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Basak US, Sattari S, Hossain MM, Horikawa K, Toda M, Komatsuzaki T. Comparison of particle image velocimetry and the underlying agents dynamics in collectively moving self propelled particles. Sci Rep 2023; 13:12566. [PMID: 37532878 PMCID: PMC10397335 DOI: 10.1038/s41598-023-39635-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Accepted: 07/28/2023] [Indexed: 08/04/2023] Open
Abstract
Collective migration of cells is a fundamental behavior in biology. For the quantitative understanding of collective cell migration, live-cell imaging techniques have been used using e.g., phase contrast or fluorescence images. Particle tracking velocimetry (PTV) is a common recipe to quantify cell motility with those image data. However, the precise tracking of cells is not always feasible. Particle image velocimetry (PIV) is an alternative to PTV, corresponding to Eulerian picture of fluid dynamics, which derives the average velocity vector of an aggregate of cells. However, the accuracy of PIV in capturing the underlying cell motility and what values of the parameters should be chosen is not necessarily well characterized, especially for cells that do not adhere to a viscous flow. Here, we investigate the accuracy of PIV by generating images of simulated cells by the Vicsek model using trajectory data of agents at different noise levels. It was found, using an alignment score, that the direction of the PIV vectors coincides with the direction of nearby agents with appropriate choices of PIV parameters. PIV is found to accurately measure the underlying motion of individual agents for a wide range of noise level, and its condition is addressed.
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Affiliation(s)
- Udoy S Basak
- Pabna University of Science and Technology, Pabna, 6600, Bangladesh
| | - Sulimon Sattari
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Kita 20, Nishi 10, Kita-ku, Sapporo, 001-0020, Japan.
| | - Md Motaleb Hossain
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Kita 20, Nishi 10, Kita-ku, Sapporo, 001-0020, Japan
- University of Dhaka, Dhaka, 1000, Bangladesh
| | - Kazuki Horikawa
- Department of Optical Imaging, Advanced Research Promotion Center, Tokushima University, Kuramoto-cho 3-18-15, Tokushima, Tokushima, 770-8503, Japan
| | - Mikito Toda
- Faculty Division of Natural Sciences, Research Group of Physics, Nara Women's University, Kita-Uoya-Nishimachi, Nara, 630-8506, Japan
- Graduate School of Information Science, University of Hyogo, 7-1-28 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo, 650-0047, Japan
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-Ku, Sapporo, 001-0020, Japan
| | - Tamiki Komatsuzaki
- Pabna University of Science and Technology, Pabna, 6600, Bangladesh.
- Graduate School of Life Science, Transdisciplinary Life Science Course, Hokkaido University, Kita 12, Nishi 6, Kita-ku, Sapporo, 060-0812, Japan.
- Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Kita 21 Nishi 10, Kita-ku, Sapporo, Hokkaido, 001-0021, Japan.
- Graduate School of Chemical Sciences and Engineering Materials Chemistry and Engineering Course, Hokkaido University, Kita 13, Nishi 8, Kita-ku, Sapporo, 060-0812, Japan.
- Institute for Open and Transdisciplinary Research Initiatives, Osaka University, Yamadaoka, Suita, Osaka, 565-0871, Japan.
- The Institute of Scientific and Industrial Research, Osaka University, Mihogaoka, 8-1, Osaka, Ibaraki, 567-0047, Japan.
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Braunstein A, Catania G, Dall'Asta L, Mariani M, Muntoni AP. Inference in conditioned dynamics through causality restoration. Sci Rep 2023; 13:7350. [PMID: 37147382 PMCID: PMC10163042 DOI: 10.1038/s41598-023-33770-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2023] [Accepted: 04/18/2023] [Indexed: 05/07/2023] Open
Abstract
Estimating observables from conditioned dynamics is typically computationally hard. While obtaining independent samples efficiently from unconditioned dynamics is usually feasible, most of them do not satisfy the imposed conditions and must be discarded. On the other hand, conditioning breaks the causal properties of the dynamics, which ultimately renders the sampling of the conditioned dynamics non-trivial and inefficient. In this work, a Causal Variational Approach is proposed, as an approximate method to generate independent samples from a conditioned distribution. The procedure relies on learning the parameters of a generalized dynamical model that optimally describes the conditioned distribution in a variational sense. The outcome is an effective and unconditioned dynamical model from which one can trivially obtain independent samples, effectively restoring the causality of the conditioned dynamics. The consequences are twofold: the method allows one to efficiently compute observables from the conditioned dynamics by averaging over independent samples; moreover, it provides an effective unconditioned distribution that is easy to interpret. This approximation can be applied virtually to any dynamics. The application of the method to epidemic inference is discussed in detail. The results of direct comparison with state-of-the-art inference methods, including the soft-margin approach and mean-field methods, are promising.
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Affiliation(s)
- Alfredo Braunstein
- DISAT, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Turin, Italy
- INFN, Sezione di Torino, Turin, Italy
- Italian Institute for Genomic Medicine, IRCCS Candiolo, SP-142, 10060, Candiolo, TO, Italy
| | - Giovanni Catania
- Departamento de Física Téorica I, Universidad Complutense, 28040, Madrid, Spain
| | - Luca Dall'Asta
- DISAT, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Turin, Italy
- INFN, Sezione di Torino, Turin, Italy
- Italian Institute for Genomic Medicine, IRCCS Candiolo, SP-142, 10060, Candiolo, TO, Italy
- Collegio Carlo Alberto, P.za Arbarello 8, 10122, Turin, Italy
| | - Matteo Mariani
- DISAT, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Turin, Italy.
| | - Anna Paola Muntoni
- DISAT, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Turin, Italy
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