From Blasdel (J. of Neuroscience 12, 1992), the optical imaging of the orientation hypercolumn structure in monkey visual cortex. |
From McLaughlin et al (PNAS 97, 2000), the response of a model visual cortex to oriented drifting grating stimulus. |
, in which the fluctuations vanish) to the fluctuation-dominated limit
(such as in small N networks). Comparison with full numerical
simulations of the original I&F network establishes that the
reduced dynamics is very accurate and numerically efficient over
all dynamic ranges. Both analytical insights and scale-up of numerical
representation can be achieved by this kinetic approach. Here,
the theory is illustrated by a study of the dynamical properties
of networks of various architectures, including excitatory and
inhibitory neurons of both simple and complex type, which exhibit
rich dynamic phenomena, such as, transitions to bistability and
hysteresis, even in the presence of large fluctuations. The implication
for possible connections between the structure of the bifurcations
and the behavior of complex cells is discussed. Finally, I&F
networks and kinetic theory are used to discuss orientation selectivity
of complex cells for "ring-model" architectures that characterize
changes in the response of neurons located from near "orientation
pinwheel centers" to far from them.Abstract: This paper reports on the consequences of high, activity dependent, synaptic conductances in neurons in a large-scale neuronal network model of an input layer of the Macaque primary visual cortex (Area V1)....
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M. Shelley and D. McLaughlin
Journal of Computational Neuroscience 12, pp. 97-122 (2002)
Abstract: We present a reduction of a large-scale network model of visual cortex developed by McLaughlin, Shapley, Shelley, and Wielaard. The reduction is from many integrate-and-fire neurons to a spatially coarse-grained system for firing rates of neuronal subpopulations. It accounts explicitly for ``disordered'' properties that vary widely from cortical neuron to cortical neuron, such as preferred spatial phase. The result is a set of nonlinear spatio-temporal integral equations for ``phase-averaged'' firing rates across the model cortex. For drifting grating stimuli, this system yields time invariant cortico-cortical conductances, with firing rates averaged over stimulus period being the natural objects. Mathematical analysis then unveils the mechanisms underlying the spatially varying firing rates and orientation selectivity observed in the large-scale point-neuron simulations. This reduction also reproduces, at far less computational cost, the salient features of the point-neuron network, and is used to study cortical response to changing stimulus contrast, noise level, and coupling length-scales.
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Abstract: To avoid the numerical errors associated with resetting the potential following a spike in simulations of integrate-and-fire neuronal networks, Hansel et al. and Shelley independently developed a modified time-stepping method. Their particular scheme consists of second-order Runge-Kutta time-stepping, a linear interpolant to find spike times, and a recalibration of post-spike potential using the spike times. Here we show analytically that such a scheme is second order, discuss the conditions under which efficient, higher-order algorithms can be constructed to treat resets, and develop a modified fourth-order scheme. To support our analysis, we simulate a system of integrate-and-fire conductance-based point neurons with all-to-all coupling. For 6-digit accuracy, our modified Runge-Kutta fourth-order scheme needs a time-step of 10^{-3} seconds, whereas to achieve comparable accuracy using a recalibrated second-order or a first-order algorithm requires time-steps of 10^{-5} seconds or 10^{-9} seconds, respectively. Furthermore, since the cortico-cortical conductances in standard integrate-and-fire neuronal networks do not depend on the value of the membrane potential, we can attain fourth-order accuracy with computational costs normally associated with second-order schemes.
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Abstract: Here, we offer an explanation for how selectivity for orientation could be produced by a model with circuitry that is based on the anatomy of V1 cortex....
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Journal of Computational Neuroscience (2000), v. 8, pp. 143-159
Abstract: In the primate
visual pathway, orientation tuning of neurons is first observed in the primary
visual cortex. The LGN cells that comprise the thalamic input to V1 are
not orientation tuned, but some V1 neurons are quite selective. Two main
classes of theoretical models have been offered to explain orientation selectivity:
feedforward models, in which inputs from spatially aligned LGN cells are summed
together by one cortical neuron; and feedback models, in which an initial
weak orientation bias due to convergent LGN input is sharpened and amplified
by intracortical feedback. Recent data on the dynamics of orientation tuning,
obtained by a cross-correlation technique, may help to distinguish between
these classes of models. To test this possibility, we simulated the measurement
of orientation tuning dynamics on various receptive field models, including
a simple Hubel-Wiesel type feedforward model: a linear spatio-temporal filter
followed by an integrate-and-fire spike generator. The computational study
reveals that simple feedforward models may account for some aspects of the
experimental data, but fail to explain many salient features of orientation
tuning dynamics in V1 cells. A simple feedback model of interacting cells
is also considered. This model is successful in explaining the appearance
of Mexican-hat orientation profiles, but other features of the data continue
to be unexplained.
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