NESTML Izhikevich tutorial

Introduction

The aim of this exercise is to obtain familiarity with NESTML by completing a partial model of the Izhikevich neuron [1].

Prerequisites

You need to have a working NEST Simulator and NESTML installation, see Installing NESTML.

You need to be able to run NESTML to generate and build model code. NESTML can be used from the command line, and via a Python API. The latter will be used in this notebook. See Running NESTML.

[1]:

%matplotlib inline
import matplotlib.pyplot as plt
import nest
import numpy as np
import os

from pynestml.codegeneration.nest_code_generator_utils import NESTCodeGeneratorUtils

/home/charl/.local/lib/python3.11/site-packages/matplotlib/projections/__init__.py:63: UserWarning: Unable to import Axes3D. This may be due to multiple versions of Matplotlib being installed (e.g. as a system package and as a pip package). As a result, the 3D projection is not available.
  warnings.warn("Unable to import Axes3D. This may be due to multiple versions of "


              -- N E S T --
  Copyright (C) 2004 The NEST Initiative

 Version: 3.6.0-post0.dev0
 Built: Mar 26 2024 08:52:51

 This program is provided AS IS and comes with
 NO WARRANTY. See the file LICENSE for details.

 Problems or suggestions?
   Visit https://www.nest-simulator.org

 Type 'nest.help()' to find out more about NEST.

Paths

We assume here that we will generate code in a temporary directory /tmp/nestml-component. You can also create a unique temporary path using the Python tempfile module.

The Izhikevich model

A simple model for spiking neurons that nevertheless can exhibit a wide variety of dynamical behaviour, depending on its parameter values [1]. It is defined as follows:

\begin{align} \frac{dv}{dt} &= 0.04 v^2 + 5 v + 140 - u + I\\ \frac{du}{dt} &= a (b v - u) \end{align}

State update:

:nbsphinx-math:`begin{align}

&text{if};; v geq V_{th}:\ &;;;; v text{ is set to } c\ &;;;; u text{ is incremented by } d\ & , \ &v text{ jumps on each spike arrival by the weight of the spike}

end{align}`

Example parameters for regular spiking (the meaning of these parameters is described in detail in the paper [1]; see also Task 2 below):

\begin{align} a&=0.02\\ b&=0.2\\ c&=-65~\text{mV}\\ d&=8 \end{align}

Task 1: Finish the model

In the file `izhikevich_task.nestml <https://raw.githubusercontent.com/nest/nestml/master/doc/tutorials/izhikevich/izhikevich_task.nestml>`__, only a subset of the parameters, state equations and update block is implemented.

Open the file in a text editor and finish the partially-completed model.

For reference, the solution is included as `izhikevich_solution.nestml <https://raw.githubusercontent.com/nest/nestml/master/doc/tutorials/izhikevich/izhikevich_solution.nestml>`__.

NESTML code generation

Assume that our NESTML input model is at izhikevich_solution.nestml. To generate code and build a dynamic library that can be loaded as a user module in NEST Simulator:

[2]:

# generate and build code
module_name, neuron_model_name = \
    NESTCodeGeneratorUtils.generate_code_for("izhikevich_solution.nestml")


              -- N E S T --
  Copyright (C) 2004 The NEST Initiative

 Version: 3.6.0-post0.dev0
 Built: Mar 26 2024 08:52:51

 This program is provided AS IS and comes with
 NO WARRANTY. See the file LICENSE for details.

 Problems or suggestions?
   Visit https://www.nest-simulator.org

 Type 'nest.help()' to find out more about NEST.

[12,izhikevich_tutorial_neuron_nestml, WARNING, [12:8;12:17]]: Variable 'a' has the same name as a physical unit!
[13,izhikevich_tutorial_neuron_nestml, WARNING, [15:8;15:17]]: Variable 'd' has the same name as a physical unit!
[17,izhikevich_tutorial_neuron_nestml, WARNING, [12:8;12:17]]: Variable 'a' has the same name as a physical unit!
[18,izhikevich_tutorial_neuron_nestml, WARNING, [15:8;15:17]]: Variable 'd' has the same name as a physical unit!
[23,izhikevich_tutorial_neuron_nestml, WARNING, [12:8;12:17]]: Variable 'a' has the same name as a physical unit!
[24,izhikevich_tutorial_neuron_nestml, WARNING, [15:8;15:17]]: Variable 'd' has the same name as a physical unit!
CMake Warning (dev) at CMakeLists.txt:93 (project):
  cmake_minimum_required() should be called prior to this top-level project()
  call.  Please see the cmake-commands(7) manual for usage documentation of
  both commands.
This warning is for project developers.  Use -Wno-dev to suppress it.

-- The CXX compiler identification is GNU 12.3.0
-- Detecting CXX compiler ABI info
-- Detecting CXX compiler ABI info - done
-- Check for working CXX compiler: /usr/bin/c++ - skipped
-- Detecting CXX compile features
-- Detecting CXX compile features - done

-------------------------------------------------------
nestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module Configuration Summary
-------------------------------------------------------

C++ compiler         : /usr/bin/c++
Build static libs    : OFF
C++ compiler flags   :
NEST compiler flags  :  -std=c++17 -Wall -fopenmp -O2 -fdiagnostics-color=auto
NEST include dirs    :  -I/home/charl/julich/nest-simulator-install/include/nest -I/usr/include -I/usr/include -I/usr/include
NEST libraries flags : -L/home/charl/julich/nest-simulator-install/lib/nest -lnest -lsli /usr/lib/x86_64-linux-gnu/libltdl.so  /usr/lib/x86_64-linux-gnu/libgsl.so /usr/lib/x86_64-linux-gnu/libgslcblas.so    /usr/lib/gcc/x86_64-linux-gnu/12/libgomp.so /usr/lib/x86_64-linux-gnu/libpthread.a

-------------------------------------------------------

You can now build and install 'nestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module' using
  make
  make install

The library file libnestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module.so will be installed to
  /tmp/nestml_target_sii6g4x1
The module can be loaded into NEST using
  (nestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module) Install       (in SLI)
  nest.Install(nestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module)   (in PyNEST)

CMake Warning (dev) in CMakeLists.txt:
  No cmake_minimum_required command is present.  A line of code such as

    cmake_minimum_required(VERSION 3.26)

  should be added at the top of the file.  The version specified may be lower
  if you wish to support older CMake versions for this project.  For more
  information run "cmake --help-policy CMP0000".
This warning is for project developers.  Use -Wno-dev to suppress it.

-- Configuring done (0.5s)
-- Generating done (0.0s)
-- Build files have been written to: /home/charl/julich/nestml-fork-integrate_specific_odes/nestml/doc/tutorials/izhikevich/target
[ 33%] Building CXX object CMakeFiles/nestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module_module.dir/nestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module.o
[ 66%] Building CXX object CMakeFiles/nestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module_module.dir/izhikevich_tutorial_neuron_nestml.o
/home/charl/julich/nestml-fork-integrate_specific_odes/nestml/doc/tutorials/izhikevich/target/izhikevich_tutorial_neuron_nestml.cpp: In member function ‘void izhikevich_tutorial_neuron_nestml::init_state_internal_()’:
/home/charl/julich/nestml-fork-integrate_specific_odes/nestml/doc/tutorials/izhikevich/target/izhikevich_tutorial_neuron_nestml.cpp:184:16: warning: unused variable ‘__resolution’ [-Wunused-variable]
  184 |   const double __resolution = nest::Time::get_resolution().get_ms();  // do not remove, this is necessary for the resolution() function
      |                ^~~~~~~~~~~~
/home/charl/julich/nestml-fork-integrate_specific_odes/nestml/doc/tutorials/izhikevich/target/izhikevich_tutorial_neuron_nestml.cpp: In member function ‘virtual void izhikevich_tutorial_neuron_nestml::update(const nest::Time&, long int, long int)’:
/home/charl/julich/nestml-fork-integrate_specific_odes/nestml/doc/tutorials/izhikevich/target/izhikevich_tutorial_neuron_nestml.cpp:318:24: warning: comparison of integer expressions of different signedness: ‘long int’ and ‘const size_t’ {aka ‘const long unsigned int’} [-Wsign-compare]
  318 |     for (long i = 0; i < NUM_SPIKE_RECEPTORS; ++i)
      |                      ~~^~~~~~~~~~~~~~~~~~~~~
/home/charl/julich/nestml-fork-integrate_specific_odes/nestml/doc/tutorials/izhikevich/target/izhikevich_tutorial_neuron_nestml.cpp:313:10: warning: variable ‘get_t’ set but not used [-Wunused-but-set-variable]
  313 |     auto get_t = [origin, lag](){ return nest::Time( nest::Time::step( origin.get_steps() + lag + 1) ).get_ms(); };
      |          ^~~~~
/home/charl/julich/nestml-fork-integrate_specific_odes/nestml/doc/tutorials/izhikevich/target/izhikevich_tutorial_neuron_nestml.cpp:303:16: warning: unused variable ‘__resolution’ [-Wunused-variable]
  303 |   const double __resolution = nest::Time::get_resolution().get_ms();  // do not remove, this is necessary for the resolution() function
      |                ^~~~~~~~~~~~
[100%] Linking CXX shared module nestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module.so
[100%] Built target nestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module_module
[100%] Built target nestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module_module
Install the project...
-- Install configuration: ""
-- Installing: /tmp/nestml_target_sii6g4x1/nestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module.so

Check the generated log output for any potential error messages or warnings.

Instantiate model in NEST Simulator and run

The generated extension module can be loaded using nest.Install().

Using the PyNEST API, the model can be instantiated and simulated in NEST. The following code will create one instance of the neuron model (nest.Create("izhikevich_tutorial")), inject a constant current and run the simulation for 250 ms.

[3]:

nest.set_verbosity("M_ALL")
nest.ResetKernel()

# load dynamic library (NEST extension module) into NEST kernel
nest.Install(module_name)

neuron = nest.Create(neuron_model_name)
voltmeter = nest.Create("voltmeter")

voltmeter.set({"record_from": ["v", "u"]})
nest.Connect(voltmeter, neuron)

cgs = nest.Create('dc_generator')
cgs.set({"amplitude": 25.})
nest.Connect(cgs, neuron)

sr = nest.Create("spike_recorder")
nest.Connect(neuron, sr)

nest.Simulate(250.)

spike_times = nest.GetStatus(sr, keys='events')[0]['times']

fig, ax = plt.subplots(nrows=2)
ax[0].plot(voltmeter.get("events")["times"], voltmeter.get("events")["v"])
ax[1].plot(voltmeter.get("events")["times"], voltmeter.get("events")["u"])
ax[0].scatter(spike_times, 30 * np.ones_like(spike_times), marker="d", c="orange", alpha=.8, zorder=99)
for _ax in ax:
    _ax.grid(True)
ax[0].set_ylabel("v [mV]")
ax[1].set_ylabel("u")
ax[-1].set_xlabel("Time [ms]")
fig.show()


Apr 19 10:44:47 Install [Info]:
    loaded module nestml_004fd3f5ec9a44b9a28667ae47e2bc9e_module

Apr 19 10:44:47 NodeManager::prepare_nodes [Info]:
    Preparing 4 nodes for simulation.

Apr 19 10:44:47 SimulationManager::start_updating_ [Info]:
    Number of local nodes: 4
    Simulation time (ms): 250
    Number of OpenMP threads: 1
    Not using MPI

Apr 19 10:44:47 SimulationManager::run [Info]:
    Simulation finished.

/tmp/ipykernel_329471/1245292433.py:33: UserWarning:FigureCanvasAgg is non-interactive, and thus cannot be shown
../../_images/tutorials_izhikevich_nestml_izhikevich_tutorial_7_2.png

Task 2: Parameter space exploration

Perform a parameter space exploration to reproduce the bottom eight panels from [1], figure 2.

References

[1] Eugene M. Izhikevich, “Simple Model of Spiking Neurons”, IEEE Transactions on Neural Networks, Vol. 14, No. 6, November 2003