Clinical application
of pharmacokinetic
and PHARMACODYNAMIC
models
Dr V. Billard[1]
Anaesthetists have a
special interest in pharmacology compared to other physicians who choose the drugs
to prescribe then often follow narrow approved guidelines to choose the doses.
Conversely, the anesthetic drugs could be administered in a wide range of
doses, and underdosage (awareness, muscle tension or pain) adequate anesthesia,
or overdosage (late recovery, side effects) can all be observed inside the
approved range of doses.
The art (or the
science ?) of the anaesthetist is to choose both the drug and the doses in
order to achieve an adequate level of anesthesia as fast as possible and
maintain it just as long as necessary.
Pharmacokinetic (PK)
and pharmacodynamic (PD) modeling could help to achieve this clinical goals
because it splits the relationship between a dose and its effects into
successive physiologic steps (dose concentration effects). Clinically, this approach is first
useful to understand what is happening when giving a dose, and how will change
the corresponding effects. Then the PKPD modeling could be used up side down to
adjust the dose to a desired level of effect at any time through target
controlled delivery systems.
PKPD
modeling to understand the dose-effect
relationship
PK or PD models are a
set of mathematical equations that link a dose of a drug to the corresponding
concentration and effects at different times.
Models are usually
established by giving a known dose of drug, measuring blood concentration and
effects over time and fitting the measured values to a "a priori"
chosen model, as 2 or 3 compartments mamillary models for PK or Hill Emax
model for PD (figure 1).
The parameters
obtained from the fitting are used to predict concentration and effects for
other patients at different times, and with different doses, if the model has
been demonstrated to be linear 1. This process assumes that the most important
factor in the dose-effect relationship is the
drug and not the patient.
This assumption is
essential because most of the patients to whom we give anesthesia come only
once. There is no way to sample for PK modeling on a first session and call
them for surgery on a second one, or to wait for a real steady state to allow
the surgeon to start to work.
Fortunately, this
basic assumption is often true for anesthetic drugs.
Rational choice of drugs and doses
based on PK models and simulation softwares
The first use of PKPD
modeling is to describe the fundamental properties of a drug and to compare the
drugs to each other in order to choose the best drug for each use.
Reading the PK parameters
(figure 1) is tricky and may induce interpretations errors 2. As anaesthetists could not all be experts in
pharmacology, the PK parameters could be incorporated into simulation softwares that display the time course of predicted
concentration when entering the drug and the doses (table 1).
Those softwares are easy to use for all anaesthetists (certified doctor,
student or nurse) to understand what they have done by giving a dose to a
patient, or what they should do to achieve stable and adequate anesthesia. Most
of the softwares use previously published 2 or 3 compartments models together
with an additional compartment for effect-site 3 and display the predicted drug concentration
in plasma and effect-site for any dose.
Simulation programs
are wonderful tools for understanding and teaching. Their clinical relevance
could be separated into 3 main areas :
-
How to deal with
delay and duration of action for short term (induction, short cases)
-
How to optimize
recovery after long term use.
-
How to adjust doses
to special patients
Use of PK models for short term procedures
The PK modeling including effect-site
compartment shows the time from an iv bolus to its maximal effect (Tmax, figure
1) 4. It indicates how long time a bolus should be
anticipated from the time the effect is needed. For example, it illustrates why
oipioids as remifentanil or alfentanil are suitable for short duration stimuli
(fast intubation, endoscopy, bone fracture reduction), just to avoid to achieve
the maximal effect when the procedure is over (figure 2).
It
also shows the decrease in concentrations after a bolus, suggesting that
fentanyl or sufentanil may be given by repeated boluses, whereas alfentanil or
remifentanil requires continuous infusion for procedures longer than a few
minutes (figure 2).
Finally,
simulating the time course of effect-site concentration after a bolus shows how
increasing the dose can shorten the onset (since the time to maximal effect is
supposed to be constant), but increases the duration of action. This property
has been widely used for choosing the doses of muscle relaxants : it resulted
in the classical choice of 2 ED95 for intubation, to optimize the
balance between a short onset to intubate quickly and a reasonable duration of
blockade to avoid post operative residual blockade. But everybody knows that
the dose may be doubled or more for emergency intubation.
Preparing
recovery after long time administrations
We
learnt at medical school that the duration of action was a constant for each
anesthetic drug, and was related to the elimination of the drug from the body.
PKPD
modeling showed us that, in realty, adequate anesthesia corresponds to a
certain concentration, and recovery occurs below another concentration
("MAC awake" or iv equivalent), although substantial amount of drug
is still present in the body. The time to go from the maintenance concentration
to the recovery concentration depends on how far they were from each other, how
fast the drug is cleared from the body, but also how much the drug accumulates
in the body, and how long time it was administered.
The
effect of the drug and the duration of infusion was illustrated by the concept
of Context Sensitive Half Time described
almost 10 years ago 5. It shows why remifentanil is suitable for
long infusion when fast recovery is required (for example for severe COPD or
obese patients), alfentanil or sufentanil may be suitable for long infusion
when intermediate delay of recovery is possible and fentanyl should be avoided
when postoperative ventilation is undesirable. It can also explain why propofol
is suitable for maintenance of anesthesia whereas thiopental is not.
For
clinical use, context sensitive half time gives an estimates of the time to
recovery only when the maintenance concentration is twice the recovery
concentration : this is often but not always true. So, the concept of CSHT has
been extended : beside the time necessary to decrease the concentration by 50%,
the decrement time was defined as
the time necessary to decrease the concentration by any percent 6.
This
parameter, available from the simulation softwares, could be helpful clinically
not only to choose a drug but to decide the level of concentration to maintain,
and the consequences of this choice on recovery times. This has been nicely
described for opioids, specially by Shafer and the Stanford group (figure 3).
-
For example, for
minor surgery with little postoperative pain, a concentration above the
recovery concentration by 20% may be sufficient. In that case, there is no
difference between fentanyl, alfentanil or sufentanil regarding recovery time
up to 120 minutes of surgery and any opioid can be used (figure 3, top).
-
If the surgical
stimulus is stronger, opioid concentration around twice the recovery
concentration may be chosen, but the physician must be aware that postoperative
ventilation may be necessary with fentanyl, and that sufentanil allows faster
recovery than alfentanil up to 8 hours of infusion (figure 3, middle).
-
When analgesia is
the main concern and postoperative sedation is usual as in cardiac surgery,
opioid concentrations 4 fold above the recovery concentration can be proposed.
Simulation shows that the recovery would be faster using alfentanil than
sufentanil for surgery longer than 2 hours, which is not very much used in
clinical practice ! (fig 3, bottom).
-
Finally, PK
calculation of decrement time show the specific behaviour of remifentanil
compared to the other opioids : this feature is an advantage when fast recovery
is the main concern, but the fast disappearance of all opioid effect must be
anticipated when postoperative analgesia is required.
Adjusting to special populations
Another
advantage of PK modeling is to show the influence of physiological variables as
weight or age on the time course of concentration.
Unfortunately,
most of initial PK studies published when the actual intravenous agents have been
released did exclude obeses and extremes ages. Some other did a class analysis
describing a set of PK parameters for young adults and another set for elderly,
but the use of these models is limited because for intermediate values of the
physiological variables, interpolation between 2 PK models is necessary.
The
most useful models to incorporate in a simulation software express the
physiological variables as a covariate of the model as could be fitted by
population analysis. 7-10.
Models
including physiological variables are very relevant in clinical practice
because they show how much the dose should be modified in special populations of
patients to achieve a chosen concentration, as illustrated for remifentanil in
figure 5.
Until
now, only simple and constant variables (age, weight, gender, lean body mass,
) are included in simulation software for iv drugs.
Changing
variables as cardiac output are included in simulation software for volatile
agents as Gasman. For iv drugs, they are only used in physiological models, and
rarely used by routine physicians. They will be developed in another
communication.
Clinical
benefits of PD modeling
PD
models described the mathematical relationship between the concentration of a
drug and its effect (for example a BIS value at 50), or the probability of
effect for binary effects (response to incision, to verbal command,).
They
first induced a change in the minds
: anaesthetists stopped to describe the effects of a drug as a function of the
dose (since this relationship is changing every second) but started to control
the concentration on one hand, and assess the corresponding response in the other
hand. Then, they had to decide if the response was adequate, and if it was not,
they adjusted the dose not as a final goal but in order to increase or decrease
the concentration.
This
process pulled up the management of intravenous anesthetics closed to the
delivery of volatile 
agents because nobody cares about the number of
milliliters of volatile agent is given, but the dose delivered is adjusted to
achieve a chosen end-tidal fraction, then to maintain it if the level of
anesthesia is considered adequate.
PD
modeling showed clinically important
features of concentration-effect relationship:
-
The requirements differ with the effect
considered. The opioid concentration necessary for intubation is higher than
for incision 11 (figure 4) and the concentration of muscle
relaxant to block the diaphragm or the larynx is higher than to block the
peripheral muscles of the hand 12. That is why at any time of the anesthesia,
doses should be adjusted to achieve the adequate concentration for the current
surgical time.
-
The potency of a drug could be modified by
physiological variables as age : for
example, the adequate concentrations are reduced by about 50% in elderly
patients for all mu-opioids 13, and by 30% for propofol 14.
-
The time to equilibration between blood and
effect site (brain) is longer in elderly
for remifentanil (figure 5) 13 and also for the hemodynamic effects of
propofol 15.
These properties
suggest that induction in elderly patients should achieve lower concentration
than in younger adults, and achieve it slower to avoid overdosage and side
effects.
The second major clinical interest of PD
modeling is to describe and quantify
interactions between drugs. The most relevant interaction is anesthesia is
the synergism between hypnotics (intravenous or volatile) and opioids. It could
be displayed as a 3 dimensional surface model where x and y are drugs
concentrations and z is effect 16.
As
for the concentration-effect relationship, interactions differ with the effect
considered :
-
Opioids reduce
only moderately the concentration of hypnotic necessary to loose consciousness
(30 to 50%) (figure 6, top) 17.
-
They reduce
markedly (60-85%) the concentration of hypnotic needed to block motor response to stimulations
-
The maximal
synergism is observed when considering the hemodynamic
response to noxious stimuli (up to 90%reduction) 18.
-
However,
synergism also occurs on side effects as hypotension 19 or respiratory depression.
So,
for every surgical event and every type of response, several combinations of
concentrations can all provide adequate anesthesia (figure 6). Whereas the
shape of the interaction curve is always the same, the values depends on both
drugs combined, and the anaesthetist can choose his strategy according to
several criteria :
-
To maintain non
moving patient and hemodynamic stability, any point of the curve is OK. Below
the curve, the patient may show signs of light anesthesia, and above
overdosage.
-
If the noxious
stimulation occurs or change rapidly, it may be interesting to shift the
balanced anesthesia to the faster reacting drug : to the opioid side (right
part of the curve) with remifentanil of alfentanil, or to the hypnotic side
(left part of the curve) with propofol, desflurane or sevoflurane.
-
If fast recovery
and discharge are the main concern, the balance should be shift to the drug
having the faster elimination.
This
property has been nicely illustrated by Vuyk & col. who performed
simulations of anesthesia for gynecologic surgery and recovery with opioids and
propofol (figure 6) 20 :
-
when fentanyl was
used, as its decrement time was much more longer than the one of propofol, the
fastest recovery was obtained with an excess of hypnotic.
-
with alfentanil
or sufentanil who have a decrement time similar to propofol, fastest recovery
was achieved for a balanced combination.
-
with remifentanil
(fast decrement time compared to propofol whatever the duration of infusion), 
the fastest recovery was obtained in excess of
opioid.
In
summary, PD modeling of interactions can help the anesthetist to choose the
optimal strategy of drug combination after having answered 2 questions :
-
what is my main
concern for the coming up surgical time?
-
How do all the
drugs I chose perform to achieve this goal?
PKPD modeling to adjust the doses to a desired concentration or effect
Target controlled infusion
The adjustment could
be done directly on the dose, using simple controllers as in industrial
processes (Proportional, Proportional-Derivative,
Proportional-Integral-Derivative) or fuzzy logic controllers 49. However, this technique needs repeated
measurements during the whole procedure, and loss of the signal could result in
crazy dose adjustments.
The second way to
build a closed loop system is to adjust not the dose but the PK or the PD model
according to the measured value. This has been described for hypnotics using,
as a quantitative effect, spectral
analysis of EEG 50, BIS 51 or auditory evoked potentials 52 . In all studies, quite stable anesthesia
could be maintained. It has also been proposed for muscle relaxants 46. Theoretically, this approach is more robust
than a closed loop adjusting the dose, because it can reduce the inter
individual variability (main cause of PD variability) and adjust the model to
each patient using very few measures. Then, even if the measured effect is
lost, the model is still appropriate for this patient, and the anesthesia
should remain stable.
However, the influence
of the opioid and the surgical stimulation on the EEG parameters and
subsequently on the adjustment of the model are uneasy to describe and should
be further studied before a routine use in clinical conditions.
Conclusion
At the stage of
research, PKPD modeling is an essential tool to understand step by step the general
behaviour of anesthetic drugs in the body, and to determine the covariates who
are relevant and those who are not.
At the bedsite, PKPD
models could be used through simulation softwares to display predicted
concentration and effect for a rational choice of the drugs and the doses.
They give to the
anesthetist the opportunity to think directly in terms of concentrations and
concentrationeffect relationship, to optimize the onset and predict the
recovery and could dramatically improve the stability of anesthesia through
target controlled delivery devices.
Table 1 : Some of the
simulation softwares available. All could be used either in dose units or in
TCI mode ; in TCI all of them can target the plasma or the effect site, and
some can target the EEG effect (Rugloop, next version) or the level of
neuromuscular blockade (Stanpump).
|
Name |
Author and request address |
Hardware |
Drugs included and specific features |
|
Stanpump |
SL Shafer http://pkpd.icon.palo-alto.med.va.gov |
PC (DOS) or MAC |
Most of iv, run 1 pump Several models / drug Bayesian for NMBA |
|
Stelpump |
J Coetzee http://pkpd.icon.palo-alto.med.va.gov |
PC (DOS) |
Most of iv, run 2 pumps Few models / drug |
|
Rugloop |
M Struys http://allserv.rug.ac.be/~mstruys |
PC (Windows) |
Most of iv Several models / drug + data management (Datex AS3, BIS,
Anemon) |
|
F Engbers http://www.eurosiva.org ou webmaster@eurosiva.org |
PC (Windows) |
Hypnotics & opioids 1 model/drug + PD interaction model |
|
|
Toolbox |
L Barvais lbarvais@ulb.ac.be or Hpital Erasme Bruxelles Belgium |
PC |
Most of iv drugs & vasoactive Run several pumps Few models / drugs + preprogrammed scenarios |
|
PAMO |
X Viviand xviviand@ap-hm.fr |
MAC or PC |
Hypnotics & opioids Run several pumps Several models / drug |
|
Gasman |
J Philips http://www.gasmanweb.com |
PC (Windows) or MAC |
Volatile agents only Simulation only Adjustable cardiac output & ventilation |
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