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| ENTERHEPATIC CIRCULATION EXAMPLES |
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The help item "Model Time examples" gives a fragment of code for mod-
elling EHC (Enterohepatic Circulation, which is also called Enterohep-
atic Recycling). It illustrates the use of MTIME parameters to model
instantaneous changes in differential equations. This help item,
"Enterhepatic circulation examples", describes two fully-worked out
control streams in the examples directory. They demonstrate how to
generalize the fragment to multiple sequential doses.
Both examples use the same data. (hillss.dat and mtimess.dat are
identical). There is a steady-state bolus dose at time 0. The inter-
dose interval II is 12, and there are enough additional doses
(ADDL=100) to continue the dosing pattern throughout the data set.
There are "other" records every 4 units till time 140 to allow com-
partment amounts to be displayed and there is a final observation
record at time 144.
mtimess.ctl
This example incorporates the fragment into a complete control
stream. MTIME parameters are used to turn on and off the EHC
terms in the differential equations. The variable FLAG is 1
between times MTIME(1) and MTIME(2) after each dose event and
turns on the EHC terms. After time MTIME(2) is reached, a new
set of MTIME's is defined which affect the next dosing interval.
MTIME parameters are not dose-related parameters and have no
effect on steady-state dose events. Even if PK computes
MTIME(i)< II, this produces future changes in the system, and
does not apply retroactively to the preceding implied doses.
(See Guide VI, Section V.F.4, Note 4).
A steady-state dose record should not be used. Instead, the SS
dose record is described as a transient dose with SS=DROP on the
$INPUT record.
hillss.ctl
This control stream does not use MTIME. Instead, a smooth step
model using Hill terms in a sigmoid emax model is used. The $DES
code has to compute all the necessary variables. Flag1 and flag2
are continuous variables that change from 0 to 1 at the times
corresponding to the MTIME's. The FLAG variable is similar to
FLAG in mtimess.ctl. The changes to the differential equations
are not instantaneous, but they are continuous. If the exponent
in the Hill term is made larger, the predictions approach those
of the MTIME model. However, very large values of the exponent
can lead to numerical difficulties in PREDPP. Smaller values of
the exponent may be more realistic physiologically. A Steady-
State dose event record is used with this model.
Note that SS dose records should only be used when the kinetics
implemented in the model coincides with the II (interdose inter-
val) of the SS record. Just as MTIME's cannot affect the differ-
ential equations retroactively, changes to the differential equa-
tions that happen in the future cannot affect the Steady-state
calculations. For example, with II=12, then the kinetics should
not be different in the interval of time 0 to 12 vs. time 12 to
24 or time 24 to 36, etc. In each interval, changes occur at
theta(8) and theta(8)+theta(9) after the start of the interval.
$DES computes the first change time for each interval using the
INT function:
mt1=II*INT(T/II)+theta(8)
NM-TRAN gives a warning about the use of the INT function in
$DES:
(WARNING 68) THE INT, MOD, MIN, OR MAX FUNCTION IS BEING USED OUT-
SIDE OF A
SIMULATION BLOCK. IF THE FUNCTION VALUE AFFECTS THE VALUE OF THE
OBJECTIVE FUNCTION, THEN AN ERROR WILL PROBABLY OCCUR.
This warning may be disregarded. Discontinuties occur at the
ends of the integration intervals, but the kinetics are unaf-
fected. For example, when T<12, the value of 12*INT(T/12) is 0.
The values of FLAG1 and FLAG2 are initially 0 and FLAG is 0. As
T approaches the end point T=12, the values of FLAG1 and FLAG2
both become 1 and FLAG is 0. At the end point when T=12, the
value of 12*INT(T/12) is 12 and both FLAG1 and FLAG2 are 0. The
discontinuity in mt1 and mt2 does not affect the FLAG variable
because FLAG1 and FLAG2 are both 0 or both 1 in the neighborhood
of the discontinuity, and the kinetics are continuous.
In these examples, EHC is driven by the dose events. The EHC changes
can also driven by the clock. Suppose every 12 hours, a new EHC cycle
begins. (The value 12 is chosen so that the two versions will give
the same predictions.) E.g., instead in mtimess.ctl, instead of
MTIME(1) = MTIME(1)+II
compute
MTIME(1) = MTIME(1)+12
In hillss.ctl, instead of
mt1=inter*INT(T/inter)+theta(8)
compute
mt1=12*INT(T/12)+theta(8)
There is no difference in the results.
REFERENCES: Guide VI Section III.F.9
REFERENCES: Guide VI Section V.F
REFERENCES: Guide IV Section V.C.5
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