  A discrete boundary-sensitive Hodge decomposition is proposed as a central
tool for the analysis of wall shear stress (WSS) vector fields in aortic blood
flows. The method is based on novel results for the smooth and discrete
Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides
the WSS vector field into five components: gradient (curl-free), co-gradient
(divergence-free), and three harmonic fields induced from the boundary, which
are called the center, Neumann and Dirichlet fields. First, an analysis of WSS
in several simulated simplified phantom geometries (duct and idealized aorta)
was performed in order to understand the impact of the five components. It was
shown that the decomposition is able to distinguish harmonic blood flow arising
from the inlet from harmonic circulations induced by the interior topology of
the geometry. Finally, a comparative analysis of 11 patients with coarctation
of the aorta (CoA) before and after treatment as well as 10 controls patient
was done.
  The study shows a significant difference between the CoA patients and the
healthy controls before and after the treatment. This means a global difference
between aortic shapes of diseased and healthy subjects, thus leading to a new
type of WSS-based analysis and classification of pathological and physiological
blood flow.
