**5. Typical computational boundary conditions for DES models**

Once the governing equations have been applied to the model domain the boundary conditions need to be allocated. Often with biological modelling it is necessary to make assumptions when applying boundary conditions. For example treating the artery wall as rigid (Mongrain et al., 2007; Devereux, 2005; Kaazempur-Mofrad and Ethier, 2001) or assuming that mass transport within the wall is modulated solely by diffusion (Balakrishnan et al., 2008, 2007, 2005; Mongrain et al., 2007, 2005) are two examples of ways commonly employed to simplify what is in reality a very complex problem. However, as previously mentioned the fundamental *in vivo* issues should be taken into account as much as possible when applying such simplifications.

## **5.1 Application of momentum boundary conditions**

### **5.1.1 Inlet: Velocity**

The heart is a muscular organ that undergoes repetitive contraction and relaxation of its walls in order to propel blood through the circulatory system. Coupled with the complex geometry of the coronary arteries, the pulsating blood velocity profile is an integral part in the mass transport behaviour of blood borne species. However, when considering the transport of drugs from a DES a common assumption to make is the presence of a steady fully developed flow profile within the lumen (Balakrishnan et al., 2008, 2007, 2005; Mongrain et al., 2007, 2005). When modelling BSMT it may be necessary to incorporate the time-dependent pulsatile nature of blood flow. However, the transient nature of blood side drug transport enables the assumption of a steady flow inlet boundary condition that in most cases will not have a considerable impact on WSMT. Arterial flow can be replicated by applying a pulsatile parabolic velocity profile at the vessels inlet.
