Geometrical and topological relationships between multiple functional maps in cat primary visual cortex

Functional organization of spatial frequency tuning in macaque V1 revealed with two-photon calcium imaging

V1 neurons are functionally organized in orientation columns in primates. Whether spatial frequency (SF) columns also exist is less clear because mixed results have been reported. A definitive solution would be SF functional maps at single-neuron resolution. Here we used two-photon calcium imaging to construct first cellular SF maps in V1 superficial layers of five awake fixating macaques, and studied SF functional organization properties and neuronal tuning characteristics. The SF maps (850 × 850 μm²) showed weak horizontal SF clustering (median clustering index = 1.43 vs. unity baseline), about one sixth as strong as orientation clustering in the same sets of neurons, which argues against a meaningful orthogonal relationship between orientation and SF functional maps. These maps also displayed nearly absent vertical SF clustering between two cortical depths (150 & 300 μm), indicating a lack of SF columnar structures within the superficial layers. The underlying causes might be that most neurons were tuned to a narrow two-octave range of medium frequencies, and many neurons with different SF preferences were often spatially mixed, which disallowed finer grouping of SF tuning. In addition, individual SF tuning functions were often asymmetric, having wider lower frequency branches, which may help encode low SF information for later decoding.

Development and Reorganization of Orientation Representation in the Cat Visual Cortex: Experience-Dependent Synaptic Rewiring in Early Life

To date, numerous mathematical models have been proposed on the basis of some types of Hebbian synaptic learning to account for the activity-dependent development of orientation maps as well as neuronal orientation selectivity. These models successfully reproduced orientation map-like spatial patterns. Nevertheless, we still have questions: (1) How does synaptic rewiring occur in the visual cortex during the formation of orderly orientation maps in early life? (2) How does visual experience contribute to the maturation of orientation selectivity of visual cortical neurons and reorganize orientation maps? (3) How does the sensitive period for orientation plasticity end? In this study, we performed animal experiments and mathematical modeling to understand the mechanisms underlying synaptic rewiring for experience-dependent formation and reorganization of orientation maps. At first, we visualized orientation maps from the intrinsic signal optical imaging in area 17 of kittens reared under single-orientation exposure through cylindrical-lens-fitted goggles. The experiments revealed that the degree of expansion of cortical domains representing the experienced orientation depends on the age at which the single-orientation exposure starts. As a result, we obtained the sensitive period profile for orientation plasticity. Next, we refined our previously proposed mathematical model for the activity-dependent self-organization of thalamo-cortical inputs on the assumption that rewiring is caused by the competitive interactions among transient synaptic contacts on the same dendritic spine. Although various kinds of molecules have been reported to be involved in such interactions, we attempt to build a mathematical model to describe synaptic rewiring focusing on brain-derived neurotrophic factor (BDNF) and its related molecules. Performing computer simulations based on the refined model, we successfully reproduced orientation maps reorganized in kittens reared under single-orientation exposure as well as normal visual experience. We also reproduced the experimentally obtained sensitive period profile for orientation plasticity. The excellent agreement between experimental observations and theoretical reproductions suggests that the BDNF-induced competitive interaction among synaptic contacts from different axons on the same spine is an important factor for the experience-dependent formation and reorganization of orientation selectivity and orientation maps.

Cell-Type-Specific Thalamocortical Inputs Constrain Direction Map Formation in Visual Cortex

Finding the relationship between individual cognitive functions and cell-type-specific neuronal circuits is a central topic in neuroscience. In cats, the lateral geniculate nucleus (LGN) contains several cell types carrying spatially and temporally precise visual information. Whereas LGN cell types lack selectivity for motion direction, neurons in the primary visual cortex (area 17) exhibit sharp direction selectivity. Whether and how such de novo formation of direction selectivity depends on LGN cell types remains unknown. Here, we addressed this question using in vivo two-photon calcium imaging in cat area 17, which consists of two compartments receiving different combinations of inputs from the LGN cell types. The direction map in area 17 showed unique fragmented organization and was present only in small and distributed cortical domains. Moreover, direction-selective domains preferentially localized in specific compartments receiving Y and W inputs carrying low spatial frequency visual information, indicating that cell-type-specific thalamocortical projections constrain the formation of direction selectivity.

Beyond Rehabilitation of Acuity, Ocular Alignment, and Binocularity in Infantile Strabismus

Infantile strabismus impairs the perception of all attributes of the visual scene. High spatial frequency components are no longer visible, leading to amblyopia. Binocularity is altered, leading to the loss of stereopsis. Spatial perception is impaired as well as detection of vertical orientation, the fastest movements, directions of movement, the highest contrasts and colors. Infantile strabismus also affects other vision-dependent processes such as control of postural stability. But presently, rehabilitative therapies for infantile strabismus by ophthalmologists, orthoptists and optometrists are restricted to preventing or curing amblyopia of the deviated eye, aligning the eyes and, whenever possible, preserving or restoring binocular vision during the critical period of development, i.e., before ~10 years of age. All the other impairments are thus ignored; whether they may recover after strabismus treatment even remains unknown. We argue here that medical and paramedical professionals may extend their present treatments of the perceptual losses associated with infantile strabismus. This hypothesis is based on findings from fundamental research on visual system organization of higher mammals in particular at the cortical level. In strabismic subjects (as in normal-seeing ones), information about all of the visual attributes converge, interact and are thus inter-dependent at multiple levels of encoding ranging from the single neuron to neuronal assemblies in visual cortex. Thus if the perception of one attribute is restored this may help to rehabilitate the perception of other attributes. Concomitantly, vision-dependent processes may also improve. This could occur spontaneously, but still should be assessed and validated. If not, medical and paramedical staff, in collaboration with neuroscientists, will have to break new ground in the field of therapies to help reorganize brain circuitry and promote more comprehensive functional recovery. Findings from fundamental research studies in both young and adult patients already support our hypothesis and are reviewed here. For example, presenting different contrasts to each eye of a strabismic patient during training sessions facilitates recovery of acuity in the amblyopic eye as well as of 3D perception. Recent data also demonstrate that visual recoveries in strabismic subjects improve postural stability. These findings form the basis for a roadmap for future research and clinical development to extend presently applied rehabilitative therapies for infantile strabismus.

Estimating Cortical Feature Maps with Dependent Gaussian Processes

A striking example of brain organisation is the stereotyped arrangement of cell preferences in the visual cortex for edges of particular orientations in the visual image. These "orientation preference maps" appear to have remarkably consistent statistical properties across many species. However fine scale analysis of these properties requires the accurate reconstruction of maps from imaging data which is highly noisy. A new approach for solving this reconstruction problem is to use Bayesian Gaussian process methods, which produce more accurate results than classical techniques. However, so far this work has not considered the fact that maps for several other features of visual input coexist with the orientation preference map and that these maps have mutually dependent spatial arrangements. Here we extend the Gaussian process framework to the multiple output case, so that we can consider multiple maps simultaneously. We demonstrate that this improves reconstruction of multiple maps compared to both classical techniques and the single output approach, can encode the empirically observed relationships, and is easily extendible. This provides the first principled approach for studying the spatial relationships between feature maps in visual cortex.

Contrast and response gain control depend on cortical map architecture

Visual cortical neurons are sensitive to visual stimulus contrast and most cells adapt their sensitivity to the prevailing visual environment. Specifically, they match the steepest region of their contrast response function to the prevailing contrast (contrast gain control), and reduce spike rates to limit saturation (response gain control). Most neurons are also tuned for stimulus orientation, and neurons with similar orientation preference are clustered together into iso-orientation zones arranged around pinwheels, i.e. points where all orientations are represented. Here we investigated the relationship between the contrast adaptation properties of neurons and their location relative to pinwheels in the orientation preference map. We measured orientation preference maps in cat cortex using optical intrinsic signal imaging. We then characterized the contrast adaptation properties of single neurons located close to pinwheels, in iso-orientation zones, and at regions in between. We found little evidence of differential contrast sensitivity of neurons adapted to zero contrast. However, after adaptation to their preferred orientation at high contrast, changes in both contrast and response gain were greater for neurons near pinwheels compared with other map regions. Therefore, in the adapted state, which is probably typical during natural viewing, there is a spatial map of contrast sensitivity that is associated with the orientation preference map. This differential adaptation revealed a new dimension of cortical functional organization, linking the contrast adaptation of cells with the orientation preference of their nearest neighbours.

Neurons in cat V1 show significant clustering by degree of tuning

Neighboring neurons in cat primary visual cortex (V1) have similar preferred orientation, direction, and spatial frequency. How diverse is their degree of tuning for these properties? To address this, we used single-tetrode recordings to simultaneously isolate multiple cells at single recording sites and record their responses to flashed and drifting gratings of multiple orientations, spatial frequencies, and, for drifting gratings, directions. Orientation tuning width, spatial frequency tuning width, and direction selectivity index (DSI) all showed significant clustering: pairs of neurons recorded at a single site were significantly more similar in each of these properties than pairs of neurons from different recording sites. The strength of the clustering was generally modest. The percent decrease in the median difference between pairs from the same site, relative to pairs from different sites, was as follows: for different measures of orientation tuning width, 29-35% (drifting gratings) or 15-25% (flashed gratings); for DSI, 24%; and for spatial frequency tuning width measured in octaves, 8% (drifting gratings). The clusterings of all of these measures were much weaker than for preferred orientation (68% decrease) but comparable to that seen for preferred spatial frequency in response to drifting gratings (26%). For the above properties, little difference in clustering was seen between simple and complex cells. In studies of spatial frequency tuning to flashed gratings, strong clustering was seen among simple-cell pairs for tuning width (70% decrease) and preferred frequency (71% decrease), whereas no clustering was seen for simple-complex or complex-complex cell pairs.

Orthogonal micro-organization of orientation and spatial frequency in primate primary visual cortex

Orientation and spatial frequency tuning are highly salient properties of neurons in primary visual cortex (V1). The combined organization of these particular tuning properties in the cortical space will strongly shape the V1 population response to different visual inputs, yet it is poorly understood. In this study, we used two-photon imaging in macaque monkey V1 to demonstrate the three-dimensional cell-by-cell layout of both spatial frequency and orientation tuning. We first found that spatial frequency tuning was organized into highly structured maps that remained consistent across the depth of layer II/III, similarly to orientation tuning. Next, we found that orientation and spatial frequency maps were intimately related at the fine spatial scale observed with two-photon imaging. Not only did the map gradients tend notably toward orthogonality, but they also co-varied negatively from cell to cell at the spatial scale of cortical columns.

Three-dimensional visual feature representation in the primary visual cortex

In the cat primary visual cortex, it is accepted that neurons optimally responding to similar stimulus orientations are clustered in a column extending from the superficial to deep layers. The cerebral cortex is, however, folded inside a skull, which makes gyri and fundi. The primary visual area of cats, area 17, is located on the fold of the cortex called the lateral gyrus. These facts raise the question of how to reconcile the tangential arrangement of the orientation columns with the curvature of the gyrus. In the present study, we show a possible configuration of feature representation in the visual cortex using a three-dimensional (3D) self-organization model. We took into account preferred orientation, preferred direction, ocular dominance and retinotopy, assuming isotropic interaction. We performed computer simulation only in the middle layer at the beginning and expanded the range of simulation gradually to other layers, which was found to be a unique method in the present model for obtaining orientation columns spanning all the layers in the flat cortex. Vertical columns of preferred orientations were found in the flat parts of the model cortex. On the other hand, in the curved parts, preferred orientations were represented in wedge-like columns rather than straight columns, and preferred directions were frequently reversed in the deeper layers. Singularities associated with orientation representation appeared as warped lines in the 3D model cortex. Direction reversal appeared on the sheets that were delimited by orientation-singularity lines. These structures emerged from the balance between periodic arrangements of preferred orientations and vertical alignment of the same orientations. Our theoretical predictions about orientation representation were confirmed by multi-slice, high-resolution functional MRI in the cat visual cortex. We obtained a close agreement between theoretical predictions and experimental observations. The present study throws a doubt about the conventional columnar view of orientation representation, although more experimental data are needed.

Quantitative investigation of the effect of the extra-cerebral vasculature in diffuse optical imaging: a simulation study

Diffuse optical imaging (DOI) is a non invasive technique allowing the recovery of hemodynamic changes in the brain. Due to the diffusive nature of photon propagation in turbid media and the fact that cerebral tissues are located around 1.5 cm under the adult human scalp, DOI measurements are subject to partial volume errors. DOI measurements are also sensitive to large pial vessels because oxygenated and deoxygenated hemoglobin are the dominant chromophores in the near infrared window. In this study, the effect of the extra-cerebral vasculature in proximity of the sagittal sinus was investigated for its impact on DOI measurements simulated over the human adult visual cortex. Numerical Monte Carlo simulations were performed on two specific models of the human head derived from magnetic resonance imaging (MRI) scans. The first model included the extra-cerebral vasculature in which constant hemoglobin concentrations were assumed while the second did not. The screening effect of the vasculature was quantified by comparing recovered hemoglobin changes from each model for different optical arrays and regions of activation. A correction factor accounting for the difference between the recovered and the simulated hemoglobin changes was computed in each case. The results show that changes in hemoglobin concentration are better estimated when the extra-cerebral vasculature is modeled and the correction factors obtained in this case were at least 1.4-fold lower. The effect of the vasculature was also examined in a high-density diffuse optical tomography configuration. In this case, the difference between changes in hemoglobin concentration recovered with each model was reduced down to 10%.

Orientation and Direction-of-Motion Response in the Middle Temporal Visual Area (MT) of New World Owl Monkeys as Revealed by Intrinsic-Signal Optical Imaging

Intrinsic-signal optical imaging was used to evaluate relationships of domains of neurons in middle temporal visual area (MT) selective for stimulus orientation and direction-of-motion. Maps of activation were elicited in MT of owl monkeys by gratings drifting back-and-forth, flashed stationary gratings and unidirectionally drifting fields of random dots. Drifting gratings, typically used to reveal orientation preference domains, contain a motion component that may be represented in MT. Consequently, this stimulus could activate groups of cells responsive to the motion of the grating, its orientation or a combination of both. Domains elicited from either moving or static gratings were remarkably similar, indicating that these groups of cells are responding to orientation, although they may also encode information about motion. To assess the relationship between domains defined by drifting oriented gratings and those responsive to direction-of-motion, the response to drifting fields of random dots was measured within domains defined from thresholded maps of activation elicited by the drifting gratings. The optical response elicited by drifting fields of random dots was maximal in a direction orthogonal to the map of orientation preference. Thus, neurons in domains selective for stimulus orientation are also selective for motion orthogonal to the preferred stimulus orientation.

A map of periodicity orthogonal to frequency representation in the cat auditory cortex

Harmonic sounds, such as voiced speech sounds and many animal communication signals, are characterized by a pitch related to the periodicity of their envelopes. While frequency information is extracted by mechanical filtering of the cochlea, periodicity information is analyzed by temporal filter mechanisms in the brainstem. In the mammalian auditory midbrain envelope periodicity is represented in maps orthogonal to the representation of sound frequency. However, how periodicity is represented across the cortical surface of primary auditory cortex (AI) remains controversial. Using optical recording of intrinsic signals, we here demonstrate that a periodicity map exists in primary AI of the cat. While pure tone stimulation confirmed the well-known frequency gradient along the rostro-caudal axis of AI, stimulation with harmonic sounds revealed segregated bands of activation, indicating spatially localized preferences to specific periodicities along a dorso-ventral axis, nearly orthogonal to the tonotopic gradient. Analysis of the response locations revealed an average gradient of - 100 degrees +/- 10 degrees for the periodotopic, and -12 degrees +/- 18 degrees for the tonotopic map resulting in a mean angle difference of 88 degrees . The gradients were 0.65 +/- 0.08 mm/octave for periodotopy and 1.07 +/- 0.16 mm/octave for tonotopy indicating that more cortical territory is devoted to the representation of an octave along the tonotopic than along the periodotopic gradient. Our results suggest that the fundamental importance of pitch, as evident in human perception, is also reflected in the layout of cortical maps and that the orthogonal spatial organization of frequency and periodicity might be a more general cortical organization principle.

Bimodal modulation and continuous stimulation in optical imaging to map direction selectivity

In the visual system, neurons with similar functional properties such as orientation and direction selectivity are clustered together to form modules. Optical imaging recordings in combination with episodic paradigms have been previously used to estimate direction selectivity, a fundamental property of visual neurons. The major drawback of the episodic approach is that the extraction of the signal from various forms of physiological noise is difficult, leading to a poor estimation of direction. Recent work, based on periodic stimulation and Fourier decomposition improved the extraction of periodic stimulus responses from noise and thus, reduced the recording time considerably. Given the success of this new paradigm in mapping orientation, the present study evaluated its reliability to measure direction selectivity in the visual cortex of anesthetized cats. Here, a model that exploits the harmonics of the Fourier decomposition is proposed where the first harmonic is related to direction responses, and the second to orientation. As expected, the first harmonic was absent when a static stimulus was presented. Contrarily, the first harmonic was present when moving stimuli were presented and the amplitude was greater with random dots kinematograms than with drifting gratings. The phase of the first harmonic showed a good agreement with direction preference measured by episodic paradigm. The ratio of the first/the second harmonic amplitude, related to a direction index, was weaker in fracture. It was also weaker in areas of the ventral pathway (areas 17 and 21a) where direction selectivity is known to be reduced. These results indicate that a periodic paradigm can be easily used to measure specific parameters in optical signals, particularly in situations when short acquisition periods are needed.

The effect of angioscotomas on map structure in primary visual cortex

When blood vessels occlude the photoreceptor layer in the retina, they cast shadows onto the photoreceptors, creating angioscotomas (regions of the visual field to which that eye is blind). Remarkably, Adams and Horton (2002) have recently shown that it is sometimes possible to observe representations of these angioscotomas anatomically in the primary visual cortices of squirrel monkeys. However, there is substantial variability in the degree and form of these representations. The source of this variability is difficult to determine experimentally, because experimental studies are unavoidably limited by small sample size. In addition, experimental studies cannot compare the map structure that would develop with and without an angioscotoma. Here, we investigate these phenomena computationally using feature-mapping models of visual cortical development, which are not subject to the same limitations. These models suggest that the primary source of variability in angioscotoma representation is the precise timing of the onset of visual experience relative to the time course of ocular dominance column segregation. Furthermore, the models predict that angioscotomas could compete for control of local column layout with other influences such as cortical shape but that they have a small effect on the structure of orientation preference maps.

Theoretical and experimental studies of relationship between pinwheel centers and ocular dominance columns in the visual cortex

In the visual cortex, pinwheel centers, which appear as point singularities in orientation maps, are likely to be found at the centers of ocular dominance columns in normal cats and monkeys. To elucidate the mechanism underlying the geometrical relationship, we performed computer simulation based on our correlation-based self-organization model. The simulation showed that pinwheel centers tended to be located at the ocular dominance centers at higher correlations of activities between the left- and right-eye specific pathways, whereas they tended to appear along the borders of ocular dominance columns at lower correlations. This tendency was mathematically analyzed with a formula describing the condition determining the geometrical relationship between pinwheel centers and ocular dominance columns. Moreover, to examine the effect of activity correlations in the eye-specific pathways on the column formation, we conducted intrinsic signal optical imaging using normally reared cats and dark-reared cats. The between-eye activity correlation in dark-reared cats is expected to be lower than that in normal cats due to the lack of common visual input in the two eyes. The statistical analysis of experimental data showed that while more pinwheel centers tended to be located in the center subregion of ocular dominance columns than in the border subregion in the normal cats, a weak tendency in the opposite direction was found in the dark-reared cats. Based on the consistent results from the model and experiment, it is suggested that the activity correlation between the left- and right-eye specific pathways has influence on the establishment of geometrical relationship in the cortical representation between orientation preference and ocular dominance.

Online analysis method for intrinsic signal optical imaging

The intrinsic optical imaging technique has been widely applied for the visualization of functional maps in the sensory cortices of mammals. Many current studies refer this mapping in order to focus thereafter on particular features, at some particular locations: a fast and accurate mapping is therefore required. However, even during a successful experiment, the recorded raw data are usually contaminated by some kinds of noise that cannot necessarily be averaged out over the trials. An adequate image data analysis method has to be applied to extract signals closely related neural activities in response to presented stimuli. Thus far two different analysis methods could be adopted: the band-pass filtering and the GIF method [Yokoo T, Knight BW, Sirovich L. An optimization approach to signal extraction from noisy multivariate data. NeuroImage 2001:14;1309-26]. While the latter one is very efficient but requires the whole data in order to maximize the signal to noise ratio, the simple band-pass filtering technically reaches its limits very quickly. Here we propose another filtering method based on the polynomial subtraction of spatially smoothly modulated components. This simple method can visualize well-organized iso-orientation domains of the cat visual cortex with reliability similar to more sophisticated ones while allowing an online visualization of the clean data.

Preservation of functional architecture in visual cortex of cats with experimentally induced hydrocephalus

We investigated how neural function is preserved or matured in the visual cortex of cats, following the induction of hydrocephalus by kaolin injection. In vivo optical imaging of intrinsic signals in 11-17-week-old hydrocephalic cats revealed orientation maps showing the orderly arrangement of preferred orientations when stimulated by grating stimuli at a low spatial frequency, whereas stimulus-evoked intrinsic signals in response to gratings at a high spatial frequency were often too weak to construct orientation maps. Furthermore, in two of the three hydrocephalic cats, initially deteriorated orientation maps became almost regular maps in the second imaging experiments conducted 8 and 11 weeks, respectively, after the first imaging. This indicates that, despite large structural deformation of the hydrocephalic brain, orientation maps are elaborated sufficiently after the age of 5-6 months, by which time the orientation map formation is usually completed in normal cats. Single unit recording from the decompressed visual cortex revealed that many neurons showed normal orientation selectivity, whereas the binocularity of these neurons was found to be reduced. These results suggested that the deformed visual cortex of hydrocephalic cats exhibits a high plasticity, retaining its functional organization.

Functional organization of visual cortex in the prosimian bush baby revealed by optical imaging of intrinsic signals

Cells in primary visual cortex (V1) of primates and carnivores respond most strongly to a visual stimulus presented to one eye, in a particular visual field location, and at a particular orientation. Each of these stimulus attributes is mapped across the cortical surface, and, in macaque monkeys and cats, strong geometrical relationships exist between these feature maps. In macaque V1 and V2, correlations between feature maps and cytochrome oxidase (CO)-rich modules have also been observed. To see if such relationships reflect a conserved principle of V1 functional architecture among primate species, we examined these maps in the prosimian bush baby, a species that has been proposed to represent the ancestral primate organization. We found that the layout of individual feature maps in bush baby V1 is similar to that of other primates, but we found an entirely different organization of orientation preference in bush baby V2 compared with that reported in simian primates. Another striking distinction between bush baby and simian species is that we observed no strong relationships among maps of orientation, ocular dominance, and CO blobs in V1. Thus our findings suggest that precise relationships between feature maps are not a common element of the functional organization in all primates and that such relationships are not necessary for achieving basic coverage of stimulus feature combinations. In addition, our results suggest that specific relationships between feature maps in V1, and the subdivision of V2 into functional compartments, may have arisen comparatively late in the evolution of primates.

Functional imaging with cellular resolution reveals precise micro-architecture in visual cortex

Neurons in the cerebral cortex are organized into anatomical columns, with ensembles of cells arranged from the surface to the white matter. Within a column, neurons often share functional properties, such as selectivity for stimulus orientation; columns with distinct properties, such as different preferred orientations, tile the cortical surface in orderly patterns. This functional architecture was discovered with the relatively sparse sampling of microelectrode recordings. Optical imaging of membrane voltage or metabolic activity elucidated the overall geometry of functional maps, but is averaged over many cells (resolution >100 microm). Consequently, the purity of functional domains and the precision of the borders between them could not be resolved. Here, we labelled thousands of neurons of the visual cortex with a calcium-sensitive indicator in vivo. We then imaged the activity of neuronal populations at single-cell resolution with two-photon microscopy up to a depth of 400 microm. In rat primary visual cortex, neurons had robust orientation selectivity but there was no discernible local structure; neighbouring neurons often responded to different orientations. In area 18 of cat visual cortex, functional maps were organized at a fine scale. Neurons with opposite preferences for stimulus direction were segregated with extraordinary spatial precision in three dimensions, with columnar borders one to two cells wide. These results indicate that cortical maps can be built with single-cell precision.

A Computational Model for the Development of Multiple Maps in Primary Visual Cortex

Primary visual cortex contains multiple maps of features of the visual scene, including visual field position, orientation, direction, ocular dominance and spatial frequency. The complex relationships between these maps provide clues to the strategies the cortex uses for representing and processing information. Here we simulate the combined development of all these map systems using a computational model, the elastic net. We show that this model robustly produces combined maps of these four variables that bear a close resemblance to experimental maps. In addition we show that the experimentally observed effects of monocular deprivation and single-orientation rearing can be reproduced in this model, and we make some testable predictions. These results provide strong support for the hypothesis that cortical representations attempt to optimize a trade-off between coverage and continuity.

Influence of Lateral Connections on the Structure of Cortical Maps

Maps of ocular dominance and orientation in primary visual cortex have a highly characteristic structure. The factors that determine this structure are still largely unknown. In particular, it is unclear how short-range excitatory and inhibitory connections between nearby neurons influence structure both within and between maps. Using a generalized version of a well-known computational model of visual cortical map development, we show that the number of excitatory and inhibitory oscillations in this interaction function critically influences map structure. Specifically, we demonstrate that functions that oscillate more than once do not produce maps closely resembling those seen biologically. This strongly suggests that local lateral connections in visual cortex oscillate only once and have the form of a Mexican hat.

Maps in the brain: what can we learn from them?

In mammalian visual cortex, neurons are organized according to their functional properties into multiple maps such as retinotopic, ocular dominance, orientation preference, direction of motion, and others. What determines the organization of cortical maps? We argue that cortical maps reflect neuronal connectivity in intracortical circuits. Because connecting distant neurons requires costly wiring (i.e., axons and dendrites), there is an evolutionary pressure to place connected neurons as close to each other as possible. Then, cortical maps may be viewed as solutions that minimize wiring cost for given intracortical connectivity. These solutions can help us in inferring intracortical connectivity and, ultimately, in understanding the function of the visual system.

Optical imaging of intrinsic signals: recent developments in the methodology and its applications

Since optical imaging (OI) of intrinsic signals was first developed in the 1980s, significant advances have been made regarding our understanding of the origins of the recorded signals. The technique has been refined and the range of its applications has been broadened considerably. Here we review recent developments in methodology and data analysis as well as the latest findings on how intrinsic signals are related to metabolic cost and electrophysiological activity in the brain. We give an overview of what optical imaging has contributed to our knowledge of the functional architecture of sensory cortices, their development and plasticity. Finally, we discuss the utility of OI for functional studies of the human brain as well as in animal models of neuropathology.

Postnatal growth and column spacing in cat primary visual cortex

The primary visual cortex (area 17) of cats continues to grow substantially during early postnatal development. To assess the implications of this growth for the organization of visual cortical maps, we analysed both postnatal growth of area 17 and the spacing of ocular dominance columns in the same animals using 2-deoxyglucose autoradiography to label cortical activation patterns. Quantitative analyses of area size and column spacing were performed on flat-mount sections of the cortical hemispheres. Our analysis of the surface area revealed an average increase of the size of area 17 between the third and tenth postnatal weeks by about 51%. About 75% of this increase occurred during the third and sixth postnatal weeks (size increase of 37%). However, the distance between adjacent columns did not exhibit a similar increase but rather remained constant during the same postnatal period. Since cortical growth is not accompanied by an increased spacing of ocular dominance columns, new functional modules must somehow be added during the first postnatal weeks to occupy the enlarging cortical sheet. Possible mechanisms underlying the formation of new modules are discussed.

Spatial coding of position and orientation in primary visual cortex

We examined the spatial distribution of population activity in primary visual cortex (V1) of tree shrews with optical imaging and electrophysiology. A line stimulus, thinner than the average V1 receptive field, evoked a broad strip of neural activity of nearly constant size for all stimulus locations tested within the central 10 degrees of visual space. Stimuli in adjacent positions activated highly overlapping populations of neurons; nevertheless, small changes in stimulus position produced orderly changes in the location of the peak of the population response. Statistically significant shifts in the population response were found for stimulus displacements an order of magnitude smaller than receptive field width, down to the limit of optical imaging resolution. Based on the pattern of population activity, we conclude that the map of visual space in V1 is orderly at a fine scale and has uniform coverage of position and orientation without local relationships in the mapping of these features.

A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images

The classical receptive fields of simple cells in the visual cortex have been shown to emerge from the statistical properties of natural images by forcing the cell responses to be maximally sparse, i.e. significantly activated only rarely. Here, we show that this single principle of sparseness can also lead to emergence of topography (columnar organization) and complex cell properties as well. These are obtained by maximizing the sparsenesses of locally pooled energies, which correspond to complex cell outputs. Thus, we obtain a highly parsimonious model of how these properties of the visual cortex are adapted to the characteristics of the natural input.

Orientation preference patterns in mammalian visual cortex: a wire length minimization approach

In the visual cortex of many mammals, orientation preference changes smoothly along the cortical surface, with the exception of singularities such as pinwheels and fractures. The reason for the existence of these singularities has remained elusive, suggesting that they are developmental artifacts. We show that singularities reduce the length of intracortical neuronal connections for some connection rules. Therefore, pinwheels and fractures could be evolutionary adaptations keeping cortical volume to a minimum. Wire length minimization approach suggests that interspecies differences in orientation preference maps reflect differences in intracortical neuronal circuits, thus leading to experimentally testable predictions. We discuss application of our model to direction preference maps.