The theory of acceleration emerged from the understanding that the theory of arterial stiffness leaves a number of important observations unaccounted for. For instance, the theory of arterial acceleration displays the vascular system as a tube narrowing towards periphery. In fact, the total cross-sectional area of the arterial system increases towards periphery. This would cause the pressure wave originating form the heart to dilute on it's way across the arterial tree. It's pulsatility would decrease and it's propagation speed would become smaller.
In real life, the opposite is true: the pulsatility of the arterial blood pressure increases towards periphery and the propagation speed of the front of the pressure wave becomes larger. It is as if extra energy is added to the systolic phase of the blood pressure signal.
This has led to the theory of arterial acceleration that proposes that smooth muscle cells in the arterial wall briefly contract (or stiffen) at the onset of systole. This temporary stiffening would cause the sys1 component within the blood pressure (of blood flow velocity) signal.