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A real-time model-based approach for the reconstruction of fluid flows induced by microorganisms


An experiment on living microorganisms is conducted to gain insight into their motion and fluid exchange characteristics. Biocompatible microscopic particle image velocimetry (PIV)-systems are used to capture images of seeded particles in the induced fluid flows. To enhance the abilities of these devices we present a model-based approach for the reconstruction of admissible flow fields from captured images. A priori knowledge of the physical model of the flow is used to iteratively refine a predicted flow field. A physics-based filter operation generates a velocity field that is consistent with the model of incompressible laminar flows described by the Navier–Stokes equations. Interactive steering of the reconstruction process is achieved by exploiting programmable graphics hardware as a co-processor for numerical computations. To validate our method, we estimate velocity vector fields from synthetic image pairs of flow scenarios for which ground truth velocity fields exist and real-world image sequences of the flow induced by sessile microorganisms.

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  1. 1.

    The Galerkin property ensures a consistent calculation on different levels of resolution, and thus it guarantees fast convergence of the multigrid scheme.

  2. 2.

    The reference image R and the template image T correspond to Im t and Im t + 1 with respect to acquisition time t.

  3. 3.

    The EDPIV software package is available at (

  4. 4.

    Ciliate is a sessile microorganism attached via stalk to the surface of granules forming up granular activated sludge. By adjusting the stalk, a ciliate can vary its inclination angle with respect to its initial orientation. This motion is referred to as nodding motion (Hartmann et al. 2007).

  5. 5.

    According to the observations in nature, the largest velocity magnitudes are expected in the vicinity of the oral cavity of the microorganism.


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The authors thank Dominique Heitz and Professor Etienne Mémin for providing the Lamb–Oseen vortex flow dataset. Support by the Deutsche Forschungsgemeinschaft (DFG) within the priority program “Bildgebende Messverfahren in der Strömungsmechanik” ( is gratefully acknowledged.

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Correspondence to P. Kondratieva.

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Kondratieva, P., Georgii, J., Westermann, R. et al. A real-time model-based approach for the reconstruction of fluid flows induced by microorganisms. Exp Fluids 45, 203–222 (2008).

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  • Particle Image Velocimetry
  • Optical Flow
  • Velocity Magnitude
  • Reconstruction Process
  • Interrogation Window