magnetic resonance imaging based upon radio waves. A new window to investigate biological tissue is the use of mechanical shear waves that travel faster through stiff tissue and slower through soft tissue. By use of shear waves it is possible to effectively carry out palpation of internal organs otherwise accessible only by surgery. However, the propagation of shear waves in biological tissue is not well understood due to the large variability in wave velocity through different tissue types, much larger than that of sound waves. This can lead to counterintuitive effects such as formation of a concussion far from the immediate area of a head blow due to focusing of shear waves reflected by the cranium. Conversely, the large variability in shear wave velocity can be leveraged to carry out detailed investigations of biological tissue outside the capabilities of other diagnostic techniques. To enable such diagnostics there is a need to obtain a fundamental understanding of the relationship between tissue structure and shear wave propagation, as investigated in this project. Project activities include mentoring of graduate student and postdoctoral participants, integration of research results into data-driven modeling courses for undergraduates, as well as presentation of information theory to the general public through outreach activities at the Morehead Planetarium and University of North Carolina Science Days.Strain-stiffening, probably due to microscopic reorganization of filamentary structures in cells and the extracellular matrix, leads to the formation of shear shock waves induced by excitation amplitudes as low as 1% strain. The subsequent wavefront steepening can readily surpass 7% strain leading to tissue injury. The shear modulus can vary by five orders of magnitude in different tissue types and is close to zero in liquid-filled interstitia that exhibit random placement in organs such as the brain. Bulk-homogenized viscoelastic models with a discrete spectrum are inapplicable outside their calibration domain and are not linked by physical principles to the specific tissue. This study pursues a combined experimental-theoretical approach to development of scale-dependent homogenized models of shear wave propagation in highly heterogeneous biological tissue. High-resolution, 1024 channel measurements at 10 kHz and 1 micrometer resolution are used to construct detailed images of shear wave propagation through biological tissue and phantoms. A multiple-scale computational model is constructed that uses information-theoretic concepts such as mutual information to link the different simulation levels, offering a new perspective on and development of traditional adaptive mesh and model refinement. Results from this investigation will be generally applicable to nonlinear, multiscale stochastic systems that do not exhibit scale separation. Both experimental results and computational code will be available through literate programming and reproducible research practices.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.