Volume of the effect compartment in simulations of neuromuscular block

Nigrovic Vladimir, Proost, Amann Anton, Bhatt

Description

The study examines the role of the volume of the effect compartment in simulations of neuromuscular block (NMB) produced by nondepolarizing muscle relaxants. Methods The molar amount of the postsynaptic receptors at the motor end plates in muscle was assumed constant; the apparent receptor concentration in the effect compartment is the ratio of this amount and the volume arbitrarily assigned to the effect compartment. The muscle relaxants were postulated to diffuse between the central and the effect compartment and to bind to the postsynaptic receptors. NMB was calculated from the free concentration of the muscle relaxant in the effect compartment. Results The simulations suggest that the time profiles of NMB and the derived pharmacokinetic and pharmacodynamic variables are dependent on the apparent receptor concentration in the effect compartment. For small, but not for large, volumes, times to peak submaximal NMB are projected to depend on the magnitude of NMB and on the binding affinities. Conclusion An experimental design to estimate the volume of the effect compartment is suggested.

Informations

• Publié par: biomed
• Publié le: 01 janvier 2005
• Nombre de lectures: 5
• Langue: English

Extrait

Theoretical Biology and Medical
BioMed CentralModelling
Open AccessResearch
Volume of the effect compartment in simulations of neuromuscular
block
1 2 3Vladimir Nigrovic* , Johannes H Proost , Anton Amann and
1Shashi B Bhatt
1 2Address: Department of Anesthesiology, Medical University of Ohio, Toledo, OH, USA, Research Group for Experimental Anesthesiology and
3Clinical Pharmacology, University Hospital Groningen, Groningen, The Netherlands and Department of Anesthesiology and Critical Care
Medicine, Leopold-Franzens University, Innsbruck, Austria, and Department of Environmental Sciences, The Swiss Federal Institute of Technology,
Zürich, Switzerland
Email: Vladimir Nigrovic* - [e-mail]; Johannes H Proost - [e-mail]; Anton Amann - [e-mail];
Shashi B Bhatt - [e-mail]
* Corresponding author
Published: 03 October 2005 Received: 02 September 2005
Accepted: 03 October 2005
Theoretical Biology and Medical Modelling 2005, 2:41 doi:10.1186/1742-4682-2-41
This article is available from: http://www.tbiomed.com/content/2/1/41
© 2005 Nigrovic et al; licensee BioMed Central Ltd.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0),
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Background: The study examines the role of the volume of the effect compartment in simulations
of neuromuscular block (NMB) produced by nondepolarizing muscle relaxants.
Methods: The molar amount of the postsynaptic receptors at the motor end plates in muscle was
assumed constant; the apparent receptor concentration in the effect compartment is the ratio of
this amount and the volume arbitrarily assigned to the effect compartment. The muscle relaxants
were postulated to diffuse between the central and the effect compartment and to bind to the
postsynaptic receptors. NMB was calculated from the free concentration of the muscle relaxant in
the effect compartment.
Results: The simulations suggest that the time profiles of NMB and the derived pharmacokinetic
and pharmacodynamic variables are dependent on the apparent receptor concentration in the
effect compartment. For small, but not for large, volumes, times to peak submaximal NMB are
projected to depend on the magnitude of NMB and on the binding affinities.
Conclusion: An experimental design to estimate the volume of the effect compartment is
suggested.
compartment using the equation of Hill. Binding of mus-Background
In the majority of the pharmacokinetic-pharmacody- cle relaxants to the postsynaptic receptors at the motor
namic (PK-PD) models proposed to simulate neuromus- end plates is not considered. Because muscle relaxants
cular block (NMB) [1-3], the volume of the effect produce NMB by binding to these receptors, considera-
compartment is postulated to be negligibly small or the tion of the interaction of muscle relaxants with the recep-
coent is postulated to contain a negligibly small tors represents a more realistic approach and an
amount of the muscle relaxant. The models simulate NMB advancement in simulations [4-6]. Donati and Meistel-
based on the concentration of the muscle relaxant in this man [5] were the first to consider binding of muscle
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relaxants to the receptors. These investigators suggested
that the receptor concentration in the effect compartment −⋅λλtt − ⋅ −⋅λ tNO PDd=⋅ose()N⋅e +O⋅e +P⋅e{}
-7 plasmaM, but the volume of the effect comparis 2.8·10
was assumed to be negligibly small. Given a fixed amount Here, N, O, and P (P = 1 - N - O) are fractions of the dose
of postsynaptic receptors, a finite receptor concentration that are eliminated from plasma with the first order rate
is not compatible with a negligibly small volume of the constants λ , λ , and λ , respectively. The dose is inN O P
-1effect compartment. mol·kg . Division of the equation by V , V expressed inC C
-1L·kg , converts the amounts in plasma to molar concen-
We decided to examine the role of the volume of the effect trations. V represents the volume of the space into whichC
compartment in a pharmacokinetic-pharmacodynamic the muscle relaxant is uniformly diluted at time t = 0, i.e.,
model for NMB and were interested in answering the fol- at the moment of bolus intravenous injection.
lowing questions: (1) Is it necessary to postulate a negligi-
bly small amount of a muscle relaxant in the effect The values assigned to the parameters in the triexponen-
compartment? (2) Do the projections from simulations tial equation were based on the following postulates: For
approximates theusing a small or a large volume of the effect compartment the hypothetical muscle relaxant D, VC
differ? If so, what are the differences? (3) Can the simula- volume of plasma and V , the volume of distribution atSS
tions suggest an experimental design suitable to test steady state, approximates the volume of the extracellular
whether the volume of the effect compartment is negligi- space. The dose that produces NMB50, i.e., ED50, is
bly small or a large volume may be more appropriate? defined by the postulate that the concentration in plasma
at 4.5 min after bolus intravenous injection is [D] =plasma
IC50. The definition of IC50 is provided below. The fol-Methods
General approach lowing values satisfy these requirements:
(1) The amount of the postsynaptic receptors at the motor
end plates in muscle, in terms of mol per kg body weight, N = 0.71; O = 0.192; P = 0.098
was assumed constant and the receptors uniformly
-1 -1 -1diluted in the effect compartment. (2) The plasma con- λ = 1.3 min ; λ = 0.31 min ; λ = 0.0231 minN O P
centrations of a hypothetical muscle relaxant after admin-
-1 -1istration of an intravenous bolus dose, defined by an V = 0.044 L·kg V = 0.28 L·kgC SS
arbitrary multiexponential equation, are labeled target
concentrations. In the simulations, the target plasma con- Compartmental interpretation of the triexponential decay
centrations fulfill the role of the experimentally deter- of the plasma concentrations yields the following param-
mined plasma concentrations. (3) A PK-PD model was eters for the standard 3-compartment pharmacokinetic
designed a priori to include an effect compartment of an model assuming a mammillary arrangement of the com-
assigned volume. The pharmacokinetic parameters in the partments and elimination only from compartment [7]:1
model were defined by the postulate that the concentra-
-1 -1tions in the central compartment (compartment1) fit the V = V = 0.044 L·kg k = 0.1848 min1 C 10
target plasma concentrations. (4) The muscle relaxant dif-
-1 -1fuses from the central to the effect compartment. (5) Phar- k = 0.3771 min k = 0.5581 min12 21
macodynamic parameters were obtained from the
-1 -1postulate that peak neuromuscular block from a bolus k = 0.4229 min k = 0.0902 min13 31
ED50 dose occurs at 4.5 minutes after injection. The peak
concentration of the muscle relaxant in the effect com- Estimation of the receptor amount
partment at this moment corresponds to the IC50 concen- The molar amount of receptors per kg body weight was
tration. (6) The relationship between NMB and the free estimated based on the following assumptions: One hun-
concentrations of the muscle relaxant in the effect com- dred g of muscle is represented as a cube with side length
partment is defined by the Hill equation. of 4.64 cm, i.e., specific density of muscle ~ 1. There is 430
g muscle per kg body weight. The muscle fibers are
The target plasma concentrations densely packed cylinders with the diameter of 50 µm and
Muscle relaxant D was postulated to display linear phar- the length of 4.64 cm (928 rows × 928 columns of fibers
macokinetics. The triexponential equation that defines in a cross section perpendicular to the length of the fib-
the time course of the molar amounts of the muscle relax- ers). Each muscle fiber has one motor end plate with
7 ant in plasma is given by (braces indicate molar 2.1·10 receptors at each end plate [8,9].
amounts):
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The PK-PD Model For an assigned volume of the effect compartment (V ),e
The pharmacokinetic model consists of four compart- the pharmacokinetic parameters in the PK-PD model were
), two peripheralments: the central (compartment estimated in a two-step procedure. In the first step, the1
(compartment and compartment ), and the effect com- parameter k was obtained using the following con-2 3 e1
partment in mammillary arrangement with elimination straints: dose = ED50, the amounts in plasma as defined
from the central compartment. The model is defined in by the triexponential equation, and the maximal NMB =
terms of the amounts of the muscle relaxant present in 50% attained at 4.5 min after administration of the mus-
each compartment and the amount eliminated from the cle relaxant. In the second step, the parameters V , k , k ,1 10 12
body. Transport between the central and the effect com- k , k , and k were estimated using the following con-21 13 31
partment