Question

Hormones control several functionalities in a biological system. The hormone insulin (H) is responsible for glucose (G) metabolism. Research has shown the rate of change of hormone level produced in the healthy body is proportional to blood glucose level. The glucose level in the body is modeled using a first order system. 1. dG + 0.0001 G-10-4H a) The time is in seconds and at t-0, the person ate six doughnuts that made blood glucose level rise to 100% (G(0-100). If the body produced insulin (H) in response at 100% and kept at that level, calculate the transfer function F(s). F(s) is the Laplace transform of the variable (G) for this step response Plot the Glucose level (G) as a function of time from 0 to 2 hours. b)

*Plot in matlab

Answer 1

MATLAB Code:

close all
clear
clc

syms s t F
F1 = s*F - 100; % L{dG/dt} = s*F(s) - G(0)
Soln = solve(F1 + 0.0001*F + 0.0001/s, F); % L{0.0001H} = 0.0001/s, since L{H} = 1/s (H = unit step function)
soln = ilaplace(Soln, s, t);
disp('Solution, G ='), disp(soln)

tt = 0:1:2*60*60; % 2 hrs. = 2*60*60 sec.
gg = subs(soln, tt);
plot(tt, gg), xlabel('Time, t (seconds)'), ylabel('Glucose Level, G(t)')
title('Glucose Metabolism')

Output:

Solution, G =
101*exp(-t/10000) - 1

Plot:

Glucose Metabolism 100 90 70 O 60 50 40 0 1000 2000 3000 4000 5000 6000 7000 8000 Time,t (seconds)