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

Algorithm 1

> restart;

Use for the varible1: 2ln(2), ln(2)/4, ln(2)/2.2 and for the varible2: ln(2)/1.6, ln(2)/5.49, ln(2)/7.38:

> a:=variable1;b:=variable2;

Specify either 6- or 24-hour drug dosage cycle by using the “signum” Maple command to sign function for (1) and (2):

> Dose1:=t->sum((signum(t-n*6)-signum(t-(n*6+0.5)),n=0..10);

           𝐃𝐨𝐬𝐞𝟏∶=𝐭⟶∑^𝟏𝟎_𝐧=𝟎(𝐬𝐢𝐠𝐧𝐮𝐦(𝐭−𝟔𝐧)−𝐬𝐢𝐠𝐧𝐮𝐦(𝐭−𝟔𝐧−𝟎.𝟓))

> Dose1:=t->sum((signum(t-n*24)-signum(t-(n*24+0.5)),n=0..10);

           𝐃𝐨𝐬𝐞𝟏∶=𝐭⟶∑^𝟏𝟎_𝐧=𝟎(𝐬𝐢𝐠𝐧𝐮𝐦(𝐭−𝟐𝟒𝐧)−𝐬𝐢𝐠𝐧𝐮𝐦(𝐭−𝟐𝟒𝐧−𝟎.𝟓))

Plot the dosage profiles for these variables:

> plot(Dose1(t),t=0..20);

> with(plots):

Use differential equations toolbox “(DEtools)” in Maple:

> with(DEtools):

Use for the varible3: Dose1(t)/12, Dose1(t)/12, and Dose1(t)/32; calculate and plot the concentration

profiles using (1) and (2):

> J:=DEplot({diff(x(t),t)=variable3-a*x(t),diff(y(t),t)=a*x(t)-b*y(t)},{x(t),y(t)},t=0..50,

{[0,0,0]},stepsize=0.5,scene=[t,x],linecolor=RED):

> K:=DEplot({diff(x(t),t)=variable3-a*x(t),diff(y(t),t)=a*x(t)-b*y(t)},{x(t),y(t)},t=0..50,

{[0,0,0]},stepsize=0.5,scene=[t,y],linecolor=BLACK):

> plots[display]({J,K},labels=["Time(hrs)",

"Concentration(μg/ml)"],labeldirections=[horizontal,vertical]);

> phaseportrait([diff(x(t),t)=(1/12)*varible4-a*x(t),diff(y(t),t)=a*x(t)-b*y(t)],[x(t),y(t)],

t=0..50,{[0,0,0]},stepsize=.5,labels=["x(t)","y(t)"]);

To determine the concentrations for analyzed substances, we calculated the phase-plane plot {𝑥(𝑡),𝑦(𝑡)}

using the following code in the Maple package (Figures 2(a)–2(c)):

> phaseportrait([diff(x(t),t)= variable4-a*x(t),diff(y(t),t)=a*x(t)-b*y(t)],[x(t),y(t)],t=0..50,

{[0,0,0]},stepsize=.5,labels=["x(t)","y(t)"]);