Fig 2. Definition of the instantaneous directionality angle.

ψ is the angle between the vector of the cell frame-to-frame displacement (${\overrightarrow{v}}_t=⟨P_t,P_{t+1}⟩$) and the gradient direction $\overrightarrow{\theta }$. In the example above, the gradient has been set to $\overrightarrow{\theta }=0°$.