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Journal of Computational Neuroscience
Published in: Journal of Computational Neuroscience 2/2024

12-04-2024 | Research

Representing stimulus motion with waves in adaptive neural fields

Authors: Sage Shaw, Zachary P Kilpatrick

Published in: Journal of Computational Neuroscience | Issue 2/2024

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Abstract

Traveling waves of neural activity emerge in cortical networks both spontaneously and in response to stimuli. The spatiotemporal structure of waves can indicate the information they encode and the physiological processes that sustain them. Here, we investigate the stimulus-response relationships of traveling waves emerging in adaptive neural fields as a model of visual motion processing. Neural field equations model the activity of cortical tissue as a continuum excitable medium, and adaptive processes provide negative feedback, generating localized activity patterns. Synaptic connectivity in our model is described by an integral kernel that weakens dynamically due to activity-dependent synaptic depression, leading to marginally stable traveling fronts (with attenuated backs) or pulses of a fixed speed. Our analysis quantifies how weak stimuli shift the relative position of these waves over time, characterized by a wave response function we obtain perturbatively. Persistent and continuously visible stimuli model moving visual objects. Intermittent flashes that hop across visual space can produce the experience of smooth apparent visual motion. Entrainment of waves to both kinds of moving stimuli are well characterized by our theory and numerical simulations, providing a mechanistic description of the perception of visual motion.
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Literature
Abouzeid, A., & Ermentrout, B. (2009). Type-ii phase resetting curve is optimal for stochastic synchrony. Physical Review E, 80(1), 011911.CrossRef
Aitken, F., Menelaou, G., Warrington, O., et al. (2020). Prior expectations evoke stimulus-specific activity in the deep layers of the primary visual cortex. PLoS biology, 18(12), e3001023.PubMedPubMedCentralCrossRef
Alamia, A., & VanRullen, R. (2023). A traveling waves perspective on temporal binding. Journal of Cognitive Neuroscience, pp 1–9.
Amari, S. (1977). Dynamics of pattern formation in lateral-inhibition type neural fields. Biological Cybernetics, 27(2), 77–87.PubMedCrossRef
Anstis, S. M. (1980). The perception of apparent movement. Philosophical Transactions of the Royal Society of London B, Biological Sciences, 290(1038), 153–168.PubMedCrossRef
Bart, E., Bao, S., & Holcman, D. (2005). Modeling the spontaneous activity of the auditory cortex. Journal of Computational Neuroscience, 19(3), 357–378.PubMedCrossRef
Ben-Yishai, R., Hansel, D., & Sompolinsky, H. (1997). Traveling waves and the processing of weakly tuned inputs in a cortical network module. Journal of computational neuroscience, 4, 57–77.PubMedCrossRef
Blom, T., Feuerriegel, D., Johnson, P., et al. (2020). Predictions drive neural representations of visual events ahead of incoming sensory information. Proceedings of the National Academy of Sciences, 117(13), 7510–7515.CrossRef
Born, R. T., & Bradley, D. C. (2005). Structure and function of visual area mt. Annu Rev Neurosci, 28, 157–189.PubMedCrossRef
Bressloff, P. C. (2001). Traveling fronts and wave propagation failure in an inhomogeneous neural network. Physica D: Nonlinear Phenomena, 155(1), 83–100.CrossRef
Bressloff, P. C. (2011). Spatiotemporal dynamics of continuum neural fields. Journal of Physics A: Mathematical and Theoretical, 45(3), 033001.CrossRef
Bressloff, P. C., & Webber, M. A. (2012). Neural field model of binocular rivalry waves. Journal of Computational Neuroscience, 32(2), 233.PubMedCrossRef
Bressloff, P. C., Folias, S. E., Prat, A., et al. (2003). Oscillatory waves in inhomogeneous neural media. Physical review letters, 91(17), 178101.PubMedCrossRef
Brown, E., Moehlis, J., & Holmes, P. (2004). On the phase reduction and response dynamics of neural oscillator populations. Neural computation, 16(4), 673–715.PubMedCrossRef
Burak, Y., & Fiete, I. R. (2009). Accurate path integration in continuous attractor network models of grid cells. PLoS computational biology, 5(2), e1000291.PubMedPubMedCentralCrossRef
Burt, P., & Sperling, G. (1981). Time, distance, and feature trade-offs in visual apparent motion. Psychological review, 88(2), 171.PubMedCrossRef
Chemla, S., Reynaud, A., Di Volo, M., et al. (2019). Suppressive traveling waves shape representations of illusory motion in primary visual cortex of awake primate. Journal of Neuroscience, 39(22), 4282–4298.PubMedCrossRef
Coombes, S. (2005). Waves, bumps, and patterns in neural field theories. Biol Cybern, 93, 91–108.PubMedCrossRef
Coombes, S., & Owen, M. R. (2004). Evans functions for integral neural field equations with heaviside firing rate function. SIAM Journal on Applied Dynamical Systems, 3(4), 574–600.CrossRef
Coombes, S., Venkov, N. A., Shiau, L., et al. (2007). Modeling electrocortical activity through improved local approximations of integral neural field equations. Physical Review E, 76(5), 051901.CrossRef
Coombes, S., Schmidt, H., & Bojak, I. (2012). Interface dynamics in planar neural field models. The Journal of Mathematical Neuroscience, 2(1), 1–27.CrossRef
Dahlem, M. A. (2013). Migraine generator network and spreading depression dynamics as neuromodulation targets in episodic migraine. Chaos: An Interdisciplinary Journal of Nonlinear Science, 23(4), 046101.
Eckert, M. P, & Zeil, J. (2001). Towards an ecology of motion vision. Motion vision: computational, neural, and ecological constraints, pp 333–369.
Ekman, M., Kok, P., & de Lange, F. P. (2017). Time-compressed preplay of anticipated events in human primary visual cortex. Nature Communications, 8(1), 15276.PubMedPubMedCentralCrossRef
Erlhagen, W., & Schöner, G. (2002). Dynamic field theory of movement preparation. Psychological review, 109(3), 545.PubMedCrossRef
Ermentrout, B. (1996). Type i membranes, phase resetting curves, and synchrony. Neural computation, 8(5), 979–1001.PubMedCrossRef
Ermentrout, B. (1998). Neural networks as spatio-temporal pattern-forming systems. Reports on progress in physics, 61(4), 353.CrossRef
Ermentrout, G. B., & Kleinfeld, D. (2001). Traveling electrical waves in cortex: Insights from phase dynamics and speculation on a computational role. Neuron, 29(1), 33–44.PubMedCrossRef
Ermentrout, G. B., & McLeod, J. B. (1993). Existence and uniqueness of travelling waves for a neural network. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 123(3), 461–478.CrossRef
Ermentrout, G. B., Jalics, J. Z., & Rubin, J. E. (2010). Stimulus-driven traveling solutions in continuum neuronal models with a general smooth firing rate function. SIAM Journal on Applied Mathematics, 70(8), 3039–3064.CrossRef
Faye, G., & Kilpatrick, Z. P. (2018). Threshold of front propagation in neural fields: An interface dynamics approach. SIAM Journal on Applied Mathematics, 78(5), 2575–2596.CrossRef
Folias, S. E. (2011). Nonlinear analysis of breathing pulses in a synaptically coupled neural network. SIAM Journal on Applied Dynamical Systems, 10(2), 744–787.CrossRef
Folias, S. E., & Bressloff, P. C. (2004). Breathing pulses in an excitatory neural network. SIAM Journal on Applied Dynamical Systems, 3(3), 378–407.CrossRef
Folias, S. E., & Bressloff, P. C. (2005). Stimulus-locked traveling waves and breathers in an excitatory neural network. SIAM journal on Applied Mathematics, 65(6), 2067–2092.CrossRef
Fortune, E. S., & Rose, G. J. (2001). Short-term synaptic plasticity as a temporal filter. Trends in neurosciences, 24(7), 381–385.PubMedCrossRef
Gepshtein, S., & Kubovy, M. (2007). The lawful perception of apparent motion. Journal of Vision, 7(8), 9–9.PubMedCrossRef
Goulet, J., & Ermentrout, G. B. (2011). The mechanisms for compression and reflection of cortical waves. Biological cybernetics, 105, 253–268.PubMedCrossRef
Huang, X., Troy, W. C., Yang, Q., et al. (2004). Spiral waves in disinhibited mammalian neocortex. Journal of Neuroscience, 24(44), 9897–9902.PubMedCrossRef
Hürlimann, F., Kiper, D. C., & Carandini, M. (2002). Testing the bayesian model of perceived speed. Vision research, 42(19), 2253–2257.PubMedCrossRef
Hutt, A., Bestehorn, M., & Wennekers, T. (2003). Pattern formation in intracortical neuronal fields. Network: Computation in Neural Systems, 14(2), 351
Itskov, V., Hansel, D., & Tsodyks, M. (2011). Short-term facilitation may stabilize parametric working memory trace. Frontiers in computational neuroscience, 5, 40.PubMedPubMedCentralCrossRef
Kane, S. A., & Zamani, M. (2014). Falcons pursue prey using visual motion cues: new perspectives from animal-borne cameras. Journal of Experimental Biology, 217(2), 225–234.PubMedPubMedCentralCrossRef
Keener, J. P. (2000a). Homogenization and propagation in the bistable equation. Physica D: Nonlinear Phenomena, 136(1), 1–17.CrossRef
Keener, J. P. (2000b). Propagation of waves in an excitable medium with discrete release sites. SIAM Journal on Applied Mathematics, 61(1), 317–334.CrossRef
Kilpatrick, Z. P. (2015). Stochastic synchronization of neural activity waves. Physical Review E, 91(4), 040701.CrossRef
Kilpatrick, Z. P. (2018). Synaptic mechanisms of interference in working memory. Scientific Reports, 8(1), 1–20.CrossRef
Kilpatrick, Z. P., & Bressloff, P. C. (2010a). Binocular rivalry in a competitive neural network with synaptic depression. SIAM Journal on Applied Dynamical Systems, 9(4), 1303–1347.CrossRef
Kilpatrick, Z. P., & Bressloff, P. C. (2010b). Effects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network. Physica D: Nonlinear Phenomena, 239(9), 547–560.CrossRef
Kilpatrick, Z. P., & Bressloff, P. C. (2010c). Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression. Journal of Computational Neuroscience, 28(2), 193–209.PubMedCrossRef
Kilpatrick, Z. P., & Bressloff, P. C. (2010d). Stability of bumps in piecewise smooth neural fields with nonlinear adaptation. Physica D: Nonlinear Phenomena, 239(12), 1048–1060.CrossRef
Kilpatrick, Z. P., & Ermentrout, B. (2012). Response of traveling waves to transient inputs in neural fields. Physical Review E, 85, 021910.CrossRef
Kilpatrick, Z. P., & Faye, G. (2014). Pulse bifurcations in stochastic neural fields. SIAM Journal on Applied Dynamical Systems, 13(2), 830–860.CrossRef
Kilpatrick, Z. P., Folias, S. E., & Bressloff, P. C. (2008). Traveling pulses and wave propagation failure in inhomogeneous neural media. SIAM Journal on Applied Dynamical Systems, 7(1), 161–185.CrossRef
Knill, D. C., & Pouget, A. (2004). The bayesian brain: the role of uncertainty in neural coding and computation. TRENDS in Neurosciences, 27(12), 712–719.PubMedCrossRef
Koffka, K. (2013). Principles of Gestalt psychology, (Vol. 44). Routledge.
Kolers, P. A. (2013). Aspects of motion perception: International series of monographs in experimental psychology, (Vol. 16). Elsevier.
Korte, A. (1915). Kinematoskopische untersuchungen. Zeitschrift fur Psychologie, 65.
Loxley, P., & Robinson, P. (2009). Soliton model of competitive neural dynamics during binocular rivalry. Physical review letters, 102(25), 258701.PubMedCrossRef
Lu, Y., Sato, Y., & Si, Amari. (2011). Traveling bumps and their collisions in a two-dimensional neural field. Neural Computation, 23(5), 1248–1260.PubMedCrossRef
Merchant, H., Battaglia-Mayer, A., & Georgopoulos, A. P. (2003). Interception of real and apparent motion targets: psychophysics in humans and monkeys. Experimental Brain Research, 152, 106–112.PubMedCrossRef
Muckli, L., Kohler, A., Kriegeskorte, N., et al. (2005). Primary visual cortex activity along the apparent-motion trace reflects illusory perception. PLoS biology, 3(8), e265.PubMedPubMedCentralCrossRef
Muller, L., Chavane, F., Reynolds, J., et al. (2018). Cortical travelling waves: mechanisms and computational principles. Nature Reviews Neuroscience, 19(5), 255–268.PubMedPubMedCentralCrossRef
Nagy, M., Ákos, Z., Biro, D., et al. (2010). Hierarchical group dynamics in pigeon flocks. Nature, 464(7290), 890–893.PubMedCrossRef
O’Reilly, J. X., Mesulam, M. M., & Nobre, A. C. (2008). The cerebellum predicts the timing of perceptual events. Journal of Neuroscience, 28(9), 2252–2260.PubMedCrossRef
Pang, Z., Alamia, A., & VanRullen, R. (2020). Turning the stimulus on and off changes the direction of \(\alpha\) traveling waves. Eneuro, 7(6).
Pinto, D. J., & Ermentrout, G. B. (2001), Spatially structured activity in synaptically coupled neuronal networks: I. traveling fronts and pulses. SIAM Journal on Applied Mathematics, 62(1), 206–225.
Ramachandran, V. S., & Anstis, S. M. (1986). The perception of apparent motion. Scientific American, 254(6), 102–109.PubMedCrossRef
Richardson, K. A., Schiff, S. J., & Gluckman, B. J. (2005). Control of traveling waves in the mammalian cortex. Physical review letters, 94(2), 028103.PubMedPubMedCentralCrossRef
Stocker, A. A., & Simoncelli, E. P. (2006). Noise characteristics and prior expectations in human visual speed perception. Nature neuroscience, 9(4), 578–585.PubMedCrossRef
Tenenbaum, J. B., Kemp, C., Griffiths, T. L., et al. (2011). How to grow a mind: Statistics, structure, and abstraction. Science, 331(6022), 1279–1285.PubMedCrossRef
Torney, C. J., Hopcraft, J. G. C., Morrison, T. A., et al. (2018). From single steps to mass migration: the problem of scale in the movement ecology of the serengeti wildebeest. Philosophical Transactions of the Royal Society B: Biological Sciences, 373(1746), 20170012.CrossRef
Townsend, R. G., Solomon, S. S., Martin, P. R., et al. (2017). Visual motion discrimination by propagating patterns in primate cerebral cortex. Journal of Neuroscience, 37(42), 10074–10084.PubMedCrossRef
Tsodyks, M., Pawelzik, K., & Markram, H. (1998). Neural networks with dynamic synapses. Neural Computation, 10(4), 821–835.PubMedCrossRef
Ullman, S. (1979). The interpretation of visual motion. Massachusetts Inst of Technology Pr.
Venkov, N. A., Coombes, S., & Matthews, P. C. (2007). Dynamic instabilities in scalar neural field equations with space-dependent delays. Physica D: Nonlinear Phenomena, 232(1), 1–15.CrossRef
Wallach, H. (1935). Über visuell wahrgenommene bewegungsrichtung. Psychologische Forschung, 20, 325–380.CrossRef
Weiss, Y., Simoncelli, E. P., & Adelson, E. H. (2002). Motion illusions as optimal percepts. Nature neuroscience, 5(6), 598–604.PubMedCrossRef
Wilson, H. R., & Cowan, J. D. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13(2), 55–80.PubMedCrossRef
Gao, X., Xu, W., Wang, Z., Takagaki, K., Li, B., Wu, J. Y. (2012). Interactions between two propagating waves in rat visual cortex. Neuroscience, 216, 57–69.PubMedCrossRef
Wu, J. Y., Huang, X., & Zhang, C. (2008a). Propagating waves of activity in the neocortex: What they are, what they do. The Neuroscientist, 14(5), 487–502.PubMedPubMedCentralCrossRef
Wu, S., Hamaguchi, K., & Si, Amari. (2008b). Dynamics and computation of continuous attractors. Neural computation, 20(4), 994–1025.PubMedCrossRef
Xie, X., Hahnloser, R. H., & Seung, H. S. (2002). Double-ring network model of the head-direction system. Physical Review E, 66(4), 041902.CrossRef
York, L. C., & van Rossum, M. C. (2009). Recurrent networks with short term synaptic depression. Journal of computational neuroscience, 27(3), 607.PubMedCrossRef
Zanos, T. P., Mineault, P. J., Nasiotis, K. T., et al. (2015). A sensorimotor role for traveling waves in primate visual cortex. Neuron, 85(3), 615–627.PubMedCrossRef
Zhang, K. (1996). Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory. Journal of Neuroscience, 16(6), 2112–2126.PubMedCrossRef
Metadata
Title
Representing stimulus motion with waves in adaptive neural fields
Authors
Sage Shaw
Zachary P Kilpatrick
Publication date
12-04-2024
Publisher
Springer US
Published in
Journal of Computational Neuroscience / Issue 2/2024
Print ISSN: 0929-5313
Electronic ISSN: 1573-6873
DOI
https://doi.org/10.1007/s10827-024-00869-z

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