Biomedical Engineering Reference
In-Depth Information
or
ln 2
K
10
¼
:
ðÞ
693
K
10
t
2
¼
ð
7
:
30
Þ
1
7.5.2 Washout Curve
A washout curve is a useful experimental technique for parameter estimation. The
experiment begins with a continuous infusion of solute until the concentration reaches
steady state. After reaching steady state, the input is stopped; the subsequent decay of
solute from its maximum back to zero is called the washout curve. In essence, the input
,
5
K
is a pulse input, z(
u
(
t
)
u
(
t
t
1
)), with a sufficiently large
t
1
much larger than
10
which has the solution
c
1
¼
q
1
p
V
u
ð
t
Þ
z
z
e
K
10
t
e
K
10
ð
t
t
1
Þ
1
¼
1
1
u
ð
t
t
1
Þ:
ð
7
:
31
Þ
V
K
V
K
1
10
1
10
The washout curve is the portion of the response from
t
1
to
1
, which is essentially an
impulse response beginning at
t
1
; ignoring the solution from 0 to
t
1
, and resetting time
t
1
to 0, the washout curve is rewritten as
z
10
e
K
10
t
u
ð
t
Þ
c
1
wo
¼
ð
7
:
32
Þ
V
K
1
From the experimental data and using Eq. (7.32), the time constant from the data gives
K
10
, and the initial value and time constant gives
V
1
. Note that the washout curve technique
described here only works for one-compartment models.
The following example considers the uptake of radioactive iodine (
131
) by the thyroid
gland in a very simplified model as depicted in Figure 7.9. We will return to modeling the
thyroid system in Section 7.7.4. The compartment represents the plasma. The thyroid gland,
located in the neck, absorbs iodine from blood and uses it to produce an iodine-containing
hormone, primarily thyroxine, which is then secreted into the blood. Thyroxine increases
the chemical reaction rate in the cell and overall metabolic rate of the body. The level of
thyroxine is closely regulated by the hypothalamus and the pituitary gland. The hypothal-
amus releases thyroid releasing hormone (TRH) in reaction to thyroid levels in the blood.
TRH stimulates the pituitary gland to release of thyroid-stimulating hormone (TSH), which
causes a reaction in the thyroid. Thus, the thyroid gland is used to regulate the body's
I
K
1T
K
1U
Thyroid
Gland
q
1
Urine
FIGURE 7.9
131
in the plasma compartment.
Illustration for Example Problem 7.5, where
q
1
equals quantity of
I
