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One way to study connectivity in visual cortical areas is by examining spontaneous neural activity. In the absence of visual input, such activity remains shaped by the underlying neural architecture and, presumably, may still reflect visuotopic organization. Here, we applied population connective field (CF) modeling to estimate the spatial profile of functional connectivity in the early visual cortex during resting state functional magnetic resonance imaging (RS-fMRI). This model-based analysis estimates the spatial integration between blood-oxygen level dependent (BOLD) signals in distinct cortical visual field maps using fMRI. Just as population receptive field (pRF) mapping predicts the collective neural activity in a voxel as a function of response selectivity to stimulus position in visual space, CF modeling predicts the activity of voxels in one visual area as a function of the aggregate activity in voxels in another visual area. In combination with pRF mapping, CF locations on the cortical surface can be interpreted in visual space, thus enabling reconstruction of visuotopic maps from resting state data. We demonstrate that V1 ➤ V2 and V1 ➤ V3 CF maps estimated from resting state fMRI data show visuotopic organization. Therefore, we conclude that-despite some variability in CF estimates between RS scans-neural properties such as CF maps and CF size can be derived from resting state data.

Human visual cortex does not represent the whole visual field with the same detail. Changes in receptive field size, population receptive field (pRF) size and cortical magnification factor (CMF) with eccentricity are well established, and associated with changes in visual acuity with eccentricity. Visual acuity also changes across polar angle. However, it remains unclear how RF size, pRF size and CMF change across polar angle. Here, we examine differences in pRF size and CMF across polar angle in V1, V2 and V3 using pRF modeling of human fMRI data. In these visual field maps, we find smaller pRFs and larger CMFs in horizontal (left and right) than vertical (upper and lower) visual field quadrants. Differences increase with eccentricity, approximately in proportion to average pRF size and CMF. Similarly, we find larger CMFs in the lower than upper quadrant, and again differences increase with eccentricity. However, pRF size differences between lower and upper quadrants change direction with eccentricity. Finally, we find slightly smaller pRFs in the left than right quadrants of V2 and V3, though this difference is very small, and we find no differences in V1 and no differences in CMF. Moreover, differences in pRF size and CMF vary gradually with polar angle and are not limited to the meridians or visual field map discontinuities. PRF size and CMF differences do not consistently follow patterns of cortical curvature, despite the link between cortical curvature and polar angle in V1. Thus, the early human visual cortex has a radially asymmetric representation of the visual field. These asymmetries may underlie consistent reports of asymmetries in perceptual abilities. •PRFs are smaller in horizontal than vertical visual field quadrants of V1, V2 & V3.•Cortical magnification is correspondingly larger in these horizontal quadrants.•Cortical magnification is larger in the lower than the upper quadrant.•The size of these differences typically increases with visual field eccentricity.•Upper versus lower quadrant PRF size differences change direction with eccentricity.

This paper proposes a methodology for estimating Neural Response Functions (NRFs) from fMRI data. These NRFs describe non-linear relationships between experimental stimuli and neuronal population responses. The method is based on a two-stage model comprising an NRF and a Hemodynamic Response Function (HRF) that are simultaneously fitted to fMRI data using a Bayesian optimization algorithm. This algorithm also produces a model evidence score, providing a formal model comparison method for evaluating alternative NRFs. The HRF is characterized using previously established \"Balloon\" and BOLD signal models. We illustrate the method with two example applications based on fMRI studies of the auditory system. In the first, we estimate the time constants of repetition suppression and facilitation, and in the second we estimate the parameters of population receptive fields in a tonotopic mapping study.

Visual spatial attention concentrates neural resources at the attended location. Recently, we demonstrated that voluntary spatial attention attracts population receptive fields (pRFs) toward its location throughout the visual hierarchy. Theoretically, both a feed forward or feedback mechanism could underlie pRF attraction in a given cortical area. Here, we use sub-millimeter ultra-high field functional MRI to measure pRF attraction across cortical depth and assess the contribution of feed forward and feedback signals to pRF attraction. In line with previous findings, we find consistent attraction of pRFs with voluntary spatial attention in V1. When assessed as a function of cortical depth, we find pRF attraction in every cortical portion (deep, center and superficial), although the attraction is strongest in deep cortical portions (near the gray-white matter boundary). Following the organization of feed forward and feedback processing across V1, we speculate that a mixture of feed forward and feedback processing underlies pRF attraction in V1. Specifically, we propose that feedback processing contributes to the pRF attraction in deep cortical portions. •Voluntary spatial attention attracts population receptive fields (pRFs) in human V1.•pRF attraction occurs throughout V1 and throughout the cortical thickness.•pRF attraction is stronger near the gray/white matter boundary in V1.•We suggest both feed forward and feedback processing underlie pRF attraction.•We suggest that feedback signals arrive in deep cortical layers.

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 R2 achieved by the qPRF compared to Benson et al. (2018) was negligible, with a median of 0.025% (R2 units being between 0% and 100%). In general, the qPRF yielded a slightly better fitting solution, achieving a greater R2 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. •We describe a system to perform PRF modeling up to 1,500 times faster than others.•The system achieves equivalent goodness-of-fit as others.•A pre-computed tree and similarity-based search strategy underlie the acceleration.

We introduce a probabilistic (Bayesian) framework and associated software toolbox for mapping population receptive fields (pRFs) based on fMRI data. This generic approach is intended to work with stimuli of any dimension and is demonstrated and validated in the context of 2D retinotopic mapping. The framework enables the experimenter to specify generative (encoding) models of fMRI timeseries, in which experimental stimuli enter a pRF model of neural activity, which in turns drives a nonlinear model of neurovascular coupling and Blood Oxygenation Level Dependent (BOLD) response. The neuronal and haemodynamic parameters are estimated together on a voxel-by-voxel or region-of-interest basis using a Bayesian estimation algorithm (variational Laplace). This offers several novel contributions to receptive field modelling. The variance/covariance of parameters are estimated, enabling receptive fields to be plotted while properly representing uncertainty about pRF size and location. Variability in the haemodynamic response across the brain is accounted for. Furthermore, the framework introduces formal hypothesis testing to pRF analysis, enabling competing models to be evaluated based on their log model evidence (approximated by the variational free energy), which represents the optimal tradeoff between accuracy and complexity. Using simulations and empirical data, we found that parameters typically used to represent pRF size and neuronal scaling are strongly correlated, which is taken into account by the Bayesian methods we describe when making inferences. We used the framework to compare the evidence for six variants of pRF model using 7 T functional MRI data and we found a circular Difference of Gaussians (DoG) model to be the best explanation for our data overall. We hope this framework will prove useful for mapping stimulus spaces with any number of dimensions onto the anatomy of the brain. •We introduce a Bayesian toolbox for population receptive field (pRF) mapping.•Neuronal and haemodynamic parameters are estimated per voxel or per region.•Hypotheses can be tested by comparing pRF models based on their evidence.•The uncertainty over parameters (such as pRF size) is estimated and visualised.•We establish face validity using simulations and test-rest reliability with 7 T fMRI.

•Multi-echo fMRI with TE-dependent denoising (ME-ICA) increases TSNR and improves pRF model fitting compared to single echo EPI.•ME-ICA improves the reliability of pRF parameter estimation.•Overall, ME-ICA may require as little as 1/3 data of single echo fMRI to achieve comparable pRF modeling performance. fMRI is an indispensable tool for neuroscience investigation, but this technique is limited by multiple sources of physiological and measurement noise. These noise sources are particularly problematic for analysis techniques that require high signal-to-noise ratio for stable model fitting, such as voxel-wise modeling. Multi-echo data acquisition in combination with echo-time dependent ICA denoising (ME-ICA) represents one promising strategy to mitigate physiological and hardware-related noise sources as well as motion-related artifacts. However, most studies employing ME-ICA to date are resting-state fMRI studies, and therefore we have a limited understanding of the impact of ME-ICA on complex task or model-based fMRI paradigms. Here, we addressed this knowledge gap by comparing data quality and model fitting performance of data acquired during a visual population receptive field (pRF) mapping (N = 13 participants) experiment after applying one of three preprocessing procedures: ME-ICA, optimally combined multi-echo data without ICA-denoising, and typical single echo processing. As expected, multi-echo fMRI improved temporal signal-to-noise compared to single echo fMRI, with ME-ICA amplifying the improvement compared to optimal combination alone. However, unexpectedly, this boost in temporal signal-to-noise did not directly translate to improved model fitting performance: compared to single echo acquisition, model fitting was only improved after ICA-denoising. Specifically, compared to single echo acquisition, ME-ICA resulted in improved variance explained by our pRF model throughout the visual system, including anterior regions of the temporal and parietal lobes where SNR is typically low, while optimal combination without ICA did not. ME-ICA also improved reliability of parameter estimates compared to single echo and optimally combined multi-echo data without ICA-denoising. Collectively, these results suggest that ME-ICA is effective for denoising task-based fMRI data for modeling analyzes and maintains the integrity of the original data. Therefore, ME-ICA may be beneficial for complex fMRI experiments, including voxel-wise modeling and naturalistic paradigms.

The relevance of human primary motor cortex (M1) for motor actions has long been established. However, it is still unknown how motor actions are represented, and whether M1 contains an ordered somatotopy at the mesoscopic level. In the current study we show that a detailed within-limb somatotopy can be obtained in M1 during finger movements using Gaussian population Receptive Field (pRF) models. Similar organizations were also obtained for primary somatosensory cortex (S1), showing that individual finger representations are interconnected throughout sensorimotor cortex. The current study additionally estimates receptive field sizes of neuronal populations, showing differences between finger digit representations, between M1 and S1, and additionally between finger digit flexion and extension. Using the Gaussian pRF approach, the detailed somatotopic organization of M1 can be obtained including underlying characteristics, allowing for the in-depth investigation of cortical motor representation and sensorimotor integration. •We find a detailed within-limb somatotopy of finger digits in primary motor cortex.•Gaussian population receptive field model was used to describe BOLD activity.•Population receptive fields were found to be larger for M1 compared to S1.•Finger digit flexion and extension result in different receptive field profiles.

The human visual system is organized as a hierarchy of maps that share the topography of the retina. Known retinotopic maps have been identified using simple visual stimuli under strict fixation, conditions different from everyday vision which is active, dynamic, and complex. This means that it remains unknown how much of the brain is truly visually organized. Here I demonstrate widespread stable visual organization beyond the traditional visual system, in default-mode network and hippocampus. Detailed topographic connectivity with primary visual cortex during movie-watching, resting-state, and retinotopic-mapping experiments revealed that visual–spatial representations throughout the brain are warped by cognitive state. Specifically, traditionally visual regions alternate with default-mode network and hippocampus in preferentially representing the center of the visual field. This visual role of default-mode network and hippocampus would allow these regions to interface between abstract memories and concrete sensory impressions. Together, these results indicate that visual–spatial organization is a fundamental coding principle that structures the communication between distant brain regions.

Neural processing is hypothesized to apply the same mathematical operations in a variety of contexts, implementing so-called canonical neural computations. Divisive normalization (DN) is considered a prime candidate for a canonical computation. Here, we propose a population receptive field (pRF) model based on DN and evaluate it using ultra-high-field functional MRI (fMRI). The DN model parsimoniously captures seemingly disparate response signatures with a single computation, superseding existing pRF models in both performance and biological plausibility. We observe systematic variations in specific DN model parameters across the visual hierarchy and show how they relate to differences in response modulation and visuospatial information integration. The DN model delivers a unifying framework for visuospatial responses throughout the human visual hierarchy and provides insights into its underlying information-encoding computations. These findings extend the role of DN as a canonical computation to neuronal populations throughout the human visual hierarchy.