Bayesian population receptive field modelling

Improving the Reliability and Accuracy of Population Receptive Field Measures Using a Logarithmically Warped Stimulus

The population receptive field method, which measures the region in visual space that elicits a BOLD signal in a voxel in retinotopic cortex, is a powerful tool for investigating the functional organization of human visual cortex with fMRI (Dumoulin & Wandell, 2008). However, recent work has shown that population receptive field (pRF) estimates for early retinotopic visual areas can be biased and unreliable, especially for voxels representing the fovea. Here, we show that a 'log-bar' stimulus that is logarithmically warped along the eccentricity dimension produces more reliable estimates of pRF size and location than the traditional moving bar stimulus. The log-bar stimulus was better able to identify pRFs near the foveal representation, and pRFs were smaller in size, consistent with simulation estimates of receptive field sizes in the fovea.

A primer on Variational Laplace (VL)

This article details a scheme for approximate Bayesian inference, which has underpinned thousands of neuroimaging studies since its introduction 15 years ago. Variational Laplace (VL) provides a generic approach to fitting linear or non-linear models, which may be static or dynamic, returning a posterior probability density over the model parameters and an approximation of log model evidence, which enables Bayesian model comparison. VL applies variational Bayesian inference in conjunction with quadratic or Laplace approximations of the evidence lower bound (free energy). Importantly, update equations do not need to be derived for each model under consideration, providing a general method for fitting a broad class of models. This primer is intended for experimenters and modellers who may wish to fit models to data using variational Bayesian methods, without assuming previous experience of variational Bayes or machine learning. Accompanying code demonstrates how to fit different kinds of model using the reference implementation of the VL scheme in the open-source Statistical Parametric Mapping (SPM) software package. In addition, we provide a standalone software function that does not require SPM, in order to ease translation to other fields, together with detailed pseudocode. Finally, the supplementary materials provide worked derivations of the key equations.

The 3D Structural Architecture of the Human Hand Area Is Nontopographic

The functional topography of the human primary somatosensory cortex hand area is a widely studied model system to understand sensory organization and plasticity. It is so far unclear whether the underlying 3D structural architecture also shows a topographic organization. We used 7 Tesla (7T) magnetic resonance imaging (MRI) data to quantify layer-specific myelin, iron, and mineralization in relation to population receptive field maps of individual finger representations in Brodman area 3b (BA 3b) of human S1 in female and male younger adults. This 3D description allowed us to identify a characteristic profile of layer-specific myelin and iron deposition in the BA 3b hand area, but revealed an absence of structural differences, an absence of low-myelin borders, and high similarity of 3D microstructure profiles between individual fingers. However, structural differences and borders were detected between the hand and face areas. We conclude that the 3D structural architecture of the human hand area is nontopographic, unlike in some monkey species, which suggests a high degree of flexibility for functional finger organization and a new perspective on human topographic plasticity.SIGNIFICANCE STATEMENT Using ultra-high-field MRI, we provide the first comprehensive in vivo description of the 3D structural architecture of the human BA 3b hand area in relation to functional population receptive field maps. High similarity of precise finger-specific 3D profiles, together with an absence of structural differences and an absence of low-myelin borders between individual fingers, reveals the 3D structural architecture of the human hand area to be nontopographic. This suggests reduced structural limitations to cortical plasticity and reorganization and allows for shared representational features across fingers.

White matter BOLD signals at 7 Tesla reveal visual field maps in optic radiation and vertical occipital fasciculus

There is growing evidence that blood-oxygen-level-dependent (BOLD) activity in the white matter (WM) can be detected by functional magnetic resonance imaging (fMRI). However, the functional relevance and significance of WM BOLD signals remain controversial. Here we investigated whether 7T BOLD fMRI can reveal fine-scale functional organizations of a WM bundle. Population receptive field (pRF) analyses of the 7T retinotopy dataset from the Human Connectome Project revealed clear contralateral retinotopic organizations of two visual WM bundles: the optic radiation (OR) and the vertical occipital fasciculus (VOF). The retinotopic maps of OR are highly consistent with post-mortem dissections and diffusion tractographies, while the VOF maps are compatible with the dorsal and ventral visual areas connected by the WM. Similar to the grey matter (GM) visual areas, both WM bundles show over-representations of the central visual field and increasing pRF size with eccentricity. Hemodynamic response functions of visual WM were slower and wider compared with those of GM areas. These findings clearly demonstrate that WM BOLD at 7 Tesla is closely coupled with neural activity related to axons, encoding highly specific information that can be used to characterize fine-scale functional organizations of a WM bundle.

Bayesian connective field modeling using a Markov Chain Monte Carlo approach

The majority of neurons in the human brain process signals from neurons elsewhere in the brain. Connective Field (CF) modelling is a biologically-grounded method to describe this essential aspect of the brain's circuitry. It allows characterizing the response of a population of neurons in terms of the activity in another part of the brain. CF modelling translates the concept of the receptive field (RF) into the domain of connectivity by assessing, at the voxel level, the spatial dependency between signals in distinct cortical visual field areas. Thus, the approach enables to characterize the functional cortical circuitry of the human cortex. While already very useful, the present CF modelling approach has some intrinsic limitations due to the fact that it only estimates the model's explained variance and not the probability distribution associated with the estimated parameters. If we could resolve this, CF modelling would lend itself much better for statistical comparisons at the level of single voxels and individuals. This is important when trying to gain a detailed understanding of the neurobiology and pathophysiology of the visual cortex, notably in rare cases. To enable this, we present a Bayesian approach to CF modeling (bCF). Using a Markov Chain Monte Carlo (MCMC) procedure, it estimates the posterior probability distribution underlying the CF parameters. Based on this, bCF quantifies, at the voxel level, the uncertainty associated with each parameter estimate. This information can be used in various ways to increase confidence in the CF model predictions. We applied bCF to BOLD responses recorded in the early human visual cortex using 3T fMRI. We estimated both the CF parameters and their associated uncertainties and show they are only weakly correlated. Moreover, we show how bCF facilitates the use of effect size (beta) as a data-driven parameter that can be used to select the most reliable voxels for further analysis. Finally, to further illustrate the functionality gained by bCF, we apply it to perform a voxel-level comparison of a single, circular symmetric, Gaussian versus a Difference-of-Gaussian model. We conclude that our bCF framework provides a comprehensive tool to study human functional cortical circuitry in health and disease.

Ramp-shaped neural tuning supports graded population-level representation of the object-to-scene continuum

We can easily perceive the spatial scale depicted in a picture, regardless of whether it is a small space (e.g., a close-up view of a chair) or a much larger space (e.g., an entire class room). How does the human visual system encode this continuous dimension? Here, we investigated the underlying neural coding of depicted spatial scale, by examining the voxel tuning and topographic organization of brain responses. We created naturalistic yet carefully-controlled stimuli by constructing virtual indoor environments, and rendered a series of snapshots to smoothly sample between a close-up view of the central object and far-scale view of the full environment (object-to-scene continuum). Human brain responses were measured to each position using functional magnetic resonance imaging. We did not find evidence for a smooth topographic mapping for the object-to-scene continuum on the cortex. Instead, we observed large swaths of cortex with opposing ramp-shaped profiles, with highest responses to one end of the object-to-scene continuum or the other, and a small region showing a weak tuning to intermediate scale views. However, when we considered the population code of the entire ventral occipito-temporal cortex, we found smooth and linear representation of the object-to-scene continuum. Our results together suggest that depicted spatial scale information is encoded parametrically in large-scale population codes across the entire ventral occipito-temporal cortex.

Intrasession and Intersession Reproducibility of Artificial Scotoma pRF Mapping Results at Ultra-High Fields

Functional magnetic resonance imaging (fMRI) combined with population receptive field (pRF) mapping allows for associating positions on the visual cortex to areas on the visual field. Apart from applications in healthy subjects, this method can also be used to examine dysfunctions in patients suffering from partial visual field losses. While such objective measurement of visual deficits (scotoma) is of great importance for, e.g., longitudinal studies addressing treatment effects, it requires a thorough assessment of accuracy and reproducibility of the results obtained. In this study, we quantified the reproducibility of pRF mapping results within and across sessions in case of central visual field loss in a group of 15 human subjects. We simulated scotoma by masking a central area of 2° radius from stimulation to establish ground-truth conditions. This study was performed on a 7T ultra-high field MRI scanner for increased sensitivity. We found excellent intrasession and intersession reproducibility for the pRF center position (Spearman correlation coefficients for x, y: >0.95; eccentricity: >0.87; polar angle: >0.98), but only modest reproducibility for pRF size (Spearman correlation coefficients around 0.4). We further examined the scotoma detection performance using an automated method based on a reference dataset acquired with full-field stimulation. For the 2° artificial scotoma, the group-averaged scotoma sizes were estimated at between 1.92° and 2.19° for different sessions. We conclude that pRF mapping of visual field losses yields robust, reproducible measures of retinal function and suggest the use of pRF mapping as an objective method for monitoring visual deficits during therapeutic interventions or disease progression.

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.

Cross-dataset reproducibility of human retinotopic maps

Population receptive field (pRF) models fit to fMRI data are used to non-invasively measure retinotopic maps in human visual cortex, and these maps are a fundamental component of visual neuroscience experiments. Here, we examined the reproducibility of retinotopic maps across two datasets: a newly acquired retinotopy dataset from New York University (NYU) (n = 44) and a public dataset from the Human Connectome Project (HCP) (n = 181). Our goal was to assess the degree to which pRF properties are similar across datasets, despite substantial differences in their experimental protocols. The two datasets simultaneously differ in their stimulus apertures, participant pool, fMRI protocol, MRI field strength, and preprocessing pipeline. We assessed the cross-dataset reproducibility of the two datasets in terms of the similarity of vertex-wise pRF estimates and in terms of large-scale polar angle asymmetries in cortical magnification. Within V1, V2, V3, and hV4, the group-median NYU and HCP vertex-wise polar angle estimates were nearly identical. Both eccentricity and pRF size estimates were also strongly correlated between the two datasets, but with a slope different from 1; the eccentricity and pRF size estimates were systematically greater in the NYU data. Next, to compare large-scale map properties, we quantified two polar angle asymmetries in V1 cortical magnification previously identified in the HCP data. The NYU dataset confirms earlier reports that more cortical surface area represents horizontal than vertical visual field meridian, and lower than upper vertical visual field meridian. Together, our findings show that the retinotopic properties of V1, V2, V3, and hV4 can be reliably measured across two datasets, despite numerous differences in their experimental design. fMRI-derived retinotopic maps are reproducible because they rely on an explicit computational model of the fMRI response. In the case of pRF mapping, the model is grounded in physiological evidence of how visual receptive fields are organized, allowing one to quantitatively characterize the BOLD signal in terms of stimulus properties (i.e., location and size). The new NYU Retinotopy Dataset will serve as a useful benchmark for testing hypotheses about the organization of visual areas and for comparison to the HCP 7T Retinotopy Dataset.

Predicting the retinotopic organization of human visual cortex from anatomy using geometric deep learning

Whether it be in a single neuron or a more complex biological system like the human brain, form and function are often directly related. The functional organization of human visual cortex, for instance, is tightly coupled with the underlying anatomy with cortical shape having been shown to be a useful predictor of the retinotopic organization in early visual cortex. Although the current state-of-the-art in predicting retinotopic maps is able to account for gross individual differences, such models are unable to account for any idiosyncratic differences in the structure-function relationship from anatomical information alone due to their initial assumption of a template. Here we developed a geometric deep learning model capable of exploiting the actual structure of the cortex to learn the complex relationship between brain function and anatomy in human visual cortex such that more realistic and idiosyncratic maps could be predicted. We show that our neural network was not only able to predict the functional organization throughout the visual cortical hierarchy, but that it was also able to predict nuanced variations across individuals. Although we demonstrate its utility for modeling the relationship between structure and function in human visual cortex, our approach is flexible and well-suited for a range of other applications involving data structured in non-Euclidean spaces.

Population receptive fields of human primary visual cortex organised as DC-balanced bandpass filters

The response to visual stimulation of population receptive fields (pRF) in the human visual cortex has been modelled with a Difference of Gaussians model, yet many aspects of their organisation remain poorly understood. Here, we examined the mathematical basis and signal-processing properties of this model and argue that the DC-balanced Difference of Gaussians (DoG) holds a number of advantages over a DC-biased DoG. Through functional magnetic resonance imaging (fMRI) pRF mapping, we compared performance of DC-balanced and DC-biased models in human primary visual cortex and found that when model complexity is taken into account, the DC-balanced model is preferred. Finally, we present evidence indicating that the BOLD signal DC offset contains information related to the processing of visual stimuli. Taken together, the results indicate that V1 pRFs are at least frequently organised in the exact constellation that allows them to function as bandpass filters, which makes the separation of stimulus contrast and luminance possible. We further speculate that if the DoG models stimulus contrast, the DC offset may reflect stimulus luminance. These findings suggest that it may be possible to separate contrast and luminance processing in fMRI experiments and this could lead to new insights on the haemodynamic response.

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.

Population Receptive Field Characteristics in the between- and Within-Digit Dimensions of the Undominant Hand in the Primary Somatosensory Cortex

Somatotopy is an important guiding principle for sensory fiber organization in the primary somatosensory cortex (S1), which reflects tactile information processing and is associated with disease-related reorganization. However, it is difficult to measure the neuronal encoding scheme in S1 in vivo in normal participants. Here, we investigated the somatotopic map of the undominant hand using a Bayesian population receptive field (pRF) model. The model was established in hand space with between- and within-digit dimensions. In the between-digit dimension, orderly representation was found, which had low variability across participants. The pRF shape tended to be elliptical for digits with high spatial acuity, for which the long axis was along the within-digit dimension. In addition, the pRF width showed different change trends in the 2 dimensions across digits. These results provide new insights into the neural mechanisms in S1, allowing for in-depth investigation of somatosensory information processing and disease-related reorganization.

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.

Combining stimulus types for improved coverage in population receptive field mapping

Retinotopy experiments using population receptive field (pRF) mapping are ideal for assigning regions in the visual field to cortical brain areas. While various designs for visual stimulation were suggested in the literature, all have specific shortcomings regarding visual field coverage. Here we acquired high-resolution 7 Tesla fMRI data to compare pRF-based coverage maps obtained with the two most commonly used stimulus variants: moving bars; rotating wedges and expanding rings. We find that stimulus selection biases the spatial distribution of pRF centres. In addition, eccentricity values and pRF sizes obtained from wedge/ring or bar stimulation runs show systematic differences. Wedge/ring stimulation results show lower eccentricity values and strongly reduced pRF sizes compared to bar stimulation runs. Statistical comparison shows significantly higher pRF centre numbers in the foveal 2° region of the visual field for wedge/ring compared to bar stimuli. We suggest and evaluate approaches for combining pRF data from different visual stimulus patterns to obtain improved mapping results.

The organizational principles of de-differentiated topographic maps in somatosensory cortex

Topographic maps are a fundamental feature of cortex architecture in the mammalian brain. One common theory is that the de-differentiation of topographic maps links to impairments in everyday behavior due to less precise functional map readouts. Here, we tested this theory by characterizing de-differentiated topographic maps in primary somatosensory cortex (SI) of younger and older adults by means of ultra-high resolution functional magnetic resonance imaging together with perceptual finger individuation and hand motor performance. Older adults' SI maps showed similar amplitude and size to younger adults' maps, but presented with less representational similarity between distant fingers. Larger population receptive field sizes in older adults' maps did not correlate with behavior, whereas reduced cortical distances between D2 and D3 related to worse finger individuation but better motor performance. Our data uncover the drawbacks of a simple de-differentiation model of topographic map function, and motivate the introduction of feature-based models of cortical reorganization.

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.

Assessing Uncertainty and Reliability of Connective Field Estimations From Resting State fMRI Activity at 3T

Connective Field (CF) modeling estimates the local spatial integration between signals in distinct cortical visual field areas. As we have shown previously using 7T data, CF can reveal the visuotopic organization of visual cortical areas even when applied to BOLD activity recorded in the absence of external stimulation. This indicates that CF modeling can be used to evaluate cortical processing in participants in which the visual input may be compromised. Furthermore, by using Bayesian CF modeling it is possible to estimate the co-variability of the parameter estimates and therefore, apply CF modeling to single cases. However, no previous studies evaluated the (Bayesian) CF model using 3T resting-state fMRI data. This is important since 3T scanners are much more abundant and more often used in clinical research compared to 7T scanners. Therefore in this study, we investigate whether it is possible to obtain meaningful CF estimates from 3T resting state (RS) fMRI data. To do so, we applied the standard and Bayesian CF modeling approaches on two RS scans, which were separated by the acquisition of visual field mapping data in 12 healthy participants. Our results show good agreement between RS- and visual field (VF)- based maps using either the standard or Bayesian CF approach. In addition to quantify the uncertainty associated with each estimate in both RS and VF data, we applied our Bayesian CF framework to provide the underlying marginal distribution of the CF parameters. Finally, we show how an additional CF parameter, beta, can be used as a data-driven threshold on the RS data to further improve CF estimates. We conclude that Bayesian CF modeling can characterize local functional connectivity between visual cortical areas from RS data at 3T. Moreover, observations obtained using 3T scanners were qualitatively similar to those reported for 7T. In particular, we expect the ability to assess parameter uncertainty in individual participants will be important for future clinical studies.

Foveal pRF properties in the visual cortex depend on the extent of stimulated visual field

Previous studies demonstrated that alterations in functional MRI derived receptive field (pRF) properties in cortical projection zones of retinal lesions can erroneously be mistaken for cortical large-scale reorganization in response to visual system pathologies. We tested, whether such confounds are also evident in the normal cortical projection zone of the fovea for simulated peripheral visual field defects. We applied fMRI-based visual field mapping of the central visual field at 3 T in eight controls to compare the pRF properties of the central visual field of a reference condition (stimulus radius: 14°) and two conditions with simulated peripheral visual field defect, i.e., with a peripheral gray mask, stimulating only the central 7° or 4° radius. We quantified, for the cortical representation of the actually stimulated visual field, the changes in the position and size of the pRFs associated with reduced peripheral stimulation using conventional and advanced pRF modeling. We found foveal pRF-positions (≤3°) to be significantly shifted towards the periphery (p<0.05, corrected). These pRF-shifts were largest for the 4° condition [visual area (mean eccentricity shift): V1 (0.9°), V2 (0.9°), V3 (1.0°)], but also evident for the 7° condition [V1 (0.5°), V2 (0.5°), V3 (0.9°)]. Further, an overall enlargement of pRF-sizes was observed. These findings indicate the dependence of foveal pRF parameters on the spatial extent of the stimulated visual field and are likely associated with methodological biases and/or physiological mechanisms. Consequently, our results imply that, previously reported similar findings in patients with actual peripheral scotomas need to be interpreted with caution and indicate the need for adequate control conditions in investigations of visual cortex reorganization.

Encoding schemes in somatosensation: From micro- to meta-topography

Encoding schemes are systematic large-scale arrangements that convert incoming sensory information into a format required for further information processing. The increased spatial resolution of brain images obtained with ultra-high field magnetic resonance imaging at 7 T (7T-MRI) and above increases the granularity and precision of processing units that mediate the link between neuronal encoding and functional readouts. Here, these new developments are reviewed with a focus on human tactile encoding schemes derived from small-scale processing units (in the order of 0.5-5 mm) that are relevant for theoretical and practical concepts of somatosensory encoding and cortical plasticity. Precisely, we review recent approaches to characterize meso-scale maps, layer units, and cortical fields in the sensorimotor cortex of the living human brain and discuss their impact on theories of perception, motor control, topographic encoding, and cortical plasticity. Finally, we discuss concepts on the integration of small-scale processing units into functional networks that span multiple topographic maps and multiple cortical areas. Novel research areas are highlighted that may help to bridge the gap between cortical microstructure and meta-topographic models on brain anatomy and function.

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.

Manipulating the structure of natural scenes using wavelets to study the functional architecture of perceptual hierarchies in the brain

Functional neuroimaging experiments that employ naturalistic stimuli (natural scenes, films, spoken narratives) provide insights into cognitive function "in the wild". Natural stimuli typically possess crowded, spectrally dense, dynamic, and multimodal properties within a rich multiscale structure. However, when using natural stimuli, various challenges exist for creating parametric manipulations with tight experimental control. Here, we revisit the typical spectral composition and statistical dependences of natural scenes, which distinguish them from abstract stimuli. We then demonstrate how to selectively degrade subtle statistical dependences within specific spatial scales using the wavelet transform. Such manipulations leave basic features of the stimuli, such as luminance and contrast, intact. Using functional neuroimaging of human participants viewing degraded natural images, we demonstrate that cortical responses at different levels of the visual hierarchy are differentially sensitive to subtle statistical dependences in natural images. This demonstration supports the notion that perceptual systems in the brain are optimally tuned to the complex statistical properties of the natural world. The code to undertake these stimulus manipulations, and their natural extension to dynamic natural scenes (films), is freely available.

A validation framework for neuroimaging software: The case of population receptive fields

Neuroimaging software methods are complex, making it a near certainty that some implementations will contain errors. Modern computational techniques (i.e., public code and data repositories, continuous integration, containerization) enable the reproducibility of the analyses and reduce coding errors, but they do not guarantee the scientific validity of the results. It is difficult, nay impossible, for researchers to check the accuracy of software by reading the source code; ground truth test datasets are needed. Computational reproducibility means providing software so that for the same input anyone obtains the same result, right or wrong. Computational validity means obtaining the right result for the ground-truth test data. We describe a framework for validating and sharing software implementations, and we illustrate its usage with an example application: population receptive field (pRF) methods for functional MRI data. The framework is composed of three main components implemented with containerization methods to guarantee computational reproducibility. In our example pRF application, those components are: (1) synthesis of fMRI time series from ground-truth pRF parameters, (2) implementation of four public pRF analysis tools and standardization of inputs and outputs, and (3) report creation to compare the results with the ground truth parameters. The framework was useful in identifying realistic conditions that lead to imperfect parameter recovery in all four pRF implementations, that would remain undetected using classic validation methods. We provide means to mitigate these problems in future experiments. A computational validation framework supports scientific rigor and creativity, as opposed to the oft-repeated suggestion that investigators rely upon a few agreed upon packages. We hope that the framework will be helpful to validate other critical neuroimaging algorithms, as having a validation framework helps (1) developers to build new software, (2) research scientists to verify the software's accuracy, and (3) reviewers to evaluate the methods used in publications and grants.

A probabilistic atlas of finger dominance in the primary somatosensory cortex

With the advent of ultra-high field (7T), high spatial resolution functional MRI (fMRI) has allowed the differentiation of the cortical representations of each of the digits at an individual-subject level in human primary somatosensory cortex (S1). Here we generate a probabilistic atlas of the contralateral SI representations of the digits of both the left and right hand in a group of 22 right-handed individuals. The atlas is generated in both volume and surface standardised spaces from somatotopic maps obtained by delivering vibrotactile stimulation to each distal phalangeal digit using a travelling wave paradigm. Metrics quantify the likelihood of a given position being assigned to a digit (full probability map) and the most probable digit for a given spatial location (maximum probability map). The atlas is validated using a leave-one-out cross validation procedure. Anatomical variance across the somatotopic map is also assessed to investigate whether the functional variability across subjects is coupled to structural differences. This probabilistic atlas quantifies the variability in digit representations in healthy subjects, finding some quantifiable separability between digits 2, 3 and 4, a complex overlapping relationship between digits 1 and 2, and little agreement of digit 5 across subjects. The atlas and constituent subject maps are available online for use as a reference in future neuroimaging studies.

Triple visual hemifield maps in a case of optic chiasm hypoplasia

In humans, each hemisphere comprises an overlay of two visuotopic maps of the contralateral visual field, one from each eye. Is the capacity of the visual cortex limited to these two maps or are plastic mechanisms available to host more maps? We determined the cortical organization of the visual field maps in a rare individual with chiasma hypoplasia, where visual cortex plasticity is challenged to accommodate three hemifield maps. Using high-resolution fMRI at 7T and diffusion-weighted MRI at 3T, we found three hemiretinal inputs, instead of the normal two, to converge onto the left hemisphere. fMRI-based population receptive field mapping of the left V1-V3 at 3T revealed three superimposed hemifield representations in the left visual cortex, i.e. two representations of opposing visual hemifields from the left eye and one right hemifield representation from the right eye. We conclude that developmental plasticity including the re-wiring of local intra- and cortico-cortical connections is pivotal to support the coexistence and functioning of three hemifield maps within one hemisphere.

Mapping sequences can bias population receptive field estimates

Population receptive field (pRF) modelling is a common technique for estimating the stimulus-selectivity of populations of neurons using neuroimaging. Here, we aimed to address if pRF properties estimated with this method depend on the spatio-temporal structure and the predictability of the mapping stimulus. We mapped the polar angle preference and tuning width of voxels in visual cortex (V1-V4) of healthy, adult volunteers. We compared sequences sweeping orderly through the visual field or jumping from location to location employing stimuli of different width (45° vs 6°) and cycles of variable duration (8s vs 60s). While we did not observe any systematic influence of stimulus predictability, the temporal structure of the sequences significantly affected tuning width estimates. Ordered designs with large wedges and short cycles produced systematically smaller estimates than random sequences. Interestingly, when we used small wedges and long cycles, we obtained larger tuning width estimates for ordered than random sequences. We suggest that ordered and random mapping protocols show different susceptibility to other design choices such as stimulus type and duration of the mapping cycle and can produce significantly different pRF results.

Studying Cortical Plasticity in Ophthalmic and Neurological Disorders: From Stimulus-Driven to Cortical Circuitry Modeling Approaches

Unsolved questions in computational visual neuroscience research are whether and how neurons and their connecting cortical networks can adapt when normal vision is compromised by a neurodevelopmental disorder or damage to the visual system. This question on neuroplasticity is particularly relevant in the context of rehabilitation therapies that attempt to overcome limitations or damage, through either perceptual training or retinal and cortical implants. Studies on cortical neuroplasticity have generally made the assumption that neuronal population properties and the resulting visual field maps are stable in healthy observers. Consequently, differences in the estimates of these properties between patients and healthy observers have been taken as a straightforward indication for neuroplasticity. However, recent studies imply that the modeled neuronal properties and the cortical visual maps vary substantially within healthy participants, e.g., in response to specific stimuli or under the influence of cognitive factors such as attention. Although notable advances have been made to improve the reliability of stimulus-driven approaches, the reliance on the visual input remains a challenge for the interpretability of the obtained results. Therefore, we argue that there is an important role in the study of cortical neuroplasticity for approaches that assess intracortical signal processing and circuitry models that can link visual cortex anatomy, function, and dynamics.

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.

Accurate and efficient extraction of fringe orientation from the poor-quality ESPI fringe pattern with a convolutional neural network

The fringe orientation is an important feature of the electronic speckle interferometry (ESPI) fringe pattern. Accurate and efficient calculation of the fringe orientation is very important for subsequent electronic speckle processing such as skeleton extraction and image filtering. To accurately and efficiently estimate fringe orientation, we propose an effective method based on a convolutional neural network. In the proposed method, the network needs clean-noisy image pairs to train and noisy images with theoretical value to test. The aligned noise-free ESPI fringe pattern orientation fields are fairly good estimations for the corresponding noise ones. After the model training is done, the other multiple ESPI fringe patterns are fed to the trained network simultaneously; the corresponding orientation results can be obtained accurately and efficiently. The advantage of using this method to extract the orientation is that the fringe orientation information can be extracted accurately and efficiently without complicated parameter adjustment. We evaluate the performance of our method via applying our method to the computer-simulated and experimentally acquired ESPI fringe patterns and comparing the results with those of three extensively used methods.

Population receptive field and connectivity properties of the early visual cortex in human albinism

In albinism, the pathological decussation of the temporal retinal afferents at the optic chiasm leads to superimposed representations of opposing hemifields in the visual cortex. Here, we assessed the equivalence of the two representations and the cortico-cortical connectivity of the early visual areas. Applying fMRI-based population receptive field (pRF)-mapping (both hemifield and bilateral mapping) and connective field (CF)-modeling, we investigated the early visual cortex in 6 albinotic participants and 4 controls. In albinism, superimposed retinotopic representations of the contra- and ipsilateral visual hemifield were observed on the hemisphere contralateral to the stimulated eye. This was confirmed by the observation of bilateral pRFs during bilateral mapping. Hemifield mapping revealed similar pRF-sizes for both hemifield representations throughout V1 to V3. The typical increase of V1-sampling extent for V3 compared to V2 was not found for the albinotic participants. The similarity of the pRF-sizes for opposing visual hemifield representations highlights the equivalence of the two maps in the early visual cortex. The altered V1-sampling extent in V3 might indicate the adaptation of cortico-cortical connections to visual pathway abnormalities in albinism. These findings thus suggest that conservative developmental mechanisms are complemented by alterations of the extrastriate cortico-cortical connectivity.

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.