Biomedical Engineering Reference
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Fig. 1.7. Top: maximum (90 %) and 50 % packing densities for circles in 2D. Bottom: 50 % con-
centration of deformable droplets (i.e., blood at a normal hemotocrit) in 3D [52]
Only time, and state-of-the-art physical and numerical experiments, will tell
whether our suppositions have merit. For now, they reinforce how the simple ques-
tioning of a widespread assumption may open up fundamental and interesting lines
of inquiry, in this case about the nature of turbulence in blood. More prosaically, they
question the role of DNS for validating our predictions about turbulent blood flow
vs. merely verifying the accuracy of our CFD solvers (“solving the right equations”
vs. merely “solving the equations right” [53]).
1.6 Conclusions
CFD modelling of large arteries has advanced to the stage where it is now almost
routine to reconstruct anatomically realistic models from medical images, or relax
traditional assumptions of rigid walls, imposed flow boundary conditions, Newto-
nian rheology, and laminar flow [54]. Nevertheless, meaningful relaxation of these
assumptions invariably requires physiological measurements that may not be avail-
able; may be difficult or impossible to obtain; or may come with sufficiently large
uncertainties as to render any perceived improvement in the predictive capability of
a hemodynamic model purely academic.
In presenting this largely personal journey of discovery regarding the limitations
and opportunities of hemodynamic assumptions, admittedly circumscribed by the
author's own experiences in modelling flow in carotid arteries and aneurysms, it is
hoped that the lessons learned and questions still-to-be-answered will inspire inves-
tigators tackling these and other vascular territories to at least consider, and then
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