September 2021
Volume 21, Issue 9
Open Access
Vision Sciences Society Annual Meeting Abstract  |   September 2021
Topological Smoothing of Retinotopic Maps
Author Affiliations & Notes
  • Yanshuai Tu
    Arizona State University
  • Duyan Ta
    Arizona State University
  • Zhong-Lin Lu
    New York University Shanghai
    New York University
    NYU-ECNU Institute of Brain and Cognitive Science at NYU Shanghai
  • Yalin Wang
    Arizona State University
  • Footnotes
    Acknowledgements  DMS-1413417, RF1AG051710, R01EB025032, R21AG065942, and DMS-1413417.
Journal of Vision September 2021, Vol.21, 2464. doi:
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      Yanshuai Tu, Duyan Ta, Zhong-Lin Lu, Yalin Wang; Topological Smoothing of Retinotopic Maps. Journal of Vision 2021;21(9):2464.

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      © ARVO (1962-2015); The Authors (2016-present)

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Retinotopic mapping (RM) is one of the central topics in vision science. Human RM can be obtained by analyzing functional magnetic resonance imaging (fMRI) signals of cortical responses to slowly moving visual stimuli on the retina. It is well-known in neurophysiology that RM is topological (i.e., neighborhood connectivity is preserved). However, the measured RM is often not topological because of the low signal-to-noise ratio and spatial resolution of fMRI. The topological violations make it difficult to precisely quantify properties of retinotopic maps. We developed a topological smoothing method for retinotopic maps. Specifically, we used Beltrami coefficient to define the topological condition, developed a mathematical model to quantify topological smoothing as a constrained optimization problem, and elaborated an efficient numerical method to solve the smoothing problem. The method can be applied to V1, V2, and V3 simultaneously. We evaluated the performance of the method using both synthetic data and retinotopy data from the Human Connectome Project (HCP). For the synthetic data, the proposed method generated topological and smooth retinotopic maps with higher accuracy than existing methods. For the HCP data, in which ~20% of the visual area is not topological, the proposed method completely fixed the topology violations without reducing the amount of variance accounted for in the fMRI time series. The method also allowed us to generate accurate and automatic boundary delineation, quantify angle distortions between the retina and visual cortex, and improve the measurement of cortical magnification factors (CMF) on the smoothed results. We found that angle distortion from the visual field to the cortical surface was less than 20° for a large part of V1, and the distortion was not symmetric along polar angle for the same eccentricity. Similarly, the CMF is also asymmetric along polar angle. Topological smoothing of retinotopic maps will enable many additional RM quantification.


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