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Proceedings Paper

Characterizing human retinotopic mapping with conformal geometry: a preliminary study
Author(s): Duyan Ta; Jie Shi; Brian Barton; Alyssa Brewer; Zhong-Lin Lu; Yalin Wang
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Paper Abstract

Functional magnetic resonance imaging (fMRI) has been widely used to measure the retinotopic organization of early visual cortex in the human brain. Previous studies have identified multiple visual field maps (VFMs) based on statistical analysis of fMRI signals, but the resulting geometry has not been fully characterized with mathematical models. Here we test whether VFMs V1 and V2 obey the least restrictive of all geometric mappings; that is, whether they are anglepreserving and therefore maintain conformal mapping. We measured retinotopic organization in individual subjects using standard traveling-wave fMRI methods. Visual stimuli consisted of black and white, drifting checkerboards comprising rotating wedges and expanding rings to measure the cortical representations of polar angle and eccentricity, respectively. These representations were then projected onto a 3D cortical mesh of each hemisphere. By generating a mapped unit disk that is conformal of the VFMs using spherical stereographic projection and computing the parameterized coordinates of the eccentricity and polar angle gradients, we computed Beltrami coefficients to check whether the mapping from the visual field to the V1 and V2 cortical representations is conformal. We find that V1 and V2 exhibit local conformality. Our analysis of the Beltrami coefficient shows that selected regions of V1 and V2 that contain reasonably smooth eccentricity and polar angle gradients do show significant local conformality, warranting further investigation of this approach for analysis of early and higher visual cortex. These results suggest that such a mathematical model can be used to characterize the early VFMs in human visual cortex.

Paper Details

Date Published: 21 March 2014
PDF: 10 pages
Proc. SPIE 9034, Medical Imaging 2014: Image Processing, 90342A (21 March 2014); doi: 10.1117/12.2043570
Show Author Affiliations
Duyan Ta, Arizona State Univ. (United States)
Jie Shi, Arizona State Univ. (United States)
Brian Barton, Univ. of California, Irvine (United States)
Alyssa Brewer, Univ. of California, Irvine (United States)
Zhong-Lin Lu, The Ohio State Univ. (United States)
Yalin Wang, Arizona State Univ. (United States)

Published in SPIE Proceedings Vol. 9034:
Medical Imaging 2014: Image Processing
Sebastien Ourselin; Martin A. Styner, Editor(s)

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