How do I solve a system of (delayed) differential equations including known functions of the independant variable.

I am trying to solve a set of 12 ODEs, where 4 of them have a 'delayed' term. I am using dde23 to solve them but I am just getting the same errors.

Here is my code:

 k=[40,60,1/60,40,60,1/60,0.0004,0.0004,1000,1,1,0.1,0.0001,5];
y0 = [0,0,0,0,0,0,0,0,0.1,0.15,1,3.5];
time = 0:0.1:20;
sol = dde23(@PL_MRI_Kinetics_ODE,5*sqrt(2*k(13)),y0',time,k');

 function ydot = PL_MRI_Kinetics_ODE(t,y,Z,k)
ydot = zeros(12,1);
ydot(1) = Inj(t)- (1/k(1))*y(1)+ k(9)*y(2)-k(10)*y(1)+Theta_z(t,k)*y(1);
%Pez
ydot(2) = - (1/k(2))*y(2)+ k(7)*y(4)-k(8)*y(2)+k(10)*y(1)-k(9)*y(2)+Theta_z(t,k)*y(2);
%Piz
ydot(3) = - (1/k(4))*y(3)+ k(11)*y(4)-k(12)*y(3)+Theta_z(t,k)*y(1);
%Lez
ydot(4) = - (1/k(5))*y(4)+ k(8)*y(2)-k(7)*y(4)+k(12)*y(3)-k(11)*y(4)+Theta_z(t,k)*y(4);
%Liz
ydot(5) = -(1/k(3))*y(5)+ k(9)*y(6)-k(10)*y(5)+Theta_xy(t,k)*Z(1);
%Pexy
ydot(6) = -(1/k(3))*y(6)+ k(9)*y(8)-k(9)*y(6)+k(10)*y(5)-k(9)*y(6)+Theta_xy(t,k)*Z(2);
%Pixy
ydot(7) = -(1/k(6))*y(7)+k(11)*y(8) -k(12)*y(7)+Theta_xy(t,k)*Z(3);
%Lexy
ydot(8) = -(1/k(6))*y(8)+k(8)*y(6)-k(7)*y(8)+k(12)*y(7)-k(11)*y(8)+Theta_xy(t,k)*Z(4);
%Lixy
ydot(9) = Inj(t)+ (1/k(1))*y(1)+(1/k(3))*y(5)+k(9)*y(10)-k(10)*y(9);
%Pet
ydot(10)= (1/k(2))*y(2)+(1/k(3))*y(6)+k(7)*y(12)-k(8)*y(10)+k(10)*y(9)-k(9)*y(10);
%Pit
ydot(11)= (1/k(4))*y(3)+(1/k(6))*y(7)+k(11)*y(12)-k(12)*k(11);
%Let
ydot(12)= (1/k(5))*y(4)+(1/k(6))*y(8)+k(8)*y(10)-k(7)*y(12)+k(12)*y(11)-k(11)*y(12);
%Lit
end

 function Th_xy= Theta_xy(t,k)
Th_xy = exp(-(t).^2/(4*k(13)))/(2*(pi*k(13))^0.5)*(sind(k(14)));
  for i=1:10
       Th_xy = Th_xy +exp(-(t-i).^2/(4*k(13)))/(2*(pi*k(13))^0.5)*(sind(k(14)));
  end
end

 function Th_z = Theta_z(t,k)
Th_z = exp(-(t).^2/(4*k(13)))/(2*(pi*k(13))^0.5)*(cosd(k(14))-1);
  for i=1:10
       Th_z = Th_z +exp(-(t-i).^2/(4*k(13)))/(2*(pi*k(13))^0.5)*(cosd(k(14))-1);
  end
end

 function Inj_fun= Inj(t)
Inj_fun = zeros(length(t),1);
 for i=1:length(t)
   if (t(i)>=0)&&(t(i)<=10)
     Inj_fun(i) = 1;
   else
     Inj_fun(i) = 0;
   end
 end
end

All I get out is a series of error messages.

 Not enough input arguments.

 Error in PL_MRI_Kinetics_ODE 
ydot(1) = Inj(t)- (1/k(1))*y(1)+ k(9)*y(2)-k(10)*y(1)+Theta_z(t,k)*y(1);

 Error in dde23 
f0 = feval(ddefun,t0,y0,Z0,varargin{:});

 Error in solver 
sol = dde23(@PL_MRI_Kinetics_ODE,5*sqrt(2*k(13)),y0',time,k');

I have a feeling the problem lies in the functions Inj(t), Theta_xy(t) and Theta_z(t) which spit arrays of numbers, rather than being just a single number. I am not sure how to deal with this.

[Torsten]

Both the call to dde23 and the list of input parameters for "PL_MRI_Kinetics_ODE" are incorrect.

Look up the documentation for dde23.

Best wishes

Torsten.