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sweeney.py
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# -*- coding: utf-8 -*-
# @Author: Theo Lemaire
# @Email: theo.lemaire@epfl.ch
# @Date: 2019-06-11 15:58:38
# @Last Modified by: Theo Lemaire
# @Last Modified time: 2019-08-26 14:45:26
import numpy as np
from ..core import PointNeuron
class SweeneyNode(PointNeuron):
''' Mammalian myelinated motor fiber fiber node.
Reference:
*Sweeney, J.D., Mortimer, J.T., and Durand, D. (1987). Modeling of mammalian myelinated nerve
for functional neuromuscular stimulation. IEEE 9th Annual Conference of the Engineering
in Medicine and Biology Society 3, 1577–1578.*
'''
# Neuron name
name = 'sweeney'
# ------------------------------ Biophysical parameters ------------------------------
# Resting parameters
Cm0 = 2.5e-2 # Membrane capacitance (F/m2)
Vm0 = -80.0 # Membrane potential (mV)
# Reversal potentials (mV)
ENa = 35.64 # Sodium
ELeak = -80.01 # Non-specific leakage
# Maximal channel conductances (S/m2)
gNabar = 1445e1 # Sodium
gLeak = 128e1 # Non-specific leakage
# ------------------------------ States names & descriptions ------------------------------
states = {
'm': 'iNa activation gate',
'h': 'iNa inactivation gate',
}
# ------------------------------ Gating states kinetics ------------------------------
@classmethod
def alpham(cls, Vm):
return (126 + 0.363 * Vm) / (1 + np.exp(-(Vm + 49) / 53)) * 1e3 # s-1
@classmethod
def betam(cls, Vm):
return cls.alpham(Vm) / (np.exp((Vm + 56.2) / 4.17)) # s-1
@classmethod
def betah(cls, Vm):
return 15.6 / (1 + np.exp(-(Vm + 56) / 10)) * 1e3 # s-1
@classmethod
def alphah(cls, Vm):
return cls.betah(Vm) / np.exp((Vm + 74.5) / 5) # s-1
# ------------------------------ States derivatives ------------------------------
@classmethod
def derStates(cls):
return {
'm': lambda Vm, x: cls.alpham(Vm) * (1 - x['m']) - cls.betam(Vm) * x['m'],
'h': lambda Vm, x: cls.alphah(Vm) * (1 - x['h']) - cls.betah(Vm) * x['h']
}
# ------------------------------ Steady states ------------------------------
@classmethod
def steadyStates(cls):
return {
'm': lambda Vm: cls.alpham(Vm) / (cls.alpham(Vm) + cls.betam(Vm)),
'h': lambda Vm: cls.alphah(Vm) / (cls.alphah(Vm) + cls.betah(Vm))
}
# ------------------------------ Membrane currents ------------------------------
@classmethod
def iNa(cls, m, h, Vm):
''' Sodium current '''
return cls.gNabar * m**2 * h * (Vm - cls.ENa) # mA/m2
@classmethod
def iLeak(cls, Vm):
''' non-specific leakage current '''
return cls.gLeak * (Vm - cls.ELeak) # mA/m2
@classmethod
def currents(cls):
return {
'iNa': lambda Vm, x: cls.iNa(x['m'], x['h'], Vm),
'iLeak': lambda Vm, _: cls.iLeak(Vm)
}

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