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Cortical_Column.cpp
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Cortical_Column.cpp
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/*
* Copyright (c) 2015 University of Lübeck
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The aboVp copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVpNT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*
* AUTHORS: Michael Schellenberger Costa: [email protected]
*
* Based on: Characterization of K-Complexes and Slow Wave Activity in a Neural Mass Model
* A Weigenand, M Schellenberger Costa, H-VV Ngo, JC Claussen, T Martinetz
* PLoS Computational Biology. 2014;10:e1003923
*
* A thalamocortical neural mass model of the EEG during NREM sleep and its response
* to auditory stimulation.
* M Schellenberger Costa, A Weigenand, H-VV Ngo, L Marshall, J Born, T Martinetz,
* JC Claussen.
* PLoS Computational Biology http://dx.doi.org/10.1371/journal.pcbi.1005022
*/
/******************************************************************************/
/* Functions of the cortical module */
/******************************************************************************/
#include "Cortical_Column.h"
/******************************************************************************/
/* Initialization of RNG */
/******************************************************************************/
void Cortical_Column::set_RNG(void) {
extern const double dt;
unsigned numRandomVariables = 2;
MTRands.reserve(2*numRandomVariables);
Rand_vars.reserve(2*numRandomVariables);
for (unsigned i=0; i < numRandomVariables; ++i){
/* Add the RNG for I_{l}*/
MTRands.push_back(randomStreamNormal(0.0, dphi*dt));
/* Add the RNG for I_{l,0} */
MTRands.push_back(randomStreamNormal(0.0, dt));
/* Get the random number for the first iteration */
Rand_vars.push_back(MTRands[2*i]());
Rand_vars.push_back(MTRands[2*i+1]());
}
}
/******************************************************************************/
/* RK noise scaling */
/******************************************************************************/
double Cortical_Column::noise_xRK(int N, int M) const{
return gamma_e * gamma_e * (Rand_vars[2*M] + Rand_vars[2*M+1]/std::sqrt(3))*B[N];
}
double Cortical_Column::noise_aRK(int M) const{
return gamma_e * gamma_e * (Rand_vars[2*M] - Rand_vars[2*M+1]*std::sqrt(3))/4;
}
/******************************************************************************/
/* Firing Rate functions */
/******************************************************************************/
/* Pyramidal firing rate */
double Cortical_Column::get_Qp (int N) const{
return Qp_max / (1 + exp(-C1 * (Vp[N] - theta_p) / sigma_p));
}
/* Inhibitory firing rate */
double Cortical_Column::get_Qi (int N) const{
return Qi_max / (1 + exp(-C1 * (Vi[N] - theta_i) / sigma_i));
}
/******************************************************************************/
/* Synaptic currents */
/******************************************************************************/
/* Excitatory input to pyramidal population */
double Cortical_Column::I_ep (int N) const{
return g_AMPA * s_ep[N] * (Vp[N] - E_AMPA);
}
/* Inhibitory input to pyramidal population */
double Cortical_Column::I_gp (int N) const{
return g_GABA * s_gp[N] * (Vp[N] - E_GABA);
}
/* Excitatory input to inhibitory population */
double Cortical_Column::I_ei (int N) const{
return g_AMPA * s_ei[N] * (Vi[N] - E_AMPA);
}
/* Inhibitory input to inhibitory population */
double Cortical_Column::I_gi (int N) const{
return g_GABA * s_gi[N] * (Vi[N] - E_GABA);
}
/******************************************************************************/
/* Intrinsic currents */
/******************************************************************************/
/* Leak current of pyramidal population */
double Cortical_Column::I_L_p (int N) const{
return g_L * (Vp[N] - E_L_p);
}
/* Leak current of inhibitory population */
double Cortical_Column::I_L_i (int N) const{
return g_L * (Vi[N] - E_L_i);
}
/* Sodium dependent potassium current */
double Cortical_Column::I_KNa (int N) const{
double w_KNa = 0.37/(1+pow(38.7/Na[N], 3.5));
return g_KNa * w_KNa * (Vp[N] - E_K);
}
/******************************************************************************/
/* Potassium pump */
/******************************************************************************/
double Cortical_Column::Na_pump (int N) const{
return R_pump*(Na[N]*Na[N]*Na[N]/(Na[N]*Na[N]*Na[N]+3375) -
Na_eq*Na_eq*Na_eq/(Na_eq*Na_eq*Na_eq+3375));
}
/******************************************************************************/
/* SRK iteration */
/******************************************************************************/
void Cortical_Column::set_RK (int N) {
extern const double dt;
Vp [N+1] = Vp [0] + A[N] * dt*(-(I_L_p(N) + I_ep(N) + I_gp(N))/tau_p - I_KNa(N));
Vi [N+1] = Vi [0] + A[N] * dt*(-(I_L_i(N) + I_ei(N) + I_gi(N))/tau_i);
Na [N+1] = Na [0] + A[N] * dt*(alpha_Na * get_Qp(N) - Na_pump(N))/tau_Na;
s_ep[N+1] = s_ep[0] + A[N] * dt*(x_ep[N]);
s_ei[N+1] = s_ei[0] + A[N] * dt*(x_ei[N]);
s_gp[N+1] = s_gp[0] + A[N] * dt*(x_gp[N]);
s_gi[N+1] = s_gi[0] + A[N] * dt*(x_gi[N]);
y [N+1] = y [0] + A[N] * dt*(x [N]);
x_ep[N+1] = x_ep[0] + A[N] * dt*(gamma_e*gamma_e * (N_pp * get_Qp(N) + N_pt * Thalamus->y[N] - s_ep[N]) - 2 * gamma_e * x_ep[N]) + noise_xRK(N, 0);
x_ei[N+1] = x_ei[0] + A[N] * dt*(gamma_e*gamma_e * (N_ip * get_Qp(N) + N_it * Thalamus->y[N] - s_ei[N]) - 2 * gamma_e * x_ei[N]) + noise_xRK(N, 1) ;
x_gp[N+1] = x_gp[0] + A[N] * dt*(gamma_g*gamma_g * (N_pi * get_Qi(N) - s_gp[N]) - 2 * gamma_g * x_gp[N]);
x_gi[N+1] = x_gi[0] + A[N] * dt*(gamma_g*gamma_g * (N_ii * get_Qi(N) - s_gi[N]) - 2 * gamma_g * x_gi[N]);
x [N+1] = x [0] + A[N] * dt*(nu * nu * ( get_Qp(N) - y [N]) - 2 * nu * x [N]);
}
void Cortical_Column::add_RK(void) {
add_RK(Vp);
add_RK(Vi);
add_RK(Na);
add_RK(s_ep);
add_RK(s_ei);
add_RK(s_gp);
add_RK(s_gi);
add_RK(y);
add_RK_noise(x_ep, 0);
add_RK_noise(x_ei, 1);
add_RK(x_gp);
add_RK(x_gi);
add_RK(x);
/* Generate noise for the next iteration */
for (unsigned i=0; i<Rand_vars.size(); ++i) {
Rand_vars[i] = MTRands[i]() + input;
}
}