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A mathematical model for blood flow through an elastic artery with multistenosis under the effect of a magnetic field in a porous medium is presented.The considered arterial segment is simulated by an anisotropically elastic cylindrical tube filled with a viscous incompressible electrically conducting fluid representing blood.An artery with mild local narrowing in its lumen forming a stenosis is analyzed.The effects of arterial wall parameters represent viscoelastic stresses along the longitudinal and circumferential directions Tt and Tθ,respectively.The degree of anisotropy of the vessel wall γ total mass of the vessel,and surrounding tissues M and contributions of the viscous and elastic constraints to the total tethering C and K respectively on resistance impedance,wall shear stress distribution,and radial and axial velocities are illustrated.Also,the effects of the stenosis shape m,the constant of permeability k,the Hartmann number Ha and the maximum height of the stenosis size δ on the fluid flow characteristics are investigated.The results show that the flow is appreciably influenced by surrounding connective tissues of the arterial wall motion,and the degree of anisotropy of the vessel wall plays an important role in determining the material of the artery.Further,the wall shear stress distribution increases with increasing Tt and γ while decreases with increasing Tθ,M,C,and K.Transmission of the wall shear stress distribution and resistance impedance at the wall surface through a tethered tube are substantially lower than those through a free tube,while the shearing stress distribution at the stenosis throat has inverse characteristic through totally tethered and free tubes.The trapping bolus increases in size toward the line center of the tube as the permeability constant k increases and decreases with the Hartmann number Ha increased.Finally,the trapping bolus appears,gradually in the case of non-symmetric stenosis,and disappears in the case of symmetric stenosis.The size of trapped bolus for the stream lines in a free isotropic tube (i.e.,a tube initially unstressed) is smaller than those in a tethered tube.