Spatial elongation of population receptive field profiles revealed by model-free fMRI back-projection

Bounded contribution of human early visual cortex to the topographic anisotropy in spatial extent perception

To interact successfully with objects, it is crucial to accurately perceive their spatial extent, an enclosed region they occupy in space. Although the topographic representation of space in the early visual cortex (EVC) has been favored as a neural correlate of spatial extent perception, its exact nature and contribution to perception remain unclear. Here, we inspect the topographic representations of human individuals' EVC and perception in terms of how much their anisotropy is influenced by the orientation (co-axiality) and radial position (radiality) of stimuli. We report that while the anisotropy is influenced by both factors, its direction is primarily determined by radiality in EVC but by co-axiality in perception. Despite this mismatch, the individual differences in both radial and co-axial anisotropy are substantially shared between EVC and perception. Our findings suggest that spatial extent perception builds on EVC's spatial representation but requires an additional mechanism to transform its topographic bias.

Radial bias in face identification

Human vision in the periphery is most accurate for stimuli that point towards the fovea. This so-called radial bias has been linked with the organization and spatial selectivity of neurons at the lowest levels of the visual system, from retinal ganglion cells onwards. Despite evidence that the human visual system is radially biased, it is not yet known whether this bias persists at higher levels of processing, or whether high-level representations are invariant to this low-level orientation bias. We used the case of face identity recognition to address this question. The specialized high-level mechanisms that support efficient face recognition are highly dependent on horizontally oriented information, which convey the most useful identity cues in the fovea. We show that face selective mechanisms are more sensitive on the horizontal meridian (to the left and right of fixation) compared to the vertical meridian (above and below fixation), suggesting that the horizontal cues in the face are better extracted on the horizontal meridian, where they align with the radial bias. The results demonstrate that the radial bias is maintained at high-level recognition stages and emphasize the importance of accounting for the radial bias in future investigation of visual recognition processes in peripheral vision.

Moving in on human motor cortex. Characterizing the relationship between body parts with non-rigid population response fields

For cortical motor activity, the relationships between different body part representations is unknown. Through reciprocal body part relationships, functionality of cortical motor areas with respect to whole body motor control can be characterized. In the current study, we investigate the relationship between body part representations within individual neuronal populations in motor cortices, following a 7 Tesla fMRI 18-body-part motor experiment in combination with our newly developed non-rigid population Response Field (pRF) model and graph theory. The non-rigid pRF metrics reveal somatotopic structures in all included motor cortices covering frontal, parietal, medial and insular cortices and that neuronal populations in primary sensorimotor cortex respond to fewer body parts than secondary motor cortices. Reciprocal body part relationships are estimated in terms of uniqueness, clique-formation, and influence. We report unique response profiles for the knee, a clique of body parts surrounding the ring finger, and a central role for the shoulder and wrist. These results reveal associations among body parts from the perspective of the central nervous system, while being in agreement with intuitive notions of body part usage.

Quantitative characterization of the human retinotopic map based on quasiconformal mapping

The retinotopic map depicts the cortical neurons' response to visual stimuli on the retina and has contributed significantly to our understanding of human visual system. Although recent advances in high field functional magnetic resonance imaging (fMRI) have made it possible to generate the in vivo retinotopic map with great detail, quantifying the map remains challenging. Existing quantification methods do not preserve surface topology and often introduce large geometric distortions to the map. In this study, we developed a new framework based on computational conformal geometry and quasiconformal Teichmüller theory to quantify the retinotopic map. Specifically, we introduced a general pipeline, consisting of cortical surface conformal parameterization, surface-spline-based cortical activation signal smoothing, and vertex-wise Beltrami coefficient-based map description. After correcting most of the violations of the topological conditions, the result was a "Beltrami coefficient map" (BCM) that rigorously and completely characterizes the retinotopic map by quantifying the local quasiconformal mapping distortion at each visual field location. The BCM provided topological and fully reconstructable retinotopic maps. We successfully applied the new framework to analyze the V1 retinotopic maps from the Human Connectome Project (n=181), the largest state of the art retinotopy dataset currently available. With unprecedented precision, we found that the V1 retinotopic map was quasiconformal and the local mapping distortions were similar across observers. The new framework can be applied to other visual areas and retinotopic maps of individuals with and without eye diseases, and improve our understanding of visual cortical organization in normal and clinical populations.

Divisive normalization unifies disparate response signatures throughout the human visual hierarchy

A canonical neural computation is a mathematical operation applied by the brain in a wide variety of contexts and capable of explaining and unifying seemingly unrelated neural and perceptual phenomena. Here, we use a combination of state-of-the-art experiments (ultra-high-field functional MRI) and mathematical methods (population receptive field [pRF] modeling) to uniquely demonstrate the role of divisive normalization (DN) as the canonical neural computation underlying visuospatial responses throughout the human visual hierarchy. The DN pRF model provides a tool to investigate and interpret the computational processes underlying neural responses in human and animal recordings, but also in clinical and cognitive dimensions.

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.

Population receptive fields in non-human primates from whole-brain fMRI and large-scale neurophysiology in visual cortex

Population receptive field (pRF) modeling is a popular fMRI method to map the retinotopic organization of the human brain. While fMRI-based pRF maps are qualitatively similar to invasively recorded single-cell receptive fields in animals, it remains unclear what neuronal signal they represent. We addressed this question in awake nonhuman primates comparing whole-brain fMRI and large-scale neurophysiological recordings in areas V1 and V4 of the visual cortex. We examined the fits of several pRF models based on the fMRI blood-oxygen-level-dependent (BOLD) signal, multi-unit spiking activity (MUA), and local field potential (LFP) power in different frequency bands. We found that pRFs derived from BOLD-fMRI were most similar to MUA-pRFs in V1 and V4, while pRFs based on LFP gamma power also gave a good approximation. fMRI-based pRFs thus reliably reflect neuronal receptive field properties in the primate brain. In addition to our results in V1 and V4, the whole-brain fMRI measurements revealed retinotopic tuning in many other cortical and subcortical areas with a consistent increase in pRF size with increasing eccentricity, as well as a retinotopically specific deactivation of default mode network nodes similar to previous observations in humans.

Extremely fast pRF mapping for real-time applications

Population receptive field (pRF) mapping is a popular tool in computational neuroimaging that allows for the investigation of receptive field properties, their topography and interrelations in health and disease. Furthermore, the possibility to invert population receptive fields provides a decoding model for constructing stimuli from observed cortical activation patterns. This has been suggested to pave the road towards pRF-based brain-computer interface (BCI) communication systems, which would be able to directly decode internally visualized letters from topographically organized brain activity. A major stumbling block for such an application is, however, that the pRF mapping procedure is computationally heavy and time consuming. To address this, we propose a novel and fast pRF mapping procedure that is suitable for real-time applications. The method is built upon hashed-Gaussian encoding of the stimulus, which tremendously reduces computational resources. After the stimulus is encoded, mapping can be performed using either ridge regression for fast offline analyses or gradient descent for real-time applications. We validate our model-agnostic approach in silico, as well as on empirical fMRI data obtained from 3T and 7T MRI scanners. Our approach is capable of estimating receptive fields and their parameters for millions of voxels in mere seconds. This method thus facilitates real-time applications of population receptive field mapping.

Topology-preserving smoothing of retinotopic maps

Retinotopic mapping, i.e., the mapping between visual inputs on the retina and neuronal activations in cortical visual areas, is one of the central topics in visual neuroscience. For human observers, the mapping is obtained by analyzing functional magnetic resonance imaging (fMRI) signals of cortical responses to slowly moving visual stimuli on the retina. Although it is well known from neurophysiology that the mapping is topological (i.e., the topology of neighborhood connectivity is preserved) within each visual area, retinotopic maps derived from the state-of-the-art methods are often not topological because of the low signal-to-noise ratio and spatial resolution of fMRI. The violation of topological condition is most severe in cortical regions corresponding to the neighborhood of the fovea (e.g., < 1 degree eccentricity in the Human Connectome Project (HCP) dataset), significantly impeding accurate analysis of retinotopic maps. This study aims to directly model the topological condition and generate topology-preserving and smooth retinotopic maps. Specifically, we adopted the Beltrami coefficient, a metric of quasiconformal mapping, to define the topological condition, developed a mathematical model to quantify topological smoothing as a constrained optimization problem, and elaborated an efficient numerical method to solve the problem. The method was then applied to V1, V2, and V3 simultaneously in the HCP dataset. Experiments with both simulated and real retinotopy data demonstrated that the proposed method could generate topological and smooth retinotopic maps.

A touch of hierarchy: population receptive fields reveal fingertip integration in Brodmann areas in human primary somatosensory cortex

Several neuroimaging studies have shown the somatotopy of body part representations in primary somatosensory cortex (S1), but the functional hierarchy of distinct subregions in human S1 has not been adequately addressed. The current study investigates the functional hierarchy of cyto-architectonically distinct regions, Brodmann areas BA3, BA1, and BA2, in human S1. During functional MRI experiments, we presented participants with vibrotactile stimulation of the fingertips at three different vibration frequencies. Using population Receptive Field (pRF) modeling of the fMRI BOLD activity, we identified the hand region in S1 and the somatotopy of the fingertips. For each voxel, the pRF center indicates the finger that most effectively drives the BOLD signal, and the pRF size measures the spatial somatic pooling of fingertips. We find a systematic relationship of pRF sizes from lower-order areas to higher-order areas. Specifically, we found that pRF sizes are smallest in BA3, increase slightly towards BA1, and are largest in BA2, paralleling the increase in visual receptive field size as one ascends the visual hierarchy. Additionally, we find that the time-to-peak of the hemodynamic response in BA3 is roughly 0.5 s earlier compared to BA1 and BA2, further supporting the notion of a functional hierarchy of subregions in S1. These results were obtained during stimulation of different mechanoreceptors, suggesting that different afferent fibers leading up to S1 feed into the same cortical hierarchy.

Population Receptive Field Shapes in Early Visual Cortex Are Nearly Circular

The visual field region where a stimulus evokes a neural response is called the receptive field (RF). Analytical tools combined with functional MRI (fMRI) can estimate the RF of the population of neurons within a voxel. Circular population RF (pRF) methods accurately specify the central position of the pRF and provide some information about the spatial extent (diameter) of the RF. A number of investigators developed methods to further estimate the shape of the pRF, for example, whether the shape is more circular or elliptical. There is a report that there are many pRFs with highly elliptical pRFs in early visual cortex (V1-V3; Silson et al., 2018). Large aspect ratios (>2) are difficult to reconcile with the spatial scale of orientation columns or visual field map properties in early visual cortex. We started to replicate the experiments and found that the software used in the publication does not accurately estimate RF shape: it produces elliptical fits to circular ground-truth data. We analyzed an independent data set with a different software package that was validated over a specific range of measurement conditions, to show that in early visual cortex the aspect ratios are <2. Furthermore, current empirical and theoretical methods do not have enough precision to discriminate ellipses with aspect ratios of 1.5 from circles. Through simulation we identify methods for improving sensitivity that may estimate ellipses with smaller aspect ratios. The results we present are quantitatively consistent with prior assessments using other methodologies.SIGNIFICANCE STATEMENT We evaluated whether the shape of many population receptive fields (RFs) in early visual cortex is elliptical and differs substantially from circular. We evaluated two tools for estimating elliptical models of the pRF; one tool was valid over the measured compliance range. Using the validated tool, we found no evidence that confidently rejects circular fits to the pRF in visual field maps V1, V2, and V3. The new measurements and analyses are consistent with prior theoretical and experimental assessments in the literature.

Modulating the global orientation bias of the visual system changes population receptive field elongations

The topographical structure of the visual system in individual subjects can be visualized using fMRI. Recently, a radial bias for the long axis of population receptive fields (pRF) has been shown using fMRI. It has been theorized that the elongation of receptive fields pointing toward the fovea results from horizontal local connections bundling orientation selective units mostly parallel to their polar position within the visual field. In order to investigate whether there is a causal relationship between orientation selectivity and pRF elongation the current study employed a global orientation adapter to modulate the orientation bias for the visual system while measuring spatial pRF characteristics. The hypothesis was that the orientation tuning change of neural populations would alter pRF elongations toward the fovea particularly at axial positions parallel and orthogonal to the affected orientation. The results indeed show a different amount of elongation of pRF units and their orientation at parallel and orthogonal axial positions relative to the adapter orientation. Within the lower left hemifield, pRF radial bias and elongation showed an increase during adaptation to a 135° grating while both parameters decreased during the presentation of a 45° adapter stimulus. The lower right visual field showed the reverse pattern. No modulation of the pRF topographies were observed in the upper visual field probably due to a vertical visual field asymmetry of sensitivity toward the low contrast spatial frequency pattern of the adapter stimulus. These data suggest a direct relationship between orientation selectivity and elongation of population units within the visual cortex.

Micro-probing enables fine-grained mapping of neuronal populations using fMRI

The characterization of receptive field (RF) properties is fundamental to understanding the neural basis of sensory and cognitive behaviour. The combination of non-invasive imaging, such as fMRI, with biologically inspired neural modelling has enabled the estimation of population RFs directly in humans. However, current approaches require making numerous a priori assumptions, so these cannot reveal unpredicted properties, such as fragmented RFs or subpopulations. This is a critical limitation in studies on adaptation, pathology or reorganization. Here, we introduce micro-probing (MP), a technique for fine-grained and largely assumption free characterization of multiple pRFs within a voxel. It overcomes many limitations of current approaches by enabling detection of unexpected RF shapes, properties and subpopulations, by enhancing the spatial detail with which we analyze the data. MP is based on tiny, fixed-size, Gaussian models that efficiently sample the entire visual space and create fine-grained probe maps. Subsequently, we derived population receptive fields (pRFs) from these maps. We demonstrate the scope of our method through simulations and by mapping the visual fields of healthy participants and of a patient group with highly abnormal RFs due to a congenital pathway disorder. Without using specific stimuli or adapted models, MP mapped the bilateral pRFs characteristic of observers with albinism. In healthy observers, MP revealed that voxels may capture the activity of multiple subpopulations RFs that sample distinct regions of the visual field. Thus, MP provides a versatile framework to visualize, analyze and model, without restrictions, the diverse RFs of cortical subpopulations in health and disease.

Data-driven models in human neuroscience and neuroengineering

Discoveries in modern human neuroscience are increasingly driven by quantitative understanding of complex data. Data-intensive approaches to modeling have promise to dramatically advance our understanding of the brain and critically enable neuroengineering capabilities. In this review, we provide an accessible primer to modern modeling approaches and highlight recent data-driven discoveries in the domains of neuroimaging, single-neuron and neuronal population responses, and device neuroengineering. Further, we suggest that meaningful progress requires the community to tackle open challenges in the realms of model interpretability and generalizability, training pipelines of data-fluent human neuroscientists, and integrated consideration of data ethics.

The Human Connectome Project 7 Tesla retinotopy dataset: Description and population receptive field analysis

About a quarter of human cerebral cortex is dedicated mainly to visual processing. The large-scale spatial organization of visual cortex can be measured with functional magnetic resonance imaging (fMRI) while subjects view spatially modulated visual stimuli, also known as "retinotopic mapping." One of the datasets collected by the Human Connectome Project involved ultrahigh-field (7 Tesla) fMRI retinotopic mapping in 181 healthy young adults (1.6-mm resolution), yielding the largest freely available collection of retinotopy data. Here, we describe the experimental paradigm and the results of model-based analysis of the fMRI data. These results provide estimates of population receptive field position and size. Our analyses include both results from individual subjects as well as results obtained by averaging fMRI time series across subjects at each cortical and subcortical location and then fitting models. Both the group-average and individual-subject results reveal robust signals across much of the brain, including occipital, temporal, parietal, and frontal cortex as well as subcortical areas. The group-average results agree well with previously published parcellations of visual areas. In addition, split-half analyses show strong within-subject reliability, further demonstrating the high quality of the data. We make publicly available the analysis results for individual subjects and the group average, as well as associated stimuli and analysis code. These resources provide an opportunity for studying fine-scale individual variability in cortical and subcortical organization and the properties of high-resolution fMRI. In addition, they provide a set of observations that can be compared with other Human Connectome Project measures acquired in these same participants.

Population receptive field tuning properties of visual cortex during childhood

Visuospatial abilities such as contrast sensitivity and Vernier acuity improve until late in childhood, but the neural mechanisms supporting these changes are poorly understood. We tested to which extent this development might reflect improved spatial sensitivity of neuronal populations in visual cortex. To do this, we measured BOLD-responses in areas V1-V4 and V3a, whilst 6- to 12-year-old children and adults watched large-field wedge and ring stimuli in the MRI scanner, and then fitted population receptive field (pRF) tuning functions to these data (Dumoulin and Wandell, 2008). Cortical magnification and pRF tuning width changed with eccentricity at all ages, as expected. However, there were no significant age differences in pRF size, shape, cortical magnification, or map consistency in any visual region. These findings thus strongly suggest that spatial vision in late childhood is not substantially limited by the spatial tuning of neuronal populations in early visual cortex. Instead, improvements in performance may reflect more efficient read-out of spatial information in early visual regions by higher-level processing stages, or prolonged tuning to more complex visual properties such as orientation. Importantly, this in-depth characterisation of the pRF tuning profiles across childhood, paves the way for in-vivo-testing of atypical visual cortex development and plasticity.

Spatial elongation of population receptive field profiles revealed by model-free fMRI back-projection

Estimates of visual field topographies in human visual cortex obtained through fMRI traveling wave techniques usually provide the parameters of population receptive field (pRF) location (polar angle, eccentricity) and receptive field size. These parameters are obtained by fitting the recorded data to a standard model population receptive field. In this work, pRF profiles are measured directly by back-projecting preprocessed fMRI time-series to sweeps of a bar across the visual field in different angles. The current data suggest that the model-free pRF profiles contain information not only about receptive field location and size but also about the pRF shape characteristics. The elongation (ellipticity) of pRFs decreases along the early visual hierarchy to a different degree for the ventral and the dorsal stream. Furthermore, ellipticity changes as a function of eccentricity. pRF orientation shows a high degree of collinearity with its angular position within the visual field. Using model-free pRF measurements, the traveling wave technique provides additional characteristics of pRF topographies that are not restricted to size and provide robust measures within the single subject.