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Correspondence  |   November 2001
Calculation of the Permeability Coefficient Should Take into Account the Fact That Most Drugs Are Weak Electrolytes
Author Affiliations & Notes
  • René J. Grouls, Ph.D.
    *
  • *Catharina Hospital, Eindhoven, The Netherlands. r.grouls@wxs.nl
Article Information
Correspondence
Correspondence   |   November 2001
Calculation of the Permeability Coefficient Should Take into Account the Fact That Most Drugs Are Weak Electrolytes
Anesthesiology 11 2001, Vol.95, 1300-1301. doi:
Anesthesiology 11 2001, Vol.95, 1300-1301. doi:
To the Editor:—
In a recent article, Bernards et al.  1 measured separately the flux of 3H-labelled R  - and S  -bupivacaine through the spinal meninges of the monkey and concluded that the meningeal permeability for the enantiomers did not differ. However, their method of calculation of the permeability coefficient does not take into account the fact that bupivacaine exists in solution as a mixture of conjugated acid (ionized) and base (unionized) forms under the chosen conditions of pH 7.4 (fig. 1).
Fig. 1. Distribution and diffusion of bupivacaine between donor and receiver compartments. The concentrations of the ionized and unionized forms of bupivacaine (symbolized as a tertiary amine R3N) in donor and receiver compartments are depicted by C1, C2, and so on.
Fig. 1. Distribution and diffusion of bupivacaine between donor and receiver compartments. The concentrations of the ionized and unionized forms of bupivacaine (symbolized as a tertiary amine R3N) in donor and receiver compartments are depicted by C1, C2, and so on.
Fig. 1. Distribution and diffusion of bupivacaine between donor and receiver compartments. The concentrations of the ionized and unionized forms of bupivacaine (symbolized as a tertiary amine R3N) in donor and receiver compartments are depicted by C1, C2, and so on.
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Partial ionization complicates the calculation of the permeability coefficient. It is known for many substances, and we have shown for local anesthetics that the unionized form of the local anesthetic predominantly diffuses through the meninges, with the contribution of the ionized form being essentially negligible. 2 By calculating the permeability coefficient (P [cm/min]) according to the equation
where Q = bupivacaine flux (μg/min), C = total bupivacaine concentration (= C1 + C2) in the donor reservoir (μg/ml), and A = tissue area (cm2).
Bernards et al.  1 underestimate the exact value of the permeability coefficient by a factor of 6 by using the total concentration C of bupivacaine in the donor compartment (= sum of C1 + C2 in fig. 1). The actual “driving force” for diffusion of bupivacaine through the meninges (C1 ≈ 0.166C) should be calculated according the Henderson-Hasselbalch equation and the pKavalue measured by Strichartz et al.  3 at 37°C.
The conclusion of this study by Bernards et al.  1 is qualitatively correct; the impact of omitting the influence of ionization is nullified because R  - and S  -bupivacaine, having the same pKa, 4 are compared. Furthermore, we independently obtained the same result using human meninges with (racemic) bupivacaine and a chiral high-pressure liquid chromatography method to measure the concurrent enantiomer concentrations individually. 5 However, it needs to be reiterated that other relevant physicochemical properties, such as aqueous solubility, cannot be assumed to be equal for the enantiomers of racemic drugs separately and in the racemic admixture. 4 
The results of previous studies, comparing the permeability coefficients of different drug molecules with widely differing pKavalues, and without correction for the unionized concentration, should be addressed cautiously. 6,7 Future studies should address this important aspect of diffusion.
References
Bernards CM, Ulma GA, Kopacz DJ: The meningeal permeability of R  - and S  -bupivacaine are not different. Anesthesiology 2000; 93: 896–7Bernards, CM Ulma, GA Kopacz, DJ
Grouls R, Korsten E, Ackerman E, Hellebrekers L, Zundert van A, Breimer D: Diffusion of n-butyl-p-aminobenzoate (BAB), lidocaine and bupivacaine through the human dura-arachnoid mater in vitro. Eur J Pharm Sciences 2000; 12: 125–31Grouls, R Korsten, E Ackerman, E Hellebrekers, L Zundert van, A Breimer, D
Strichartz GR, Sanchez V, Arthur GR, Chafetz R, Martin D: Fundamental properties of local anesthetics, II: Measured octanol:buffer partition coefficients and pKa values of clinically used drugs. Anesth Analg 1990; 71: 158–70Strichartz, GR Sanchez, V Arthur, GR Chafetz, R Martin, D
Friberger P, Åberg G: Some physicochemical properties of the racemates and the optically active isomers of two local anaesthetic compounds. Acta Pharm Suecica 1971; 8: 361–4Friberger, P
Grouls RJE, Mather LE, Korsten HM, Gu X-Q: Diffusion of R- and S-bupivacaine through the human dura-arachnoid (abstract). Br J Clin Pharmacol 2000; 50: 494–5Grouls, RJE Mather, LE Korsten, HM Gu, X-Q
Bernards CM, Hill HF: Physical and chemical properties of drug molecules governing their diffusion through the spinal meninges. Anesthesiology 1992; 77: 750–6Bernards, CM Hill, HF
McEllistrem RF, Bennington RG, Roth SH: In vitro determination of human dura mater permeability to opioids and local anaesthetics. Can J Anaesth 1993; 40: 165–9McEllistrem, RF Bennington, RG Roth, SH
Fig. 1. Distribution and diffusion of bupivacaine between donor and receiver compartments. The concentrations of the ionized and unionized forms of bupivacaine (symbolized as a tertiary amine R3N) in donor and receiver compartments are depicted by C1, C2, and so on.
Fig. 1. Distribution and diffusion of bupivacaine between donor and receiver compartments. The concentrations of the ionized and unionized forms of bupivacaine (symbolized as a tertiary amine R3N) in donor and receiver compartments are depicted by C1, C2, and so on.
Fig. 1. Distribution and diffusion of bupivacaine between donor and receiver compartments. The concentrations of the ionized and unionized forms of bupivacaine (symbolized as a tertiary amine R3N) in donor and receiver compartments are depicted by C1, C2, and so on.
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