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Revisiting horizontal connectivity rules in V1: from like-to-like towards like-to-all. Brain Struct Funct 2022; 227:1279-1295. [PMID: 35122520 DOI: 10.1007/s00429-022-02455-4] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2021] [Accepted: 01/03/2022] [Indexed: 01/15/2023]
Abstract
Horizontal connections in the primary visual cortex of carnivores, ungulates and primates organize on a near-regular lattice. Given the similar length scale for the regularity found in cortical orientation maps, the currently accepted theoretical standpoint is that these maps are underpinned by a like-to-like connectivity rule: horizontal axons connect preferentially to neurons with similar preferred orientation. However, there is reason to doubt the rule's explanatory power, since a growing number of quantitative studies show that the like-to-like connectivity preference and bias mostly observed at short-range scale, are highly variable on a neuron-to-neuron level and depend on the origin of the presynaptic neuron. Despite the wide availability of published data, the accepted model of visual processing has never been revised. Here, we review three lines of independent evidence supporting a much-needed revision of the like-to-like connectivity rule, ranging from anatomy to population functional measures, computational models and to theoretical approaches. We advocate an alternative, distance-dependent connectivity rule that is consistent with new structural and functional evidence: from like-to-like bias at short horizontal distance to like-to-all at long horizontal distance. This generic rule accounts for the observed high heterogeneity in interactions between the orientation and retinotopic domains, that we argue is necessary to process non-trivial stimuli in a task-dependent manner.
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Multi-Frequency Image Completion via a Biologically-Inspired Sub-Riemannian Model with Frequency and Phase. J Imaging 2021; 7:jimaging7120271. [PMID: 34940739 PMCID: PMC8704454 DOI: 10.3390/jimaging7120271] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2021] [Revised: 11/24/2021] [Accepted: 12/01/2021] [Indexed: 11/16/2022] Open
Abstract
We present a novel cortically-inspired image completion algorithm. It uses five-dimensional sub-Riemannian cortical geometry, modeling the orientation, spatial frequency and phase-selective behavior of the cells in the visual cortex. The algorithm extracts the orientation, frequency and phase information existing in a given two-dimensional corrupted input image via a Gabor transform and represents those values in terms of cortical cell output responses in the model geometry. Then, it performs completion via a diffusion concentrated in a neighborhood along the neural connections within the model geometry. The diffusion models the activity propagation integrating orientation, frequency and phase features along the neural connections. Finally, the algorithm transforms the diffused and completed output responses back to the two-dimensional image plane.
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Baspinar E, Sarti A, Citti G. A sub-Riemannian model of the visual cortex with frequency and phase. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2020; 10:11. [PMID: 32728818 PMCID: PMC7391467 DOI: 10.1186/s13408-020-00089-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Accepted: 07/19/2020] [Indexed: 06/11/2023]
Abstract
In this paper, we present a novel model of the primary visual cortex (V1) based on orientation, frequency, and phase selective behavior of V1 simple cells. We start from the first-level mechanisms of visual perception, receptive profiles. The model interprets V1 as a fiber bundle over the two-dimensional retinal plane by introducing orientation, frequency, and phase as intrinsic variables. Each receptive profile on the fiber is mathematically interpreted as rotated, frequency modulated, and phase shifted Gabor function. We start from the Gabor function and show that it induces in a natural way the model geometry and the associated horizontal connectivity modeling of the neural connectivity patterns in V1. We provide an image enhancement algorithm employing the model framework. The algorithm is capable of exploiting not only orientation but also frequency and phase information existing intrinsically in a two-dimensional input image. We provide the experimental results corresponding to the enhancement algorithm.
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Affiliation(s)
- E. Baspinar
- MathNeuro Team, INRIA Sophia Antipolis, Valbonne, France
| | | | - G. Citti
- MathNeuro Team, INRIA Sophia Antipolis, Valbonne, France
- Department of Mathematics, University of Bologna, Bologna, Italy
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Milleret C, Bui Quoc E. Beyond Rehabilitation of Acuity, Ocular Alignment, and Binocularity in Infantile Strabismus. Front Syst Neurosci 2018; 12:29. [PMID: 30072876 PMCID: PMC6058758 DOI: 10.3389/fnsys.2018.00029] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2017] [Accepted: 06/15/2018] [Indexed: 11/13/2022] Open
Abstract
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.
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Affiliation(s)
- Chantal Milleret
- Center for Interdisciplinary Research in Biology, Centre National de la Recherche Scientifique, College de France, INSERM, PSL Research University, Paris, France
| | - Emmanuel Bui Quoc
- Department of Ophthalmology, Robert Debré University Hospital, Assistance Publique - Hôpitaux de Paris Paris, France
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5
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Rankin J, Chavane F. Neural field model to reconcile structure with function in primary visual cortex. PLoS Comput Biol 2017; 13:e1005821. [PMID: 29065120 PMCID: PMC5669491 DOI: 10.1371/journal.pcbi.1005821] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2017] [Revised: 11/03/2017] [Accepted: 10/14/2017] [Indexed: 11/19/2022] Open
Abstract
Voltage-sensitive dye imaging experiments in primary visual cortex (V1) have shown that local, oriented visual stimuli elicit stable orientation-selective activation within the stimulus retinotopic footprint. The cortical activation dynamically extends far beyond the retinotopic footprint, but the peripheral spread stays non-selective-a surprising finding given a number of anatomo-functional studies showing the orientation specificity of long-range connections. Here we use a computational model to investigate this apparent discrepancy by studying the expected population response using known published anatomical constraints. The dynamics of input-driven localized states were simulated in a planar neural field model with multiple sub-populations encoding orientation. The realistic connectivity profile has parameters controlling the clustering of long-range connections and their orientation bias. We found substantial overlap between the anatomically relevant parameter range and a steep decay in orientation selective activation that is consistent with the imaging experiments. In this way our study reconciles the reported orientation bias of long-range connections with the functional expression of orientation selective neural activity. Our results demonstrate this sharp decay is contingent on three factors, that long-range connections are sufficiently diffuse, that the orientation bias of these connections is in an intermediate range (consistent with anatomy) and that excitation is sufficiently balanced by inhibition. Conversely, our modelling results predict that, for reduced inhibition strength, spurious orientation selective activation could be generated through long-range lateral connections. Furthermore, if the orientation bias of lateral connections is very strong, or if inhibition is particularly weak, the network operates close to an instability leading to unbounded cortical activation.
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Affiliation(s)
- James Rankin
- Department of Mathematics, University of Exeter, Exeter, United Kingdom
- Center for Neural Science, New York University, New York, New York, United States of America
| | - Frédéric Chavane
- Institut de Neurosciences de la Timone, CNRS & Aix-Marseille Université, Faculté de Médecine, Marseille, France
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Sauvage A, Hubert G, Touboul J, Ribot J. The hemodynamic signal as a first-order low-pass temporal filter: Evidence and implications for neuroimaging studies. Neuroimage 2017; 155:394-405. [PMID: 28343986 DOI: 10.1016/j.neuroimage.2017.03.053] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2016] [Revised: 02/28/2017] [Accepted: 03/23/2017] [Indexed: 01/26/2023] Open
Abstract
Neuronal activation triggers local changes in blood flow and hemoglobin oxygenation. These hemodynamic signals can be recorded through functional magnetic resonance imaging or intrinsic optical imaging, and allows inferring neural activity in response to stimuli. These techniques are widely used to uncover functional brain architectures. However, their accuracy suffers from distortions inherent to hemodynamic responses and noise. The analysis of these signals currently relies on models of impulse hemodynamic responses to brief stimuli. Here, in order to infer precise functional architectures, we focused on integrated signals associated to the dynamic response of functional maps. To this end, we recorded orientation and direction maps in cat primary visual cortex and compared two protocols: the conventional episodic stimulation technique and a continuous, periodic stimulation paradigm. Conventional methods show that the dynamics of activation and deactivation of the functional maps follows a linear first-order differential equation representing a low-pass filter. Comparison with the periodic stimulation methods confirmed this observation: the phase shifts and magnitude attenuations extracted at various frequencies were consistent with a low-pass filter with a 5s time constant. This dynamics presumably reflects the variations in deoxyhemoglobin mediated by arterial dilations. This dynamics open new avenues in the analysis of neuroimaging data that differs from common methods based on the hemodynamic response function. In particular, we demonstrate that inverting this first-order low-pass filter minimized the distortions of the signal and enabled a much faster and accurate reconstruction of functional maps.
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Affiliation(s)
- Antoine Sauvage
- Mathematical Neuroscience Team, CIRB - Collège de France (CNRS UMR 7241, INSERM U1050, UPMC ED 158, MEMOLIFE PSL), 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Guillaume Hubert
- Mathematical Neuroscience Team, CIRB - Collège de France (CNRS UMR 7241, INSERM U1050, UPMC ED 158, MEMOLIFE PSL), 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Jonathan Touboul
- Mathematical Neuroscience Team, CIRB - Collège de France (CNRS UMR 7241, INSERM U1050, UPMC ED 158, MEMOLIFE PSL), 11 Place Marcelin Berthelot, 75005 Paris, France; INRIA Mycenae Team, Paris-Rocquencourt, France
| | - Jérôme Ribot
- Mathematical Neuroscience Team, CIRB - Collège de France (CNRS UMR 7241, INSERM U1050, UPMC ED 158, MEMOLIFE PSL), 11 Place Marcelin Berthelot, 75005 Paris, France.
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Romagnoni A, Ribot J, Bennequin D, Touboul J. Parsimony, Exhaustivity and Balanced Detection in Neocortex. PLoS Comput Biol 2015; 11:e1004623. [PMID: 26587664 PMCID: PMC4654526 DOI: 10.1371/journal.pcbi.1004623] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2015] [Accepted: 10/23/2015] [Indexed: 11/18/2022] Open
Abstract
The layout of sensory brain areas is thought to subtend perception. The principles shaping these architectures and their role in information processing are still poorly understood. We investigate mathematically and computationally the representation of orientation and spatial frequency in cat primary visual cortex. We prove that two natural principles, local exhaustivity and parsimony of representation, would constrain the orientation and spatial frequency maps to display a very specific pinwheel-dipole singularity. This is particularly interesting since recent experimental evidences show a dipolar structures of the spatial frequency map co-localized with pinwheels in cat. These structures have important properties on information processing capabilities. In particular, we show using a computational model of visual information processing that this architecture allows a trade-off in the local detection of orientation and spatial frequency, but this property occurs for spatial frequency selectivity sharper than reported in the literature. We validated this sharpening on high-resolution optical imaging experimental data. These results shed new light on the principles at play in the emergence of functional architecture of cortical maps, as well as their potential role in processing information.
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Affiliation(s)
- Alberto Romagnoni
- Mathematical Neuroscience Team, CIRB—Collège de France (CNRS UMR 7241, INSERM U1050, Labex MEMOLIFE), PSL, Paris, France
- Group for Neural Theory, Laboratoire des Neurosciences Cognitives, INSERM Unité 960, Département d’Études Cognitives, École Normale Supérieure, PSL, Paris, France
- * E-mail:
| | - Jérôme Ribot
- Mathematical Neuroscience Team, CIRB—Collège de France (CNRS UMR 7241, INSERM U1050, Labex MEMOLIFE), PSL, Paris, France
| | - Daniel Bennequin
- Géométrie et dynamique, Université Paris Diderot (Paris VII), Paris, France
| | - Jonathan Touboul
- Mathematical Neuroscience Team, CIRB—Collège de France (CNRS UMR 7241, INSERM U1050, Labex MEMOLIFE), PSL, Paris, France
- INRIA Mycenae Team, Paris-Rocquencourt, France
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