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PHARMACOKINETIC MODELS: SIMPLE OR COMPLEX ?
BRITISH JOURNAL OF ANAESTHESIA
88
METHOHEXITONE
Sir,—I was surprised to read Dr Whitwam's statement in your editorial of July 1976 that "there are no published accounts of any anaphylactoid reactions to methohexitone in the United Kingdom" as Dr Watkins and I reported just such a case in your October 1975 issue. Those of us who aim at brevity, as requested in your same July issue, will be discouraged to learn that material in letter form is apparently not read, or even acknowledged. Since our report was published, another case of anaphylactoid reaction to methohexitone has come to my notice, in my own area. I do not believe my experience to be unique, and reiterate our plea for reporting of all cases of such reactions, not just those involving the newer agents. Only in this way can misapprehensions such as those of your distinguished guest editor be set aside. RICHARD WYATT Leicester REFERENCE
Wyatt, R., and Watkins, J. (1975). Reaction to methohexitone. Br.J. Anaesth., 47, 1119. PHARMACOKINETIC MODELS: SIMPLE OR COMPLEX ?
Sir,—Beneken Kolmer and his colleagues (1975) reported in this Journal an interesting study of the uptake and elimination of halothane in dogs. They claimed that their results could be described adequately by equations involving only two exponentials and, therefore, in terms of a twocompartment system. They went on to expound the advantages of a two-compartment system over a multi-compartment system such as that originally propounded by Kety (1951). However, the choice between a simple and a complex model depends upon the object of the study. If the object is only to provide an empirical description of experimental results then a simple equation may well be adequate—at least if the constants in the equation are chosen on the basis of what will fit the data best. Since Beneken Kolmer's equations have four or five constants it is not surprising that, by choosing different values of the constants for each animal and for each sampling site, they get a good fit of the calculated curves to the measured tensions in restricted circumstances, that is during 2£ h of uptake with constant inspired concentrations and, with another set of constants, during
1J h of elimination. Indeed, Lowe (1972) has gone even further and claimed good fits for a range of anaesthetic agents given at constant alveolar concentration with an equation of the form at05 (where t is time). This equation includes only one arbitrary constant, a. Empirical equations are valid only for the circumstances in which they were derived. For an equation to be applicable over a wide range of circumstances it must be based on sound theory; then it can be used to predict uptake and elimination from a knowledge of the physiological properties of the body and the physical properties of the anaesthetic. For predictions of this kind to agree with experiment, multi-compartment models are necessary (Mapleson, 1962; Eger, 1963; Cowles, Borgstedt and Gillies, 1972); and it now appears that even these may be inadequate if they allow communication between compartments only by perfusion; direct diffusion between compartments may need to be taken into account (Allott, Steward and Mapleson, 1976). A further advantage of a theoretical model is that it can be used to make predictions of the effects of changes of circumstances; but how could the effect of obesity, for instance, be deduced from Beneken Kolmer's equation ? Thus, the complexity of the equation required depends upon the use to be made of it: by all means use a simple equation where this is adequate but, because a simple equation fits in some circumstances, do not think that it will fit in all circumstances. Finally, it is a little quixotic that, at the same time that Beneken Kolmer and his colleagues are drawing attention to the merits of simple empirical models, non-anaesthetic pharmacokineticists, who have traditionally used such models, are beginning to appreciate the merits of theoretical models (Benowitz et al., 1974). W. W. MAPLESON Cardiff REFERENCES
Allott, P. R., Steward, A., and Mapleson, W. W. (1976). Pharmacokinetics of halothane in the dog. Br.J. Anaesth., 48, 279. Beneken Kolmer, H. H., Burm, A. G., Cramers, C. A., Ramakers, J. M., and Vader, H. L. (1975). The uptake and elimination of halothane in dogs: a two or multicompartment system? II: Evaluation of wash-in and wash-out curves. Br.J. Anaesth., 47, 1169. Benowitz, N., Forsyth, R. P., Melmon, K. L., and Rowland, M. (1974). Lidocaine disposition kinetics in monkey and man. I: Prediction by a perfusion model. Clin. Pharmacol. Ther., 16, 87. Cowles, A. L., Borgstedt, H. H., and Gillies, A. J. (1972). The uptake and distribution of four inhalation anesthetics in dogs. Anesthesiology, 36, 558. Eger, E. I., II (1963). A mathematical model of uptake and distribution; in Uptake and Distribution of Anesthetic Agents (eds E. M. Papper and R. J. Kitz), p. 72. New York: McGraw-Hill. Kety, S. S. (1951). The theory and applications of the exchange of inert gas at the lungs and tissues. Pharmacol. Rev., 3, 1. Lowe, H. J. (1972). Dose-regulated Penthrane Anesthesia, p. 43. Chicago: Abbott Laboratories. Mapleson, W. W. (1962). The rate of uptake of halothane vapour in man. Br.J. Anaesth., 34, 11.
Downloaded from http://bja.oxfordjournals.org/ at University of California, San Fransisco on March 27, 2015
Lorenz, W., Doenicke, A., Messmer, K., Reimann, H. J., Therman, M., Lahn, W., Berr, J., Schmal, A., Dorman, P., Regenfuss, P., and Hamelmann, H. (1976). Histamine release in human subjects by modified gelatin (Haemaccel) and Dextran: an explanation for anaphylactoid reactions observed under clinical conditions. Br. J. Anaesth., 48, 151. Watkins, J., Appleyard, T. N., and Ward, A. M. (1975). Complement involvement in patients showing hypersensitivity responses to Althesin and methohexitone (1975). Br. J. Anaesth., 47, 903. Watt, H. K. (1973). Anaphylactic shock from gallamine. N.Z. Soc. Anaesth. Newsletter, 20, 21. Watt, J. M. (1975). Anaphylactic reactions after use of CT 1341 (Althesin). Br. Med.J., 2, 205.
88
METHOHEXITONE
Sir,—I was surprised to read Dr Whitwam's statement in your editorial of July 1976 that "there are no published accounts of any anaphylactoid reactions to methohexitone in the United Kingdom" as Dr Watkins and I reported just such a case in your October 1975 issue. Those of us who aim at brevity, as requested in your same July issue, will be discouraged to learn that material in letter form is apparently not read, or even acknowledged. Since our report was published, another case of anaphylactoid reaction to methohexitone has come to my notice, in my own area. I do not believe my experience to be unique, and reiterate our plea for reporting of all cases of such reactions, not just those involving the newer agents. Only in this way can misapprehensions such as those of your distinguished guest editor be set aside. RICHARD WYATT Leicester REFERENCE
Wyatt, R., and Watkins, J. (1975). Reaction to methohexitone. Br.J. Anaesth., 47, 1119. PHARMACOKINETIC MODELS: SIMPLE OR COMPLEX ?
Sir,—Beneken Kolmer and his colleagues (1975) reported in this Journal an interesting study of the uptake and elimination of halothane in dogs. They claimed that their results could be described adequately by equations involving only two exponentials and, therefore, in terms of a twocompartment system. They went on to expound the advantages of a two-compartment system over a multi-compartment system such as that originally propounded by Kety (1951). However, the choice between a simple and a complex model depends upon the object of the study. If the object is only to provide an empirical description of experimental results then a simple equation may well be adequate—at least if the constants in the equation are chosen on the basis of what will fit the data best. Since Beneken Kolmer's equations have four or five constants it is not surprising that, by choosing different values of the constants for each animal and for each sampling site, they get a good fit of the calculated curves to the measured tensions in restricted circumstances, that is during 2£ h of uptake with constant inspired concentrations and, with another set of constants, during
1J h of elimination. Indeed, Lowe (1972) has gone even further and claimed good fits for a range of anaesthetic agents given at constant alveolar concentration with an equation of the form at05 (where t is time). This equation includes only one arbitrary constant, a. Empirical equations are valid only for the circumstances in which they were derived. For an equation to be applicable over a wide range of circumstances it must be based on sound theory; then it can be used to predict uptake and elimination from a knowledge of the physiological properties of the body and the physical properties of the anaesthetic. For predictions of this kind to agree with experiment, multi-compartment models are necessary (Mapleson, 1962; Eger, 1963; Cowles, Borgstedt and Gillies, 1972); and it now appears that even these may be inadequate if they allow communication between compartments only by perfusion; direct diffusion between compartments may need to be taken into account (Allott, Steward and Mapleson, 1976). A further advantage of a theoretical model is that it can be used to make predictions of the effects of changes of circumstances; but how could the effect of obesity, for instance, be deduced from Beneken Kolmer's equation ? Thus, the complexity of the equation required depends upon the use to be made of it: by all means use a simple equation where this is adequate but, because a simple equation fits in some circumstances, do not think that it will fit in all circumstances. Finally, it is a little quixotic that, at the same time that Beneken Kolmer and his colleagues are drawing attention to the merits of simple empirical models, non-anaesthetic pharmacokineticists, who have traditionally used such models, are beginning to appreciate the merits of theoretical models (Benowitz et al., 1974). W. W. MAPLESON Cardiff REFERENCES
Allott, P. R., Steward, A., and Mapleson, W. W. (1976). Pharmacokinetics of halothane in the dog. Br.J. Anaesth., 48, 279. Beneken Kolmer, H. H., Burm, A. G., Cramers, C. A., Ramakers, J. M., and Vader, H. L. (1975). The uptake and elimination of halothane in dogs: a two or multicompartment system? II: Evaluation of wash-in and wash-out curves. Br.J. Anaesth., 47, 1169. Benowitz, N., Forsyth, R. P., Melmon, K. L., and Rowland, M. (1974). Lidocaine disposition kinetics in monkey and man. I: Prediction by a perfusion model. Clin. Pharmacol. Ther., 16, 87. Cowles, A. L., Borgstedt, H. H., and Gillies, A. J. (1972). The uptake and distribution of four inhalation anesthetics in dogs. Anesthesiology, 36, 558. Eger, E. I., II (1963). A mathematical model of uptake and distribution; in Uptake and Distribution of Anesthetic Agents (eds E. M. Papper and R. J. Kitz), p. 72. New York: McGraw-Hill. Kety, S. S. (1951). The theory and applications of the exchange of inert gas at the lungs and tissues. Pharmacol. Rev., 3, 1. Lowe, H. J. (1972). Dose-regulated Penthrane Anesthesia, p. 43. Chicago: Abbott Laboratories. Mapleson, W. W. (1962). The rate of uptake of halothane vapour in man. Br.J. Anaesth., 34, 11.
Downloaded from http://bja.oxfordjournals.org/ at University of California, San Fransisco on March 27, 2015
Lorenz, W., Doenicke, A., Messmer, K., Reimann, H. J., Therman, M., Lahn, W., Berr, J., Schmal, A., Dorman, P., Regenfuss, P., and Hamelmann, H. (1976). Histamine release in human subjects by modified gelatin (Haemaccel) and Dextran: an explanation for anaphylactoid reactions observed under clinical conditions. Br. J. Anaesth., 48, 151. Watkins, J., Appleyard, T. N., and Ward, A. M. (1975). Complement involvement in patients showing hypersensitivity responses to Althesin and methohexitone (1975). Br. J. Anaesth., 47, 903. Watt, H. K. (1973). Anaphylactic shock from gallamine. N.Z. Soc. Anaesth. Newsletter, 20, 21. Watt, J. M. (1975). Anaphylactic reactions after use of CT 1341 (Althesin). Br. Med.J., 2, 205.