Arterial drug concentration distribution determines local toxicity. The safety issues dealing with Drug-Eluting Stents reveal the needs for investigation on the effective factors contributing to fluctuations in arterial drug uptake. The current study focuses on the importance of hypertension as an important and controversial risk factor among researchers on the efficacy of Heparin-Eluting Stents. For this purpose, the effect of blood pressure is systematically investigated in certain cardiac cycle modes. A comprehensive study is conducted on two classes, pulsatile (time-dependent), to have a more realistic simulation, and non-pulsatile (time-independent) blood flow, each one in four modes. The governing equations applied to drug release dynamics are obtained based on porous media theory. The equations are solved numerically using the Finite Volume Method. Results reveal that there is a significant difference when the plasma flow considered, and when it is neglected (regardless of time dependency). Moreover, the concentration level is more decreased in pulsatile blood flow rather than the non-pulsatile blood flow, although the penetration depth for pressure and concentration are nearly 20% and 5% of the wall thickness, respectively. In other words, the mass experienced by the arterial wall is lower in pulsatile blood flow in comparison to non-pulsatile blood flow. As a consequence, the risk of toxicity is declined as the blood pressure increases. Also, it can be seen that the polymer is Diffusion-dominated so that no significant changes in the release characteristics are observed in the presence of the plasma filtration.