# Two-level time-domain decomposition based distributed method for numerical solutions of pharmacokinetic models

Liu, Li, Lai, Choi-Hong, Zhou, Shao-Dan, Xie, Fen and Lu, Rui
(2011)
*Two-level time-domain decomposition based distributed method for numerical solutions of pharmacokinetic models.*
Computers in Biology and Medicine, 41.
pp. 221-227.
ISSN 0010-4825 (online)

## Abstract

In order to predict variations of drug concentration during a given period of time, numerical solutions of pharmacokinetic models need to be obtained efficiently. Analytical solutions of linear pharmacokinetic models are usually obtained using the Laplace transform and inverse Laplace tables. The derivations of solutions to complex nonlinear models are tedious, and such solutions process may be difficult to implement as a robust software code. For nonlinear models, the fourth-order Runge-Kutta (RK4) is the most classical numerical method in obtaining approximate numerical solutions, which is impossible to be implemented in distributed computing environments without much modification. The reason is that numerical solutions obtained by using RK4 can only be computed in sequential time steps. In this paper, time-domain decomposition methods are adapted for nonlinear pharmacokinetic models. The numerical Laplace method of PharmacoKinetic models (ILPK) is implemented to solve pharmacokinetic models with iterative inverse Laplace transform in each time interval. The distributed ILPK algorithm, which is based on a two-level time-domain decomposition concept, is proposed to improve its efficiency. Solutions on the coarser temporal mesh at the top level are obtained one by one, and then those on the finer temporal mesh at the bottom level are calculated concurrently by using those initial solutions that have been obtained at the top level decomposition. Accuracy and efficiency of the proposed algorithm and its distributed equivalent are investigated by using several test models. Results indicate that the ILPK algorithm and its distributed equivalent are good candidates for both linear and nonlinear pharmacokinetic models.

Item Type: | Article |
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Uncontrolled Keywords: | pharmacokinetics, distributed computing, numerical inverseLaplace, runge-kutta |

Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics > QA75 Electronic computers. Computer science Q Science > QH Natural history > QH301 Biology R Medicine > R Medicine (General) |

School / Department / Research Groups: | School of Computing & Mathematical Sciences Faculty of Architecture, Computing & Humanities > School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Department of Mathematical Sciences Faculty of Architecture, Computing & Humanities > School of Computing & Mathematical Sciences > Department of Mathematical Sciences |

Related URLs: | |

Last Modified: | 17 Feb 2012 11:58 |

URI: | http://gala.gre.ac.uk/id/eprint/7535 |

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