#include "modelHHneuron.h" #include "math.h" #include "iostream.h" void modelHHneuron(double t,double *x,double *dx,double *parameter,double *extra) { double am,bm,ah,bh,an,bn,v; double s; v=x[0]; if(parameter[12]==1 ) //traub model { s=1; am=.32*(13-(v-parameter[11]))/(exp((13-(v-parameter[11]))/4.)-1); bm=.28*((v-parameter[11])-40)/(exp(((v-parameter[11])-40)/5)-1); ah=.128*exp((17-(v-parameter[11]))/18); bh=4.0/(1+exp((40-(v-parameter[11]))/5)); an=0.032*(15-(v-parameter[11]))/(exp((15-(v-parameter[11]))/5)-1); bn=.5*exp((10-(v-parameter[11]))/40); } else if(parameter[12]==2 ) //henry model { s=1; am=-.1*(35+v)/(exp(-(35+v)/10)-1); bm=4.*exp(-(60+v)/18); ah=.07*exp(-(60+v)/20); bh=1./(exp(-(30+v)/10)+1); an=-0.01*(50+v)/(exp(-(50+v)/10)-1); bn=.125*exp(-(60+v)/80); } else if (parameter[12]==3) //Wang Buzsaki model { s=5; am=-.1*(35+v)/(exp(-(35+v)/10)-1); bm=4.*exp(-(60+v)/18); ah=.07*exp(-(58+v)/20); bh=1./(exp(-(28+v)/10)+1); an=-0.01*(34+v)/(exp(-(34+v)/10)-1); bn=.125*exp(-(44+v)/80); } if (parameter[12]==3) x[1]=am/(am+bm); dx[0]=(parameter[7]+parameter[2]*pow(x[1],3)*x[2]*(parameter[1]-x[0])+ parameter[4]*pow(x[3],4)*(parameter[3]-x[0])+parameter[6]*(parameter[5]-x[0])+1.0*extra[1]+1.0*extra[2]+1.0*extra[3]+0.0*extra[5])/parameter[0]; dx[1]=s*(am*(1-x[1])-bm*x[1]); dx[2]=s*(ah*(1-x[2])-bh*x[2]); dx[3]=s*(an*(1-x[3])-bn*x[3]); dx[4]=(parameter[8]-x[4])/parameter[9]+1.*extra[4]; } /* Traub model with Vth=-67 gNa=215;gK=43;gL=.813;ENa=50;Ek=-95;El=-64;CM=1;Co=1; am=-.32*(52+x[0])/(exp(-(x[0]+52)/4)-1); bm=.28*(25+x[0])/(exp((25+x[0])/5)-1); ah=.128*exp(-(x[0]+48)/18); bh=4.0/(1+exp(-(x[0]+25)/5)); an=-.032*(50+x[0])/(1+exp(-(50+x[0])/5)); bn=.5*exp(-(55+x[0])/40); The reduced model for this system can be obtained as replace m variable with minf, and the following relation between h and n variables n=-.8154h+.8114 Std HH model gNa=20;gK=6.2;gL=.03;ENa=50.;Ek=-77.;El=-49.4;CM=1;Co=1; am=-.1*(35+v)/(exp(-(35+v)/10)-1); bm=4.*exp(-(60+v)/18); ah=.07*exp(-(60+v)/20); bh=1./(exp(-(30+v)/10)+1); an=-0.01*(50+v)/(exp(-(50+v)/10)-1); bn=.125*exp(-(60+v)/80); The reduced model can againbe obtianed by replacing m with minf and the following relation between h and the n variables. n=-.8314h+.7499 */