Diffeomorphic registration for retinotopic maps of multiple visual regions

Adaptive smoothing of retinotopic maps based on Teichmüller parametrization

Retinotopic mapping, the mapping between visual inputs on the retina and neural responses on the cortical surface, is one of the fundamental topics in visual neuroscience. In human studies, retinotopic maps are conventionally constructed and processed by decoding blood oxygenation-level dependent (BOLD) functional magnetic resonance imaging (fMRI) responses to designed visual stimuli on the cortical surface. However, these methods frequently generate retinotopic maps that do not preserve topology, contradicting a fundamental property of retinotopic maps observed in neurophysiology. To address this problem, we propose an integrated approach to simultaneously refine the flattening from the 3D cortical surface to the 2D parametric space and adaptively smooth retinotopic perception centers in the visual space to make the retinotopic maps topological. One key element of the approach is the enhanced error tolerant Teichmüller mapping, which refines the parametrization by minimizing angle distortions and maximizing alignment to noisy landmarks. We validated our overall approach with synthetic and real retinotopic mapping datasets and applied it to compute cortical magnification factor (CMF). The results showed that the proposed approach was superior to other conventional retinotopic mapping methods in predicting BOLD fMRI time series and preserving topology.

Protocol for quantitative characterization of human retinotopic maps using quasiconformal mapping

High-field functional magnetic resonance imaging generates in vivo retinotopic maps, but quantifying them remains challenging. Here, we present a pipeline based on conformal geometry and Teichmüller theory for the quantitative characterization of human retinotopic maps. We describe steps for cortical surface parameterization and surface-spline-based smoothing. We then detail Beltrami coefficient-based mapping, which provides a quantitative and re-constructible description of the retinotopic maps. This framework has been successfully used to analyze the Human Connectome Project's V1 retinotopic maps. For complete details on the use and execution of this protocol, please refer to Ta et al. (2022).¹.