A fundamental study to characterize the flow around an oscillating cylinder in a pulsatile flow environment is investigated. This work is motivated by a new proposed design of the total artificial lung (TAL), which is envisioned to provide better gas exchange. The Navier-Stokes computations in a moving frame of reference were performed to compute the dynamic flow field surrounding the cylinder. Cylinder oscillations and pulsatile free-stream velocity were represented by two sinusoidal waves with amplitudes A and B and frequencies ω(c) and ω, respectively. The Keulegan-Carpenter number (K(c)=U(o)∕Dω(c)) was used to describe the frequency of the oscillating cylinder while the pulsatile free-stream velocity was fixed by imposing ω∕K(c)=1 for all cases investigated. The parameters of interest and their values were amplitude (0.5D<A<D), the Keulegan-Carpenter number (0.33<K(c)<1), and the Reynolds number (5<Re<20) corresponding to operating conditions of the TAL. It was observed that an increase in amplitude and a decrease in K(c) are associated with an increase in vorticity (up to 246%) for every Re suggesting that mixing could be enhanced by the proposed TAL design. The drag coefficient was found to decrease for higher amplitudes and lower K(c) for all cases investigated. In some cases the drag coefficient values were found to be lower than the stationary cylinder values (A=0.5, K(c)=0.3, and Re=10 and 20). A lock-in phenomenon (cylinder oscillating frequency matched the vortex shedding frequency) was found when K(c)=1 for all cases. This lock-in condition was attributed to be the cause of the rise in drag observed in that operating regime. For optimal performance of the modified TAL design it is recommended to operate the device at higher fiber oscillation amplitudes and lower K(c) (avoiding the lock-in regime).