## Fluid-poroelastic interface modelling for an implantable medical device: Application to brain tumours treatment

 Titre Fluid-poroelastic interface modelling for an implantable medical device: Application to brain tumours treatment Type de publication Communication Type Communication sans actes dans un congrès Année 2018 Langue Anglais Date du colloque 19-22/06/2018 Titre du colloque 3rd Mathematical Biology Modelling days of Besançon Auteur Rolland, Julien Yves 1, Lozinski, Alexei 1, Calvignac, Brice 2, Gimel, Jean-Christophe 2, Franconi, Florence 2, 3, Lemaire, Laurent 2 Pays France Ville Besançon Résumé en anglais In order to overcome biological barriers and improve the local delivery of drugs for the treatment of solid tumours such as glioblastoma, the use of an innovative medical injection device composed by microneedles array as been proposed by MINT. This work will focus on the mathematical modelling of the drug transport and diffusion in the region of interest. Mathematically, the injection of a drug into the brain can be described by the system of equations comprising the Biot equations - for displacements of the elastic matrix and for the intraporous flow - and the Stokes equations - for fluid flow inside the needle and in the gap between the wall and the poroelastic tissue. These equations are coupled by Biot-Darcy interface conditions and a dynamic contact condition at the triple line defined by the tissue, the fluid and the wall of a needle. We have developed a monolithic scheme using continuous finite elements to discretise both the Biot and Stokes systems. The choice of finite elements space and the implementation of the Biot-Stokes interface conditions allow us to avoid stabilisation terms, unlike other approaches available in the recent literature[1]. The critical difficulty is the triple line treatment. Our modelling assumption is that each point at the edge of the tissue-wall interface is either: • attached to the wall, if the normal component of the force exerted on the wall by the tissue is opposite to the normal outgoing wall, • detached from the wall; in this case, the fluid is assumed to fill the created gap. Numerically, unknowns are represented on two dynamic meshes: One for elastic displacements and pressure in the tissue, the other for the fluid velocity. The former evolves in time by moving the initial mesh nodes, the latter is reconstructed at each time step to allow for geometric evolution of the fluid domain. This system allows us to model the crucial phenomena of “backflow”[2]: Under specific conditions, the triple line may creep up the needle wall, exit the region of interest and thus, would lead to an inefficiency of the locoregional drug delivery in the brain. URL de la notice http://okina.univ-angers.fr/publications/ua17313 Lien vers le document en ligne https://lmb.univ-fcomte.fr/3rd-Mathematical-Biology-Modelling