  Cell migration is an indispensable physiological and pathological process for
normal tissue development and cancer metastasis, which is greatly regulated by
intracellular signal pathways and extracellular microenvironment (ECM).
However, there is a lack of adequate tools to analyze the time-varying cell
migration characteristics because of the effects of some factors, i.e., the ECM
including the time-dependent local stiffness due to microstructural remodeling
by migrating cells. Here, we develop an approach to derive the time-dependent
motility parameters from cellular trajectories, based on the time-varying
persistent random walk model. In particular, we employ the wavelet denoising
and wavelet transform to investigate cell migration velocities and obtain the
wavelet power spectrum. The time-dependent motility parameters are subsequently
derived via Lorentzian power spectrum. Our analysis shows that the combination
of wavelet denoising, wavelet transform and Lorentzian power spectrum provides
a powerful tool to derive accurately the time-dependent motility parameters,
which reflects the time-varying microenvironment characteristics to some
extent.
