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J R Soc Interface. 2017 Dec;14(137). pii: 20170564. doi: 10.1098/rsif.2017.0564.

Model-based image analysis of a tethered Brownian fibre for shear stress sensing.

Author information

School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
Institute for Metabolism and Systems Research, University of Birmingham, Birmingham B15 2TT, UK.
Centre for Human Reproductive Science, Birmingham Women's and Children's NHS Foundation Trust, Birmingham B15 2TG, UK.
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK.
School of Medicine, University of Nottingham, Nottingham NG7 2UH, UK.
Biofisika Institute (CSIC UPV/EHU), University of the Basque Country, 48080 Bilbao, Spain.
Research Centre for Experimental Marine Biology and Biotechnology, University of the Basque Country, 48080 Bilbao, Spain.


The measurement of fluid dynamic shear stress acting on a biologically relevant surface is a challenging problem, particularly in the complex environment of, for example, the vasculature. While an experimental method for the direct detection of wall shear stress via the imaging of a synthetic biology nanorod has recently been developed, the data interpretation so far has been limited to phenomenological random walk modelling, small-angle approximation, and image analysis techniques which do not take into account the production of an image from a three-dimensional subject. In this report, we develop a mathematical and statistical framework to estimate shear stress from rapid imaging sequences based firstly on stochastic modelling of the dynamics of a tethered Brownian fibre in shear flow, and secondly on a novel model-based image analysis, which reconstructs fibre positions by solving the inverse problem of image formation. This framework is tested on experimental data, providing the first mechanistically rational analysis of the novel assay. What follows further develops the established theory for an untethered particle in a semi-dilute suspension, which is of relevance to, for example, the study of Brownian nanowires without flow, and presents new ideas in the field of multi-disciplinary image analysis.


Brownian dynamics; image analysis; mathematical modelling; regularized stokeslets; viscous fluid dynamics; wall shear stress

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