Brain oscillations might be traveling waves propagating in cortex. Studying their propagation within single cortical areas has mostly been restricted to invasive measurements. Their investigation in healthy humans, however, requires non-invasive recordings, such as MEG or EEG. Identifying traveling waves with these techniques is challenging because source summation, volume conduction, and low signal-to-noise ratios make it difficult to localize cortical activity from sensor responses. The difficulty is compounded by the lack of a known ground truth in traveling wave experiments. Rather than source-localizing cortical responses from sensor activity, we developed a two-part model-based neuroimaging approach: (1) The putative neural sources of a propagating oscillation were modeled within primary visual cortex (V1) via retinotopic mapping from functional MRI recordings (encoding model); and (2) the modeled sources were projected onto MEG and EEG sensors to predict the resulting signal using a biophysical head model. We tested our model by comparing its predictions against the MEG-EEG signal obtained when participants viewed visual stimuli designed to elicit either fovea-to-periphery or periphery-to-fovea traveling waves or standing waves in V1, in which ground truth cortical waves could be reasonably assumed. Correlations on within-sensor phase and amplitude relations between predicted and measured data revealed good model performance. Crucially, the model predicted sensor data more accurately when the input to the model was a traveling wave going in the stimulus direction compared to when the input was a standing wave, or a traveling wave in a different direction. Furthermore, model accuracy peaked at the spatial and temporal frequency parameters of the visual stimulation. Together, our model successfully recovers traveling wave properties in cortex when they are induced by traveling waves in stimuli. This provides a sound basis for using MEG-EEG to study endogenous traveling waves in cortex and test hypotheses related with their role in cognition.

Primary visual cortex (V1) has long served as a model system for understanding cortical organization. Although its structural and functional properties vary markedly across its surface, patterns of covariation suggest possible underlying constancies. Such constancies would imply that V1 is composed of multiple identical units whose visual properties differ only due to differences in their inputs. To test this, we used fMRI to investigate how V1 cortical magnification and preferred spatial frequency covary with eccentricity and polar angle, measured in 40 observers. V1 cortical magnification and preferred spatial frequency were strongly correlated across eccentricity and around polar angle, however their relation differed between these dimensions: they were proportional across eccentricity but not polar angle. The constant ratio of cortical magnification to preferred spatial frequency when measured as a function of eccentricity suggests a shared underlying cause of variation in the two properties, e.g., the gradient of retinal ganglion cell density across eccentricity. In contrast, the deviation from proportionality around polar angle implies that cortical variation differs from that in retina along this dimension. Thus, a constancy hypothesis is supported for one of the two spatial dimensions of V1, highlighting the importance of examining the full 2D-map to understand how V1 is organized.

Neural responses in visual cortex adapt to prolonged and repeated stimuli. While adaptation occurs across the visual cortex, it is unclear how adaptation patterns and computational mechanisms differ across the visual hierarchy. Here we characterize two signatures of short-term neural adaptation in time-varying intracranial electroencephalography (iEEG) data collected while participants viewed naturalistic image categories varying in duration and repetition interval. Ventral- and lateral-occipitotemporal cortex exhibit slower and prolonged adaptation to single stimuli and slower recovery from adaptation to repeated stimuli compared to V1-V3. For category-selective electrodes, recovery from adaptation is slower for preferred than non-preferred stimuli. To model neural adaptation we augment our delayed divisive normalization (DN) model by scaling the input strength as a function of stimulus category, enabling the model to accurately predict neural responses across multiple image categories. The model fits suggest that differences in adaptation patterns arise from slower normalization dynamics in higher visual areas interacting with differences in input strength resulting from category selectivity. Our results reveal systematic differences in temporal adaptation of neural population responses between lower and higher visual brain areas and show that a single computational model of history-dependent normalization dynamics, fit with area-specific parameters, accounts for these differences.

An influential account of neuronal responses in primary visual cortex is the normalized energy model. This model is often implemented as a multi-stage computation. The first stage is linear filtering. The second stage is the extraction of contrast energy, whereby a complex cell computes the squared and summed outputs of a pair of the linear filters in quadrature phase. The third stage is normalization, in which a local population of complex cells mutually inhibit one another. Because the population includes cells tuned to a range of orientations and spatial frequencies, the result is that the responses are effectively normalized by the local stimulus contrast. Here, using evidence from human functional MRI, we show that the classical model fails to account for the relative responses to two classes of stimuli: straight, parallel, band-passed contours (gratings), and curved, band-passed contours (snakes). The snakes elicit fMRI responses that are about twice as large as the gratings, yet a traditional divisive normalization model predicts responses that are about the same. Motivated by these observations and others from the literature, we implement a divisive normalization model in which cells matched in orientation tuning ("tuned normalization") preferentially inhibit each other. We first show that this model accounts for differential responses to these two classes of stimuli. We then show that the model successfully generalizes to other band-pass textures, both in V1 and in extrastriate cortex (V2 and V3). We conclude that even in primary visual cortex, complex features of images such as the degree of heterogeneity, can have large effects on neural responses.

Visual performance varies around the visual field. It is best near the fovea compared to the periphery, and at iso-eccentric locations it is best on the horizontal, intermediate on the lower, and poorest on the upper meridian. The fovea-to-periphery performance decline is linked to the decreases in cone density, retinal ganglion cell (RGC) density, and V1 cortical magnification factor (CMF) as eccentricity increases. The origins of polar angle asymmetries are not well understood. Optical quality and cone density vary across the retina, but recent computational modeling has shown that these factors can only account for a small percentage of behavior. Here, we investigate how visual processing beyond the cone photon absorptions contributes to polar angle asymmetries in performance. First, we quantify the extent of asymmetries in cone density, midget RGC density, and V1 CMF. We find that both polar angle asymmetries and eccentricity gradients increase from cones to mRGCs, and from mRGCs to cortex. Second, we extend our previously published computational observer model to quantify the contribution of phototransduction by the cones and spatial filtering by mRGCs to behavioral asymmetries. Starting with photons emitted by a visual display, the model simulates the effect of human optics, cone isomerizations, phototransduction, and mRGC spatial filtering. The model performs a forced choice orientation discrimination task on mRGC responses using a linear support vector machine classifier. The model shows that asymmetries in a decision maker's performance across polar angle are greater when assessing the photocurrents than when assessing isomerizations and are greater still when assessing mRGC signals. Nonetheless, the polar angle asymmetries of the mRGC outputs are still considerably smaller than those observed from human performance. We conclude that cone isomerizations, phototransduction, and the spatial filtering properties of mRGCs contribute to polar angle performance differences, but that a full account of these differences will entail additional contribution from cortical representations.

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.

Visual performance depends on polar angle, even when eccentricity is held constant; on many psychophysical tasks observers perform best when stimuli are presented on the horizontal meridian, worst on the upper vertical, and intermediate on the lower vertical meridian. This variation in performance 'around' the visual field can be as pronounced as that of doubling the stimulus eccentricity. The causes of these asymmetries in performance are largely unknown. Some factors in the eye, e.g. cone density, are positively correlated with the reported variations in visual performance with polar angle. However, the question remains whether these correlations can quantitatively explain the perceptual differences observed 'around' the visual field. To investigate the extent to which the earliest stages of vision-optical quality and cone density-contribute to performance differences with polar angle, we created a computational observer model. The model uses the open-source software package ISETBIO to simulate an orientation discrimination task for which visual performance differs with polar angle. The model starts from the photons emitted by a display, which pass through simulated human optics with fixational eye movements, followed by cone isomerizations in the retina. Finally, we classify stimulus orientation using a support vector machine to learn a linear classifier on the photon absorptions. To account for the 30% increase in contrast thresholds for upper vertical compared to horizontal meridian, as observed psychophysically on the same task, our computational observer model would require either an increase of ~7 diopters of defocus or a reduction of 500% in cone density. These values far exceed the actual variations as a function of polar angle observed in human eyes. Therefore, we conclude that these factors in the eye only account for a small fraction of differences in visual performance with polar angle. Substantial additional asymmetries must arise in later retinal and/or cortical processing.

Visual neurons respond to static images with specific dynamics: neuronal responses sum sub-additively over time, reduce in amplitude with repeated or sustained stimuli (neuronal adaptation), and are slower at low stimulus contrast. Here, we propose a simple model that predicts these seemingly disparate response patterns observed in a diverse set of measurements-intracranial electrodes in patients, fMRI, and macaque single unit spiking. The model takes a time-varying contrast time course of a stimulus as input, and produces predicted neuronal dynamics as output. Model computation consists of linear filtering, expansive exponentiation, and a divisive gain control. The gain control signal relates to but is slower than the linear signal, and this delay is critical in giving rise to predictions matched to the observed dynamics. Our model is simpler than previously proposed related models, and fitting the model to intracranial EEG data uncovers two regularities across human visual field maps: estimated linear filters (temporal receptive fields) systematically differ across and within visual field maps, and later areas exhibit more rapid and substantial gain control. The model is further generalizable to account for dynamics of contrast-dependent spike rates in macaque V1, and amplitudes of fMRI BOLD in human V1.

Visual neuroscientists have discovered fundamental properties of neural representation through careful analysis of responses to controlled stimuli. Typically, different properties are studied and modeled separately. To integrate our knowledge, it is necessary to build general models that begin with an input image and predict responses to a wide range of stimuli. In this study, we develop a model that accepts an arbitrary band-pass grayscale image as input and predicts blood oxygenation level dependent (BOLD) responses in early visual cortex as output. The model has a cascade architecture, consisting of two stages of linear and nonlinear operations. The first stage involves well-established computations-local oriented filters and divisive normalization-whereas the second stage involves novel computations-compressive spatial summation (a form of normalization) and a variance-like nonlinearity that generates selectivity for second-order contrast. The parameters of the model, which are estimated from BOLD data, vary systematically across visual field maps: compared to primary visual cortex, extrastriate maps generally have larger receptive field size, stronger levels of normalization, and increased selectivity for second-order contrast. Our results provide insight into how stimuli are encoded and transformed in successive stages of visual processing.