The Scientific World Journal / 2013 / Article / Alg 2

Research Article

Pharmacokinetic Delivery and Metabolizing Rate of Nicardipine Incorporated in Hydrophilic and Hydrophobic Cyclodextrins Using Two-Compartment Mathematical Model

Algorithm 2

> restart;
Use linear algebra package “(linalg)” in Maple.
>  with(linalg);
>  with(plots);
Enter the governing equations (5) and (6) as follow:
> eq 4 :=diff(C[A](t),t)=-k1*C[A](t);
           
> eq 5 :=diff(C[B](t),t)=k1*C[A](t)-k2*C[B](t);
           
Store the variables in “vars”:
> vars:=[C[A](t),C[B](t)];
             
Next, store the right hand sides of (5) and (6) in “eqs”:
> eqs:=[rhs(eq 4 ),rhs(eq 5 )];
         
Now use the “genmatrix” command in Maple to produce the coefficient matrix :
> A:=genmatrix(eqs,vars);
Specify the initial conditions.
> Y0:=matrix(2,1,[1,0]);
Use “exponential ( )” command in Maple to produce exponential ( ) matrix:
> mat:=exponential(A,t);
Calculate the solution vector using “evalm” command and matrix multiplication “&*”:
> sol:=evalm(&*(mat,Y0));
The first row of “sol” is the solution for the concentration of species ( ) and the
second row is the concentration of species ( ):
> ca:=sol[1,1];
            
> cb:=sol[2,1];
           
The concentration of species is obtained from the material balance equation (7):
> cc:=1-ca-cb;
         
Note that the concentration of the species are obtained as functions of the kinetic constants from the Tables 1 and 2
and the independent variable . Use the “pars” command to illustrate the results:
> pars:={k1,k2};
Next, substitute these values for the kinetic constants into the concentrations store as , , and :
> Ca:=subs(pars,ca);
> Cb:=subs(pars,cb);
> Cc:=subs(pars,cc);
Plot the concentration profiles for these values of the kinetic constants:
> plot(Ca,t=0..10);
> plot(Cb,t=0..10);
> plot(Cc,t=0..10);

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