%
%  heafib.m   Steve Cox, 2/1/07
%
% solve the active fiber problem via sparse hybrid euler
%
% usage:	heafib(a,ell,N,dt,t1,t2,T,Iapp,pinc)
%
%		a = fiber radius (cm)
%		ell = fiber length (cm)
%             	N = number of compartments
%               dt = timestep (ms)
%		t1 = start of current pulse (ms)
%		t2 = end of current pulse (ms)
%               T = stopping time (ms)
%		Iapp = size of current pulse (micro amps)
%               pinc = number of time steps between plots
%                      if pinc > 0 then 3D full
%                      if pinc < 0 then 2D movie
%
% example:	heafib(.0001,.5,200,.01,1,2,15,.001,-20)
%

function heafib(a,ell,N,dt,t1,t2,T,Iapp,pinc)

Cm = 1;		% micro F / cm^2
R2 = 0.034;		% k Ohm cm
dx = ell/N;		% patch length
A = 2*pi*a*dx;		% patch surface area
x = dx/2:dx:ell-dx/2;	% vector of patch midpoints

vK = -6;        % mV
vNa = 127;      % mV
vCl = 3;        % mV

GK = 36;        % mS/(cm)^2
GNa = 40;      % mS/(cm)^2
GL = 0.3;      % mS/(cm)^2
GK = GK/GL;
GNa = GNa/GL;
tau = Cm/GL;
lam2 = a/2/R2/GL;

e = ones(N,1);
v = 0*e;		% initial conditions
n = 0.3177*e;
m = 0.0529*e;
h = 0.5961*e;

B = spdiags([-e 2*e -e], -1:1, N, N)/dx/dx;
B(1,1) = 1/dx/dx;
B(N,N) = 1/dx/dx;
B = dt*lam2*B/tau;
dB = diag(B);

t = 0;
tcnt = 0;
if pinc > 0
   plot3(x,t*ones(N,1),v)
   hold on
end
vcnt = 1;

while (t <= T)

      t = t + dt;

      Istim = Iapp*(t>t1)*(t<t2);

      ant = an(v);
      amt = am(v);
      aht = ah(v);
      n = ( n + dt*ant )./(1 + dt*(ant+bn(v)) );
      m = ( m + dt*amt )./(1 + dt*(amt+bm(v)) );
      h = ( h + dt*aht )./(1 + dt*(aht+bh(v)) );

      cNa = GNa * m.^3 .* h;
      cK = GK * n.^4;

      ed = 1 + dt*(1 + cNa + cK)/tau;

      B(1:N+1:end) = dB + ed;	      % update the diagonal

      rhs = v + dt*(cNa*vNa + cK*vK + vCl)/tau;
      rhs(1) = rhs(1) + dt*Istim/A;

      v = B \ rhs;

      tcnt = tcnt + 1;

      if mod(tcnt,pinc) == 0
         if pinc > 0
            plot3(x,t*ones(N,1),v)
         else
            plot(x,v)
            axis([0 ell -10 100])
            drawnow
         end
      end
end

if pinc > 0
   xlabel('x  (cm)','fontsize',16)
   ylabel('t  (ms)','fontsize',16)
   zlabel('v  (mV)','fontsize',16)
end

hold off

return

function val = an(v)
val = .01*(10-v)./(exp(1-v/10)-1);

function val = bn(v)
val = .125*exp(-v/80);

function val = am(v)
val = .1*(25-v)./(exp(2.5-v/10)-1);

function val = bm(v)
val = 4*exp(-v/18);

function val = ah(v)
val = 0.07*exp(-v/20);

function val = bh(v)
val = 1./(exp(3-v/10)+1);