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How do i create an Explore plot?...

DONTWORRYBEKABU 15 Maple
ode explore dsolve
December 14 2024
1 0

I am trying to model the change in bloodglucose when performing a OGTT (Oral glucose tolerance test). In connection to this I've created a compartmentmodel consisting of two compartments; one for the stomach and one for the blood. Based on this compartmentmodel I've formulated two differentialequations describing how the glucose concentration in respectively the stomach and the blood changes. I've then solved this system of differential equations and I'm now trying to adjust the variables to make the graphs look like the one from a glucose tolerance test but I'm having trouble creating an Explore-plot.

restart

 

 

 

Absorption from stomach

diff(Cm(t), t) = -Ka*Cm(t)                                  (1)

 

Solution to (1)

Cm = c*exp(-Ka*t)                                              (2)

 

Glucose concentration in blood

diff(Cb(t), t) = Ka*Cm(t)-Ku*Cb(t)                (3)

 

(2) Is put into (3)

diff(Cb(t), t) = Ka*c*exp(-Ka*t)-Ku*Cb(t)          (4)

 

(Ku*Cb(t)) gets added

diff(Cb(t), t)+Ku*Cb(t) = Ka*c*exp(-Ka*t)        (5)

 

Solution to (5)

"Cb(t):=(e)^(-∫Ku ⅆt)*∫Ka*( c0*(e)^(-Ka*t))*(e)^(∫Ku ⅆt) ⅆt+c*(e)^(-∫Ku ⅆt)" = proc (t) options operator, arrow, function_assign; exp(-(int(Ku, t)))*(int(Ka*c0*exp(-Ka*t)*exp(int(Ku, t)), t))+c*exp(-(int(Ku, t))) end procNULL

 

Solution to (1)

  "Cm(t):= c0*(e)^(-Ka*t)" = proc (t) options operator, arrow, function_assign; c0*exp(-Ka*t) end procNULL

  NULL

Explore(plot([Cb(t), Cm(t)], t = 0 .. 100, y = 0 .. 50), parameters = [Ka = 0 .. 10, Ku = 0 .. 10, c0 = 0 .. 20, c = 0 .. 20], initialvalues = [Ka = 1, Ku = 1, c0 = 1, c = 1])Warning, expecting only range variable t in expression -exp(-Ku*t)*Ka*c0/(Ka-Ku)*exp(-Ka*t+Ku*t)+c*exp(-Ku*t) to be plotted but found names [Ka, Ku, c, c0]

 

Download Explore_plot.mw

How do i solve this system of differenti...

DONTWORRYBEKABU 15 Maple 2024
ode dsolve differential-equations
December 12 2024
1 0

I'm having trouble solving this system of differential equations. I haven't solved systems of differential equations before but i tried defining the system and then using dsolve, but it couldn't solve all the equations.

Hope you can help.

NULL

diff(Q1(t), t) = -k1*Q1(t)

 

diff(Q2(t), t) = k1*Q1+k3/Q2(t)-k2*Q2(t)-k4*Q2(t)

 

diff(Q3(t), t) = k4*Q2

 

diff(Q4(t), t) = k2*Q2-k3/Q2

 

NULL

Download System_Of_Differential_Equations.mw

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