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A Poroelasticity Theory Approach to Study the Mechanisms Leading to Elevated Interstitial Fluid Pressure in Solid Tumours

  • Special Issue: Mathematical Oncology
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Abstract

Although the mechanisms responsible for elevated interstitial fluid pressure (IFP) in tumours remain obscure, it seems clear that high IFP represents a barrier to drug delivery (since the resulting adverse pressure gradient implies a reduction in the driving force for transvascular exchange of both fluid and macromolecules). R. Jain and co-workers studied this problem, and although the conclusions drawn from their idealized mathematical models offered useful insights into the causes of elevated IFP, they by no means gave a definitive explanation for this phenomenon. In this paper, we use poroelasticity theory to also develop a macroscopic mathematical model to describe the time evolution of a solid tumour, but focus our attention on the mechanisms responsible for the rise of the IFP, from that for a healthy interstitium to that measured in malignant tumours. In particular, we discuss a number of possible time scales suggested by our mathematical model and propose a tumour-dependent time scale that leads to results in agreement with experimental observations. We apply our mathematical model to simulate the effect of “vascular normalization” (as proposed by Jain in Nat Med 7:987–989, 2001) on the IFP profile and discuss and contrast our conclusions with those of previous work in the literature.

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Acknowledgements

SS is grateful to NSERC for support of this research through a Discovery Grant.

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Authors and Affiliations

  1. Mathematical and Computational Sciences, University of Toronto, Mississauga, ON, L5M 5G9, Canada

    Andrijana Burazin

  2. Engineering Science and Mechanics, Pennsylvania State University, University Park, PA, 16802, USA

    Corina S. Drapaca

  3. Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Giuseppe Tenti & Siv Sivaloganathan

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  1. Andrijana Burazin
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  2. Corina S. Drapaca
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  3. Giuseppe Tenti
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  4. Siv Sivaloganathan
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Correspondence to Siv Sivaloganathan.

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Burazin, A., Drapaca, C.S., Tenti, G. et al. A Poroelasticity Theory Approach to Study the Mechanisms Leading to Elevated Interstitial Fluid Pressure in Solid Tumours. Bull Math Biol 80, 1172–1194 (2018). https://doi.org/10.1007/s11538-017-0383-1

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