Tu Yanshuai, Ta Duyan, Lu Zhong-Lin, Wang Yalin
School of Computing, Informatics, Decision Systems Engineering, Arizona State Univ., Tempe, AZ.
Division of Arts and Sciences, NYU Shanghai, Shanghai, China.
Proc IEEE Int Symp Biomed Imaging. 2020 Apr;2020:534-538. doi: 10.1109/isbi45749.2020.9098316. Epub 2020 May 22.
Retinotopic mapping, the mapping of visual input on the retina to cortical neurons, is an important topic in vision science. Typically, cortical neurons are related to visual input on the retina using functional magnetic resonance imaging (fMRI) of cortical responses to slowly moving visual stimuli on the retina. Although it is well known from neurophysiology studies that retinotopic mapping is locally diffeomorphic (i.e., smooth, differentiable, and invertible) within each local area, the retinotopic maps from fMRI are often not diffeomorphic, especially near the fovea, because of the low signal-noise ratio of fMRI. The aim of this study is to develop and solve a mathematical model that produces diffeomorphic retinotopic mapping from fMRI data. Specifically, we adopt a geometry concept, the Beltrami coefficient, as the tool to define diffeomorphism, and model the problem in an optimization framework. Efficient numerical methods are proposed to solve the model. Experimental results with both synthetic and real retinotopy data demonstrate that the proposed method is superior to conventional smoothing methods.
视网膜拓扑映射，即将视网膜上的视觉输入映射到皮层神经元，是视觉科学中的一个重要课题。通常，利用对视网膜上缓慢移动的视觉刺激的皮层反应的功能磁共振成像（fMRI），将皮层神经元与视网膜上的视觉输入联系起来。尽管从神经生理学研究中已知视网膜拓扑映射在每个局部区域内是局部微分同胚的（即光滑、可微且可逆），但由于fMRI的低信噪比，来自fMRI的视网膜拓扑图通常不是微分同胚的，尤其是在中央凹附近。本研究的目的是开发并求解一个从fMRI数据生成微分同胚视网膜拓扑映射的数学模型。具体而言，我们采用一个几何概念，即贝尔特拉米系数，作为定义微分同胚的工具，并在一个优化框架中对该问题进行建模。提出了有效的数值方法来求解该模型。对合成和真实视网膜拓扑数据的实验结果表明，所提出的方法优于传统的平滑方法。
