Pharmacokinetic and pharmacodynamic modeling has prospered in anesthesia because of the types of drugs used in our profession, our ability to make meaningful measurements, and our ability to perform high-resolution studies, e.g. the opportunity to sample arterial blood frequently. In the past two decades, much seminal work has been performed using muscle relaxants. In this session, I will review a number of these seminal studies. I make no attempt to provide a comprehensive overview of all issues related to kinetic/dynamic (PK/PD) modeling of relaxants. Instead I review those studies that have impacted most significantly on our understanding of modeling.
Effect compartment modeling
An intuitive approach to modeling effect of a drug that works
directly is to assume that the plasma concentration of the drug
relates to effect. If drug concentration changes quite slowly
(e.g. if the drug is administered orally and measurements are
made only at steady state), this assumption is reasonable. However,
most anesthetic drugs and most muscle relaxants are not used in
this manner. Hence, using the plasma concentration to represent
effect site concentration is presumably flawed. Although the introduction
of this concept to modeling is credited to Segre, widespread application
of this concept in all of pharmacology (i.e. not just in anesthesia)
resulted from seminal manuscripts by Hull et al.[1]and by Sheiner
et al.[2] Of note, Sheiner et al. administered d-tubocurarine
by brief infusion so as to obtain information about the largest
fraction of the Cp/effect hysteresis curve.
Semiparametric modeling
Most PK/PD modeling assumes that the plasma concentration vs.
time curve can be described as the sum of exponentials. In many
situations this is appropriate. However, if the time shortly
after drug administration is critical (as it typically is for
anesthetic drugs), then the assumption is flawed. Studies by Henthorn
et al.[3] demonstrate that arterial plasma concentration of drugs
administered intravenously increases during the first 30 sec,
then oscillates before decreasing monotonically; this contrasts
to the continuous monotonic decrease mandated by traditional exponential
models. If Cp is not described appropriately by the sum of exponentials,
then PD based on exponential models for Cp is flawed. Fortunately,
techniques exist to address this issue. If arterial plasma samples
are obtained at the appropriate intervals after drug administration
(e.g. at critical times during the first min), the Cp vs. time
curve can be described by a series of splines (smoothed curves)
or lines connecting the measured plasma concentration values.
The rate constant keo is then used to convolve these plasma concentrations
(in a manner similar to that with the exponential models) to estimate
the concentration in the effect compartment. If a drug is administered
by bolus and if effect occurs sometime before Cp decreases monotonically,
then this approach to necessary to obtain meaningful values for
keo.
Modeling without Cp data
The traditional approach to modeling PK/PD is to measure both
plasma concentrations and effect, then to model the dose/Cp relationship
(pharmacokinetics) and the Cp/effect relationship (equilibration,
pharmacodynamics). However, this is costly because it requires
measurement of Cp. Verotta[4] proposed that the sequential PK/PD
model could be modified to estimate the steady state infusion
rate that produced a certain effect (for example, the infusion
rate depressing twitch tension 50%, IR50), a parameter of more
clinical utility than either plasma clearance or the steady state
concentration depressing twitch tension 50%. Data from Donati
et al.[5,6] for laryngeal muscle function and adductor pollicis
twitch depression provided Bragg et al.[7] the opportunity to
evaluate whether this could be applied to real data. This study
provided estimates of both the relative sensitivities of the
two muscle groups and the relative rates of equilibration and
offered insight into the time course of paralysis at the two muscle
groups. However, the analysis suggested one aberrant finding,
that IR50 varied with the initial bolus dose. To verify or refute
this finding, we[8] repeated Donati's studies with measurements
of arterial plasma concentrations of the muscle relaxant. To our
surprise, we learned C50 (and IR50) varied with dose, a finding
for which no explanation is presently available. The ability to
model effect without plasma concentration represents an extreme
example of the sparse plasma sampling approach available with
population techniques.
The role of metabolites
Segredo et al.[9] study in critically ill patients demonstrated
that vecuronium's metabolite cumulated in patients with renal
failure and probably contributed to the prolonged paralysis seen
with chronic administration of vecuronium. However, verification
of this hypothesis depended on estimation of the potency of this
metabolite compared to the parent compound. An elegant study
by Caldwell et al.[10] determined this potency ratio by administering
the parent compound and the metabolite to volunteers using a crossover
design. A less powerful design, administering parent compound
to one group and metabolite to another group, was used recently
by Schiere et al.[11] to estimate the potency of the metabolite
of rapacuronium.
Modeling of antagonists: All the pharmacodynamic models discussed
previously assume that the concentration of the drug (either in
plasma or at the effect site) produces the effect directly. For
muscle relaxants, in which the mechanism of effect is well known,
this assumption is reasonable and can be modeled as:
Dose => Cp <=> Ce <=> Effect (1)
However, for neostigmine, the relationship is more complicated. Administration of neostigmine produces a plasma (and effect site) concentration which "poisons" cholinesterase. In turn, the decreased activity of cholinesterase increases the concentration of acetylcholine at the neuromuscular junction, thereby producing an effect. This can be summarized as:
Dose => Cp <=> Ce => Cholinesterase Inhibition
=> Acetylcholine (2)
Muscle Relaxant => Effect (3)
Thus, there is no direct effect of the antagonist; instead, the time course of recovery is mediated by the regeneration of cholinesterase rather than the rate at which plasma neostigmine concentration's decrease. This is know as an indirect model. These models have been invoked only rarely in anesthesia[12] (but frequently in other areas, such as coagulation); however, they are necessary to explain certain types of effects.
In summary, kinetic/dynamic modeling has been used extensively in the area of muscle relaxants. The availability of well-defined and easy-to-obtain effect measures, the ability to sample arterial blood, and the knowledge of the "model" have permitted significant advances in this area.
References
1. Hull CJ, Van Beem HB, McLeod K, Sibbald A, Watson MJ: A pharmacodynamic
model for pancuronium. Br J Anaesth 1978;50:1113-23
2. Sheiner LB, Stanski DR, Vozeh S, Miller RD, Ham J: Simultaneous
modeling of pharmacokinetics and pharmacodynamics: Application
to d-tubocurarine. Clin Pharmacol Ther 1979;25:358-71
3. Henthorn TK, Avram MJ, Krejcie TC, Shanks CA, Asada A, Kaczynski
DA: Minimal compartmental model of circulatory mixing of indocyanine
green. Am J Physiol 1992;262:H903-10
4. Verotta D: An inequality-constrained least-squares deconvolution
method. J Pharmacokinet Biopharm 1989;17:269-89
5. Donati F, Meistelman C, Plaud B: Vecuronium neuromuscular blockade
at the diaphragm, the orbicularis oculi, and adductor pollicis
muscles. Anesthesiology 1990;73:870-5
6. Donati F, Meistelman C, Plaud B: Vecuronium neuromuscular blockade
at the adductor muscles of the larynx and adductor pollicis.
Anesthesiology 1991;74:833-7
7. Bragg P, Fisher DM, Shi J, Donati F, Meistelman C, Lau M, Sheiner
LB: Comparison of twitch depression of the adductor pollicis and
the respiratory muscles. Pharmacodynamic modeling without plasma
concentrations. Anesthesiology 1994;80:310-9
8. Fisher DM, Wright PM: Are plasma concentration values necessary
for pharmacodynamic modeling of muscle relaxants? Anesthesiology
1997;86:567-75
9. Segredo V, Caldwell JE, Matthay MA, Sharma ML, Gruenke LD,
Miller RD: Persistent paralysis in critically ill patients after
long-term administration of vecuronium. N Engl J Med 1992;327:524-8
10. Caldwell JE, Szenohradszky J, Segredo V, Wright PM, McLoughlin
C, Sharma ML, Gruenke LD, Fisher DM, Miller RD: The pharmacodynamics
and pharmacokinetics of the metabolite 3-desacetylvecuronium (ORG
7268) and its parent compound, vecuronium, in human volunteers.
J Pharmacol Exp Ther 1994;270:1216-22
11. Schiere S, Proost JH, Wierda JMKH: Pharmacokinetics and pharmacokinetic/
pharmacodynamic (PK/PD) relationship of ORG 9488, the 3-desacetyl
metabolite of ORG 9487 (abstract). Anesthesiology 1997;87:A377
12. Verotta D, Kitts J, Rodriguez R, Coldwell J, Miller RD, Sheiner
LB: Reversal of neuromuscular blockade in humans by neostigmine
and edrophonium: a mathematical model. J Pharmacokinet Biopharm
1991;19:713-29