/*
* 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 above 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 EVENT 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: mschellenbergercosta@gmail.com
*
* Based on: 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 thalamic module */
/******************************************************************************/
#include "Thalamic_Column.h"
/******************************************************************************/
/* Initialization of RNG */
/******************************************************************************/
void Thalamic_Column::set_RNG(void) {
extern const double dt;
unsigned numRandomVariables = 1;
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 Thalamic_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 Thalamic_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 */
/******************************************************************************/
double Thalamic_Column::get_Qt (int N) const{
return Qt_max/ (1 + exp(-C1 * (Vt[N] - theta_t) / sigma_t));
}
double Thalamic_Column::get_Qr (int N) const{
return Qr_max / (1 + exp(-C1 * (Vr[N]- theta_r) / sigma_r));
}
/******************************************************************************/
/* Synaptic currents */
/******************************************************************************/
/* Excitatory input to TC population */
double Thalamic_Column::I_et (int N) const{
return g_AMPA * s_et[N]* (Vt[N]- E_AMPA);
}
/* Inhibitory input to TC population */
double Thalamic_Column::I_gt (int N) const{
return g_GABA * s_gt[N]* (Vt[N]- E_GABA);
}
/* Excitatory input to RE population */
double Thalamic_Column::I_er (int N) const{
return g_AMPA * s_er[N]* (Vr[N]- E_AMPA);
}
/* Inhibitory input to RE population */
double Thalamic_Column::I_gr (int N) const{
return g_GABA * s_gr[N]* (Vr[N]- E_GABA);
}
/******************************************************************************/
/* I_T gating functions */
/******************************************************************************/
/* Activation in TC population after Destexhe 1996 */
double Thalamic_Column::m_inf_T_t (int N) const{
return 1/(1+exp(-(Vt[N]+59)/6.2));
}
/* Activation in RE population after Destexhe 1996 */
double Thalamic_Column::m_inf_T_r (int N) const{
return 1/(1+exp(-(Vr[N]+52)/7.4));
}
/* Deactivation in TC population after Destexhe 1996 */
double Thalamic_Column::h_inf_T_t (int N) const{
return 1/(1+exp( (Vt[N]+81)/4));
}
/* Deactivation in RE population after Destexhe 1996 */
double Thalamic_Column::h_inf_T_r (int N) const{
return 1/(1+exp( (Vr[N]+80)/5));
}
/* Deactivation time in RE population after Destexhe 1996 */
double Thalamic_Column::tau_h_T_t (int N) const{
return (30.8 + (211.4 + exp((Vt[N]+115.2)/5))/(1 + exp((Vt[N]+86)/3.2)))/3.7371928;
}
/* Deactivation time in RE population after Destexhe 1996 */
double Thalamic_Column::tau_h_T_r (int N) const{
return (85 + 1/(exp((Vr[N]+48)/4) + exp(-(Vr[N]+407)/50)))/3.7371928;
}
/******************************************************************************/
/* I_h gating functions */
/******************************************************************************/
/* Activation in TC population after Destexhe 1993 */
double Thalamic_Column::m_inf_h (int N) const{
return 1/(1+exp( (Vt[N]+75)/5.5));
}
/* Activation time for slow components in TC population after Chen2012 */
double Thalamic_Column::tau_m_h (int N) const{
return (20 + 1000/(exp((Vt[N]+ 71.5)/14.2) + exp(-(Vt[N]+ 89)/11.6)));
}
/* Instantaneous calcium binding onto messenger protein after Chen2012 */
double Thalamic_Column::P_h (int N) const{
//return k1 * pow(Ca[N], n_P)/(k1*pow(Ca[N], n_P)+k2);
return k1 * Ca[N] * Ca[N] * Ca[N] * Ca[N]/(k1 * Ca[N] * Ca[N] * Ca[N] * Ca[N]+k2);
}
/* Return I_h activation */
double Thalamic_Column::act_h (void) const{
return m_h[0] + g_inc * m_h2[0];
}
/******************************************************************************/
/* Intrinsic currents */
/******************************************************************************/
/* Leak current of TC population */
double Thalamic_Column::I_L_t (int N) const{
return g_L * (Vt[N]- E_L_t);
}
/* Potassium leak current of TC population */
double Thalamic_Column::I_LK_t (int N) const{
return g_LK * (Vt[N]- E_K);
}
/* Leak current of RE population */
double Thalamic_Column::I_L_r (int N) const{
return g_L * (Vr[N]- E_L_r);
}
/* Potassium leak current of RE population */
double Thalamic_Column::I_LK_r (int N) const{
return g_LK * (Vr[N]- E_K);
}
/* T-type current of TC population */
double Thalamic_Column::I_T_t (int N) const{
return g_T_t * m_inf_T_t(N) * m_inf_T_t(N) * h_T_t[N] * (Vt[N]- E_Ca);
}
/* T-type current of RE population */
double Thalamic_Column::I_T_r (int N) const{
return g_T_r * m_inf_T_r(N) * m_inf_T_r(N) * h_T_r[N] * (Vr[N]- E_Ca);
}
/* h-type current of TC population */
double Thalamic_Column::I_h (int N) const{
return g_h * (m_h[N] + g_inc * m_h2[N]) * (Vt[N]- E_h);
}
/******************************************************************************/
/* SRK iteration */
/******************************************************************************/
void Thalamic_Column::set_RK (int N) {
extern const double dt;
Vt [N+1] = Vt [0] + A[N]*dt*(-(I_L_t(N) + I_et(N) + I_gt(N))/tau_t - C_m * (I_LK_t(N) + I_T_t(N) + I_h(N)));
Vr [N+1] = Vr [0] + A[N]*dt*(-(I_L_r(N) + I_er(N) + I_gr(N))/tau_r - C_m * (I_LK_r(N) + I_T_r(N)));
Ca [N+1] = Ca [0] + A[N]*dt*(alpha_Ca * I_T_t(N) - (Ca[N] - Ca_0)/tau_Ca);
h_T_t [N+1] = h_T_t[0] + A[N]*dt*(h_inf_T_t(N) - h_T_t[N])/tau_h_T_t(N);
h_T_r [N+1] = h_T_r[0] + A[N]*dt*(h_inf_T_r(N) - h_T_r[N])/tau_h_T_r(N);
m_h [N+1] = m_h [0] + A[N]*dt*((m_inf_h(N) * (1 - m_h2[N]) - m_h[N])/tau_m_h(N) - k3 * P_h(N) * m_h[N] + k4 * m_h2[N]);
m_h2 [N+1] = m_h2 [0] + A[N]*dt*(k3 * P_h(N) * m_h[N] - k4 * m_h2[N]);
s_et [N+1] = s_et [0] + A[N]*dt*(x_et[N]);
s_er [N+1] = s_er [0] + A[N]*dt*(x_er[N]);
s_gt [N+1] = s_gt [0] + A[N]*dt*(x_gt[N]);
s_gr [N+1] = s_gr [0] + A[N]*dt*(x_gr[N]);
x_et [N+1] = x_et [0] + A[N]*dt*(gamma_e*gamma_e * ( - s_et[N]) - 2 * gamma_e * x_et[N]) + noise_xRK(N,0);
x_er [N+1] = x_er [0] + A[N]*dt*(gamma_e*gamma_e * (N_rt * get_Qt(N) - s_er[N]) - 2 * gamma_e * x_er[N]);
x_gt [N+1] = x_gt [0] + A[N]*dt*(gamma_g*gamma_g * (N_tr * get_Qr(N) - s_gt[N]) - 2 * gamma_g * x_gt[N]);
x_gr [N+1] = x_gr [0] + A[N]*dt*(gamma_g*gamma_g * (N_rr * get_Qr(N) - s_gr[N]) - 2 * gamma_g * x_gr[N]);
}
/****************************************************************************************************/
/* end */
/****************************************************************************************************/
void Thalamic_Column::add_RK(void) {
add_RK(Vt);
add_RK(Vr);
add_RK(Ca);
add_RK(s_et);
add_RK(s_er);
add_RK(s_gt);
add_RK(s_gr);
add_RK_noise(x_et, 0);
add_RK(x_er);
add_RK(x_gt);
add_RK(x_gr);
add_RK(h_T_t);
add_RK(h_T_r);
add_RK(m_h);
add_RK(m_h2);
/* Generate noise for the next iteration */
for (unsigned i=0; i<Rand_vars.size(); ++i) {
Rand_vars[i] = MTRands[i]() + input;
}
}
void Thalamic_Column::iterate_ODE(void) {
/* First calculating every ith RK moment. Has to be in order, 1th moment first */
for (unsigned i=0; i<4; ++i) {
set_RK(i);
}
add_RK();
}