Neural mass model of the sleeping thalamocortical system (Schellenberger Costa et al 2016)

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Accession:226474
This paper generates typical human EEG data of sleep stages N2/N3 as well as wakefulness and REM sleep.
References:
1 . Weigenand A, Schellenberger Costa M, Ngo HV, Claussen JC, Martinetz T (2014) Characterization of K-complexes and slow wave activity in a neural mass model. PLoS Comput Biol 10:e1003923 [PubMed]
2 . Schellenberger Costa M, Weigenand A, Ngo HV, Marshall L, Born J, Martinetz T, Claussen JC (2016) A Thalamocortical Neural Mass Model of the EEG during NREM Sleep and Its Response to Auditory Stimulation. PLoS Comput Biol 12:e1005022 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neural mass;
Brain Region(s)/Organism: Thalamus; Neocortex;
Cell Type(s): Neocortex L2/3 pyramidal GLU cell; Thalamus reticular nucleus GABA cell; Thalamus geniculate nucleus/lateral principal GLU cell; Neocortex U1 L6 pyramidal corticalthalamic GLU cell; Neocortex layer 2-3 interneuron;
Channel(s): I Calcium; Na/K pump; I_K,Na;
Gap Junctions:
Receptor(s): AMPA; Gaba; NMDA;
Gene(s):
Transmitter(s):
Simulation Environment: Network; C or C++ program (web link to model); MATLAB (web link to model);
Model Concept(s): Calcium dynamics; Sleep; Activity Patterns; Oscillations; Bifurcation; Spindles; Audition;
Implementer(s): Schellenberger Costa, Michael [mschellenbergercosta at gmail.com];
Search NeuronDB for information about:  Thalamus geniculate nucleus/lateral principal GLU cell; Thalamus reticular nucleus GABA cell; Neocortex L2/3 pyramidal GLU cell; Neocortex U1 L6 pyramidal corticalthalamic GLU cell; AMPA; NMDA; Gaba; I Calcium; I_K,Na; Na/K pump;
/*
 *	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:	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
 */

/******************************************************************************/
/*						Implementation of a cortical module					  */
/******************************************************************************/
#pragma once
#include <cmath>
#include <vector>

#include "Random_Stream.h"
#include "Thalamic_Column.h"
class Thalamic_Column;

class Cortical_Column {
public:
    Cortical_Column(double* Param, double* Con)
        :sigma_p 	(Param[0]),	g_KNa	(Param[1]), 	  dphi	(Param[2]),
          N_pt		(Con[2]),	N_it	(Con[3])
    {set_RNG();}

    /* Connect to the thalamic module */
    void	get_Thalamus(Thalamic_Column& T) {Thalamus = &T;}

    /* ODE functions */
    void 	set_RK		(int);
    void 	add_RK	 	(void);

private:
    /* Declaration of private functions */
    /* Initialize the RNGs */
    void 	set_RNG		(void);

    /* Firing rates */
    double 	get_Qp		(int) const;
    double 	get_Qi		(int) const;

    /* Currents */
    double 	I_ep		(int) const;
    double 	I_ei		(int) const;
    double 	I_gp		(int) const;
    double 	I_gi		(int) const;
    double 	I_L_p		(int) const;
    double 	I_L_i		(int) const;
    double 	I_KNa		(int) const;

    /* Potassium pump */
    double 	Na_pump		(int) const;

    /* Noise functions */
    double 	noise_xRK 	(int,int) const;
    double 	noise_aRK 	(int) const;

    /* Helper functions */
    inline std::vector<double> init (double value)
    {return {value, 0.0, 0.0, 0.0, 0.0};}

    inline void add_RK (std::vector<double>& var)
    {var[0] = (-3*var[0] + 2*var[1] + 4*var[2] + 2*var[3] + var[4])/6;}

    inline void add_RK_noise (std::vector<double>& var, unsigned noise)
    {var[0] = (-3*var[0] + 2*var[1] + 4*var[2] + 2*var[3] + var[4])/6 + noise_aRK(noise);}

    /* Declaration and Initialization of parameters */
    /* Membrane time in ms */
    const double 	tau_p 		= 30;
    const double 	tau_i 		= 30;

    /* Maximum firing rate in ms^-1 */
    const double 	Qp_max		= 30.E-3;
    const double 	Qi_max		= 60.E-3;

    /* Sigmoid threshold in mV */
    const double 	theta_p		= -58.5;
    const double 	theta_i		= -58.5;

    /* Sigmoid gain in mV */
    const double 	sigma_p		= 4;
    const double 	sigma_i		= 6;

    /* Scaling parameter for sigmoidal mapping (dimensionless) */
    const double 	C1          = (M_PI/sqrt(3));

    /* parameters of the firing adaption */
    const double 	alpha_Na	= 2;			/* Sodium influx per spike			in mM ms 	*/
    const double 	tau_Na		= 1.7;			/* Sodium time constant 			in ms 		*/

    const double 	R_pump   	= 0.09;        	/* Na-K pump  constant              in mM/ms 	*/
    const double 	Na_eq    	= 9.5;         	/* Na-eq concentration              in mM 		*/

    /* PSP rise time in ms^-1 */
    const double 	gamma_e		= 70E-3;
    const double 	gamma_g		= 58.6E-3;

    /* Axonal flux time constant */
    const double 	nu			= 120E-3;

    /* Leak weight in aU*/
    const double 	g_L    		= 1.;

    /* Synaptic weight in ms */
    const double 	g_AMPA 		= 1.;
    const double 	g_GABA 		= 1.;

    /* Conductivity */
    /* KNa in mS/cm^2 */
    const double	g_KNa		= 1.33;

    /* Reversal potentials in mV */
    /* Synaptic */
    const double 	E_AMPA  	= 0;
    const double 	E_GABA  	= -70;

    /* Leak */
    const double 	E_L_p 		= -64;
    const double 	E_L_i 		= -64;

    /* Potassium */
    const double 	E_K    		= -100;

    /* Noise parameters in ms^-1 */
    const double 	mphi		= 0E-3;
    const double	dphi		= 20E-1;
    double			input		= 0.0;

    /* Connectivities (dimensionless) */
    const double 	N_pp		= 115;
    const double 	N_ip		= 72;
    const double 	N_pi		= 90;
    const double 	N_ii		= 90;
    const double 	N_pt		= 2.5;
    const double 	N_it		= 2.5;

    /* Pointer to thalamic column */
    Thalamic_Column* Thalamus;

    /* Parameters for SRK4 iteration */
    const std::vector<double> A = {0.5,  0.5,  1.0, 1.0};
    const std::vector<double> B = {0.75, 0.75, 0.0, 0.0};

    /* Random number generators */
    std::vector<randomStreamNormal> MTRands;

    /* Container for noise */
    std::vector<double>	Rand_vars;

    /* Population variables */
    std::vector<double> Vp	= init(E_L_p),	/* excitatory membrane voltage						*/
                        Vi	= init(E_L_i),	/* inhibitory membrane voltage						*/
                        Na	= init(Na_eq),	/* Na concentration									*/
                        s_ep= init(0.0),	/* PostSP from excitatory to excitatory population	*/
                        s_ei= init(0.0),	/* PostSP from excitatory to inhibitory population	*/
                        s_gp= init(0.0),	/* PostSP from inhibitory to excitatory population	*/
                        s_gi= init(0.0),	/* PostSP from inhibitory to inhibitory population	*/
                        y	= init(0.0),	/* axonal flux										*/
                        x_ep= init(0.0),	/* derivative of s_ep								*/
                        x_ei= init(0.0),	/* derivative of s_ei								*/
                        x_gp= init(0.0),	/* derivative of s_gp				 				*/
                        x_gi= init(0.0),	/* derivative of s_gi								*/
                        x	= init(0.0);	/* derivative of y									*/

    /* Data storage access */
    friend void get_data (int, Cortical_Column&, Thalamic_Column&, std::vector<double*>);

    /* Stimulation protocol access */
    friend class Stim;
    friend class Thalamic_Column;
};

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