Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A new method for assessment of drug disposition in muscle: Application of statistical moment theory to local perfusion systems


A new experimental system is used to determine exact information concerning local drug disposition. Rabbit hind leg is perfused in situusing a single-pass technique, and outflow curves of drugs are analyzed using statistical moment theory. By the introduction of Chromatographic concepts and the application of the well-stirred model to the local perfusion system, physiologically and/or physicochemically meaningful parameters are derived from the first three moments. Moreover, in the assessment, drug disposition is divided into elimination and distribution. The elimination process is also evaluated with respect to rate and extent. This system is used to elucidate the disposition characteristics of mitomycin C and its lipophilic derivative nonyloxycarbonyl mitomycin C.

This is a preview of subscription content, log in to check access.


  1. 1.

    R. L. Juliano (ed.).Drug Delivery System, Oxford University Press, New York, 1980.

  2. 2.

    G. Gregoriadis. Targeting of drugs.Nature 265:407–411 (1977).

  3. 3.

    M. Hashida, S. Muranishi, H. Sezaki, N. Tanigawa, K. Satomura, and Y. Hikasa. Increased lymphatic delivery of bleomycin by microsphere in oil emulsion and its effect on lymph node metastasis.Int. J. Pharm. 2:245–256 (1979).

  4. 4.

    T. Yoshioka, M. Hashida, S. Muranishi, and H. Sezaki. Specific delivery of mitomycin C to the liver, spleen, and lung; nano- and microspherical carriers of gelatin.Int. J. Pharm. 8:131–141 (1981).

  5. 5.

    Y. Takakura, S. Matsumoto, M. Hashida, and H. Sezaki. Enhanced lymphatic delivery of mitomycin C conjugated with dextran.Cancer Res. 44:2505–2510 (1984).

  6. 6.

    M. Hashida, A. Kato, Y. Takakura, and H. Sezaki. Disposition and pharmacokinetics of a polymeric prodrug of mitomycin C, mitomycin C-dextran conjugate, in the rat.Drug Metab. Dispos. 12:492–499 (1984).

  7. 7.

    H. Sasaki, E. Muaki, M. Hashida, T. Kimura, and H. Sezaki. Development of lipophilic prodrugs of mitomycin C.I. Synthesis and antitumor activity of la-N-substituted derivatives with aromatic pro-moiety.Int. J. Pharm. 15:49–59 (1983).

  8. 8.

    H. Sasaki, M. Fukumoto, M. Hashida, T. Kimura, and H. Sezaki. Development of lipophilic prodrugs of mitomycin C. III. Physicochemical and biological properties of newly synthesized alkoxycarbonyl derivatives.Chem. Pharm. Bull. 31:4083–4090 (1983).

  9. 9.

    M. Hashida and H. Sezaki. Specific delivery of mitomycin C: Combined use of prodrugs and spherical delivery systems. In: S. S. Davis, L. Illum, J. G. McVie, and E. Tomlinson (eds.),Microspheres and Drug Therapy, Elsevier/North-Holland Biomedical Press, Amsterdam, 1984, Chapter 8.

  10. 10.

    C. T. Klopp, T. C. Alford, J. Bateman, G. N. Berry, and T. Winship. Fractionated intra-arterial cancer; chemotherapy with methyl bis amine hydrochloride; a preliminary report.Ann. Surg. 132:811–832 (1950).

  11. 11.

    O. Creech, Jr., E. T. Krementz, R. F. Ryan, and J. N. Winblad. Chemotherapy of cancer: Regional perfusion utilizing an extracorporeal circuit.Ann. Surg. 148:616–632 (1958).

  12. 12.

    T. Kato, R. Nemoto, H. Mori, M. Takahashi, and Y. Tamakawa. Transcatheter arterial. chemoembolization of renal cell carcinoma with microencapsulated mitomycin C.J. Urol. 125:19–24 (1981).

  13. 13.

    K.B. Bischoff and R.L. Dedrick. Thiopental pharmacokinetics.J. Pharm. Sci. 57:1346–1351 (1968).

  14. 14.

    K.B. Bischoff and R.G. Brown. Drug distribution in mammals.Chem. Eng. Prog. Symp. Ser. 62:32–45 (1968).

  15. 15.

    F.B. Freedman and J.A. Johnson. Equilibrium and kinetic properties of the Evans blue-albumin system.Am. J. Physiol. 216:675–681 (1969).

  16. 16.

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

  17. 17.

    D.P. Vaughan and I. Hope. Applications of a recirculatory stochastic pharmacokinetic model: Limitations of compartmental models.J. Pharmacokin. Biopharm. 7:207–225 (1979).

  18. 18.

    D. M. Himmelblau and K. B. Bischoff.Process Analysis and Simulation: Deterministic System, Wiley, New York, 1968.

  19. 19.

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

  20. 20.

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

  21. 21.

    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).

  22. 22.

    M. Rowland and G. Tucker. Symbols in pharmacokinetics.J. Pharmacokin. Biopharm. 8:497–507 (1980).

  23. 23.

    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).

  24. 24.

    G. W. Robertz, K. B. Larson, and E. E. Spaeth. The interpretation of mean transit time measurements for multiphase tissue systems.J. Theor. Biol. 39:447–475 (1973).

  25. 25.

    K.L. Zierler. Equations for measuring blood flow by external monitoring of radioisotopes.Circ. Res. 16:309–321 (1965).

  26. 26.

    M. Rowland, L. Z. Benet, and G. G. Graham. Clearance concepts in pharamacokinetics.J. Pharmacokin. Biopharm. 1:123–136 (1973).

  27. 27.

    K. S. Pang and M. Rowland. Hepatic clearance of drugs. I. Theoretical considerations of a “well-stirred” model and “parallel tube” model. Influence of hepatic blood flow, plasma and blood cell binding, and the hepatocellular enzymatic activity on hepatic drug clearance.J. Pharmacokin. Biopharm. 5:625–653 (1977).

  28. 28.

    K. Yamaoka and T. Nakagawa. Statistical moments in linear equilibrium chromatography.J. Chromatogr. 93:1–6 (1974).

  29. 29.

    K. Yamaoka and T. Nakagawa. Moment vectors in linear gas chromatography.J. Chromatogr. 100:1–9 (1974).

  30. 30.

    L. R. Snyder and J. J. Kirkland.Introduction to Modern Liquid Chromatography, 2nd ed., Wiley, New York, 1979.

  31. 31.

    R. O. Law. Techniques and applications of extracellular space determination in mammalian tissues.Experientia 38:411–421 (1982).

  32. 32.

    D.L. Yudilevich and G.E. Mann. Unidirectional uptake of substrates at the blood side of secretory epithelia: Stomach, salivary gland, pancreas.Fed. Proc. 41:3045–3053 (1982).

  33. 33.

    C. Trainor and M. Silverman. Transcapillary exchange of molecular weight markers in the postglomerular circulation: Application of a barrier-limited model.Am. J. Physiol. 242:F436-F446 (1982).

  34. 34.

    C.A. Goresky and G.G. Bach. Membrane transport and the hepatic circulation.Ann. N. Y. Acad. Sci. 170:18–47 (1970).

  35. 35.

    M. Weiss and W. Forster. Pharmacokinetic model based on circulatory transport.Eur. J. Clin. Pharmacol. 16:287–293 (1979).

  36. 36.

    K.K. Chan. A simple integrated method for drug and derived metabolite kinetics: An application of the statistical moment theory.Drug Metab. Dispos. 10:474–479 (1982).

  37. 37.

    P. S. Collier. Some considerations on the estimation of steady state apparent volume of distribution and the relationships between volume terms.J. Pharmacokin. Biopharm. 11:93–105 (1983).

  38. 38.

    L. Z. Benet and R. L. Galeazzi. Noncompartmental determination of the steady-state volume of distribution.J. Pharm. Sci. 68:1071–1074 (1979).

  39. 39.

    D. P. Vaughan. Theorems on the apparent volume of distribution of a linear system.J. Pharm. Sci. 71:793–795 (1982).

  40. 40.

    D. P. Ganote and P. W. Lucker. A new mathematical approach to describe transmural gastric potential difference changes (great moments in pharmacodynamics).Arzneim. Forsch. 32:552–556 (1982).

  41. 41.

    D. Brockmeier, D. Vogele, and H. M. von Hattingberg.In vitro-in vivo correlation, a time scaling problem?: Basic techniques for testing equivalence.Arzneim. Forsch. 33:598–601 (1983).

  42. 42.

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

  43. 43.

    J. B. Bassingthwaighte. A concurrent flow model for extraction during transcapillary passage.Circ. Res. 35: 483–503 (1974).

  44. 44.

    C. P. Rose, C. A. Goresky, and G. G. Bach. The capillary and sarcolemmal barriers in the heart: An exploration of labeled water permeability.Circ. Res. 41:515–533 (1977).

  45. 45.

    M. Silverman and C. Trainor.In vivo determination of cellular uptake in the kidney.Fed. Proc. 41:3054–3060 (1982).

  46. 46.

    J. B. Bassingthwaighte. Cellular influx and efflux in the heart.Fed. Proc. 41:3040–3044 (1982).

  47. 47.

    J.R. Gillette. Factors affecting drug metabolism.Ann. N. Y. Acad. Sci. 179:43–66 (1971).

  48. 48.

    G. T. Tucker. Empirical vs. compartmental vs. physiological models. In: D. D. Breimer and P. S. Speiser (eds.),Topics in Pharmaceutical Sciences, Elsevier/North-Holland Biomedical Press, Amsterdam, 1981.

  49. 49.

    H. S. G. Chen, and J. F. Gross. Estimation of tissue-to-plasma partition coefficients used in physiological pharmacokinetic models.J. Pharmacokin. Biopharm. 7:117–125 (1979).

  50. 50.

    H. M. von Hattingberg and D. Brockmeier. The pharmacokinetic basis of optimal antibiotic dosage.Eur. J. Clin. Study Treat. Infect. 8:S21-S24 (1980).

  51. 51.

    M. Weiss. Hemodynamic influences upon the variance of disposition residence time distribution of drugs.J. Pharmacokin. Biopharm. 11:63–75 (1983).

  52. 52.

    R. L. Schoenfeld. Linear network theory and tracer analysis.Ann. N. Y. Acad. Sci. 108:69–91 (1963).

  53. 53.

    A. Rescigno, and G. Segre.Drug and Tracer Kinetics. Blaisdell, Waltham, 1966.

Download references

Author information

Correspondence to Hitoshi Sezaki.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kakutani, T., Yamaoka, K., Hashida, M. et al. A new method for assessment of drug disposition in muscle: Application of statistical moment theory to local perfusion systems. Journal of Pharmacokinetics and Biopharmaceutics 13, 609–631 (1985).

Download citation

Key words

  • local perfusion system
  • statistical moment theory
  • drug disposition
  • rabbit muscle tissue
  • mitomycin C
  • lipophilic derivative
  • tissue distribution ratio
  • mean elimination time
  • dispersion ratio