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:

> eq4:=diff(C[A](t),t)=-k1*C[A](t);

> eq5:=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(eq4),rhs(eq5)];

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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