Investigating the Reliability of Population Receptive Field Size Estimates Using fMRI

In functional MRI (fMRI), population receptive field (pRF) models allow a quantitative description of the response as a function of the features of the stimuli that are relevant for each voxel. The most popular pRF model used in fMRI assumes a Gaussian shape in the features space (e.g., the visual field) reducing the description of the voxel's pRF to the Gaussian mean (the pRF preferred feature) and standard deviation (the pRF size). The estimation of the pRF mean has been proven to be highly reliable. However, the estimate of the pRF size has been shown not to be consistent within and between subjects. While this issue has been noted experimentally, here we use an optimization theory perspective to describe how the inconsistency in estimating the pRF size is linked to an inherent property of the Gaussian pRF model. When fitting such models, the goodness of fit is less sensitive to variations in the pRF size than to variations in the pRF mean. We also show how the same issue can be considered from a bias-variance perspective. We compare different estimation procedures in terms of the reliability of their estimates using simulated and real fMRI data in the visual (using the Human Connectome Project database) and auditory domain. We show that, the reliability of the estimate of the pRF size can be improved considering a linear combination of those pRF models with similar goodness of fit or a permutation based approach. This increase in reliability of the pRF size estimate does not affect the reliability of the estimate of the pRF mean and the prediction accuracy.