.. currentmodule:: brian2

.. cylinder:

Example: cylinder
=================


        .. only:: html

            .. |launchbinder| image:: http://mybinder.org/badge.svg
            .. _launchbinder: https://mybinder.org/v2/gh/brian-team/brian2-binder/master?filepath=examples/compartmental/cylinder.ipynb

            .. note::
               You can launch an interactive, editable version of this
               example without installing any local files
               using the Binder service (although note that at some times this
               may be slow or fail to open): |launchbinder|_

        

A short cylinder with constant injection at one end.

::

    from brian2 import *
    
    defaultclock.dt = 0.01*ms
    
    # Morphology
    diameter = 1*um
    length = 300*um
    Cm = 1*uF/cm**2
    Ri = 150*ohm*cm
    N = 200
    morpho = Cylinder(diameter=diameter, length=length, n=N)
    
    # Passive channels
    gL = 1e-4*siemens/cm**2
    EL = -70*mV
    eqs = '''
    Im = gL * (EL - v) : amp/meter**2
    I : amp (point current)
    '''
    
    neuron = SpatialNeuron(morphology=morpho, model=eqs, Cm=Cm, Ri=Ri,
                           method='exponential_euler')
    neuron.v = EL
    
    la = neuron.space_constant[0]
    print("Electrotonic length: %s" % la)
    
    neuron.I[0] = 0.02*nA # injecting at the left end
    run(100*ms, report='text')
    
    plot(neuron.distance/um, neuron.v/mV, 'kx')
    # Theory
    x = neuron.distance
    ra = la * 4 * Ri / (pi * diameter**2)
    theory = EL + ra * neuron.I[0] * cosh((length - x) / la) / sinh(length / la)
    plot(x/um, theory/mV, 'r')
    xlabel('x (um)')
    ylabel('v (mV)')
    show()
    

.. image:: ../resources/examples_images/compartmental.cylinder.1.png