Introduction

This is a model of a planar neural field that simulates evolution of activity rate of neurons implemented using the Amari equation.

This project is written in C++ and it uses CMake to generate platform-specific build files. Program uses OpenGL 3.3 or higher for rendering and ImGui library for the UI. Linear outlines are produced using the Marching squares algorithm. Matrix algebra and marching squares use OpenMP API for paralleling calculations on CPU.

Sceenshots

Description of the Amari Neural Field

Planar neural field is modeled using an Amari model that uses the solution of the Cauchy problem for integro-differential equation:

• u(x,t) - activity function,
• h - equilibrium potential,
• H(x) - Heaviside function,
• w - weight function,
• s - external inhibition,
• phi - initial distribution of an electric potential at t=0,
• x - coordinate in the area Omega.

Prerequisites

You need CMake to generate platform-specific makefiles or project files. This repository bundles most of the dependencies as git submodules, which includes:

• glad - OpenGL Function Loader.
• glfw - Windowing and Input.
• glm - OpenGL Mathematics.
• plog - Logging library.
• imgui - UI library.
• inih - INI file parsing.

Building for Linux

Dependencies

The following instructions apply to:

• Ubuntu or Debian

apt-get install \
    build-essential \
    cmake \
    xorg-dev \
    libgl1-mesa-dev \
    libfreetype6-dev

The following instructions apply to:

• RedHat-based systems (Fedora, CentOS):

dnf install \
    cmake \
    gcc-c++ \
    mesa-libGL-devel \
    libXrandr-devel \
    libXinerama-devel \
    libXcursor-devel \
    libXi-devel \
    freetype-devel

Dependencies for OpenCL build

Build with USE_OPENCL option requires additional dependencies.

• Install development libraries:

On Ubuntu or Debian:

apt install opencl-headers ocl-icd-opencl-dev

On RedHat-based systems (Fedora, CentOS):

dnf install mesa-libOpenCL-devel ocl-icd-devel

• Install platform-specific driver, e.g. driver for Intel:

On Ubuntu or Debian:

apt install intel-opencl-icd

On RedHat-based systems (Fedora, CentOS):

dnf install intel-opencl

Cloning Repository

git clone --recursive https://github.com/Postrediori/NeuralField.git
cd NeuralField

The --recursive option automatically clones the required Git submodules too.

Building Project

The program is built with the commands below. CMake requires the directory with the main project's CMakeLists.txt file as an argument. Then the CMake creates the build files for the GNU make which build an executable.

mkdir build && cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
make

Additional build options

The following options are available when running CMake:

• USE_OPENMP (default value: ON) - Make parallel code with OpenMP. This option is disabled on macOS.
• USE_OPENCL (default value: OFF) - Use OpenCL for calculations.

Example usage:

mkdir build && cd build
cmake .. -DUSE_OPENMP=OFF -DUSE_OPENCL=ON

Running Project

After the successful build the binary NeuralField will end up in <source dir>/bundle directory.

./bundle/NeuralField

All of the files required for an executable to run are stored in the <PathToProject>/bundle:

cd <PathToProject>/bundle
tree
.
├── NeuralField
└── data
    ├── amari.conf
    ├── plane.frag
    ├── plane.vert
    └── ...

2 directories, 7 files

Building for macOS

Generate makefiles for the build:

mkdir build && cd build
cmake .. -DCMAKE_OSX_ARCHITECTURES=x86_64 -DCMAKE_BUILD_TYPE=Release

Configuration

The parameters of the model can be adjusted in the data/amari.conf file:

# size = 128 | 256 | 512
size = 128

# h = 0..-0.3
h = -0.2

k = 0.05
K = 0.125
m = 0.025

# M = 0.05..0.07, 0.0625 - optimal
M = 0.065

# mode = wrap | reflect | mirror
mode = wrap

• size - Size of discrete neural field.
• M - Activation spread parameter. Smaller values stand for easily activated naural field, larger values lead to smaller activity spread from the same activity initiator.
• h - Discrepancy parameter. Zero stands for no discrepancies and leads to symmetric model. Smaller values lead to unsymmetric development of an activity.
• mode - Behavior on the neural field boundaries. wrap stands for the possibility of boundary neurons to influence the opposite boundary. reflect stands for boundary as the line of an active neurons.

h=0	h=-0.15	h=-0.3

Controls

• F1 - Toggle fullscreen mode.
• F2 - Show/hide help on the screen.
• Space or RMB - Clear the model.
• LMB - Initiate the activity in a pointunder cursor.
• 1..5 - Switch between output modes.
• B - Toggle blurring for the textured mode.

Links

• S. Amari, Dynamics of pattern formation in lateral-inhibition type neural filed, 1977.
• Konstantin Doubrovinski, Dynamics, Stability and Bifurcation Phenomena in the Nonlocal Model of Cortical Activity, 2005.
• Dequan Jin, Dong Liang, Jigen Peng, Existence and Properties of Stationary Solution of Dynamical Neural Field, 2011.
• Stephen Coombes, Helmut Schmidt, Ingo Bojak, Interface Dynamics in Planar Neural Field Models, 2012.
• Luca Salasnich, Power Spectrum and Diffusion of the Amari Neural Field, 2019.

TODO

• Build instructions for Windows.
• Matrix algebra using hardware acceleration (OpenCL, OpenGL Compute Shaders, texture rendering&framebuffers, shader feedback, etc.)
• Export results to images and videos.
• Expand description of the model.