Page 70 - Control Theory in Biomedical Engineering

56 Control theory in biomedical engineering

by about 30% of dietary cholesterol. Thus, in this case, to estimate the
amount of cholesterol returning via the portal vein to the liver, the amount
ejected from the gallbladder, enrichment by 30% of the dietary amount, and
the amount removed along with fecal masses should all be taken into
account.
The amount of cholesterol absorbed from the diet can be calculated
* *
analogously as the other parameters M in and M out (Eq. 16):
t
ð k
2 t eabs t babs
m diet ¼ M diet sin ω diet t t babs Þð ð Þdt ¼ M diet (16)
2
t p
where m diet is the total dose of cholesterol consumed at time t 0 , and t babs and
t eabs are the time of beginning and end of absorption, respectively.
An exemplary profile of change in cholesterol concentration in the sec-
ond compartment (c 2 ) and the accompanying change in the rate of de novo
cholesterol synthesis in the liver is shown in Fig. 4A and B. We calculated the
concentration of cholesterol for a person weighing 70kg with an initial mass

Fig. 4 Profiles of changes in total cholesterol concentration c 2 after a meal containing 1g
of cholesterol (A) and the rate of de novo cholesterol synthesis, k/m 1 (B). This
figure presents solution for a two-compartment model with the following set of
1
1
1
1
2
parameters: k¼450mg min , k 12 ¼3.58min ; k 21 ¼1min ; m tis ¼0.243mgmin ;
1
1
1
M in ¼1.96mgmin ; M out ¼9.6mgmin ; M diet ¼2.3mgmin ; t 1 ¼50min; t 2 ¼70min;
t 3 ¼300min; t 4 ¼400min; and t 5 ¼530min.