Mathematical modeling of the cardiovascular system is useful in understanding its physiological and pathological processes. Pressure and flow waves carry valuable information regarding the physical properties of the system, which is helpful in diagnosis and treatment of disease. Pulse wave propagation is studied extensively using one-dimensional blood flow models. On the other hand, Left Ventricular Assist Devices (LVAD) are constant flow devices with no pulse and the patients are prone to stroke. In this paper we focus on modelling the LVAD flow along with pulsatile flow using the one dimensional blood flow model. The effect of introducing pulsatility to LVAD and its influence on the mean pressure is then studied. The model is then used to simulate absence of one or more arteries in cerebral circulation and incision of LVAD at different locations in arterial tree. Simulation results show that mean blood pressure in LVAD is higher compared to pulsatile flow, which agrees with the results reported in literature. Also, introduction of pulse to LVAD has lowered the mean blood pressure, which is desired and can reduce LVAD related complications. One dimensional models can serve as a valuable noninvasive diagnostic tool for surgical planning and simulating pathology. © 2019 by SCITEPRESS - Science and Technology Publications, Lda.