  The measurement of 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 3D 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
novel model-based image analysis, which reconstructs phage 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 multidisciplinary image analysis.
