# Special issue: mathematical pharmacology

Special issue: mathematical pharmacology Journal of Pharmacokinetics and Pharmacodynamics (2018) 45:1 https://doi.org/10.1007/s10928-017-9566-5(0123456789().,-volV)(0123456789().,-volV) EDITORIAL 1 2 Wojciech Krzyzanski J. G. Coen van Hasselt Received: 27 December 2017 / Accepted: 29 December 2017 / Published online: 3 January 2018 Springer Science+Business Media, LLC, part of Springer Nature 2018 Pharmacology as a biomedical science has not yet received estimation of model parameters are introduced in the context the attention of applied mathematicians such as has been of structural identiﬁability analysis. Numerical approaches to the case for the ﬁeld of mathematical biology. In recog- alternative methods of solving ordinary differential equations nition of increasing relevance of mathematical ideas and are represented by the inductive linearization technique. methods in the realm of pharmacology van der Graaf et al. Methods of fractional calculus are explained using examples coined the term Mathematical Pharmacology for the ﬁeld of fractional differential equations. Markov processes and of study that is aimed at using mathematical approaches to stochastic differential equations are applied in mixed effects achieve a better understanding of pharmacological pro- hidden Markov models. Optimal control theory demonstrates cesses [1]. Although examples of tools applicable for utility of calculus of variations. Techniques of model reduc- mathematical pharmacology have been limited to deter- tion such as proper lumping and input response index are ministic dynamical systems, a much broader arsenal of applied to systems pharmacology models. The special issue techniques is available. More importantly, many of these concludes with a review of Boolean networks techniques of methods have been successfully applied in biomedical modeling signaling pathways in complex pharmacological sciences and they continue to attract more users. The systems. Although majority of articles are original research purpose of this special issue of Journal of Pharmacokinetics publications, several contributions to this special issue are and Pharmacodynamics is to increase awareness of mod- written in a format of review. elers of currently applied mathematical techniques and to By no means selection of presented topics is compre- popularize Mathematical Pharmacology as a discipline of hensive, but rather merely representative of a broader spec- mathematical biology. We focused on both the application trum of problems speciﬁc to mathematical pharmacology of mathematical approaches as well as overlap with that can be solved by existing mathematical techniques and advanced statistical methods. To this aim, we invited inspire development of new ones. Examples of methods that experts in their ﬁelds to contribute to this special issue a have not been included are chaotic dynamical systems [2] manuscript that would brieﬂy introduce a mathematical and partial differential equations [3]. We hope that future technique of interest and provide examples of applications issues of Journal of Pharmacokinetics and Pharmacody- to pharmacological problems. namics will contain growing number of contributions falling Mathematical techniques presented in this special issue into the scope of mathematical pharmacology. have been organized according to their level of mathematical Acknowledgements We would like to thank 43 reviewers, particu- complexity rather than therapeutic areas or similarity of larly those of mathematical background, for their constructive com- pharmacological systems they describe. Classical methods of ments which help us to uphold mathematical rigor in all articles of dynamical systems analysis are followed by delay differential this special issue. equations and distributed delay differential equations with examples of bifurcation analysis. Problems arising in References 1. van der Graaf PH, Benson N, Peletier LA (2016) Topics in & Wojciech Krzyzanski mathematical pharmacology. J Dyn Diff Equat 28:1337–1356 wk@buffalo.edu 2. Dokoumetzidis A, Iliadis A, Macheras P (2001) Nonlinear dynamics and chaos theory: concepts and applications relevant Department of Pharmaceutical Sciences, University at to pharmacodynamics. Pharm Res 18(4):415–426 Buffalo, Buffalo, NY, USA 3. Krzyzanski W (2015) Pharmacodynamic models of age-structured Division of Systems Biomedicine and Pharmacology, Leiden cell populations. J Pharmacokinet Pharmacodyn 42:573–589 Academic Centre for Drug Research, Leiden University, Leiden, The Netherlands http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Pharmacokinetics and Pharmacodynamics Springer Journals

# Special issue: mathematical pharmacology

, Volume 45 (1) – Jan 3, 2018
1 page

1 Page

/lp/springer_journal/special-issue-mathematical-pharmacology-E0eaws9rM1
Publisher
Springer Journals
Subject
Biomedicine; Pharmacology/Toxicology; Pharmacy; Veterinary Medicine/Veterinary Science; Biomedical Engineering; Biochemistry, general
ISSN
1567-567X
eISSN
1573-8744
D.O.I.
10.1007/s10928-017-9566-5
Publisher site
See Article on Publisher Site

### Abstract

Journal of Pharmacokinetics and Pharmacodynamics (2018) 45:1 https://doi.org/10.1007/s10928-017-9566-5(0123456789().,-volV)(0123456789().,-volV) EDITORIAL 1 2 Wojciech Krzyzanski J. G. Coen van Hasselt Received: 27 December 2017 / Accepted: 29 December 2017 / Published online: 3 January 2018 Springer Science+Business Media, LLC, part of Springer Nature 2018 Pharmacology as a biomedical science has not yet received estimation of model parameters are introduced in the context the attention of applied mathematicians such as has been of structural identiﬁability analysis. Numerical approaches to the case for the ﬁeld of mathematical biology. In recog- alternative methods of solving ordinary differential equations nition of increasing relevance of mathematical ideas and are represented by the inductive linearization technique. methods in the realm of pharmacology van der Graaf et al. Methods of fractional calculus are explained using examples coined the term Mathematical Pharmacology for the ﬁeld of fractional differential equations. Markov processes and of study that is aimed at using mathematical approaches to stochastic differential equations are applied in mixed effects achieve a better understanding of pharmacological pro- hidden Markov models. Optimal control theory demonstrates cesses [1]. Although examples of tools applicable for utility of calculus of variations. Techniques of model reduc- mathematical pharmacology have been limited to deter- tion such as proper lumping and input response index are ministic dynamical systems, a much broader arsenal of applied to systems pharmacology models. The special issue techniques is available. More importantly, many of these concludes with a review of Boolean networks techniques of methods have been successfully applied in biomedical modeling signaling pathways in complex pharmacological sciences and they continue to attract more users. The systems. Although majority of articles are original research purpose of this special issue of Journal of Pharmacokinetics publications, several contributions to this special issue are and Pharmacodynamics is to increase awareness of mod- written in a format of review. elers of currently applied mathematical techniques and to By no means selection of presented topics is compre- popularize Mathematical Pharmacology as a discipline of hensive, but rather merely representative of a broader spec- mathematical biology. We focused on both the application trum of problems speciﬁc to mathematical pharmacology of mathematical approaches as well as overlap with that can be solved by existing mathematical techniques and advanced statistical methods. To this aim, we invited inspire development of new ones. Examples of methods that experts in their ﬁelds to contribute to this special issue a have not been included are chaotic dynamical systems [2] manuscript that would brieﬂy introduce a mathematical and partial differential equations [3]. We hope that future technique of interest and provide examples of applications issues of Journal of Pharmacokinetics and Pharmacody- to pharmacological problems. namics will contain growing number of contributions falling Mathematical techniques presented in this special issue into the scope of mathematical pharmacology. have been organized according to their level of mathematical Acknowledgements We would like to thank 43 reviewers, particu- complexity rather than therapeutic areas or similarity of larly those of mathematical background, for their constructive com- pharmacological systems they describe. Classical methods of ments which help us to uphold mathematical rigor in all articles of dynamical systems analysis are followed by delay differential this special issue. equations and distributed delay differential equations with examples of bifurcation analysis. Problems arising in References 1. van der Graaf PH, Benson N, Peletier LA (2016) Topics in & Wojciech Krzyzanski mathematical pharmacology. J Dyn Diff Equat 28:1337–1356 wk@buffalo.edu 2. Dokoumetzidis A, Iliadis A, Macheras P (2001) Nonlinear dynamics and chaos theory: concepts and applications relevant Department of Pharmaceutical Sciences, University at to pharmacodynamics. Pharm Res 18(4):415–426 Buffalo, Buffalo, NY, USA 3. Krzyzanski W (2015) Pharmacodynamic models of age-structured Division of Systems Biomedicine and Pharmacology, Leiden cell populations. J Pharmacokinet Pharmacodyn 42:573–589 Academic Centre for Drug Research, Leiden University, Leiden, The Netherlands

### Journal

Journal of Pharmacokinetics and PharmacodynamicsSpringer Journals

Published: Jan 3, 2018

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