Macrophages trajectories smoothing by evolving curves

TL;DR

This paper introduces a mathematical and numerical approach to smooth noisy macrophage cell trajectories using evolving curves, improving the analysis of cell movement data.

Contribution

It presents a novel curve evolution model combining smoothing and trajectory attraction, with a finite volume discretization for macrophage trajectory smoothing.

Findings

Effective smoothing of noisy macrophage trajectories

Accurate computation of cell velocities on smoothed curves

Demonstrated robustness of the method on biological data

Abstract

When analyzing cell trajectories, we often have to deal with noisy data due to the random motion of the cells and possible imperfections in cell center detection. To smooth these trajectories, we present a mathematical model and numerical method based on evolving open-plane curve approach in the Lagrangian formulation. The model contains two terms: the first is the smoothing term given by the influence of local curvature, while the other attracts the curve to the original trajectory. We use the flowing finite volume method to discretize the advection-diffusion partial differential equation. The PDE includes the asymptotically uniform tangential redistribution of curve grid points. We present results for macrophage trajectory smoothing and define a method to compute the cell velocity for the discrete points on the smoothed curve.