/* * 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]); y [N+1] = y [0] + A[N]*dt*(x [N]); x_et [N+1] = x_et [0] + A[N]*dt*(gamma_e*gamma_e * ( + N_tp * Cortex->y[N] - 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) + N_rp * Cortex->y[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]); x [N+1] = x [0] + A[N]*dt*(nu * nu * ( get_Qt(N) - y [N]) - 2 * nu * x [N]); } 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(y); add_RK_noise(x_et, 0); add_RK(x_er); add_RK(x_gt); add_RK(x_gr); add_RK(x); 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