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Modeling Blood Glucose Levels

​
rate constants
k
1
, digestion
0.0453
k
2
, insulin release
0.0224
initial concentrations
C
0
​, blood glucose
90
G
0
​, stomach carbohydrate
120
blood glucose
stomach carbohydrates
It is proposed that the kinetics of the reaction steps are first order, so that
dC
dt
=-
k
1
C
and
dG
dt
=
k
1
C-
k
2
(G-
G
0
)
, where
C
is the concentration of carbohydrates in the stomach and
G
is the concentration of glucose in the blood.
G
0
is the baseline value of
G
at time
t=0
. After an average meal,
G
0
=90
mg/dL and
C
0
=120
mg/dL. The rate constant
k
1
is related to how quickly the food is digested, while the rate constant
k
2
is associated with how quickly insulin is released.
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