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Mathematical and computational models of drug transport in tumours

Groh, C.M.; Hubbard, Matthew E.; Jones, P.F.; Loadman, P.M.; Periasamy, N.; Sleeman, B.D.; Smye, S.W.; Twelves, C.J.; Phillips, R.M.


C.M. Groh

Professor of Computational and Applied Mathematics

P.F. Jones

P.M. Loadman

N. Periasamy

B.D. Sleeman

S.W. Smye

C.J. Twelves

R.M. Phillips


The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and schedule of drug administration, an in silico tool that can predict the drug administration schedule that results in optimal drug delivery to tumours would streamline clinical trial design. This paper investigates the application of mathematical and computational modelling techniques to help improve our understanding of the fundamental mechanisms underlying drug delivery, and compares the performance of a simple model with more complex approaches. Three models of drug transport are developed, all based on the same drug binding model and parametrized by bespoke in vitro experiments. Their predictions, compared for a ‘tumour cord’ geometry, are qualitatively and quantitatively similar. We assess the effect of varying the PK profile of the supplied drug, and the binding affinity of the drug to tumour cells, on the concentration of drug reaching cells and the accumulated exposure of cells to drug at arbitrary distances from a supplying blood vessel. This is a contribution towards developing a useful drug transport modelling tool for informing strategies for the treatment of tumour cells which are ‘pharmacokinetically resistant’ to chemotherapeutic strategies.


Groh, C., Hubbard, M. E., Jones, P., Loadman, P., Periasamy, N., Sleeman, B., …Phillips, R. (2014). Mathematical and computational models of drug transport in tumours. Interface, 11(94), Article 20131173.

Journal Article Type Article
Acceptance Date Feb 20, 2014
Publication Date Mar 12, 2014
Deposit Date Feb 24, 2017
Publicly Available Date Feb 24, 2017
Journal Interface
Electronic ISSN 1742-5662
Publisher The Royal Society
Peer Reviewed Peer Reviewed
Volume 11
Issue 94
Article Number 20131173
Keywords Computational modelling; Mathematical modelling; Drug delivery; Drug transport;
Drug binding; Pharmacokinetic profiles
Public URL
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