Multi-scale modelling of nanoparticle delivery and heat transport in vascularised tumours

Al Sariri, T. and Penta, R. (2022) Multi-scale modelling of nanoparticle delivery and heat transport in vascularised tumours. Mathematical Medicine and Biology, 39(4), pp. 332-367. (doi: 10.1093/imammb/dqac009) (PMID:35862063)

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We focus on modelling of cancer hyperthermia driven by the application of the magnetic field to iron oxide nanoparticles. We assume that the particles are interacting with the tumour environment by extravasating from the vessels into the interstitial space. We start from Darcy’s and Stokes’ problems in the interstitial and fluid vessels compartments. Advection–diffusion of nanoparticles takes place in both compartments (as well as uptake in the tumour interstitium), and a heat source proportional to the concentration of nanoparticles drives heat diffusion and convection in the system. The system under consideration is intrinsically multi-scale. The distance between adjacent vessels (the micro-scale) is much smaller than the average tumour size (the macro-scale). We then apply the asymptotic homogenisation technique to retain the influence of the micro-structure on the tissue scale distribution of heat and particles. We derive a new system of homogenised partial differential equations (PDEs) describing blood transport, delivery of nanoparticles and heat transport. The new model comprises a double Darcy’s law, coupled with two double advection–diffusion–reaction systems of PDEs describing fluid, particles and heat transport and mass, drug and heat exchange. The role of the micro-structure is encoded in the coefficients of the model, which are to be computed solving appropriate periodic problems. We show that the heat distribution is impaired by increasing vessels’ tortuosity and that regularization of the micro-vessels can produce a significant increase (1–2 degrees) in the maximum temperature. We quantify the impact of modifying the properties of the magnetic field depending on the vessels’ tortuosity.

Item Type:Articles
Additional Information:T.A. acknowledges the Ministry of higher education and innovation of Oman for the scholarship that supports this research. R.P. is partially supported by the Engineering and Physical Sciences Research Council grants EP/S030875/1 and EP/T017899/1 and conducted the research according to the inspiring scientific principles of the national Italian mathematics association Indam (‘Istituto nazionale di Alta Matematica’).
Glasgow Author(s) Enlighten ID:Al Sariri, Tahani Mohammed Sulaiman and Penta, Dr Raimondo
Authors: Al Sariri, T., and Penta, R.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematical Medicine and Biology
Publisher:Oxford University Press
ISSN (Online):1477-8602
Published Online:21 July 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Mathematical Medicine and Biology 39(4) 332-367
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
303232EPSRC Centre for Multiscale soft tissue mechanics with MIT and POLIMI (SofTMech-MP)Xiaoyu LuoEngineering and Physical Sciences Research Council (EPSRC)EP/S030875/1M&S - Mathematics
308255The SofTMech Statistical Emulation and Translation HubDirk HusmeierEngineering and Physical Sciences Research Council (EPSRC)EP/T017899/1M&S - Statistics