Page 63 - Control Theory in Biomedical Engineering

50 Control theory in biomedical engineering

derived for compartment I, blood should be collected from the blood vessels
of the liver, which requires significant surgical intervention.

4 Estimating the values of the model parameters
We assumed that the model refers to a 70-kg healthy subject with a total
cholesterol concentration not exceeding 190mg/dL of blood plasma. For
such a person, the volume of blood plasma in the liver is estimated to be
approximately 6.5dL, while the volume of plasma in the peripheral blood
is 23.5dL. As an initial condition, we assumed that the cholesterol concen-
tration in both the compartments is the same. According to this assumption,
the initial cholesterol mass is m 1 (t 0 )¼1235 and m 2 (t 0 )¼4465mg in compart-
ments I and II, respectively.
In the next step, we have to determine the values of kinetic parameters.
Because the rate of de novo cholesterol synthesis is higher when the amount
of cholesterol in the liver is less, we expressed this relationship as k/m 1 ,
where k is the kinetic constant. As the rate of cholesterol synthesis varies
from 0.324 to 0.624mgmin 1 (Yashiro et al., 1994; Jones and Schoeller,
1990), the values of kinetic constant k vary in the range of
1
2
390–751mg min .
Analysis of the two-compartment model in a study (Hrydziuszko et al.,
2015) indicated a significant influence of the parameters describing the out-
flow (m out ) and inflow (m in ) of the cholesterol from and to the liver on the
total cholesterol in the second compartment (peripheral blood). If parame-
1
ters m out and m in exceeded 1.2 and 0.8mgmin , respectively, the total cho-
lesterol concentration was lower than 200mg/dL. Generally, m out is
expected to be greater than m in because about 95% of cholesterol leaving
the liver with bile returns via the portal vein enriched by cholesterol derived
from the membranes of dead enterocytes and partly by cholesterol in the
dietary pool.
As mentioned in Section 1, almost every cell shows a cholesterol
demand, which is fulfilled by the appropriate receptors that capture the cho-
lesterol from the bloodstream. In the model, the tissue demand is described
by the parameter m tis, which takes a value of 0.243mgmin 1 (Sabine, 1977).
Another source of external cholesterol is the diet based on animal products
(in the diet based on plants and microorganisms, cholesterol is absent)
(Sabine, 1977). The daily cholesterol content in the diet is estimated to
be 3g; however, only about up to 30% of it is absorbed in the intestine.
The process of absorption of cholesterol from the diet into the plasma is
delayed (because of the time required for the digestion and initial absorption