Accounting for Bias in the Estimation of r 2 between Two Sets of Noisy Neural Responses.

The Pearson correlation coefficient squared, r 2, is an important tool used in the analysis of neural data to quantify the similarity between neural tuning curves. Yet this metric is biased by trial-to-trial variability; as trial-to-trial variability increases, measured correlation decreases. Major lines of research are confounded by this bias, including those involving the study of invariance of neural tuning across conditions and the analysis of the similarity of tuning across neurons. To address this, we extend an estimator, [Formula: see text], that was recently developed for estimating model-to-neuron correlation, in which a noisy signal is compared with a noise-free prediction, to the case of neuron-to-neuron correlation, in which two noisy signals are compared with each other. We compare the performance of our novel estimator to a prior method developed by Spearman, commonly used in other fields but widely overlooked in neuroscience, and find that our method has less bias. We then apply our estimator to demonstrate how it avoids drastic confounds introduced by trial-to-trial variability using data collected in two prior studies (macaque, both sexes) that examined two different forms of invariance in the neural encoding of visual inputs-translation invariance and fill-outline invariance. Our results quantify for the first time the gradual falloff with spatial offset of translation-invariant shape selectivity within visual cortical neuronal receptive fields and offer a principled method to compare invariance in noisy biological systems to that in noise-free models.SIGNIFICANCE STATEMENT Quantifying the similarity between two sets of averaged neural responses is fundamental to the analysis of neural data. A ubiquitous metric of similarity, the correlation coefficient, is attenuated by trial-to-trial variability that arises from many irrelevant factors. Spearman recognized this problem and proposed corrected methods that have been extended over a century. We show this method has large asymptotic biases that can be overcome using a novel estimator. Despite the frequent use of the correlation coefficient in neuroscience, consensus on how to address this fundamental statistical issue has not been reached. We provide an accurate estimator of the correlation coefficient and apply it to gain insight into visual invariance.

Perceptual Texture Dimensions Modulate Neuronal Response Dynamics in Visual Cortical Area V4.

Texture is an important visual attribute for surface pattern discrimination and therefore object segmentation, but the neural bases of texture perception are largely unknown. Previously, we demonstrated that the responses of V4 neurons to naturalistic texture patches are sensitive to four key features of human texture perception: coarseness, directionality, regularity, and contrast. To begin to understand how distinct texture perception emerges from the dynamics of neuronal responses, in 2 macaque monkeys (1 male, 1 female), we investigated the relative contribution of the four texture attributes to V4 responses in terms of the strength and timing of response modulation. We found that the different feature dimensions are associated with different temporal dynamics. Specifically, the response modulation associated with directionality and regularity was significantly delayed relative to that associated with coarseness and contrast, suggesting that the latter are fundamentally simpler feature dimensions. The population of texture-selective neurons could be grouped into multiple clusters based on the combination of feature dimensions encoded, and those subpopulations displayed distinct temporal dynamics characterized by the weighted combinations of multiple features. Finally, we applied a population decoding approach to demonstrate that texture category information can be obtained from short temporal windows across time. These results demonstrate that the representation of different perceptually relevant texture features emerge over time in the responses of V4 neurons. The observed temporal organization provides a framework to interpret how the processing of surface features unfolds in early and midlevel cortical stages, and could ultimately inform the interpretation of perceptual texture dynamics.SIGNIFICANCE STATEMENT To delineate how neuronal responses underlie our ability to perceive visual textures, we related four key perceptual dimensions (coarseness, directionality, regularity, and contrast) of naturalistic textures to the strength and timing of modulation of neuronal responses in area V4, an intermediate stage in the form-processing, ventral visual pathway. Our results provide the first characterization of V4 temporal dynamics for texture encoding along perceptually defined axes.

Accounting for Biases in the Estimation of Neuronal Signal Correlation.

Signal correlation (rs) is commonly defined as the correlation between the tuning curves of two neurons and is widely used as a metric of tuning similarity. It is fundamental to how populations of neurons represent stimuli and has been central to many studies of neural coding. Yet the classic estimate, Pearson's correlation coefficient, [Formula: see text], between the average responses of two neurons to a set of stimuli suffers from confounding biases. The estimate [Formula: see text] can be downwardly biased by trial-to-trial variability and also upwardly biased by trial-to-trial correlation between neurons, and these biases can hide important aspects of neural coding. Here we provide analytic results on the source of these biases and explore them for ranges of parameters that are relevant for electrophysiological experiments. We then provide corrections for these biases that we validate in simulation. Furthermore, we apply these corrected estimators to make the following novel experimental observation in cortical area MT: pairs of nearby neurons that are strongly tuned for motion direction tend to have high signal correlation, and pairs that are weakly tuned tend to have low signal correlation. We dismiss a trivial explanation for this and find that an analogous trend holds for orientation tuning in the primary visual cortex. We also consider the potential consequences for encoding whereby the association of signal correlation and tuning strength naturally regularizes the dimensionality of downstream computations.SIGNIFICANCE STATEMENT Fundamental to how cortical neurons encode information about the environment is their functional similarity, that is, the redundancy in what they encode and their shared noise. These properties have been extensively studied theoretically and experimentally throughout the nervous system, but here we show that a common estimator of functional similarity has confounding biases. We characterize these biases and provide estimators that do not suffer from them. Using our improved estimators, we demonstrate a novel result, that is, there is a positive relationship between tuning curve similarity and amplitude for nearby neurons in the visual cortical motion area MT. We provide a simple stochastic model explaining this relationship and discuss how it would naturally regularize the dimensionality of neural encoding.

The unbiased estimation of the fraction of variance explained by a model.

The correlation coefficient squared, r2, is commonly used to validate quantitative models on neural data, yet it is biased by trial-to-trial variability: as trial-to-trial variability increases, measured correlation to a model's predictions decreases. As a result, models that perfectly explain neural tuning can appear to perform poorly. Many solutions to this problem have been proposed, but no consensus has been reached on which is the least biased estimator. Some currently used methods substantially overestimate model fit, and the utility of even the best performing methods is limited by the lack of confidence intervals and asymptotic analysis. We provide a new estimator, [Formula: see text], that outperforms all prior estimators in our testing, and we provide confidence intervals and asymptotic guarantees. We apply our estimator to a variety of neural data to validate its utility. We find that neural noise is often so great that confidence intervals of the estimator cover the entire possible range of values ([0, 1]), preventing meaningful evaluation of the quality of a model's predictions. This leads us to propose the use of the signal-to-noise ratio (SNR) as a quality metric for making quantitative comparisons across neural recordings. Analyzing a variety of neural data sets, we find that up to ∼ 40% of some state-of-the-art neural recordings do not pass even a liberal SNR criterion. Moving toward more reliable estimates of correlation, and quantitatively comparing quality across recording modalities and data sets, will be critical to accelerating progress in modeling biological phenomena.

Neural Coding for Shape and Texture in Macaque Area V4.

The distinct visual sensations of shape and texture have been studied separately in cortex; therefore, it remains unknown whether separate neuronal populations encode each of these properties or one population carries a joint encoding. We directly compared shape and texture selectivity of individual V4 neurons in awake macaques (1 male, 1 female) and found that V4 neurons lie along a continuum from strong tuning for boundary curvature of shapes to strong tuning for perceptual dimensions of texture. Among neurons tuned to both attributes, tuning for shape and texture were largely separable, with the latter delayed by ∼30 ms. We also found that shape stimuli typically evoked stronger, more selective responses than did texture patches, regardless of whether the latter were contained within or extended beyond the receptive field. These results suggest that there are separate specializations in mid-level cortical processing for visual attributes of shape and texture.SIGNIFICANCE STATEMENT Object recognition depends on our ability to see both the shape of the boundaries of objects and properties of their surfaces. However, neuroscientists have never before examined how shape and texture are linked together in mid-level visual cortex. In this study, we used systematically designed sets of simple shapes and texture patches to probe the responses of individual neurons in the primate visual cortex. Our results provide the first evidence that some cortical neurons specialize in processing shape whereas others specialize in processing textures. Most neurons lie between the ends of this continuum, and in these neurons we find that shape and texture encoding are largely independent.

Modeling diverse responses to filled and outline shapes in macaque V4.

Visual area V4 is an important midlevel cortical processing stage that subserves object recognition in primates. Studies investigating shape coding in V4 have largely probed neuronal responses with filled shapes, i.e., shapes defined by both a boundary and an interior fill. As a result, we do not know whether form-selective V4 responses are dictated by boundary features alone or if interior fill is also important. We studied 43 V4 neurons in two male macaque monkeys ( Macaca mulatta) with a set of 362 filled shapes and their corresponding outlines to determine how interior fill modulates neuronal responses in shape-selective neurons. Only a minority of neurons exhibited similar response strength and shape preferences for filled and outline stimuli. A majority responded preferentially to one stimulus category (either filled or outline shapes) and poorly to the other. Our findings are inconsistent with predictions of the hierarchical-max (HMax) V4 model that builds form selectivity from oriented boundary features and takes little account of attributes related to object surface, such as the phase of the boundary edge. We modified the V4 HMax model to include sensitivity to interior fill by either removing phase-pooling or introducing unoriented units at the V1 level; both modifications better explained our data without increasing the number of free parameters. Overall, our results suggest that boundary orientation and interior surface information are both maintained until at least the midlevel visual representation, consistent with the idea that object fill is important for recognition and perception in natural vision. NEW & NOTEWORTHY The shape of an object's boundary is critical for identification; consistent with this idea, models of object recognition predict that filled and outline versions of a shape are encoded similarly. We report that many neurons in a midlevel visual cortical area respond differently to filled and outline shapes and modify a biologically plausible model to account for our data. Our results suggest that representations of boundary shape and surface fill are interrelated in visual cortex.

A Model of Binocular Motion Integration in MT Neurons.

UNLABELLED: Primate cortical area MT plays a central role in visual motion perception, but models of this area have largely overlooked the binocular integration of motion signals. Recent electrophysiological studies tested binocular integration in MT and found surprisingly that MT neurons lose their hallmark "pattern motion" selectivity when stimuli are presented dichoptically and that many neurons are selective for motion-in-depth (MID). By unifying these novel observations with insights from monocular, frontoparallel motion studies concurrently in a binocular MT motion model, we generated clear, testable predictions about the circuitry and mechanisms underlying visual motion processing. We built binocular models in which signals from left- and right-eye streams could be integrated at various stages from V1 to MT, attempting to create the simplest plausible circuits that accounted for the physiological range of pattern motion selectivity, that explained changes across this range for dichoptic stimulus presentation, and that spanned the spectrum of MID selectivity observed in MT. Our successful models predict that motion-opponent suppression is the key mechanism to account for the striking loss of pattern motion sensitivity with dichoptic plaids, that opponent suppression precedes binocular integration, and that opponent suppression will be stronger in inputs to pattern cells than to component cells. We also found an unexpected connection between circuits for pattern motion selectivity and MID selectivity, suggesting that these two separately studied phenomena could be related. These results also hold in models that include binocular disparity computations, providing a platform for future exploration of binocular response properties in MT. SIGNIFICANCE STATEMENT: The neural pathways underlying our sense of visual motion are among the most studied and well-understood parts of the primate cerebral cortex. Nevertheless, our understanding is incomplete because electrophysiological research has focused mainly on motion in the 2D frontoparallel plane, even though real-world motion often occurs in three dimensions, involving a change in distance from the viewer. Recent studies have revealed a specialization for sensing 3D motion in area MT, the cortical area most tightly linked to the processing and perception of visual motion. Our study provides the first model to explain how 3D motion sensitivity can arise in MT neurons and predicts how essential features of 2D motion integration may relate to 3D motion processing.

Mechanisms for Rapid Adaptive Control of Motion Processing in Macaque Visual Cortex.

A key feature of neural networks is their ability to rapidly adjust their function, including signal gain and temporal dynamics, in response to changes in sensory inputs. These adjustments are thought to be important for optimizing the sensitivity of the system, yet their mechanisms remain poorly understood. We studied adaptive changes in temporal integration in direction-selective cells in macaque primary visual cortex, where specific hypotheses have been proposed to account for rapid adaptation. By independently stimulating direction-specific channels, we found that the control of temporal integration of motion at one direction was independent of motion signals driven at the orthogonal direction. We also found that individual neurons can simultaneously support two different profiles of temporal integration for motion in orthogonal directions. These findings rule out a broad range of adaptive mechanisms as being key to the control of temporal integration, including untuned normalization and nonlinearities of spike generation and somatic adaptation in the recorded direction-selective cells. Such mechanisms are too broadly tuned, or occur too far downstream, to explain the channel-specific and multiplexed temporal integration that we observe in single neurons. Instead, we are compelled to conclude that parallel processing pathways are involved, and we demonstrate one such circuit using a computer model. This solution allows processing in different direction/orientation channels to be separately optimized and is sensible given that, under typical motion conditions (e.g., translation or looming), speed on the retina is a function of the orientation of image components. SIGNIFICANCE STATEMENT: Many neurons in visual cortex are understood in terms of their spatial and temporal receptive fields. It is now known that the spatiotemporal integration underlying visual responses is not fixed but depends on the visual input. For example, neurons that respond selectively to motion direction integrate signals over a shorter time window when visual motion is fast and a longer window when motion is slow. We investigated the mechanisms underlying this useful adaptation by recording from neurons as they responded to stimuli moving in two different directions at different speeds. Computer simulations of our results enabled us to rule out several candidate theories in favor of a model that integrates across multiple parallel channels that operate at different time scales.

Refinement and Pattern Formation in Neural Circuits by the Interaction of Traveling Waves with Spike-Timing Dependent Plasticity.

Traveling waves in the developing brain are a prominent source of highly correlated spiking activity that may instruct the refinement of neural circuits. A candidate mechanism for mediating such refinement is spike-timing dependent plasticity (STDP), which translates correlated activity patterns into changes in synaptic strength. To assess the potential of these phenomena to build useful structure in developing neural circuits, we examined the interaction of wave activity with STDP rules in simple, biologically plausible models of spiking neurons. We derive an expression for the synaptic strength dynamics showing that, by mapping the time dependence of STDP into spatial interactions, traveling waves can build periodic synaptic connectivity patterns into feedforward circuits with a broad class of experimentally observed STDP rules. The spatial scale of the connectivity patterns increases with wave speed and STDP time constants. We verify these results with simulations and demonstrate their robustness to likely sources of noise. We show how this pattern formation ability, which is analogous to solutions of reaction-diffusion systems that have been widely applied to biological pattern formation, can be harnessed to instruct the refinement of postsynaptic receptive fields. Our results hold for rich, complex wave patterns in two dimensions and over several orders of magnitude in wave speeds and STDP time constants, and they provide predictions that can be tested under existing experimental paradigms. Our model generalizes across brain areas and STDP rules, allowing broad application to the ubiquitous occurrence of traveling waves and to wave-like activity patterns induced by moving stimuli.

Spectral receptive fields do not explain tuning for boundary curvature in V4.

The midlevel visual cortical area V4 in the primate is thought to be critical for the neural representation of visual shape. Several studies agree that V4 neurons respond to contour features, e.g., convexities and concavities along a shape boundary, that are more complex than the oriented segments encoded by neurons in the primary visual cortex. Here we compare two distinct approaches to modeling V4 shape selectivity: one based on a spectral receptive field (SRF) map in the orientation and spatial frequency domain and the other based on a map in an object-centered angular position and contour curvature space. We test the ability of these two characterizations to account for the responses of V4 neurons to a set of parametrically designed two-dimensional shapes recorded previously in the awake macaque. We report two lines of evidence suggesting that the SRF model does not capture the contour sensitivity of V4 neurons. First, the SRF model discards spatial phase information, which is inconsistent with the neuronal data. Second, the amount of variance explained by the SRF model was significantly less than that explained by the contour curvature model. Notably, cells best fit by the curvature model were poorly fit by the SRF model, the latter being appropriate for a subset of V4 neurons that appear to be orientation tuned. These limitations of the SRF model suggest that a full understanding of midlevel shape representation requires more complicated models that preserve phase information and perhaps deal with object segmentation.

Ultra-high density electrodes improve detection, yield, and cell type identification in neuronal recordings.

To understand the neural basis of behavior, it is essential to sensitively and accurately measure neural activity at single neuron and single spike resolution. Extracellular electrophysiology delivers this, but it has biases in the neurons it detects and it imperfectly resolves their action potentials. To minimize these limitations, we developed a silicon probe with much smaller and denser recording sites than previous designs, called Neuropixels Ultra (NP Ultra). This device samples neuronal activity at ultra-high spatial density (~10 times higher than previous probes) with low noise levels, while trading off recording span. NP Ultra is effectively an implantable voltage-sensing camera that captures a planar image of a neuron's electrical field. We use a spike sorting algorithm optimized for these probes to demonstrate that the yield of visually-responsive neurons in recordings from mouse visual cortex improves up to ~3-fold. We show that NP Ultra can record from small neuronal structures including axons and dendrites. Recordings across multiple brain regions and four species revealed a subset of extracellular action potentials with unexpectedly small spatial spread and axon-like features. We share a large-scale dataset of these brain-wide recordings in mice as a resource for studies of neuronal biophysics. Finally, using ground-truth identification of three major inhibitory cortical cell types, we found that these cell types were discriminable with approximately 75% success, a significant improvement over lower-resolution recordings. NP Ultra improves spike sorting performance, detection of subcellular compartments, and cell type classification to enable more powerful dissection of neural circuit activity during behavior.

Inter-neuronal correlation distinguishes mechanisms of direction selectivity in cortical circuit models.

Direction selectivity is a fundamental physiological property that arises from primary visual cortex (V1) circuitry, yet basic questions of how direction-selective (DS) receptive fields are constructed remain unanswered. We built a set of simple, plausible neuronal circuits that produce DS cells via different mechanisms and tested these circuits to determine how they can be distinguished experimentally. Our models consisted of populations of spiking units representing physiological cell classes ranging from LGN cells to V1 complex DS cells. They differed in network architecture and DS mechanism, including linear summation of non-DS simple-cell inputs or nonlinear pairwise combinations of non-DS inputs. The circuits also varied in the location of the DS time delay and whether the DS interaction was facilitatory or suppressive. We tested the models with visual stimuli often used experimentally, including sinusoidal gratings and flashed bars, and computed shuffle-corrected cross-correlograms (CCGs) of spike trains from pairs of units that would be accessible to extracellular recording. We found that CCGs revealed fundamental features of the DS models, including the location of signal delays in the DS circuit and the sign (facilitatory or suppressive) of DS interactions. We also found that correlation was strongly stimulus-dependent, changing with direction and temporal frequency in a manner that generalized across model architectures. Our models make specific predictions for designing, optimizing, and interpreting electrophysiology experiments aimed at resolving DS circuitry and provide new insights into mechanisms that could underlie stimulus-dependent correlation. The models are available and easy to explore at www.imodel.org.

Long-range clustered connections within extrastriate visual area V5/MT of the rhesus macaque.

Visual area V5/MT in the rhesus macaque has a distinct functional organization, where neurons with specific preferences for direction of motion and binocular disparity are co-organized in columns or clusters. Here, we analyze the pattern of intrinsic connectivity within cortical area V5/MT in both parasagittal sections of the intact brain and tangential sections from flatmounted cortex using small injections of the retrograde tracer cholera toxin subunit b. Labeled cells were predominantly found in cortical layers 2, 3, and 6. Going along the cortical layers, labeled cells were concentrated in regularly spaced clusters. The clusters nearest to the injection site were approximately 2 mm from its center. In flatmounted cortex, along the dorsoventral axis of V5/MT, we identified further clusters of labeled cells up to 10 mm from the injection site. Quantitative analysis of parasagittal sections estimated average cluster spacing at 2.2 mm; in cortical flatmounts, spacing was 2.3 mm measured radially from the injection site. The results suggest a regular pattern of intrinsic connectivity within V5/MT, which is consistent with connectivity between sites with a common preference for both direction of motion and binocular depth. The long-range connections can potentially account for the large suppressive surrounds of V5/MT neurons.

Dissociation in neuronal encoding of object versus surface motion in the primate brain.

A paradox exists in our understanding of motion processing in the primate visual system: neurons in the dorsal motion processing stream often strikingly fail to encode long-range and perceptually salient jumps of a moving stimulus. Psychophysical studies suggest that such long-range motion, which requires integration over more distant parts of the visual field, may be based on higher-order motion processing mechanisms that rely on feature or object tracking. Here, we demonstrate that ventral visual area V4, long recognized as critical for processing static scenes, includes neurons that maintain direction selectivity for long-range motion, even when conflicting local motion is present. These V4 neurons exhibit specific selectivity for the motion of objects, i.e., targets with defined boundaries, rather than the motion of surfaces behind apertures, and are selective for direction of motion over a broad range of spatial displacements and defined by a variety of features. Motion direction at a range of speeds can be accurately decoded on single trials from the activity of just a few V4 neurons. Thus, our results identify a novel motion computation in the ventral stream that is strikingly different from, and complementary to, the well-established system in the dorsal stream, and they support the hypothesis that the ventral stream system interacts with the dorsal stream to achieve the higher level of abstraction critical for tracking dynamic objects.

Microscale visualization of cellular features in adult macaque visual cortex.

Expansion microscopy and light sheet imaging enable fine-scale resolution of intracellular features that comprise neural circuits. Most current techniques visualize sparsely distributed features across whole brains or densely distributed features within individual brain regions. Here, we visualize dense distributions of immunolabeled proteins across early visual cortical areas in adult macaque monkeys. This process may be combined with multiphoton or magnetic resonance imaging to produce multimodal atlases in large, gyrencephalic brains.

Equiluminance cells in visual cortical area v4.

We report a novel class of V4 neuron in the macaque monkey that responds selectively to equiluminant colored form. These "equiluminance" cells stand apart because they violate the well established trend throughout the visual system that responses are minimal at low luminance contrast and grow and saturate as contrast increases. Equiluminance cells, which compose ∼22% of V4, exhibit the opposite behavior: responses are greatest near zero contrast and decrease as contrast increases. While equiluminance cells respond preferentially to equiluminant colored stimuli, strong hue tuning is not their distinguishing feature-some equiluminance cells do exhibit strong unimodal hue tuning, but many show little or no tuning for hue. We find that equiluminance cells are color and shape selective to a degree comparable with other classes of V4 cells with more conventional contrast response functions. Those more conventional cells respond equally well to achromatic luminance and equiluminant color stimuli, analogous to color luminance cells described in V1. The existence of equiluminance cells, which have not been reported in V1 or V2, suggests that chromatically defined boundaries and shapes are given special status in V4 and raises the possibility that form at equiluminance and form at higher contrasts are processed in separate channels in V4.

Direction opponency, not quadrature, is key to the 1/4 cycle preference for apparent motion in the motion energy model.

Sensitivity to visual motion is a fundamental property of neurons in the visual cortex and has received wide attention in terms of mathematical models. A key feature of many popular models for cortical motion sensors is the use of pairs of functions that are related by a 90 degrees phase shift. This phase relationship, known as quadrature, is the hallmark of the motion energy model and played an important role in the development of a class of model dubbed elaborated Reichardt detectors. For decades, the literature has supported a link between quadrature and the observation that motion detectors and human observers often prefer a 1/4 cycle displacement of an apparent motion stimulus that consists of a pair of sinusoidal gratings. We show that there is essentially no link between quadrature and this preference. Quadrature is neither necessary nor sufficient for a motion sensor to prefer 1/4 cycle displacement, and motion energy is not maximized for a 1/4 cycle step. Other properties of motion sensors are the key: the opponent subtraction of two oppositely tuned stages that individually have sinusoidal displacement tuning curves. Thus, psychophysical and neurophysiological data revealing a preference at or near 1/4 cycle displacement do not offer specific support for common quadrature or energy-based motion models. Instead, they point to a broader class of model.

Neuronal responses during and after the presentation of static visual stimuli in macaque primary visual cortex.

Viewing static visual scenes for several seconds or longer can induce a wide variety of striking percepts, including negative afterimages, fading, and motion aftereffects. To characterize the neuronal bases of such phenomena and elucidate functional circuitry in the visual system, we recorded responses of neurons in primary visual cortex (V1) of anesthetized macaques during and after the presentation of prolonged static visual stimuli. We found that 72% of cells generated significant after-responses (ARs) that outlasted classical off-transients after the cessation of stimuli, and AR amplitude grew with stimulus duration. After the longest stimuli tested (32 s), the amplitude and the time course of the AR were on average comparable to, and correlated with, those of the maintained response evoked while stimuli were present. These observations generally held regardless of cell class: simple, complex, direction selective (DS) or non-DS. The average decay time constant of the AR for orientation-tuned cells was 0.65 s. This is strikingly shorter than time constants observed in the lateral geniculate nucleus, which were on the order of tens of seconds. Cells in V1 that lacked orientation tuning displayed an intermediate time course, with a mean time constant of 4.3 s. These results are consistent with a multistage model in which cells at successive stages adapt to their inputs with progressively shorter time constants. Our findings suggest that the perceptual phenomena of fading and afterimages are shaped by both cortical and subcortical dynamics and provide a physiological framework for the interpretation of recent and long-standing psychophysical observations.

Responses to static visual images in macaque lateral geniculate nucleus: implications for adaptation, negative afterimages, and visual fading.

Adaptation to static scenes is a familiar and fundamental aspect of visual perception that causes negative afterimages, fading, and many other visual illusions. To establish a foundation for understanding the neuronal bases of such phenomena and to constrain the contributions of retinal versus cortical processing, we studied the responses of neurons in the dorsal lateral geniculate nucleus during and after the presentation of prolonged static visual stimuli. We found that parvocellular (P) cells (the more numerous and color-sensitive pathway) showed response adaptation with a time constant on the order of tens of seconds and that their response after the removal of a visual stimulus lasting 1 min was similar in amplitude and time course to the response evoked by the photographic negative stimulus. Magnocellular (M) cells (the faster-conducting and achromatic pathway) had after responses that were substantially weaker than responses evoked by patterned visual stimuli. This difference points to the existence of an adaptive mechanism in the P-pathway that is absent or impaired in the M-pathway and is inconsistent with full adaptation of photoreceptors, which feed both pathways. Cells in both pathways often maintained a substantial tonic response throughout 1 min stimuli, suggesting that these major feedforward inputs to cortex adapt too slowly to account for visual fading. Our findings suggest that faster-adapting mechanisms in cortex are likely to be required to account for the dynamics of perception during and after the viewing of prolonged static images.

Spiking neural network simulation: numerical integration with the Parker-Sochacki method.

Mathematical neuronal models are normally expressed using differential equations. The Parker-Sochacki method is a new technique for the numerical integration of differential equations applicable to many neuronal models. Using this method, the solution order can be adapted according to the local conditions at each time step, enabling adaptive error control without changing the integration timestep. The method has been limited to polynomial equations, but we present division and power operations that expand its scope. We apply the Parker-Sochacki method to the Izhikevich 'simple' model and a Hodgkin-Huxley type neuron, comparing the results with those obtained using the Runge-Kutta and Bulirsch-Stoer methods. Benchmark simulations demonstrate an improved speed/accuracy trade-off for the method relative to these established techniques.