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Physiologic-Pharmacologic Interpretation of the Constants in the Hill Equation for Neuromuscular Block: A Hypothesis

  • Vladimir NigrovicEmail author
  • Anton Amann
Article

Abstract

Neuromuscular block (NMB) is simulated in pharmacodynamic models using the concentration of a muscle relaxant (MR) in the effect compartment and two constants, γ and IC50. No physiologic or pharmacologic interpretation is offered for either constant. We desired to explore whether the constants are properties of the muscle or the MR and to simulate NMB when the MR binds to two sites at a single receptor. Based on steady state conditions, we defined receptor occupancy using the equilibrium dissociation constants. Two concepts are introduced: threshold occupancy and occupancy at half-maximal NMB, OccNMB50. Threshold occupancy is defined as receptor occupancy at the motor end plate of a muscle fiber when the fiber fails to contract and OccNMB50 as the median threshold occupancy. NMB may be simulated as a function of either the concentration of the muscle relaxant or receptor occupancy. We suggest: (1) The distribution of threshold occupancies is an intrinsic property of a muscle and is characterized by two constants (γO and OccNMB50); (2) γO is numerically equal to the slope of the NMB vs. concentration curves and is independent of the equilibrium dissociation constants. IC50 is codetermined by OccNMB50 and by the equilibrium dissociation constants. (3) Binding of a muscle relaxant to the second binding site influences only the estimate of IC50 but not γ.

neuromuscular blocking drugs simulation of neuromuscular block neuromuscular transmission skeletal muscle postsynaptic receptors 

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REFERENCES

  1. 1.
    G. Fletcher and J. Steinbach. Ability of nondepolarizing neuromuscular blocking drugs to act as partial agonists at fetal and adult mouse muscle nicotinic receptors. Mol. Pharmacol. 49:938-947 (1996).PubMedGoogle Scholar
  2. 2.
    S. Pedersen and J. Cohen. D-tubocurarine binding sites are located at alpha-gamma and alpha-delta subunit interfaces of the nicotinic acetylcholine receptor. Proc. Natl. Acad. Sci. U.S.A. 87:2785-2789 (1990).PubMedGoogle Scholar
  3. 3.
    A. Le Dain, B. Madsen, and R. Edeson. Kinetics of (+)-tubocurarine blockade at the neuromuscular junction. Br. J. Pharmacol. 103:1607-1613 (1991).PubMedGoogle Scholar
  4. 4.
    D. Armstrong and H. Lester. The kinetics of tubocurarine action and restricted diffusion within the synaptic cleft. J. Physiol. 294:365-386 (1979).PubMedGoogle Scholar
  5. 5.
    J. Min, I. Bekavac, M. Glavinovic, F. Donati, and D. Bevan. Iontophoretic study of speed of action of various muscle relaxants. Anesthesiology 77:351-356 (1992).PubMedGoogle Scholar
  6. 6.
    A. Kopman, M. Klewicka, and G. Neuman. An alternate method for estimating the doseresponse relationships of neuromuscular blocking drugs. Anesth. Analg. 90:1191-1197 (2000).PubMedGoogle Scholar
  7. 7.
    A. Kopman, M. Klewicka, K. Ghori, F. Flores, and G. Neuman. Dose-response and onset_offset characteristics of rapacuronium. Anesthesiology 93:1017-1021 (2000).PubMedGoogle Scholar
  8. 8.
    L. Sheiner, D. Stanski, S. Vozeh, R. Miller, and J. Ham. Simultaneous modeling of pharmacokinetics and pharmacodynamics: Application to d-tubocurarine. Clin. Pharmacol. Ther. (St. Louis) 25:358-371 (1979).Google Scholar
  9. 9.
    P. Wright, R. Brown, M. Lau, and D. Fisher. A pharmacodynamic explanation for the rapid onset_offset of rapacuronium bromide. Anesthesiology 90:16-23 (1999).PubMedGoogle Scholar
  10. 10.
    B. Plaud, J. Proost, J. Wierda, J. Barre, B. Debaene, and C. Meistelman. Pharmacokinetics and pharmacodynamics of rocuronium at the vocal cords and the adductor pollicis in humans. Clin. Pharmacol. Ther. (St Louis) 58:185-191 (1995).Google Scholar
  11. 11.
    D. Fisher, J. Szenohradszky, P. Wright, M. Lau, R. Brown, and M. Sharma. Pharmacodynamic modeling of vecuronium-induced twitch depression. Rapid plasma-effect site equilibration explains faster onset at resistant laryngeal muscles than at the adductor pollicis. Anesthesiology 86:558-566 (1997).PubMedGoogle Scholar
  12. 12.
    J. Kuipers, F. Boer, E. Olofsen, J. Bovill, and A. Burm. Recirculatory pharmacokinetics and pharmacodynamics of rocuronium in patients. Anesthesiology 94:47-55 (2001).PubMedGoogle Scholar
  13. 13.
    E. Vizi and B. Lendvai. Side effects of nondepolarizing muscle relaxants: Relationship to their antinicotinic and antimuscarinic actions. Pharmacol. Ther. 73:75-89 (1997).PubMedGoogle Scholar
  14. 14.
    E. Bradshaw, N. Harper, B. Pleuvry, and C. Modla. Differing potencies of muscle relaxants on rat and guinea-pig phrenic nerve diaphragm preparations. J. Pharm. Pharmacol. 38:623-624 (1986).PubMedGoogle Scholar
  15. 15.
    G. Bikhazi, I. Leung, C. Flores, H. Mikati, and F. Foldes. Potentiation of neuromuscular blocking agents by calcium channel blockers in rats. Anesth. Analog. 67:1-8 (1988).Google Scholar
  16. 16.
    S. Matsuo, D. Rao, I. Chaudry, and F. Foldes. Interaction of muscle relaxants and local anesthetics at the neuromuscular junction. Anesth. Analog. 57:580-587 (1978).Google Scholar
  17. 17.
    L. Aziz, Y. Ohta, T. Yamada, K. Morita, and M. Hirakawa. The effect of isoflurane and temperature on the actions of muscle relaxants in rat in vitro. Anesth. Analog. 80:1181-1186 (1995).Google Scholar
  18. 18.
    R. Treffers, A. Frankhuyzen, and L. Booij. Effects of neostigmine, edrophonium, 4-aminopyridine and their combinations. Acta Anaesth. Belg. 39:55-58 (1988).PubMedGoogle Scholar
  19. 19.
    D. Stanski, J. Ham, R. Miller, and L. Sheiner. Pharmacokinetics and pharmacodynamics of d-tubocurarine during nitrous oxide-narcotic and halothane anesthesia in man. Anesthesiology 51:235-241 (1979).PubMedGoogle Scholar
  20. 20.
    D. Fisher, O. K. C. D. Stanski, R. Cronnelly, R. Miller, and G. Gregory. Pharmacokinetics and pharmacodynamics of d-tubocurarine in infants, children, and adults. Anesthesiology 57:203-208 (1982).PubMedGoogle Scholar
  21. 21.
    S. Rupp, K. Castagnoli, D. Fisher, and R. Miller. Pancuronium and vecuronium pharmacokinetics and pharmacodynamics in younger and elderly adults. Anesthesiology 67:45-49 (1987).PubMedGoogle Scholar
  22. 22.
    C. Hull, B. H. Van, K. McLeod, A. Sibbald, and M. Watson. A pharmacodynamic model for pancuronium. Br. J. Anaesth. 50:1113-1123 (1978).PubMedGoogle Scholar
  23. 23.
    F. Donati, F. Varin, J. Ducharme, S. Gill, Y. Theoret, and D. Bevan. Pharmacokinetics and pharmacodynamics of atracurium obtained with arterial and venous blood samples. Clin. Pharmacol. Ther. (St. Louis) 49:515-522 (1991).Google Scholar
  24. 24.
    B. Weatherley, S. Williams, and E. Neill. Pharmacokinetics, pharmacodynamics and doseresponse relationships of atracurium administered i.v. Br. J. Anaesth. 55 Suppl 1:39S-45S (1983).PubMedGoogle Scholar
  25. 25.
    J. Kitts, D. Fisher, P. Canfell, M. Spellman, J. Caldwell, T. Heier, M. Fahey, and R. Miller. Pharmacokinetics and pharmacodynamics of atracurium in the elderly. Anesthesiology 72:272-275 (1990).PubMedGoogle Scholar
  26. 26.
    D. Fisher, P. Canfell, M. Spellman, and R. Miller. Pharmacokinetics and pharmacodynamics of atracurium in infants and children. Anesthesiology 73:33-37 (1990).PubMedGoogle Scholar
  27. 27.
    R. Matteo, W. Brotherton, K. Nishitateno, H. Khambatta, and J. Dias. Pharmacodynamics and pharmacokinetics of metocurine in humans: Comparison to d-tubocurarine. Anesthesiology 57:183-190 (1982).PubMedGoogle Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  1. 1.Departments of Anesthesiology and PharmacologyMedical College of OhioToledoUSA
  2. 2.Department of Anesthesiology and Intensive CareUniversity of InnsbruckInnsbruckAustria
  3. 3.Swiss Federal Institute of TechnologyZurichSwitzerland

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