Bulletin of Mathematical Biology

, Volume 80, Issue 12, pp 3184–3226 | Cite as

A Continuum Mechanics Model of Enzyme-Based Tissue Degradation in Cancer Therapies

  • Manon Deville
  • Roberto Natalini
  • Clair PoignardEmail author


We propose a mathematical model to describe enzyme-based tissue degradation in cancer therapies. The proposed model combines the poroelastic theory of mixtures with the transport of enzymes or drugs in the extracellular space. The effect of the matrix-degrading enzymes on the tissue composition and its mechanical response are accounted for. Numerical simulations in 1D, 2D and axisymmetric (3D) configurations show how an injection of matrix-degrading enzymes alters the porosity of a biological tissue. We eventually exhibit numerically the main consequences of a matrix-degrading enzyme pretreatment in the framework of chemotherapy: the removal of the diffusive hindrance to the penetration of therapeutic molecules in tumors and the reduction of interstitial fluid pressure which improves transcapillary transport. Both effects are consistent with previous biological observations.


Mathematical biology Poroelasticity ECM degradation Interstitial fluid pressure Drug distribution in tissue 

Mathematics Subject Classification

65M06 65M12 92C37 



The authors thank Professor E. Signori for her advices and fruitful discussions on the experimental features of drug injection in tumor and muscles. M.D. is partly granted by “Université Franco-Italienne,” Project VINCI C2-25. M.D. and C.P. are partly granted by the Plan Cancer DYNAMO (Inserm 9749) and Plan Cancer NUMEP (Inserm 11099). This study has been carried out within the scope of the European Associate Lab EBAM and the Inria Associate Team Num4SEP.


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Team MONC, INRIA Bordeaux-Sud-Ouest, Institut de Mathématiques de Bordeaux, CNRS UMR 5251Université de BordeauxTalence CedexFrance
  2. 2.Istituto per le Applicazioni del Calcolo “M. Picone”Consiglio Nazionale delle RicercheRomeItaly

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