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MuscleSpindle.py
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MuscleSpindle.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]
'''
import numpy as np
import math
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 MuscleSpindle(object):
'''
Class that implements a muscle spindle model.
'''
def __init__(self, conf, muscle):
'''
Constructor
- Inputs:
+ **conf**: Configuration object with the simulation parameters.
+ **muscle**: string with the muscle to which the muscle spindle belongs.
'''
## Configuration object with the simulation parameters.
self.conf = conf
self.muscle = muscle
self.beta0Bag1 = float(conf.parameterSet('beta0Bag1', muscle, 0))
self.beta0Bag2 = float(conf.parameterSet('beta0Bag2', muscle, 0))
self.beta0Chain = float(conf.parameterSet('beta0Chain', muscle, 0))
self.beta1Bag1 = float(conf.parameterSet('beta1Bag1', muscle, 0))
self.beta2Bag2 = float(conf.parameterSet('beta2Bag2', muscle, 0))
self.beta2Chain = float(conf.parameterSet('beta2Chain', muscle, 0))
self.GAMMA1Bag1 = float(conf.parameterSet('GAMMA1Bag1', muscle, 0))
self.GAMMA2Bag2 = float(conf.parameterSet('GAMMA2Bag2', muscle, 0))
self.GAMMA2Chain = float(conf.parameterSet('GAMMA2Chain', muscle, 0))
self.freq_bag1_Hz = float(conf.parameterSet('freqBag1', muscle, 0))
self.freq_bag2_Hz = float(conf.parameterSet('freqBag2', muscle, 0))
self.freq_Chain_Hz = float(conf.parameterSet('freqChain', muscle, 0))
self.tauBag1_s = float(conf.parameterSet('tauBag1', muscle, 0))
self.tauBag2_s = float(conf.parameterSet('tauBag2', muscle, 0))
self.KsrBag1 = float(conf.parameterSet('KsrBag1', muscle, 0))
self.KsrBag2 = float(conf.parameterSet('KsrBag2', muscle, 0))
self.KsrChain = float(conf.parameterSet('KsrChain', muscle, 0))
self.MBag1 = float(conf.parameterSet('MBag1', muscle, 0))
self.MBag2 = float(conf.parameterSet('MBag2', muscle, 0))
self.MChain = float(conf.parameterSet('MChain', muscle, 0))
self.L0SrBag1 = float(conf.parameterSet('L0SrBag1', muscle, 0))
self.L0SrBag2 = float(conf.parameterSet('L0SrBag2', muscle, 0))
self.L0SrChain = float(conf.parameterSet('L0SrChain', muscle, 0))
self.L0PrBag1 = float(conf.parameterSet('L0PrBag1', muscle, 0))
self.L0PrBag2 = float(conf.parameterSet('L0PrBag2', muscle, 0))
self.L0PrChain = float(conf.parameterSet('L0PrChain', muscle, 0))
self.LNSrBag1 = float(conf.parameterSet('LNSrBag1', muscle, 0))
self.LNSrBag2 = float(conf.parameterSet('LNSrBag2', muscle, 0))
self.LNSrChain = float(conf.parameterSet('LNSrChain', muscle, 0))
self.LNPrBag2 = float(conf.parameterSet('LNPrBag2', muscle, 0))
self.LNPrChain = float(conf.parameterSet('LNPrChain', muscle, 0))
self.RBag1 = float(conf.parameterSet('RBag1', muscle, 0))
self.RBag2 = float(conf.parameterSet('RBag2', muscle, 0))
self.RChain = float(conf.parameterSet('RChain', muscle, 0))
self.KPrBag1 = float(conf.parameterSet('KPrBag1', muscle, 0))
self.KPrBag2 = float(conf.parameterSet('KPrBag2', muscle, 0))
self.KPrChain = float(conf.parameterSet('KPrChain', muscle, 0))
self.GPrimaryBag1 = float(conf.parameterSet('GPrimaryBag1', muscle, 0))
self.GPrimaryBag2 = float(conf.parameterSet('GPrimaryBag2', muscle, 0))
self.GPrimaryChain = float(conf.parameterSet('GPrimaryChain', muscle, 0))
self.SOcclusionFactor = float(conf.parameterSet('SOcclusionFactor', muscle, 0))
self.betaBag1 = 0
self.betaBag2 = 0
self.betaChain = 0
self.GAMMABag1 = 0
self.GAMMABag2 = 0
self.GAMMAChain = 0
self.primaryPotentialBag1 = 0
self.primaryPotentialBag2 = 0
self.primaryPotentialChain = 0
self.secondaryPotentialBag1 = 0
self.secondaryPotentialBag2 = 0
self.secondaryPotentialChain = 0
## Vector with the activation of each fusimotor fiber. The first
# element is the frequency of Bag1, the second of Bag2 and the
# third of the Chain.
self.fusimotorActivation = np.zeros((3), dtype=np.float64)
## Vector with the tensions and tensions derivatives of each
# fusimotor fiber. The first two elements correspond to the Bag1,
# the third and fourth to Bag2 and the last ones to the Chain.
self.fiberTension = np.zeros((6), dtype=np.float64)
self.IaFR_Hz = 0.0
self.IIFR_Hz = 0.0
print 'Muscle spindle from muscle ' + self.muscle + ' built.'
def atualizeMuscleSpindle(self, t, fascicleLength, fascicleVelocity,
fascicleAcceleration, gammaMNDynamicFR, gammaMNStaticFR):
'''
Atualize the dynamical and nondynamical (delay) parts of the motor unit.
- Inputs:
+ **t**: current instant, in ms.
'''
self.computeFusimotorActivation(t, gammaMNDynamicFR, gammaMNStaticFR)
self.betaBag1 = self.beta0Bag1 + self.beta1Bag1 * self.fusimotorActivation[0]
self.betaBag2 = self.beta0Bag2 + self.beta2Bag2 * self.fusimotorActivation[1]
self.betaChain = self.beta0Chain + self.beta2Chain * self.fusimotorActivation[2]
self.GAMMABag1 = self.GAMMA1Bag1 * self.fusimotorActivation[0]
self.GAMMABag2 = self.GAMMA2Bag2 * self.fusimotorActivation[1]
self.GAMMAChain = self.GAMMA2Chain * self.fusimotorActivation[2]
self.computeFiberTension(t, fascicleLength, fascicleVelocity, fascicleAcceleration)
self.IaFR_Hz = self.computeIa(t)
#self.IIFR = self.computeII(t)
def computeC(self, fascicleVelocity, dT, Ksr):
if (fascicleVelocity - dT/Ksr) > 0:
C = 1.0
else:
C = 0.42
return C
def computeFusimotorActivation(self, t, gammaMNDynamicFR, gammaMNStaticFR):
'''
'''
df = self.dfdt(t,gammaMNDynamicFR, gammaMNStaticFR)
self.fusimotorActivation[0] += self.conf.timeStep_ms / 1000.0 * df[0]
self.fusimotorActivation[1] += self.conf.timeStep_ms / 1000.0 * df[1]
self.fusimotorActivation[2] = gammaMNStaticFR**2/(gammaMNStaticFR**2 + self.freq_Chain_Hz**2)
def dfdt(self, t, gammaMNDynamicFR, gammaMNStaticFR):
'''
'''
df = np.zeros((2))
df[0] = ((gammaMNDynamicFR**2)/(gammaMNDynamicFR**2 + self.freq_bag1_Hz**2) - self.fusimotorActivation[0]) / self.tauBag1_s
df[1] = ((gammaMNStaticFR**2)/(gammaMNStaticFR**2 + self.freq_bag2_Hz**2) - self.fusimotorActivation[1]) / self.tauBag2_s
return df
def computeFiberTension(self, t, fascicleLength, fascicleVelocity, fascicleAcceleration):
'''
'''
dT = self.dTdt(t, fascicleLength, fascicleVelocity, fascicleAcceleration)
self.fiberTension += self.conf.timeStep_ms / 1000 * dT
def dTdt(self, t, fascicleLength, fascicleVelocity, fascicleAcceleration):
'''
'''
dT = np.zeros((6))
dT[0] = self.fiberTension[1]
dT[1] = self.KsrBag1 / self.MBag1 * (self.computeC(fascicleVelocity, self.fiberTension[1], self.KsrBag1) * self.betaBag1 * np.sign(fascicleVelocity - self.fiberTension[1]/self.KsrBag1)
* (math.fabs(fascicleVelocity - self.fiberTension[1]/self.KsrBag1)**0.3) *
(fascicleLength - self.L0SrBag1 - self.fiberTension[0]/self.KsrBag1 - self.RBag1)
+ self.KPrBag1 * (fascicleLength - self.L0SrBag1 - self.fiberTension[0]/self.KsrBag1 - self.L0PrBag1)
+ self.MBag1 * fascicleAcceleration + self.GAMMABag1 - self.fiberTension[0]
)
dT[2] = self.fiberTension[3]
dT[3] = self.KsrBag2 / self.MBag2 * (self.computeC(fascicleVelocity, self.fiberTension[3], self.KsrBag2) * self.betaBag2 * np.sign(fascicleVelocity - self.fiberTension[3]/self.KsrBag2)
* (math.fabs(fascicleVelocity - self.fiberTension[3]/self.KsrBag2)**0.3) *
(fascicleLength - self.L0SrBag2 - self.fiberTension[2]/self.KsrBag2 - self.RBag2)
+ self.KPrBag2 * (fascicleLength - self.L0SrBag2 - self.fiberTension[2]/self.KsrBag2 - self.L0PrBag2)
+ self.MBag2 * fascicleAcceleration + self.GAMMABag2 - self.fiberTension[2]
)
dT[4] = self.fiberTension[5]
dT[5] = self.KsrChain / self.MChain * (self.computeC(fascicleVelocity, self.fiberTension[5], self.KsrChain) * self.betaChain * np.sign(fascicleVelocity - self.fiberTension[5]/self.KsrChain)
* (math.fabs(fascicleVelocity - self.fiberTension[5]/self.KsrChain)**0.3) *
(fascicleLength - self.L0SrChain - self.fiberTension[4]/self.KsrChain - self.RChain)
+ self.KPrChain * (fascicleLength - self.L0SrChain - self.fiberTension[4]/self.KsrChain - self.L0PrChain)
+ self.MChain * fascicleAcceleration + self.GAMMAChain - self.fiberTension[4]
)
return dT
def computeIa(self, t):
'''
'''
self.computePrimaryActivity(t)
if (self.primaryPotentialBag1 >= (self.primaryPotentialBag2 + self.primaryPotentialChain)):
larger = self.primaryPotentialBag1
smaller = self.primaryPotentialBag2 + self.primaryPotentialChain
else:
smaller = self.primaryPotentialBag1
larger = self.primaryPotentialBag2 + self.primaryPotentialChain
return self.SOcclusionFactor * smaller + larger
def computeII(self, t):
'''
'''
def computePrimaryActivity(self, t):
'''
'''
self.primaryPotentialBag1 = self.GPrimaryBag1 * (self.fiberTension[0] / self.KsrBag1 -
self.LNSrBag1 + self.L0SrBag1
)
self.primaryPotentialBag2 = self.GPrimaryBag2 * (self.fiberTension[2] / self.KsrBag2 -
self.LNSrBag2 + self.L0SrBag2
)
self.primaryPotentialChain = self.GPrimaryChain * (self.fiberTension[4] / self.KsrChain -
self.LNSrChain + self.L0SrChain
)
def reset(self, t):
'''
'''
self.betaBag1 = 0
self.betaBag2 = 0
self.betaChain = 0
self.GAMMABag1 = 0
self.GAMMABag2 = 0
self.GAMMAChain = 0
self.primaryPotentialBag1 = 0
self.primaryPotentialBag2 = 0
self.primaryPotentialChain = 0
self.secondaryPotentialBag1 = 0
self.secondaryPotentialBag2 = 0
self.secondaryPotentialChain = 0
self.fusimotorActivation = np.zeros((3), dtype=np.float64)
self.fiberTension = np.zeros((6), dtype=np.float64)
self.IaFR_Hz = 0.0
self.IIFR_Hz = 0.0