Phase and Amplitude Modulation in a Neural Oscillatory Model of the

Orientation MapDr. V Srinivasa Chakravarthy, Bhadra S Kumar,

Avinash Kori, Sundari Elong

Overview

▪Classical cortical map models▪Need for dynamic map model▪Proposed model ▪ Information encoding using AM▪ Information encoding using PM▪Relevance and future work

Classical cortical map models

▪There are neurons in mammalian visual cortex that respond to selected orientations➢ Hubel and Wiesel

▪The mapping of the orientations on the 2-D surface of primary visual cortex➢ Orientation map

▪Computational models which simulate orientation map➢ Spectral models➢ Correlation models➢ Self organizing map (SOM)➢ Laterally interconnected synergistically self

organizing map (LISSOM)

Need for dynamic map model

▪Visual cortical maps are static representations of neurons to visual stimuli▪Fundamental building block of cortical computation➢ Single spike?➢ Or collective activity of a neuronal ensemble(LFP)?

▪LFP oscillations shows➢ Adaptation to stimulus➢ Ability to predict time of reward presentation➢ In general a significant role in cortical computation

▪ In this light static cortical maps seems a bit outmoded▪Can we reframe the cortical representation of visual stimulus in terms of oscillatory activity?

Proposed model

▪Requirement ➢ A dynamic model with spatiotemporal characteristics which can capture the

features of the stimulus.

▪Neural field models (NFM) ➢ Network of oscillators to capture the spatiotemporal evolution of neural

response

▪The model thus has➢ A two dimensional NFM with Fitzhugh Nagumo (FN) neurons as individual

units➢ The neurons are laterally interconnected➢ The network can operate in two modes

• Excitatory mode• Oscillatory mode

▪The network is trained on oriented bar stimuli

Model Outline

Input stimuli

0° 45° 90° 135°

Information encoding using PM

▪

Waveform of individual neurons Unwrapped phase difference across time

Mean relative phase (MRP)

ExcitatoryNFM

OscillatoryNFM

Classification accuracy using phase information of NFM

Classification accuracy on new test data Average classification accuracy

Information encoding using AM

▪

ExcitatoryRegime

OscillatoryRegime

Variance here is high

Variance here is low

Classification accuracy using amplitude information of NFM

Classification accuracy on new test data Average classification accuracy

Relevance and future work

▪Brain is a dynamical system➢ Cortical responses display spatiotemporal characteristics

▪Some intriguing experimental observations➢ Freeman’s experiment on olfactory bulb of rabbits (Freeman et al 1989)

• Responses observed in olfactory bulb showed stable and repeatable spatio-temporal patterns➢ André M. CRAVO et al 2013

• Phase of delta oscillations overlying human visual cortex (1 to 4 Hz) was predictive of the quality of target processing.

• Temporal rhythms increase phase entrainment of oscillatory activity at electrodes overlying human visual cortex.

▪ In this model, fundamental unit of neural computation is reconsidered➢ Output of a neuronal ensemble is considered instead of single neuron response➢ The oscillator units could be designed to oscillate at low frequency bands to

simulate the experiment by CRAVO➢ The network with its spatiotemporal characteristics could be easily modified to

model Freeman’s observation➢ The whole perspective of neural computation could be rephrased in terms of

neural oscillations using this model

Thank You..

Equations and Parameters