Mathematical and Statistical Modeling and Methodology for Topics in Diffusion Tensor Imaging

Diffusion tensor imaging is a non-invasive magnetic resonance imaging technology that can be used to analyze the complex neuronal network of the brain. Currently, brain connectivity measurements are complicated and are difficult to validate due to a high level of noise. This project aims to model the noise in measurements and substantially improve the ability of scientific and medical end-users to make confident decisions about fiber tracts in the brain.

Ultimately, this project aspires to improve early diagnostic tools for brain diseases and disorders such as Alzheimer's disease, traumatic brain injury, and multiple sclerosis. The results of the research are expected to help further develop diffusion tensor imaging technology as a reliable and practical routine clinical procedure. The investigators, with expertise in statistics, mathematics, imaging physics, engineering, and neuroscience, are also training an interdisciplinary team of young researchers, who will gain valuable exposure to both mathematical and neuroscience aspects of this project through regular meetings, graduate courses in nonparametric statistics and image processing, and other research group activities.

The group also plans to stimulate interest of K-12 students on how to use "math and stat" to understand brain wiring structures.

Integral curves are natural models for a variety of scientific phenomena, from axonal fibers in the brain, to jet streams in the atmosphere, to road outlines for self-driving cars. Traditionally, they are modeled as solutions to the orientation distribution functions defined on fields of direction vectors that are observed with noise in a 3D domain.

Advances in brain imaging technology can now provide highly complex directional information, such as longitudinal data, manifolds constructed out of integral curves, and graphic structures of the underlying axonal anatomy. Individual integral curves as well as their bundles traced using this enhanced directional data provide the potential to dramatically increase our understanding of biological phenomena such as the structural integrity of the axonal fibers and to assist in selecting an optimal scanning protocol in brain MRI.

However, the estimators for the statistical properties of individual integral curves and their bundles based on the new data are not well understood. In this project, the PIs aim to provide a solid theoretical foundation for linking integral curve estimation in 3D-4D-6D fields of complex directional data with underlying graphical noise structures and to apply the new methodology to address several practical problems in diffusion tensor imaging (DTI) and high angular resolution diffusion imaging (HARDI), technologies commonly used in brain MRI.

Specifically, the goals are (1) longitudinal modeling of the structural integrity of the axonal fibers, (2) modeling and assessing the uncertainty of a bundle of fibers, (3) searching for optimal numbers of diffusion directions and shells within a reasonable scan time, (4) equalizing methods for the fiber tracking characterization, and (5) deriving statistically optimal designs for data acquisition protocols. This project strives to improve DTI/HARDI not only as a reliable neuroscience research tool but also as a reliable and practical imaging technique for routine clinical applications.

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.