Skip to main content
Log in

A non-markovian model for calcium kinetics in the body

  • Published:
Journal of Pharmacokinetics and Biopharmaceutics Aims and scope Submit manuscript

Abstract

We present a new generalized compartmental model for calcium kinetics as measured by tracer concentration in blood plasma. The parameter measuring incorporation of calcium in bone discriminates between different levels of physical development in female teenagers and between teenagers and adults.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K. Godfrey.Compartmental Models and their Applications, Academic Press. New York, 1983.

    Google Scholar 

  2. M. E. Wise. Negative power functions of time in pharmacokinetics and their implications.J. Pharmacokin. Biopharm 13:309–346 (1985).

    Article  CAS  Google Scholar 

  3. J. H. Marshall. Calcium pools and the power function. In Per-E. E. Bergner and C. C. Lushbaugh (eds.),Compartments, Pools and Spaces in Medical Physiology, Vol. 11, 1967, pp. 451–468.

  4. M. Weiss. Modeling of initial distribution of drugs following intravenous bolus injection.Eur. J. Clin. Pharmacol. 23:121–126 (1983).

    Article  Google Scholar 

  5. J. Reeve, R. Wootton, and R. Hesp. A new method for calculating the accretion rate of bone calcium and some observations on the suitability of strontium-85 as a tracer for bone calcium.Calcif. Tiss. Res. 20:121–135 (1976).

    Article  CAS  Google Scholar 

  6. R. E. Goans, S. A. Abrams, N. E. Vieira, J. C. Marini, M. D. Perez, and A. L. Yergey. A three hour measurement to evaluate bone calcium turnover.Bone 16:33–38 (1995).

    Article  CAS  PubMed  Google Scholar 

  7. R. M. Neer, M. Berman, L. Fisher, and L. E. Rosenberg. Multicompartmental analysis of calcium kinetics in normal adult males.J. Clin. Invest. 41:1364–1379 (1967).

    Article  Google Scholar 

  8. E. B. Reeve and H. R. Bailey. Mathematical models describing the distribution ofI 131 in man.J. Lab. Clin. Med. 60:923–943 (1962).

    CAS  PubMed  Google Scholar 

  9. A. H. Marcus. Power laws in compartmental models. I. A unified stochastic model.Math. Biosci. 23:337–350 (1975).

    Article  Google Scholar 

  10. A. H. Marcus and A. Becker. Power laws in compartmental models. II. Numerical evaluation of semi-Markov models.Math. Biosci. 35:27–45 (1977).

    Article  Google Scholar 

  11. A. H. Marcus and A. Becker. Alkaline earth metabolism: The ICRP model reformulated as a semi-Markov model.Health Physics 38:825–832. (1980).

    Article  CAS  PubMed  Google Scholar 

  12. W. R. Gillespie. Generalized pharmacokinetic modelling for drugs with nonlinear binding. 1. Theoretical framework.J. Pharmacokin. Biopharm. 21:99–124 (1993).

    Article  CAS  Google Scholar 

  13. G. H. Weiss. On a generalized transport equation for chromatographic systems. In J. Klafter, R. J. Rubin, and M. F. Shlesinger (eds.),Transport and Relaxation in Random Materials, World Scientific, Singapore, 1986, pp. 394–406.

    Google Scholar 

  14. M. Gitterman and G. H. Weiss, Generalized theory of the kinetics of tracers in biological systems.J. Math. Biol. 56:171–186 (1994).

    Article  CAS  Google Scholar 

  15. J. H. Matis and T. E. Wehrly. Generalized stochastic compartmental models with Erlang transit times.J. Pharmacokin, Biopharm.18:589–607 (1990).

    Article  CAS  Google Scholar 

  16. S. A. Abrams. Pubertal changes in calcium kinetics in girls assessed using42Ca.Pediatr. Res. 34:455–459 (1993).

    Article  CAS  PubMed  Google Scholar 

  17. J. M. Tanner.Growth at Adolescence, 2nd ed., Blackwell, Oxford, 1962.

    Google Scholar 

  18. F. Bronner and W. D. Stein. Modulation of bone calcium-binding sites regulates plasma calcium: an hypothesis.Calcif. Tissue Int. 50:483–492 (1992).

    Article  CAS  PubMed  Google Scholar 

  19. A. Jung, P. Bartholdi, B. Mermillod, J. Reeve, and R. Neer. Critical analysis of methods for analyzing human calcium kinetics.J. Theoret. Biol. 73:131–57 (1978).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weiss, G.H., Goans, R.E., Gitterman, M. et al. A non-markovian model for calcium kinetics in the body. Journal of Pharmacokinetics and Biopharmaceutics 22, 367–379 (1994). https://doi.org/10.1007/BF02353861

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02353861

Keywords

Navigation