A Generic Model of Visual Selective Attention

Abstract

We present a computational model for the understanding of the fundamental principles of visual selective attention. The model has important medical, social and engineering applications that could benefit the general public. The design of the model is guided by the state of the art in neurophysiological evidence and its performance has been evaluated by comparisons to behavioral data from psychological studies.

The model effectively links low level neural interactions with behavioral data, thus providing concrete explanations for psychological phenomena. The model was used to simulate finding from several behavioral experiments on visual selective attention, with emphasis on those eliciting controversies in the scientific literature.

Appendices

Appendix

The basic computational unit used in the model is the graded response neuron, defined by the membrane Eq. A1.

$$ \tau_{m} \frac{dV}{dt} = E_{L} - V(t) + R_{m} I_{s} (t) $$

(A1)

V is the membrane potential of each neuron, τ_m is the membrane time constant, and E_L is the resting potential of the membrane. The membrane potential can be seen as a measure of the extent to which a node is excited. I_s(t) represents the total synaptic current and is a simple combination of pre-synaptic excitation and bias currents that increase the membrane potential, with inhibition currents that reduce the membrane potential of the node. The total summation of the excitatory and inhibitory currents influences the actual membrane potential at each time instance. Finally, Rm is the membrane resistance of the neuron. In brief, Eq. 1 determines how the membrane potential V of each neuron develops over time after an input current Is is applied. The value of the membrane potential increases until it reaches a specific threshold (V_th) at which a spike is emitted and V resets to its initial condition or resting potential V_res. Subsequently, a refractory period of 2 ms is applied before the neuron model is allowed to integrate again any pre-synaptic currents.

The term I_s in Eq. A1 quantifies the synaptic currents that are mediated by the excitatory receptors AMPA and NMDA (activated by glutamate, gAMPA and gNMDA) and the inhibitory receptor GABAA and GABAB, as shown in Eq. A2.

$$ I_{s} \left( t \right) = \left( {I_{AMPA} \left( t \right) + I_{NMDA} \left( t \right) + I_{{GABA_{A} }} \left( t \right) + I_{{GABA_{B} }} \left( t \right)} \right) $$

(A2)

For the following analysis, the synaptic inputs will be considered as the total excitatory and inhibitory synaptic currents (I_exc(t) + I_inh(t)).

In the framework of the integrate-and-fire model, each pre-synaptic spike generates a post-synaptic current pulse that is driven towards the input of the following neuron as shown in (A3).

$$ I_{s} \left( t \right) = \left( {I_{exc} \left( t \right) + I_{inh} \left( t \right) = g_{exc} \left( t \right)(Es_{exc} - V) + g_{inh} \left( t \right)(Es_{inh} - V)} \right) $$

(A3)

Where

$$ g_{exc} \left( t \right) = \bar{g}_{exc} w_{exc} P_{s} \left( t \right),g_{inh} \left( t \right) = \bar{g}_{inh} w_{inh} P_{s} \left( t \right) $$

(A4)

is the maximal excitatory or inhibitory conductance and w_exc, w_inh refer to the excitatory and inhibitory synaptic weights.

P_s(t) determines the synaptic conductivity and can be modeled by a simple exponential decay with time constant τs as shown in (A5).

$$ P_{s} = \frac{1}{{e^{{\frac{t}{{\tau_{s} }}}} }} + \frac{{(\Theta (t - t_{k} )e^{{\frac{{t_{k} }}{{\tau_{s} }}}} )}}{{e^{{\frac{t}{{\tau_{s} }}}} }} $$

(A5)

In (A5), Θ represents the Heaviside step function (zero for negative arguments, unity for zero or positive arguments

$$ \Theta (x) = \left\{ {\begin{array}{*{20}c} 0 \\ 1 \\ \end{array} \, \begin{array}{*{20}c} {x < 0} \\ {x >= 0} \\ \end{array} } \right. $$

(A6)

Coincidence Detector Nodes

Traditionally, coincidence detector neurons are modeled with a very short membrane time constant τ_m that can change rapidly. However, another way to model coincidence detection is based on a simple case in which separate inputs converge on a common target.

More precisely, if Ψ(t) is a binary row vector denoting the states of neuron A and B at time t and C(t + 1) the state of neuron C at t + 1.

$$ C(t + 1) =\Theta (\varPsi (t) - \theta ) $$

(A7)

With Θ being the Heaviside step function, and θ the specific threshold for a number of pre-synaptic spikes that are needed to arrive synchronously in order for the output neuron C to induce a spike.