Engineering, 2012, 5, 150-152
doi:10.4236/eng.2012.410B039 Published Online October 2012 (
Copyright © 2012 SciRes. ENG
An iterative Approach to Deriving Drug Infusions
David P. Crankshaw
Department of Pharmacology, The University of Melbourne, Melbourne, Victoria, Australia
Received 2012
A simple iter ative process c an be used t o generate intravenous drug infusion profiles. It overcomes limitations in deriving compart-
mental pharmacokin etic models and has application to evaluatio n of new drugs and to clin ical practice.
Keywords: Pharmacokinetics; Drug Delivery; Intravenous Infusion
1. Introduction
Compartmental pharmacokinetic models (CPM) commonly of
three compartments together with inter-compartmental rate
constants are usually derived from data obtained during the
elimination phase following administration of a single dose of a
drug. The CPM is widely used to predict the intravenous in-
fusion rate for delivery of hypnotics and opioids during anaes-
thesia and in intensive therapy units. Assumptions are made
that the CPM accurately describes the distrib ution and elimina-
tion of the drug during infusion as predicted from a single dose.
This approach has proved effective in clinical situations where
the operator is free to adjust the target concentration according
to clinical impressions of dosing requirements [1]. However,
it has b een observed that drug levels based on predictions from
a CPM commonly result in higher blood levels. This appears
to b e due to an over est imation of the cen tral co mpartment (V1)
together with an over estimation of the rate of elimination [2].
In a widely used commercial application of the CPM, an arbi-
trary reduction in the size of V1 was incorporated to overcome
this problem [3]. Such an approach to programmed delivery,
while expedient and clinically effective for drugs with a large
therapeutic index, has considerable limitations if used in a ri-
gorous way for experimental or regulatory purposes.
Further points are that therapeutic agents may have consi-
derable effect o n the cardio vascular syste m resultin g in concen-
tration dependent changes in distribution and elimination. In
particular, the cardiac output may differ at different concentra-
tions and directly or indirectly influence the flow of drug to
various organs of the body particularly the liver and kidneys.
Further, the metabolism of drugs may be concentration depen-
dent. If a CPM is derived during the elimination phase follow-
ing a single bolus dose, cardiac output may be considerably
higher than at therapeutic levels during an infusion. Similarly,
if drug metabolism is concentration dependent, a higher rate of
metabol ism at lo wer con cent rati ons may lead t o an o ver esti ma-
tion of infusion requirements when concentrations are higher.
Population pharmacokinetic modeling such as STANPUMP
[4] u sing NONMEM software [5] can be u sed to create mod els
that are concentration dependent. But implementation requires
specialized knowledge, is computationally intense, time con-
suming and complex.
We have described a method which requires no more than
simple arithmetic to create a table of values infusion rates
against time suitable for manual implementation with a stan-
dard syringe pu mp [6] . We have termed this iterati ve metho d
for developing infusion profiles at specific predetermined con-
centrations the Plasma Drug Efflux (PDE) method. The me-
thod has been described by us for a range of drugs infused into
human patients during the conduct of clinical anaesthesia [6-8].
2. Methods
Following published methodology [6] an arbitrary fixed rate
infusion of the drug under investigation is administered to the
first individual as a continuous fixed rate infusion with dosage
based on total body mass (TBM) or estimated lean body mass
(LBM). Arterial blood is sampled at frequent intervals from the
commencement until the end of the infusion period and assayed
for total blood concentration (Cm).
The intravenous infusion site is considered the reference
point so each measured art erial bl oo d con cen trat ion is co rrect ed
by an arbitrary value of minus one minute to allow for vein to
artery transit time. The delivery rate (mg.min-1.kgLBM-1) is then
divided by the time corrected arterial plasma concentration
(mg.L-1). This calcu lation is successively app lied to all concen-
tration measurements during the study period in order to deter-
mine the Plasma Drug Efflux values (Ep) (L.min- 1.kgLBM-1).
The values for the first subject are plotted as a function of time
and a set of values o f Ep at one min u te int ervals is generat ed b y
linear interpolation. These values were transferred to a pro-
grammable infusion device [8]. An infusion is then adminis-
tered to a second group of around two subjects with a nomi-
nated target concentration (CTGT). The delivery rate (mg.min-1)
for each subject is produced by continuous multiplication of
successive values of Ep (read from the memory each minute)
by CTGT (mg.L-1) and by the TBM or LBM (kilogram) of the
particu lar subject. A tabl e may be produ ced for a range of sub-
ject weights and target concentrations and the infusion imple-
mented by manual setting of a standard infusion pump at times
obtained from the table [9].
Engineering, 2012, 5, 150-152
doi:10.4236/eng.2012.410B039 Published Online October 2012 (
Copyright © 2012 SciRes. ENG
Ta ble I. Bolus doses (ml) and infusion rate, in seven steps from zero to 150 min, derived from published data of thiopental [7], methohexi tal
[7], alfentanil [8] and propofol [6] in order to achieve a clinically appropriate target concentration in an anaesthetized subject o f 50kg LBM.
Infusion per iod (min)
0-5 5-10 10-20 20-30 30-60 60-90 90-120 120-150
Drug Target conc. (mg.L-1) Bolus (ml) Infusion rate (
( 10 4.0 38 26 19 16 14 13 12 11
( 5 5.0 57 46 38 32 28 26 25 24
( 0.1 0.87 15 10 6 4 3 - - -
( 3 4.3 66 57 47 42 42 42 42 42
Successive groups of subjects are then infused using same
process with the infusion rate-time profile calculated from the
immediatel y previous group of subjects. The size of each group
is cho sen to increase progressively du ring the iterat ive process.
The decision to accept an infusion profile as optimal and stop
the it erative pro cess can b e made b y comparin g valu es of Cm at
each sampling point using Wilcoxon's matched pairs test
(CSS-Statsoft) to identify bias from CTGT. A non-significant
result (P>0.05) is used to ter min ate the iterative p r ocess.
When determining the Ep profile for propofol, groups of 1, 2,
5 and 11 were used to obtain a sui ta bl e end po i nt [ 6 ].
3. Results
Previously published data for thiopental [7], methohexital [7],
alfentanil [8] and propofol [6] has been used to develop bolus
and infusion rates for each drug. Table I shows an application
of such data in a form suitable for clinical implementation. An
initial bolus dose and subsequent infusion rates, as a series of
steps suitable for implementation with a simple syringe pump,
are shown for a patient of 50kg lean body mass. For further
flexibility, a simple spread sheet could be based on th es e data to
develop data for a range o f pati ent weights and a range o f target
4. Discussion
This iterative process has been used to determine infusion re-
quirements for a number of drugs commonly used in anaesthet-
ic practice. The method is highly efficient in proceeding to-
wards a defined endpoint. The values of Plasma Drug Efflux
(Ep) r epresent, at a con stant plasma con centrat ion, th e expected
time varying, rate of loss of drug from the site of intravenous
injection in units of drug clearance. The values represent
“clearance” from the intravenous site of injection whether the
loss is by redistribution, binding to tissues, metabolism, or eli-
mination from any organ.
Data, obtained with this time and resource efficient method,
can be processed with NONMEM to yield standard CPM pa-
rameters (see [ 6]) and are of immediate pr actical use in a num-
ber of ways.
A pharmacoki netic mod el generated in this way is free of the
major deficiencies of standard methods which fail to define the
concentration at which the model is determined. Models de-
rived over a range of concentrations, for drugs with significant
cardio vascul ar e ffects, are i n fact no t accu rat e at an y con cent ra-
If the PDE method is used in a series of studies over a range
of concentrations, effects of the drug under well controlled
conditions can be observed. Data from this approach can then
be used in the design of more accurate preprogrammed infusion
The method can also be used to determine optimal drug infu-
sion profiles for a wide range of drugs in both animal and hu-
man subjects. This has application in drug development.
Constant drug levels can be used to investigate the actions of
drugs on a wide range of organ systems.
Finally, the efficiency of the method allows researchers to
investigate variability due to species, age, gender and race as
well as drug interactions.
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Copyright © 2012 SciRes. ENG
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