The stability of blood vessels under the lumen blood pressure load is essential to the maintenance of normal arterial function. It has been well documented that arteries and veins collapse when the internal lumen pressure is too low and/or the external pressure become higher than the internal pressure [1–3]. It has been demonstrated recently that arteries and veins also buckle (bend) due to hypertensive pressure or a reduced axial stretch ratio [4]. Buckling equations have been established recently for linear and nonlinear elastic artery and vein models based on assumed sinusoidal mode shapes [4–6]. However, the theoretical base for the assumption is lacking. It is necessary to determine whether arteries can bifurcate into the buckled shape under internal pressure.

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