# Team : reo

## Section: New Results

### Blood flows

Participants : Adel Blouza, Laurent Dumas, Jean-Frédéric Gerbeau, Marc Thiriet.

#### Fluid-structure interaction

In [18], we have proposed a practical method to apply our new fluid-structure algorithms on geometries coming from medical imaging, in particular cerebral aneurisms and carotid bifurcation. Figure 2 shows for example the propagation of a pressure wave in an aneurism.

#### Stent optimization

In order to reduce the effects of atherosceloris, a vascular disesase that partially obturate an artery, the deployment of a device called stent by a catheter technique is now commonly used. Unfortunately, a re-stenosis is observed, in some cases, few mounths after the operation. In order to reduce this failure, the optimization of the shape of the stent is investigated on two aspects: structural and fluid. On the first aspect, the minimization can deal with the mass, the mechanical stresses and/or the dissipation energy with respect to the geometry of the structure namely its chart and its thickness. On the second aspect, the minimization can deal with the flow recirculation length appearing or the regions of low wall shear stress with respect to the geometry of the stent.

**Work in progress**: the optimization of a simplified 2D stent is under
investigation, first from an hemodynamic viewpoint. The total vorticity of
a pulsatile incompressible viscous flow has been minimized with respect
to three parameters defining the stent: the strut height, the strut
pitch and the strut width. The optimization method that has been chosen
is the genetic algorithm method, in order to obtain a global optimum and
to avoid gradient computations.

**Future work**: the influence of the stent structure will be
incorporated in the actual fluid simulation. Then a 3D fluid
optimization will be investigated. In this case, due to the higher cost
of each computation, a hybrid optimization method that has already been
described in [1] will be used: the general idea is to couple a genetic
algorithm with a deterministic descent method which will explore more
rapidly the local minima of the functional. In order to maintain the
stochastic aspect of the GA and for computational time reasons, the
descent method is only and eventually applied at the best current
element of the population after each generation.

#### Collapsed tube flow

The laminar steady flow of incompressible Newtonian fluid has been studied in rigid pipes with cross configuration of a collapsed tube to determine both the entry length and the wall shear stress (WSS). Entry length, axial and cross variations in WSS are indeed computed to design flow chambers in order to explore the mechanotransduction function of the endothelial cells. The cross section shapes have been defined from the collapse of an infinitely long elastic tube subjected to an uniform transmural pressure. Cross variation in wall curvature, which are also observed in collapsed tubes due to the transverse bending of the wall, induces transverse gradient of the WSS axial component. The cross-section configuration is not aimed at mimicing actual collapsed veins but creates at the cell scale a shear stress which generates two forces applied at the cell inertia center: (i) a shear force which stretches the cell in the streamwize direction and (ii) a shear torque which twists the cell perpendicularly to the cell plane, induced by the WSS transverse gradient. Five characteristic collapsed configurations, from the unstressed down to the point-contact states, with a finite and infinite curvature radius at the contact point, are investigated. The numerical tests are performed with the same value of the volume flow rate whatever the tube configuration. The entry length was estimated by introducing three indices: (i) the first is defined by using the axial fluid velocity, (ii) the second by using the wall shear stress and (iii) the third by the pressure field, the pressure decease being non-linear in the entrance region. The results are analyzed in order to exhibit the mechanical environment of cultured endothelial cells in the flow chamber for which the test conditions will be well-defined.

#### Carotid bifurcation simulations

Blood flow simulations have been performed in a carotid artery network (Fig. 3). Mesh influence on the numerical results have been shown, using the same YAMS tool but different control parmeters, especially influences induced by the mesh of the carotid stem. Such a network will be very useful to compar full 3D detailed models with coupled models of shorter 3D segments and simplified 1D-0D model of vessel parts at distance form branching sites.