Fractional dynamics pharmacokinetics-pharmacodynamic models.
While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics-pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics.
Verotta
Davide
D
Department of Bioengineering and Therapeutic Sciences, University of California, Box 0912, San Francisco, CA, USA. davide.verotta@ucsf.edu
D004341:Drug Evaluation / Q000379:methods*; D008954:Models, Biological; D008962:Models, Theoretical
Crit Rev Biomed Eng. 2004;32(2):105-93
15373276
Biometrics. 1990 Sep;46(3):673-87
2242409
Farmaco Sci. 1968 Oct;23(10):907-18
5712792
J Pharmacokinet Pharmacodyn. 2005 Aug;32(3-4):501-20
16320102
J Pharmacokinet Biopharm. 1993 Aug;21(4):457-78
8133465
Biophys J. 1995 Jan;68(1):46-53
7711266
Drug Metab Dispos. 2009 Feb;37(2):386-90
19022942
J Pharmacokinet Pharmacodyn. 2002 Aug;29(4):383-402
12518710
J Pharmacokinet Pharmacodyn. 2006 Jun;33(3):227-79
16404503
Crit Rev Biomed Eng. 2004;32(3-4):195-377
15651636
Am J Physiol. 1990 Apr;258(4 Pt 1):E727-36
2333964
J Pharmacokinet Pharmacodyn. 2010 Apr;37(2):209-15; discussion 217-20
20405313
J Pharmacokinet Pharmacodyn. 2009 Apr;36(2):165-78
19340400
J Pharmacokinet Pharmacodyn. 2010 Apr;37(2):119-34
20072802