Numerical simulations of three distinct models of excitable media (two-variable Oregonator, with both variables diffusing equally; and piecewise linear A and B kinetics, with only the propagator variable diffusing) are used here to investigate the dynamics of scroll filaments, with emphasis on the role of twist. In all three models, initially uncurved filaments uniformly twisted more than a threshold amount 'sproing' into radially expanding helices, some of which stabilize at finite radius. By monitoring the evolution of these helices with a differential geometry 'tool kit', we attempt to discern the presumed causal dependence of filament motion (resolved into velocities along the normal and binormal directions of the local Frenet frame) and rotor spin rate, on local filament geometry (curvature and torsion) and twist. Twist can reverse the direction of normal velocity from that seen in untwisted scroll rings; binormal velocity is either reversed (A kinetics), abolished (B kinetics), or engendered (Oregonator). In all cases twist increased spin rate, as predicted by theory. Our efforts to perceive a functional dependence of the dynamical variables on filament geometry and twist have met with limited success, but we believe our attempts have uncovered some useful methodology and exposed some pitfalls relevant to any such investigation. The existence and properties of a novel class of stable organizing centers, as well as the existence of a threshold of twist for their induction, should be of interest to theorists. In addition, our findings here based on models suggest new phenomena to look for in various excitable media, such as the Belousov–Zhabotinsky reagent or heart muscle.