Towards a biologically plausible model of LGN-V1 pathways (Lian et al 2019)

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Accession:247970
"Increasing evidence supports the hypothesis that the visual system employs a sparse code to represent visual stimuli, where information is encoded in an efficient way by a small population of cells that respond to sensory input at a given time. This includes simple cells in primary visual cortex (V1), which are defined by their linear spatial integration of visual stimuli. Various models of sparse coding have been proposed to explain physiological phenomena observed in simple cells. However, these models have usually made the simplifying assumption that inputs to simple cells already incorporate linear spatial summation. This overlooks the fact that these inputs are known to have strong non-linearities such as the separation of ON and OFF pathways, or separation of excitatory and inhibitory neurons. Consequently these models ignore a range of important experimental phenomena that are related to the emergence of linear spatial summation from non-linear inputs, such as segregation of ON and OFF sub-regions of simple cell receptive fields, the push-pull effect of excitation and inhibition, and phase-reversed cortico-thalamic feedback. Here, we demonstrate that a two-layer model of the visual pathway from the lateral geniculate nucleus to V1 that incorporates these biological constraints on the neural circuits and is based on sparse coding can account for the emergence of these experimental phenomena, diverse shapes of receptive fields and contrast invariance of orientation tuning of simple cells when the model is trained on natural images. The model suggests that sparse coding can be implemented by the V1 simple cells using neural circuits with a simple biologically plausible architecture."
Reference:
1 . Lian Y, Grayden DB, Kameneva T, Meffin H, Burkitt AN (2019) Toward a Biologically Plausible Model of LGN-V1 Pathways Based on Efficient Coding Frontiers in Neural Circuits 13:13
Model Information (Click on a link to find other models with that property)
Model Type: Connectionist Network;
Brain Region(s)/Organism: Neocortex;
Cell Type(s): Abstract rate-based neuron;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: MATLAB;
Model Concept(s): Hebbian plasticity;
Implementer(s): Lian, Yanbo [yanbol at student.unimelb.edu.au];
function [ S1, U1, S_L, U_L, S1_history] = Compute_S_U_LGN_V1_UpDown( S1, U1, S_L, U_L, ...
                    X, A_Up, A_Down, lambda1, s_b, uEta, nU, threshType, s1Max, sL_Max, histFlag)
% [ S1, U1, S_L, U_L] = Compute_S_U_LGN_V1_UpDown( S1, U1, S_L, U_L, X, A_Up, A_Down, lambda1, s_b, uEta, nU, threshType, s1Max, sL_Max)
% This function computes the membrane potentials and firing rates of simple
% cells and LGN cells in the model
%
% S1, U1: firing rates and membrane potentials of V1 simple cells
% S_L, U_L: firing rates and membrane potentials of LGN cells
% X: ON and OFF input for LGN cells from early visual system
% A_Up: feedforward connections between LGN and V1 simple cells
% A_Down: feedback connections between LGN and V1 simple cells
% lambda1: threshold of simple cells that controls the sparseness of simple cells
% s_b: background firing rate
% uEta: updating rate of membrane potentials U
% nU: number of iterations of calculating membrane potentials U
% threshType: type of thresholding function that computes firing rates of simple cells from membrane potentials


for n = 1 : nU
    
    V_Leak = - A_Up' * repmat(s_b, size(S_L,1), size(S_L,2)); % membrane potential caused by leakage current
    
    % Dynamics of V1 simple cells: compute membrane potentials
    U1 = (1-uEta) * U1 + uEta * ( V_Leak + A_Up' * S_L + 1*S1 );
    
    % record the trajectory of the first simple cell
    if exist('histFlag','var')
        if histFlag==1
            %         S_history(:,i,:)=S;
            %         U_history(:,i,:)=U;
            S1_history(n,:) = S1(:,1);
        end
    end
    
    % Compute firing rates of simple cells S1 by thresholding U1
    if isequal( threshType, 'soft' ) % soft thresholding at lambda
        S1 = wthresh( U1, 's', lambda1 );
    elseif isequal( threshType, 'hard' ) % hard thresholding at lambda
        S1 = wthresh( U1, 'h', lambda1);
    elseif isequal( threshType, 'sigmoid' ) % sigmoid thresholding at lambda
        alpha = 1/20; beta = 20;
        S1 = alpha * log( 1 + exp( beta*(U1-lambda1) ) );
    else
        S1 = max(U1-lambda1,0); % non-negative soft thresholding at lambda
    end
    S1 = min(S1, s1Max); % keep the response below maximal firing rate
    
    % Dynamics of LGN cells: compute membrane potentials
    U_L = (1-uEta) * U_L + uEta * (X + A_Down * S1 + s_b);
    
    % Compute firing rates of LGN cells S_L by rectifying U_L
    S_L = max(U_L,0);
    
    S_L = min(S_L, sL_Max); % keep the response below maximal firing rate
    
end
    

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