.. currentmodule:: brian2

.. infinite_cable:

Example: infinite_cable
=======================


        .. only:: html

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

        

An (almost) infinite cable with pulse injection in the middle.

::

    from brian2 import *
    
    defaultclock.dt = 0.001*ms
    
    # Morphology
    diameter = 1*um
    Cm = 1*uF/cm**2
    Ri = 100*ohm*cm
    N = 500
    morpho = Cylinder(diameter=diameter, length=3*mm, 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
    
    taum = Cm  /gL  # membrane time constant
    print("Time constant: %s" % taum)
    la = neuron.space_constant[0]
    print("Characteristic length: %s" % la)
    
    # Monitors
    mon = StateMonitor(neuron, 'v', record=range(0, N//2, 20))
    
    neuron.I[len(neuron) // 2] = 1*nA  # injecting in the middle
    run(0.02*ms)
    neuron.I = 0*amp
    run(10*ms, report='text')
    
    t = mon.t
    plot(t/ms, mon.v.T/mV, 'k')
    # Theory (incorrect near cable ends)
    for i in range(0, len(neuron)//2, 20):
        x = (len(neuron)/2 - i) * morpho.length[0]
        theory = (1/(la*Cm*pi*diameter) * sqrt(taum / (4*pi*(t + defaultclock.dt))) *
                  exp(-(t+defaultclock.dt)/taum -
                      taum / (4*(t+defaultclock.dt))*(x/la)**2))
        theory = EL + theory * 1*nA * 0.02*ms
        plot(t/ms, theory/mV, 'r')
    xlabel('Time (ms)')
    ylabel('v (mV')
    show()
    

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