qPRF: A system to accelerate population receptive field modeling

Abstract

BOLD response can be fitted using the population receptive field (PRF) model to reveal how visual input is represented on the cortex (Dumoulin and Wandell, 2008). Fitting the PRF model costs considerable time, often requiring days to analyze BOLD signals for a small cohort of subjects. We introduce the qPRF (“quick PRF”), a system for accelerated PRF modeling that reduced the computation time by a factor $>1,000$ without losing goodness-of-fit when compared to another widely available PRF modeling package (Kay et al., 2013) on a benchmark of data from the Human Connectome Project (HCP; Van Essen et al. (2013). The system achieves this level of acceleration by pre-computing a tree-like data structure, which it rapidly searches during the fitting step for an optimal parameter combination. We tested the method on a constrained four-parameter version of the PRF model (Strategy 1 herein) and an unconstrained five-parameter PRF model, which the qPRF fitted at comparable speed (Strategy 2). We show how an additional search step can guarantee optimality of qPRF solutions with little additional time cost (Strategy 3). To assess the quality of qPRF solutions, we compared our Strategy 1 solutions to those provided by Benson et al. (2018) who performed a similar four-parameter fit. Both hemispheres of the 181 subjects in the HCP dataset (a total of 10,753,572 vertices, each with a unique BOLD time series of 1800 frames) were analyzed by qPRF in 12.82 h on an ordinary CPU. The absolute difference in $R^2$ achieved by the qPRF compared to Benson et al. (2018) was negligible, with a median of 0.025% ($R^2$ units being between 0% and 100%). In general, the qPRF yielded a slightly better fitting solution, achieving a greater $R^2$ on 70.2% of vertices. We also assess the qPRF method’s model-recovery ability using a simulated dataset. The qPRF may facilitate the development and use of more elaborate models based on the PRF framework and may pave the way for novel clinical applications.