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MODELING APPLICATIONS

Kalman Smoother Based Force Localization and Mapping Using Intravital Video Microscopy

[+] Author and Article Information
Dejan Lj. Milutinović1

Department of Applied Mathematics and Statistics, Baskin School of Engineering, University of California, Santa Cruz, CA 95064dejan@soe.ucsc.edu

Devendra P. Garg

Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27707dpgarg@duke.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(6), 061503 (Oct 29, 2010) (8 pages) doi:10.1115/1.4002485 History: Received October 03, 2008; Revised April 10, 2010; Published October 29, 2010; Online October 29, 2010

Motility is an important property of immune system cells. It provides cells with the ability to perform their function not only at the right time but also at the right place. In this paper, we introduce the problem of modeling and estimating an effective force field directing cell movement by the analysis of intravital video microscopy. A computational approach is proposed for solving this problem without dealing with a parametrized spatial model of the field in order to avoid potential errors due to inaccurate spatial model assumptions. We consider the dynamics of cells similar to the dynamics of distributed agents typically used in the field of swarm robotics. The method utilizes a fixed-interval Kalman filter based smoother. Its application results in a map giving the intensity and direction of the effective force field. The results show that real-time video images are a source of data, enabling us to visualize intriguing spatiotemporal phenomena inside immune system organs. The proposed approach can fill the existing gap between contemporary technology and quantitative data analyses present in the field of biosystems.

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Copyright © 2010 by American Society of Mechanical Engineers
Topics: Force
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Figures

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Figure 1

Computer-generated image of a cellular interaction inside the lymph node: T-cells (red), and dendritic cells (green) (4)

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Figure 2

Two-dimensional projection of 40 cell tracks from the 200×150×50 μm3 visual field provided by a two-photon video microscopy (model generated). Each track is translated so that the track begins at the diagram origin. The cells can move in all directions, therefore, the limits for plotting translated trajectories are ±200 μm and ±150 μm along x and y axes, respectively.

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Figure 3

Time-continuous cell motility model: (a) general model and (b) stochastic motility model

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Figure 4

Cell displacements versus the square root of traveled time: parameters σ=10 and c=0.1, 1, 10, and 100

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Figure 5

The force estimation σF=0 (top) and σF=0.1 (bottom): true force (red), the forward (Kalman filter) iteration (green), and the backward iteration (blue). The true force is defined by expression 11.

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Figure 6

The force estimation σF=1 (top) and σF=5 (bottom): true force (red), the forward (Kalman filter) iteration (green), and the backward iteration (blue). The true force is defined by expression 11.

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Figure 7

The standard deviation of the constant force estimation component; the fixed-interval smoother parameter σF=0

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Figure 8

Result of the force field estimation: the cell trajectories (green), the constant force F¯ (red arrows), the smoother estimation F̂ (blue thick arrows), and the interval smoother parameter σF=0.1. The true field is defined by expression 19.

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