Ebers, DaVinci, and Euler: Calculating the Pulse. Assumptions, Challenges, and Opportunities in Mathematical Modeling...

Mathematical modeling of flow in the circulatory system, particularly the arterial system, has long relied on old equations derived from the study of fluid mechanics in rigid tubes, which does not account for the cyclic distension of the vessel or the effects of intraluminal forces on wall components. An understanding of the current scientific evidence and the limitations of such assumptions is essential for adequate computational modeling of the circulatory system. Improved interdisciplinary communication among the basic science, medical, surgical, and biomedical engineering communities should prove to be beneficial in developing safer, more effective, and more reliable tools and devices that are more consistent with physiological processes within the body.