Boundary Conditions


The easiest boundary condition to determine is the artery wall. We simply need to define the wall regions of this model and set it to “wall”. From a physical viewpoint, the “wall” condition dictates that the velocity at the wall is zero.


As we know, mammalian blood flow is pulsatile and cyclic in nature. Thus the velocity at the inlet is not set to be a constant, but instead, in this case, it is a time-varying periodic profile. The pulsatile profile within each period is considered to be a combination of two phases. During the systolic phase, the velocity at the inlet varies in a sinusoidal pattern. The sine wave during the systolic phase has a peak velocity of 0.5 m/s and a minimum velocity of 0.1 m/s. Assuming a heartbeat rate of 120 per minute, the duration of each period is 0.5 s. This model for pulsatile blood flow is proposed by Sinnott et, al. [3] A figure of the profile within two periods is given below:

To describe the profile more clearly, a mathematical description is also given below:


The systolic pressure of a healthy human is around 120 mm Hg and the diastolic pressure of a healthy human is around 80 mm Hg. Thus, taking the average pressure of the two phases, we use 100 mm Hg (around 13332 Pascal) as the static gauge pressure at the outlets.