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Interneuron.py
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Interneuron.py
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'''
Neuromuscular simulator in Python.
Copyright (C) 2017 Renato Naville Watanabe
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Contact: [email protected]
'''
from Compartment import Compartment
import numpy as np
from AxonDelay import AxonDelay
import math
from scipy.sparse import lil_matrix
import time
def runge_kutta(derivativeFunction, t, x, timeStep, timeStepByTwo, timeStepBySix):
'''
Function to implement the fourth order Runge-Kutta Method to solve numerically a
differential equation.
- Inputs:
+ **derivativeFunction**: function that corresponds to the derivative of the differential equation.
+ **t**: current instant.
+ **x**: current state value.
+ **timeStep**: time step of the solution of the differential equation, in the same unit of t.
+ **timeStepByTwo**: timeStep divided by two, for computational efficiency.
+ **timeStepBySix**: timeStep divided by six, for computational efficiency.
This method is intended to solve the following differential equation:
\f{equation}{
\frac{dx(t)}{dt} = f(t, x(t))
\f}
First, four derivatives are computed:
\f{align}{
k_1 &= f(t,x(t))\\
k_2 &= f(t+\frac{\Delta t}{2}, x(t) + \frac{\Delta t}{2}.k_1)\\
k_3 &= f(t+\frac{\Delta t}{2}, x(t) + \frac{\Delta t}{2}.k_2)\\
k_4 &= f(t+\Delta t, x(t) + \Delta t.k_3)
\f}
where \f$\Delta t\f$ is the time step of the numerical solution of the
differential equation.
Then the value of \f$x(t+\Delta t)\f$ is computed with:
\f{equation}{
x(t+\Delta t) = x(t) + \frac{\Delta t}{6}(k_1 + 2k_2 + 2k_3+k_4)
\f}
'''
k1 = derivativeFunction(t, x)
k2 = derivativeFunction(t + timeStepByTwo, x + timeStepByTwo * k1)
k3 = derivativeFunction(t + timeStepByTwo, x + timeStepByTwo * k2)
k4 = derivativeFunction(t + timeStep, x + timeStep * k3)
return x + timeStepBySix * (k1 + k2 + k2 + k3 + k3 + k4)
class Interneuron(object):
'''
Class that implements a motor unit model. Encompasses a motoneuron
and a muscle unit.
'''
def __init__(self, conf, pool, index):
'''
Constructor
- Inputs:
+ **conf**: Configuration object with the simulation parameters.
+ **pool**: string with Interneuron pool to which the motor
unit belongs. It can
be *RC* (Renshaw cell), *IaIn* (Ia Interneuron), *IbIn* (Ib Interneuron) and
*gII*.
+ **index**: integer corresponding to the motor unit order in
the pool, according to the Henneman's principle (size principle).
'''
## Configuration object with the simulation parameters.
self.conf = conf
self.pool = pool
self.kind = ''
# Neural compartments
## The instant of the last spike of the Motor unit
## at the Soma compartment.
self.tSomaSpike = float("-inf")
compartmentsList = ['soma']
## Vector with the instants of spikes at the soma.
self.somaSpikeTrain = []
## Integer corresponding to the Interneuron order in the pool.
self.index = int(index)
## Vector of Compartment of the Motor Unit.
self.compartment = dict()
## Value of the membrane potential, in mV, that is considered a spike.
self.threshold_mV = conf.parameterSet('threshold', pool, index)
## Anatomical position of the neuron, in mm.
self.position_mm = conf.parameterSet('position', pool, index)
for i in xrange(len(compartmentsList)):
self.compartment[i] = Compartment(compartmentsList[i], self.conf, self.pool, self.index, self.kind)
## Number of compartments.
self.compNumber = len(self.compartment)
## Vector with membrane potential,in mV, of all compartments.
self.v_mV = np.zeros((self.compNumber), dtype = np.float64)
gLeak = np.zeros_like(self.v_mV, dtype = 'd')
capacitance_nF = np.zeros_like(self.v_mV, dtype = 'd')
EqPot = np.zeros_like(self.v_mV, dtype = 'd')
for i in xrange(len(self.compartment)):
capacitance_nF[i] = self.compartment[i].capacitance_nF
gLeak[i] = self.compartment[i].gLeak_muS
EqPot[i] = self.compartment[i].EqPot_mV
## Vector with the inverse of the capacitance of all compartments.
self.capacitanceInv = 1 / capacitance_nF
## Vector with current, in nA, of each compartment coming from other elements of the model. For example
## from ionic channels and synapses.
self.iIonic = np.full_like(self.v_mV, 0.0)
## Vector with the current, in nA, injected in each compartment.
self.iInjected = np.zeros_like(self.v_mV, dtype = 'd')
#self.iInjected = np.array([0, 10.0])
GL = -np.diag(gLeak)
## Matrix of the conductance of the motoneuron. Multiplied by the vector self.v_mV,
## results in the passive currents of each compartment.
self.G = np.float64(GL)
self.EqCurrent_nA = np.dot(-GL, EqPot)
## index of the soma compartment.
self.somaIndex = compartmentsList.index('soma')
## Refractory period, in ms, of the motoneuron.
self.RefPer_ms = float(conf.parameterSet(self.pool + 'SomaRefPer', pool, index))
## Vector with the instants of spikes at the terminal.
self.terminalSpikeTrain = []
## Build synapses
self.SynapsesOut = []
self.transmitSpikesThroughSynapses = []
self.indicesOfSynapsesOnTarget = []
def atualizeInterneuron(self, t, v_mV):
'''
Atualize the dynamical and nondynamical (delay) parts of the motor unit.
- Inputs:
+ **t**: current instant, in ms.
'''
self.atualizeCompartments(t, v_mV)
def atualizeCompartments(self, t, v_mV):
'''
Atualize all neural compartments.
- Inputs:
+ **t**: current instant, in ms.
'''
self.v_mV[:] = v_mV
if self.v_mV[self.somaIndex] > self.threshold_mV and t-self.tSomaSpike > self.RefPer_ms:
self.addSomaSpike(t)
def addSomaSpike(self, t):
'''
When the soma potential is above the threshold a spike is added to the soma.
- Inputs:
+ **t**: current instant, in ms.
'''
self.tSomaSpike = t
self.somaSpikeTrain.append([t, int(self.index)])
self.transmitSpikes(t)
for channel in self.compartment[self.somaIndex].Channels:
for channelState in channel.condState: channelState.changeState(t)
def transmitSpikes(self, t):
'''
- Inputs:
+ **t**: current instant, in ms.
'''
for i in xrange(len(self.indicesOfSynapsesOnTarget)):
self.transmitSpikesThroughSynapses[i].receiveSpike(t, self.indicesOfSynapsesOnTarget[i])