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UID:1787@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20170530T110000
DTEND;TZID=Europe/Paris:20170530T120000
DTSTAMP:20170515T090000Z
URL:https://www.i2m.univ-amu.fr/evenements/free-boundary-problem-for-cance
 r-cell-protrusion-formation-mathematical-model-and-numerical-aspects-for-r
 esolution/
SUMMARY: (...): Free boundary problem for cancer cell protrusion formation.
  Mathematical model and numerical aspects for resolution.
DESCRIPTION:: Metastatic cells are cancer cells that leave a primary tumor.
  They are able to invade sub-epithelial basement membranes and then to mig
 rate through the healthy tissue towards the blood network or lymphatic sys
 tem before invading the rest of the body and creating metastases. Numerous
  biological phenomena are involved inside the cell and they are strongly c
 oupled to microenvironmental processes via the cell membrane. They lead to
  protrusion formation which are the early stages of invasion and direction
 al migration\, depending on though the protrusion is localized and proteol
 ytic (invadopodia) or wider and non-proteolytic (pseudopodia).For both inv
 adopodia and pseudopodia\, the protrusion formation at the cellular level 
 can be mathematically described thanks to a free-boundary model based on P
 DEs. In our model\, an interface accounts for the cell membrane\, which is
  the main area of interest. This interface is between two harmonic phases.
  One phase stands for the outer phenomena: in the case of invadopodia\, it
  accounts for the ligands which are created if some cellular MT1-MMP enzym
 es are embedded in the membrane and degrade the extracellular matrix. In t
 he case of pseudopodia\, the outer phase is a chemotactic signal which is 
 diffused by a distant blood network or immune cells. In both cases\, the o
 uter phase is given with a Neumann boundary condition on the interface and
  provides the data of the Dirichlet boundary condition for the inner phase
 . The inner phase accounts for a cytoplasmic signal\, which is triggered b
 y the binding of outer ligands to receptors at the cell membrane. This sig
 nal is a simplification to describe the internal signalling pathways that 
 lead to actin polymerization. The force exerted by the actin filaments on 
 the membrane results in the protrusion formation. The interface velocity i
 s then given as the gradient of the inner phase.The positive feedback loop
  between inner and outer phases results in a strong mathematical coupling.
  From the numerical point of view\, the coupling and successive derivation
 s at each time step may result in nonconsistent solutions. The main focus 
 of the presentation is to give the hints for building suitable numerical m
 ethods\, which make it possible to overcome the issue thanks to the use of
  superconvergence properties. These methods are based on finite difference
 s for solving the protrusion formation problem on Cartesian grid. A level 
 set function is used to implicitly describe the interface in the usual Eul
 erian formalism. The core of the methods is the stabilization of the stand
 ard Ghost Fluid Method (Fedkiw et al.\,1999)\, the use of a specific veloc
 ity extension\, and linear\, quadratic or cubic extrapolations of the ghos
 t values. They result in different numerical schemes with different superc
 onvergent behaviors. Hence\, depending on the scheme\, the solutions are e
 ither first order or second order accurate. Finally\, the cubic method eve
 n leads to a second order accuracy of the interface curvature\, which make
 s it possible to consider using interface regularization techniques to mod
 el the subsequent stages of cell migration. The presentation will be illus
 trated by convergence tests and simulation results showing the formation o
 f membrane protrusions.http://www.math.u-bordeaux.fr/imb/fiche-personnelle
 ?uid=ogallina
CATEGORIES:Séminaire,Analyse Appliquée
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