Collaborative Research: Quantifying Human Retinotopic Mapping by Conformal Geometry

Project: Research project

Project Details


Project Summary The advent of functional magnetic resonance imaging (fMRI), a non-invasive, high spatial resolution technique for measuring brain activities, has provided a wealth of data on visual cortical organizations. Although numerous studies have been devoted to discovering and validating different retinotopic maps in the visual cortex, limited progress has been made in theoretical modeling of the maps to obtain quantitative descriptions and discover the relationship between the retinotopic maps of different visual areas. This proposal focuses on discovering, investigating, and exploring computational theorems and algorithms in conformal geometry, and produce theoretically sound and practically efficient solutions for quantifying retinotopic maps. Intellectual Merit. Analyses of retinotopic maps pose a number of exciting research questions that will be studied in this proposal: How to model retinotopic maps to capture the underlying neuronal anatomical structure? How to model the relationship between retinotopic maps of different visual areas? How to obtain quantitative descriptions of retinotopic maps in a population based study to establish biologically meaningful biomarkers for normal and abnormal visual functions or therapeutic efficacies? To address these questions, we propose an integrated research and education plan with three components: (1) the Ricci flow method to compute hyperbolic conformal mapping of the retinotopic map on the cortical surface to the Poincare disk. One key feature of the proposed formulation is that it computes the intrinsic surface geometrical metrics that are determined by the underlying anatomical structure. (2) a Mobius transformation based solution for mapping between different retinotopic visual areas, in which a least squares formulation is employed for robust estimations; (3) a Teichmuller theory approach to quantify population properties of the retinotopic maps, in which extremal quasiconformal mapping is explored to build quantitative models for fMRI responses in individual subjects. The major contribution in computational mathematics is to discover theorems and invent computational algorithms for quasiconformal Teichmuller theory, which has significant applications in a number of fields. The major contribution in neuroscience is the development of a coherent mathematical theory for modeling neuronal organizations, which may lead to non-invasive biomarkers of visual functions and eventually help improve and cure visual deficits. The success of this project will largely improve the state-of-the-art in computational quasiconformal Teichmuller theory and theoretical approach to retinotopic mapping, and broaden these research areas by opening up and addressing many new research themes. Broader Impact. The work outlined in this proposal will have applications in a number of research fields, including (1) Conformal geometry: The proposed research unifies and connects a variety of computational conformal geometry techniques and tackles several open problems. We anticipate that the proposed research will help create an exciting interdisciplinary environment for graduate and undergraduate students as well as postdocs and an ideal framework for teaching conformal geometry, providing students with a broader context in which various components may fit together. (2) Visual neuroscience: The algorithms and tools developed in this project will have a direct impact on visual neuroscience, as they will be applied to analyze and quantify the retinotopic maps in early visual areas. It will enable researchers to develop normative models of retinotopy and discover quantitative relationship between retinotopic maps and visual deficits. (3) Related Fields: conformal geometry has applications in many other fields, including computer vision, computer graphics, and wireless sensor network. (4) Integrated Education: This project will facilitate the development of new courses and laboratory infrastructure for knowledge discovery from brain imaging data. It will provide a unique opportunity for students/researchers from computer science to learn neuroscience more efficiently and more effectively. The funding will allow continuation of ongoing efforts to actively recruit and advise students from under-represented groups.
Effective start/end date7/1/146/30/18


  • National Science Foundation (NSF): $208,000.00

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