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Accueil > Interactions > Interdisciplinaires > Health Care and Biology : modeling and simulation blood rheology

Health Care and Biology : modeling and simulation blood rheology    fr

The team "Partial Differential Equations and Control Theory" has developed collaborations in these three areas:
- the simulation of blood flows in the human vascular system,
- the numerical rheology of the blood and
- the mass transfer from the vascular system (through the blood) to the surrounding tissues.

These different collaborations share many similarities and common toolchains and software are being setup.

Blood Rheology

- Research team : partial differential equations and control theory
- Contact : Christophe Prud’homme

Cytosquelette d'une globule rouge Unlike ordinary liquids and elastic solids, complex fluids exhibit several puzzling behaviours that critically depend on the underlying structures that compose the fluids. Indeed, many complex fluids are made of microscopic entities (such as rigid or soft particles, biological cells, macromolecules etc...) which are suspended in a liquid, and whose individual and collective behaviours strongly impact on the overall rheological properties of the fluid at the global scale. It is this feedback from the microscale to the macroscale that confers to complex fluids nontrivial behaviours that continue to pose a formidable challenge to theoretical modelling. Typical examples of complex fluids are suspensions (rigid particles suspended in a Newtonian fluid), emulsions (droplets suspended in a Newtonian fluid), blood (red blood cells suspended in the plasma), and so on. Complex fluids are the rule in the industrial and biological worlds, conferring thus to this topic an important interest in various domains ranging from the fundamental to the technological level.
Forme biconcave d'une globule rouge A significant challenge in complex fluids lies in the understanding of the fluid/structure interaction at the individual level and the spatio-temporal organisation of the entities (i.e. their collective behaviours, like jamming, formation of bands...) composing the complex fluid.

Images : Cytosquelette d’une globule rouge et forme biconcave d’une globule rouge

Over the last few years we have been developing numerical methods, models and a software platform (Feel++) for the numerical simulation of blood rheology in the vascular system : The aim of this project is to simulate suspensions of a large number of vesicles --- acting as models for blood cells --- in moving domains. It has indeed been shown that there are several similarities between vesicles and red blood cells (RBC) particularly from the mechanical point of view. For example, like RBC, vesicles under shear flow exhibit various dynamics : tank treading, tumbling, and vacillating breathing. Within 5 years, we plan to be able to simulate tens of deformable vesicles (RBC) within 3D flows in arteries with moving boundaries on hundreds of processors and within 10 years hundreds of deformable vesicles in 3D flows in arteries with moving boundaries. The scope is to study pulsed blood flow in medium to small arteries. In this context great displacements of the membrane (over 10% of the radius) of arteries coexist together with confinement of blood flow. This work currently build on four ingredients:
- high order discretization methods in space, time and geometry applied to flows in moving domains,
- leveset and fictitious domain methods,
- efficient domain decomposition methods and parallel solver strategies and
- efficient use of high performance computing architectures --- e.g. distributed, parallel and GPU computing.

This work is done in collaboration with physicists in Grenoble (LIPHY) and is funded at the moment by Ministry of High Education and Research, Region Rhone-Alpes (2009-2012) and the ANR project HAMM (2010-2014).

These two images show simulation of pulsed blood flow in an arterie :

Champ de pression exercé par le fluide dans une coupe du domaine où s'écoule le sang

Champ de pression exercé par le fluide dans une coupe du domaine où s’écoule le sang.

Déformation de la paroi artérielle

Déformation de la paroi arterielle.

Dernière mise à jour le 14-12-2011