We propose in this Note a method of identifying leak zones in a saturated and homogeneous porous domain by solving a Cauchy problem. The method is based on the minimisation of an energy-like error functional procedure developed in 2006 by Andrieux and Baranger.

We consider a computational multiscale framework of a bio-chemo-mechanical model for intimal hyperplasia. With respect to existing models, we investigate the interactions between hemodynamics, cellular dynamics and biochemistry on the development of the pathology. Within the arterial wall, we propose a mathematical model consisting of kinetic differential equations for key vascular cell types, collagen and growth factors. The luminal hemodynamics is modelled with the Navier-Stokes equations. Coupling hypothesis among time and space scales are proposed to build a tractable modelling of such a complex multifactorial and multiscale pathology. A one-dimensional numerical test-case is presented for validation by comparing the results of the framework with experiments at short and long timescales. Our model permits to capture many cellular phenomena which have a central role in the physiopathology of intimal hyperplasia. Results are quantitatively and qualitatively consistent with experimental findings at both short and long timescales.

Abstract. In this work, we aim to identificate leaks at a boundary of homogeneous porous media saturated with fluid. The identification is hold on by solving a Cauchy problem on the Darcy equation with pressure formulation.