A study on discrete and discrete fractional pharmacokinetics-pharmacodynamics models for tumor growth and anti-cancer effects

Computational and Mathematical Biophysics

Nguyen Ngoc¹  Atıcı Ferhan M.¹  Zhoroev Tilekbek¹  Koch Gilbert²  Atıcı Mustafa³ 

[1] Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101-3576 USA;Pediatric Clinical Pharmacology, University Children’s Hospital, Basel, Switzerland;School of Engineering and Applied Sciences, Western Kentucky University, Bowling Green, Kentucky 42101-3576 USA;

关键词: discrete fractional calculus;    parameter estimations;    data fitting;    sensitivity analysis;    markov chain monte carlo;    random walk metropolis;    delayed rejection adaptive metropolis;    39a12;    34a25;    26a33;    62g05;    65c05;    65c20;   

DOI  :  10.1515/cmb-2019-0002

来源: DOAJ

【 摘 要 】

We study the discrete and discrete fractional representation of a pharmacokinetics - pharmacodynamics (PK-PD) model describing tumor growth and anti-cancer effects in continuous time considering a time scale hℕ0h$h\mathbb{N}_0^h$, where h > 0. Since the measurements of the tumor volume in mice were taken daily, we consider h = 1 and obtain the model in discrete time (i.e. daily). We then continue with fractionalizing the discrete nabla operator to obtain the model as a system of nabla fractional difference equations. The nabla fractional difference operator is considered in the sense of Riemann-Liouville definition of the fractional derivative. In order to solve the fractional discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. For the data fitting purpose, we use a new developed method which is known as an improved version of the partial sum method to estimate the parameters for discrete and discrete fractional models. Sensitivity analysis is conducted to incorporate uncertainty/noise into the model. We employ both frequentist approach and Bayesian method to construct 90 percent confidence intervals for the parameters. Lastly, for the purpose of practicality, we test the discrete models for their efficiency and illustrate their current limitations for application.

【 授权许可】

Unknown