Stationary Flow of Blood in a Rigid Vessel in the Presence of an External Magnetic Field: Considerations about the Forces and Wall Shear StressesReportar como inadecuado




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1 Biomécanique et Bioingéniérie 2 LMAC - Laboratoire de Mathématiques Appliquées Compiegne 3 IR4M - Imagerie par Résonance Magnétique Médicale et Multi-Modalités

Abstract : The magnetohydrodynamics laws govern the motion of a conducting fluid, such as blood, in an externally applied static magnetic field B 0. When an artery is exposed to a magnetic field, the blood charged particles are deviated by the Lorentz force thus inducing electrical currents and voltages along the vessel walls and in the neighboring tissues. Such a situation may occur in several bio-medical applications: magnetic resonance imaging MRI, magnetic drug transport and targeting, tissue engineering… In this paper, we consider the steady unidirectional blood flow in a straight circular rigid vessel with non-conducting walls, in the presence of an exterior static magnetic field. The exact solution of Gold 1962 with the induced fields not neglected is revisited. It is shown that the integration over a cross section of the vessel of the longitudinal projection of the Lorentz force is zero, and that this result is related to the existence of current return paths, whose contributions compensate each other over the section. It is also demonstrated that the classical definition of the shear stresses cannot apply in this situation of magnetohydrodynamic flow, because, due to the existence of the Lorentz force, the axisymmetry is broken.

Keywords : Wall Shear Stresses Magnetic Field in Biomedical Applications Magnetohydrodynamic Flow of Blood





Autor: Agnès Drochon - Vincent Robin - Odette Fokapu - Dima Abi-Abdallah Rodriguez -

Fuente: https://hal.archives-ouvertes.fr/



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