Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

In vitro characterisation and expansion of human regulatory T cells for their in vivo application in the induction of tolerance in haematopoietic stem cell and solid organ transplantation

Solid organ transplantation (SOT) is considered the treatment of choice for many end-stage organ diseases. Thus far, short term results are excellent, with patient survival rates greater than 90% one year post-surgery, but there are several problems with the long term acceptance and use of immunosuppressive drugs. Hematopoietic Stem Cells Transplantation (HSCT) concerns the infusion of haematopoietic stem cells to re-establish acquired and congenital disorders of the hematopoietic system. The main side effect is the Graft versus Host Disease (GvHD) where donor T cells can cause pathology involving the damage of host tissues. Patients undergoing acute or chronic GvHD receive immunosuppressive regimen that is responsible for several side effects. The use of immunosuppressive drugs in the setting of SOT and GvHD has markedly reduced the incidence of acute rejection and the tissue damage in GvHD however, the numerous adverse side effects observed boost the development of alternative strategies to improve the long-term outcome. To this effect, the use of CD4+CD25+FOXP3+ regulatory T cells (Treg) as a cellular therapy is an attractive approach for autoimmunity disease, GvHD and limiting immune responses to allograft after transplantation. Treg have a pivotal role in maintaining peripheral immunological tolerance, by preventing autoimmunity and chronic inflammation. Results of my thesis provide the characterization and cell processing of Tregs from healthy controls and patients in waiting list for liver transplantation, followed by the development of an efficient expansion-protocol and the investigation of the impact of the main immunosuppressive drugs on viability, proliferative capacity and function of expanded cells after expansion. The conclusion is that ex vivo expansion is necessary to infuse a high Treg dose and although many other factors in vivo can contribute to the success of Treg therapy, the infusion of Tregs during the administration of the highest dose of immunosuppressants should be carefully considered.