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Linear and nonlinear system approaches in pharmacokinetics: How much do they have to offer? I. General considerations

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Abstract

System approaches in pharmacokinetics are defined as generalizing and simplifying modeling approaches that mathematically model a general property of the pharmacokinetic system without modeling specifically the individual kinetic processes responsible for the general property considered. The rationale for the use of system approaches is discussed and the kinetic basis of some of the approaches is presented. An overview of the approaches is presented together with a comparison to classical approaches involving specific pharmacokinetic models. Examples are given from different application areas involving problems in linear and nonlinear pharmacokinetics and in pharmacodynamics. The advantages, disadvantages, and limitations of the system approaches are discussed. In several application areas the system approach offers some rational methods and procedures with distinct advantages over more traditional approaches.

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References

  1. D. Cutler. Linear system analysis in pharmacokinetics.J. Pharmacokin. Biopharm. 6:227–241 (1978).

    Article  CAS  Google Scholar 

  2. G. Amidon, M. Paul, and P. Welling. Model-independent methods in pharmacokinetics: Theoretical considerations.Math. Biosci. 25:259–272 (1975).

    Article  Google Scholar 

  3. P. Veng-Pedersen. Theorems and implications of a model independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions: I. Derivation and theoretical analyses.J. Pharmacokin. Biopharm. 12:627–648 (1984).

    Article  CAS  Google Scholar 

  4. W. R. Gillespie and P. Veng-Pedersen. Theorems and implications of a model independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions: II. Clearance concepts applied to the evaluation of distribution kinetics.J. Pharmacokin. Biopharm. 13:441–451 (1985).

    Article  CAS  Google Scholar 

  5. W. R. Gillespie, P. Veng-Pedersen, and T. P. Gibson. Deconvolution applied to the evaluation of extracorporal drug removal. Haemodialysis of Cefsulidin.Eur. J. Clin. Pharmacol. 29:503–509 (1985).

    Article  CAS  PubMed  Google Scholar 

  6. W. R. Gillespie, P. Veng-Pedersen, M. J. Berg, and D. D. Schottelius. Linear system approach to the analysis of an induced drug removal process. Phenobarbital removal by oral activated charcoal.J. Pharmacokin. Biopharm. 14:19–28 (1986).

    Article  CAS  Google Scholar 

  7. D. Cutler. Assessment of rate and extent of drug absorption.Pharmacol. Ther. 14:123–160 (1981).

    Article  CAS  PubMed  Google Scholar 

  8. D. Cutler. A linear recirculation model for drug disposition.J. Pharmacokin. Biopharm. 7:101–116 (1979).

    Article  CAS  Google Scholar 

  9. D. P. Vaughan and I. Hope. Application of a recirculatory stochastic pharmacokinetic model: limitation of compartment models.J. Pharmacokin. Biopharm. 7:207–225 (1979).

    Article  CAS  Google Scholar 

  10. D. J. Cutler. Properties of the recirculation model: calculation of the amount of drug in the body from blood concentration data, with application to absorption rate calculations.J. Pharmacokin. Biopharm. 9:225–234 (1981).

    Article  CAS  Google Scholar 

  11. P. Veng-Pedersen. Pharmacokinetic analyses by linear system approach I: Cimetidine bioavailability and second peak phenomena.J. Pharm. Sci. 70:32–38 (1981).

    Article  CAS  PubMed  Google Scholar 

  12. P. Veng-Pedersen. Model independent method of analyzing input in linear pharmacokinetic systems having a polyexponential impulse response. I. Theoretical analysis.J. Pharm. Sci. 69:298–304 (1980).

    Article  CAS  Google Scholar 

  13. P. Veng-Pedersen. Model independent method of analyzing input in linear pharmacokinetic systems having a polyexponential impulse response. II. Numerical evaluation.J. Pharm. Sci. 69:305–311 (1980).

    Article  CAS  Google Scholar 

  14. P. Veng-Pedersen. Novel deconvolution method for linear pharmacokinetic systems with polyexponential impulse response.J. Pharm. Sci. 69:312–317 (1980).

    Article  CAS  Google Scholar 

  15. P. Veng-Pedersen. An algorithm and computer program for deconvolution in linear pharmacokinetics.J. Pharmacokin. Biopharm. 8:463–481 (1980).

    Article  CAS  Google Scholar 

  16. W. R. Gillespie and P. Veng-Pedersen. A polyexponential deconvolution method. Evaluation of “gastrointestinal bioavailability” and meanin vivo dissolution time of some ibuprofen dosage forms.J. Pharmacokin. Biopharm. 13:289–307 (1985).

    Article  CAS  Google Scholar 

  17. W. R. Gillespie and P. Veng-Pedersen. Gastrointestinal bioavailability: determination ofin vivo release profiles of solid oral dosage forms by deconvolution.Biopharm. Drug Dispos. 6:351–355 (1985).

    Article  CAS  PubMed  Google Scholar 

  18. P. Veng-Pedersen and W. R. Gillespie. A note on appropriate constraints on the initial input response when applying deconvolution.J. Pharmacokin. Biopharm. 14:441–447 (1986).

    Article  CAS  Google Scholar 

  19. D. Vaughan and M. Dennis. Mathematical basis of point-area deconvolution method for determiningin vivo input functions.J. Pharm. Sci. 67:663–665 (1978).

    Article  CAS  PubMed  Google Scholar 

  20. P. Veng-Pedersen and L. Suarez. Novel method of calculating the absolute bioavailability in nonlinear pharmacokinetics.J. Pharm. Sci. 74:90–94 (1983).

    Article  Google Scholar 

  21. P. Veng-Pedersen. Drug absorption evaluation in presence of changes in clearance. An algorithm and computer program for deconvolution with exact clearance correction.Biopharm. Drug Dispos. 8:185–203 (1987).

    Article  CAS  PubMed  Google Scholar 

  22. D. Cutler. Numerical deconvolution by least squares: use of prescribed functions.J. Pharmacokin. Biopharm. 6:227–241 (1978).

    Article  CAS  Google Scholar 

  23. D. Cutler. Numerical deconvolution by least squares: use of polynomials to represent the input function.J. Pharmacokin. Biopharm. 6:243–263 (1978).

    Article  CAS  Google Scholar 

  24. P. Veng-Pedersen. A nonlinear system approach for analyzing drug disposition.IEEE Trans. Biomed. Eng. 30:541 (1983).

    Google Scholar 

  25. P. Veng-Pedersen. Model independent method of predicting peak, trough and mean steady state levels in multiple i.v. bolus dosing in nonlinear pharmacokinetics.J. Pharm. Sci. 72:1098–1102 (1984).

    Article  Google Scholar 

  26. P. Veng-Pedersen. Model independent steady state plasma level predictions in autonomic nonlinear pharmacokinetics I. Derivation and theoretical analysis.J. Pharm. Sci. 73:761–765 (1984).

    Article  CAS  PubMed  Google Scholar 

  27. S. Hwang and K. Kwan. Further considerations on model-independent bioavailability estimation.J. Pharm. Sci. 69:77–80 (1980).

    Article  CAS  PubMed  Google Scholar 

  28. P. Veng-Pedersen and R. Miller. Deconvolution at steady state: Determination of gastrointestinal bioavailability of sustained release theophylline.Clin. Pharmac. Toxicol. 25:233–237 (1987).

    CAS  Google Scholar 

  29. P. Veng-Pedersen and R. Miller. Relative deconvolution. An explicit method for bioavailability comparison not requiring intravenous administration.Clin. Pharmac. Toxicol. 25:10–14 (1987).

    CAS  Google Scholar 

  30. C. Waterhouse and J. Keilson. Transfer times across the human body.Bull. Math. Biophys. 34:33–44 (1972).

    Article  CAS  PubMed  Google Scholar 

  31. K. Yamaoka, T. Nakagawa, and T. Uno. Statistical moments in pharmacokinetics.J. Pharmacokin. Biopharm. 6:547–558 (1978).

    Article  CAS  Google Scholar 

  32. D. Cutler. Theory of mean absorption time, an adjunct to conventional bioavailability studies.J. Pharm. Pharmacol. 30:476–478 (1978).

    Article  CAS  PubMed  Google Scholar 

  33. M. Weiss. Residence time and accumulation of drugs in the body.Int. J. Clin. Pharmacol. 19:82–85 (1981).

    CAS  Google Scholar 

  34. M. Weiss. Moments of physiological transit time distributions and the time course of drug disposition in the body.J. Math. Biol. 15:305–318 (1982).

    Article  CAS  PubMed  Google Scholar 

  35. P. Veng-Pedersen and W. Gillespie. The mean residence time of drug in the systemic circulation.J. Pharm. Sci. 74:791–792 (1985).

    Article  CAS  PubMed  Google Scholar 

  36. P. Veng-Pedersen and W. Gillespie. Mean residence time in peripheral tissue: a linear disposition parameter useful for evaluating a drug's tissue distribution.J. Pharmacokin. Biopharm. 12:535–544 (1984).

    Article  CAS  Google Scholar 

  37. P. Veng-Pedersen and W. Gillespie. Single pass mean residence time in peripheral tissues: A distribution parameter intrinsic to the tissue affinity of a drug.J. Pharm. Sci. 75:1119–1126 (1986).

    Article  CAS  PubMed  Google Scholar 

  38. S. Riegelman and P. Collier. The application of statistical moment theory to the evaluation ofin vivo dissolution time and absorption time.J. Pharmacokin. Biopharm. 8:509–534 (1980).

    Article  CAS  Google Scholar 

  39. P. Veng-Pedersen. A simple method for obtaining the mean residence time of metabolites in the body.J. Pharm. Sci. 75:818–821 (1986).

    Article  CAS  PubMed  Google Scholar 

  40. D. Pfeffer. Estimation of mean residence time from data obtained when multiple dosing steady state has been reached.J. Pharm. Sci. 73:854–856 (1984).

    Article  CAS  PubMed  Google Scholar 

  41. V. Smolen. Theoretical and computational basis for drug bioavailability determinations using pharmacologic data I. General considerations and procedures.J. Pharmacokin. Biopharm. 4:337–353 (1976).

    Article  CAS  Google Scholar 

  42. V. Smolen. Theoretical and computational basis for drug bioavailability determinations using pharmacologic data II. Drug input-response relationships.J. Pharmacokin. Biopharm. 4:355–375 (1976).

    Article  CAS  Google Scholar 

  43. V. Smolen, B. D. Turrie, and W. A. Weigand. Drug input optimization: Bioavailability effected time-optimal control of multiple, simultaneous, pharmacological effects and their interrelationship.J. Pharm. Sci. 61:1941–1952 (1972).

    Article  CAS  PubMed  Google Scholar 

  44. D. Cutler. Drug availability to noneliminating tissue and sites of action following an intravenous dose.J. Pharm. Sci. 75:1141–1144 (1986).

    Article  CAS  PubMed  Google Scholar 

  45. P. Veng-Pederen, R. E. Brashear, and M. D. Karol. Theophylline blood-brain barrier transfer kinetics in dogs.J. Pharm. Sci. 72:951–953 (1983).

    Article  Google Scholar 

  46. M. D. Karol, P. Veng-Pedersen, and R. E. Brashear. Diffusion and flow transfer of theophylline across the blood-brain barrier: Pharmacokinetic analysis.J. Pharmacokin. Biopharm. 11:273–287 (1983).

    Article  CAS  Google Scholar 

  47. P. Veng-Pedersen. Pulmonary absorption and excretion of compounds in the gas phase. A theoretical pharmacokinetic and toxicokinetic analysis.J. Pharm. Sci. 73:1136–1141 (1984).

    Article  CAS  PubMed  Google Scholar 

  48. P. Veng-Pedersen, D. J. Paustenbach, G. P. Carlson, and L. Suarez. A linear system approach to analyzing the pharmacokinetics of carbon tetrachloride in the rat following repeated exposures of 8 and 11.5 hr/day.Arch. Toxicol. 60:355–365 (1987).

    Article  CAS  PubMed  Google Scholar 

  49. C. D. Thron. Linearity and superposition in pharmacokinetics.Pharmacol. Rev. 26:3–31 (1974).

    CAS  PubMed  Google Scholar 

  50. H. Knolle. A new estimation method for noncompartmental pharmacokinetic analysis.Biomed. J. 28:31–38 (1986).

    Google Scholar 

  51. J. Wagner and E. Nelson. Percent absorbed time plots derived from blood level and/or urinary excretion data.J. Pharm. Sci. 52:610–611 (1963).

    Article  CAS  PubMed  Google Scholar 

  52. J. Keilson and A. Kester. A circulatory model for human metabolism. Working paper series no. 7724. Department of Statistics, University of Rochester, Minnesota, 1977.

    Google Scholar 

  53. R. G. Gun, S. P. Clifford, and J. Z. Hearon. The logarithmic convexity of the washout function in tracer kinetics.Math. Biosci. 4:1–6 (1969).

    Article  Google Scholar 

  54. J. Z. Hearon. Theorems on linear systems.Ann. N.Y. Acad. Sci. 108:36–68 (1963).

    Article  CAS  PubMed  Google Scholar 

  55. P. Veng-Pedersen and W. Gillespie. The determination of mean residence time using statistical moments: it is correct.J. Pharmacokin. Biopharm. 13:549–554 (1985).

    Article  Google Scholar 

  56. T. A. Shepard, R. H. Reuning, and L. J. Aarons. Interpretation of area under the curve measurements for drugs subject to enterohepatic cycling.J. Pharm. Sci. 74:227–228 (1985).

    Article  CAS  PubMed  Google Scholar 

  57. J. Loo and S. Riegelman. New method for calculating the intrinsic absorption rate of drugs.J. Pharm. Sci. 57:918–928 (1968).

    Article  CAS  PubMed  Google Scholar 

  58. V. K. Batra, J. D. Haynes, and E. Purich. Noncompartmental determination of the absorption rate.J. Pharm. Sci. 75:1014–1016 (1986).

    Article  CAS  PubMed  Google Scholar 

  59. P. Veng-Pedersen. Curve fitting and modeling in pharmacokinetics and some practical experiences with NONLIN and a new program FUNFIT.J. Pharmacokin. Biopharm. 5:513–531 (1977).

    Article  Google Scholar 

  60. P. Veng-Pedersen and R. Miller. Pharmacokinetics and bioavailability of cimitidine in man.J. Pharm. Sci. 69:394–400 (1980).

    Article  Google Scholar 

  61. P. Veng-Pedersen and W. Gillespie. Theorems and implications of a model independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. III. Peripheral bioavailability and distribution time concepts applied to the evaluation of distribution kinetics.J. Pharmacokin. Biopharm. 15:281–304 (1987).

    Article  CAS  Google Scholar 

  62. W. A. Colburn. Simultaneous pharmacokinetic and pharmacodynamic modeling.J. Pharmacokin. Biopharm. 9:367–388 (1981).

    Article  CAS  Google Scholar 

  63. A. W. Hixon and J. H. Crowell. Dissolution of solid particles.Ind. Eng. Chem. 23:923–928 (1931).

    Article  Google Scholar 

  64. P. Veng-Pedersen and W. Gillespie. Theorems and implications of a model independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. IV. Exact relationship between the terminal log-linear slope parameter beta and drug clearance.J. Pharmacokin. Biopharm. 15:305–325 (1987).

    Article  CAS  Google Scholar 

  65. P. Veng-Pedersen and W. Gillespie. A system approach to pharmacodynamics I: Theoretical framework.J. Pharm. Sci. 77:39–47 (1988).

    Article  CAS  PubMed  Google Scholar 

  66. W. Gillespie, P. Veng-Pedersen, E. J. Antal, and J. P. Phillips. A system approach to pharmacodynamics II. Glyburide pharmacodynamics and estimation of optimal drug delivery.J. Pharm. Sci. 77:48–55 (1988).

    Article  CAS  PubMed  Google Scholar 

  67. P. Veng-Pedersen. Application of linear and nonlinear system analysis in pharmacodynamic research. In P. D. Kroboth, R. B. Smith, and R. P. Juhl (eds.),Pharmacodynamic Research: Current Problems and Potential Solutions, Harvey Whitney Books, Cincinnati, 1987 (in press).

    Google Scholar 

  68. P. G. Coxson, Lumpability and observability of linear system.J. Math. Anal. Appl. 99:435–446 (1984).

    Article  Google Scholar 

  69. P. G. Coxson. Model reduction: Indentifying partitions for structured aggregates.IEEE Trans. Autom. Control AC-305:478–481 (1985).

    Article  Google Scholar 

  70. B. C. Moore. Principal component analysis in linear systems: controllability, observability and model reduction.IEEE Trans. Autom. Control AC-261:17–31 (1981).

    Article  Google Scholar 

  71. P. G. Coxson and K. B. Bischoff. Lumping strategy part I: Introductory techniques and applications of cluster analysis.Ind. Eng. Chem. Res. May (1987).

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Authors and Affiliations

  1. College of Pharmacy, University of Iowa, 52242, Iowa City, Iowa

    Peter Veng-Pedersen

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This work was in part supported by grant no. 1 RO1 DA04083-01 from NIH.

Part II of this article will appear in theJournal of Pharmacokinetics and Biopharmaceutics, Vol. 16, No. 5; commentaries on both parts and a rebuttal by P.V.P. will appear in JPB, Vol. 16, No. 6.

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Veng-Pedersen, P. Linear and nonlinear system approaches in pharmacokinetics: How much do they have to offer? I. General considerations. Journal of Pharmacokinetics and Biopharmaceutics 16, 413–472 (1988). https://doi.org/10.1007/BF01062554

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