<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Macrophages Trajectories Smoothing by Evolving Curves

Department of Mathematics and Descriptive Geometry

Slovak University of Technology in Bratislava

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Macrophages Trajectories Smoothing by Evolving Curves"}

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...

Macrophages Trajectories Smoothing by Evolving Curves

Published Online: Oct 31, 2023

Page range: -

Received: Nov 24, 2022

Accepted: Oct 16, 2023

DOI: https://doi.org/10.2478/tmmp-2023-0031

Keywords
smoothing, macrophage, velocity, finite volume method

© 2023 Giulia Lupi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Macrophages Trajectories Smoothing by Evolving Curves

Published Online: Oct 31, 2023

Page range: -

Received: Nov 24, 2022

Accepted: Oct 16, 2023

DOI: https://doi.org/10.2478/tmmp-2023-0031

Keywordssmoothing, macrophage, velocity, finite volume method

© 2023 Giulia Lupi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
smoothing, macrophage, velocity, finite volume method