Image-based CFD tends to rely on lots of explicit and implicit
assumptions, and there are also various overt and hidden sources of
uncertainty. As part of our ongoing attempts to understand the impact of these, in
2006 we published a study asking, and we thought answering, whether for "
Inlet Conditions for Image-Based CFD Models of the Carotid Bifurcation: Is it Reasonable to Assume Fully Developed Flow". Then, in
2009 a paper came out saying that "
Choice of In Vivo Versus Idealized Velocity Boundary Conditions Influences Physiologically Relevant Flow Patterns in a Subject-Specific Simulation of Flow in the Human Carotid Bifurcation".
Well, we thought, that's bad news, not only because it
seemed to contradict our work, but because it's tough to acquire and impose subject-specific velocity conditions, at least in comparison to acquiring or assuming flow rates and imposing fully-developed (idealized) velocity conditions. Admittedly, one of the
drawbacks of our study was that we perturbed the fully-developed inlet conditions by imposing ideally curved and helical inlet sections. And we since had learned that common carotid artery (CCA) inlet segments are rarely so ideally curved, and
their velocity profiles can be quite complex. So we decided to
revisit the question, but now with the advantage of the high quality carotid MRI scans available through our collaborations on the
VALIDATE study.
Specifically, in "
Effect of Common Carotid Artery Inlet Length on Normal Carotid Bifurcation Hemodynamics", we started with carotid bifurcations (a dozen of 'em, more than either of the earlier studies -- we wanted to leave no doubt :-) having their actual CCA segments almost down to their aortic arch origins. As shown in the
figure above, these were progressively truncated, and CFD simulations carried out on the whole lot (60 simulations in total!) using fully-developed inlet conditions. In the end we found that
three diameters of CCA inlet length are required before it is reasonable to impose fully-developed flow, at least for the purposes of quantifying common measures of "disturbed flow" within the uncertainty of the image-based CFD pipeline itself.
So why the difference of opinion? Both earlier studies had looked at different hemodynamic quantities for sure, but we believe the big difference was in their inlet lengths: we estimated that the CCA in the 2009 paper was closer to one diameter in length, whereas those in our 2006 paper were (lucky for us) closer to three diameters. This doesn't mean that one paper is more right or wrong than the other. It just means that one needs to consider the
(formerly) hidden variable of CCA length before deciding whether it's reasonable or not to impose fully-developed flow.
Thanks to our friend and self-styled quasi-media activist Roberta Buiani, currently transplanted to Cambridge, for sending this link to "William Harvey and the circulation of blood", a great 1978 film from the Wellcome Collection. (Note early on the comments about Galen being so revered for centuries that no one dared question his presumptions about the circulation. Guess it didn't hurt that Harvey had tenure and the ear of the king :-)
