Numerical simulation of MagnetoHydroDynamics inside cardiovascular and respiratory systems

In the present work, we have studied the influence of the magnetic field, on the fluid dynamic properties for a Newtonian fluid. We have studied Navier-Stokes’ equations coupled with Maxwell’s ones. Firstly, we have compared the analytical solution comes from Shercliff’s papers, with the numerical one. We have run numerical simulations with simple geometries as two-dimensional rectangular ducts and three-dimensional rectangular and cylinder ducts. We have used an open-source software OpenFOAM, in order to run the simulations. We have done a series of tests to validate the software and the solution of the problem, using different boundary conditions. In detail, we have used a uniform and a non-uniform magnetic fields, also we have tried different patches where applied the magnetic fields. This, it has been done because the velocity profile is subjected to the applied magnetic field direction. After, we have focused our attention on biological geometry. In specific, we have analysed the effects on the blood flow and on the air, when it is applied an external magnetic field. Starting from DICOM images, we have reconstructed a section of the Descending Aorta and of the Trachea. For the first geometry, we have concentrated our efforts on the Coeliac trunk and its bifurcation into the Hepatic artery. To obtain the reconstructed geometries, we have used an open-source software VMTK (The Vascular Modelling Toolkit). Once we have made the geometries with the grids, we have run steady and unsteady simulations. For the first set of simulations, we have imposed for the inlet a parabolic velocity profile, whereas for the second set we have imposed a Womersley’s or periodic velocity profile to the inlet. For the outlet boundary conditions, we have set up a constant flow rate dependent from the arteries for the first geometry whereas for the second one we have fixed the value of the air velocity. About the magnetic field, we have run simulations with uniform magnetic field generated by a rectangular coil. In the last step of the work we have verified the correct adsorption of nano-particles, as we wanted to mimic the behaviour of nano-drugs. Future works about Magneto-Hydrodynamics applied to human body, could be: the investigation of the probes used to create the magnetic field; different pathologies involved in this alternative treatment.