Abstract
The population receptive field (pRF) model is the state-of-the-art retinotopic map analysis method. However, because of the relatively low signal-to-noise ratio and low spatial resolution in fMRI signals, large portions of the retinotopic maps from the voxel-wise decoding pRF solutions often violate the topological condition observed in neurophysiology, that is, nearby neurons have nearby receptive fields. It is advantageous but challenging to impose the topological condition when decoding fMRI time series. Here, we propose a topological receptive field (tRF) framework to impose both topological conditions by combining topology-preserving segmentation and topological fMRI decoding iteratively, using the Beltrami coefficient, a metric used in quasiconformal theory, to quantify topological conditions. We validated the proposed framework on both synthetic and real human retinotopy data. The synthetic data were generated using the double-sech model with two levels of fMRI noise and then decoded with both tRF and pRF. We found that tRF performed better than pRF, with a smaller average visual coordinate recovery error (2.485 vs 2.924 degrees) and no violation of the topological condition (0 vs 393 flipped triangles, out of a total of 2798). We also compared the performance of the two methods on the 12 visual areas retinotopic maps of the first three observers in the Human Connectome Project 7T Retinotopic dataset. The results also showed that the tRF provided better fits to the fMRI time series than the pRF (average RMSE=0.273 vs 0.276) and generate no topological violations (0 vs 870 flipped triangles out of a total of 19640). To our knowledge, this is the first work that enforces the topological condition in decoding retinotopic fMRI signals, and the first automatic visual area segmentation method that preserves the topology graph. The general framework can be extended to other sensory maps.