Euclid, Da Vinci and the aortic root

In the September 2018 issue of the journal, Peterson et al. [1] presented the first study documenting the changes in the aortic annulus during the cardiac cycle. This cyclic expansion of the annulus demonstrates that the aortic root responds to pulsations in a similar fashion as the aortic tree, with dilatation of its anatomical boundaries. The study also demonstrates the eccentricity of the aortic valve annulus and the circumferential pattern of the expansion of its aperture during the systole, from the right sinus, to the left sinus to the non-coronary sinus. Current understanding of this flow is based largely on the Hagenbach–Poiseuille and the Navier–Stokes equations [2, 3], which have the following assumptions: 1. The conduit (i.e. the aortic root) has a cross-section of a perfect circle and regular, rigid walls without change in shape. 2. The flow inside this conduit is steady-state, fully developed, uniaxial and axisymmetric with the highest velocity in the centre (corresponding to the lowest shear) and the lowest velocity at the periphery. 3. The aortic valve is a passive structure that opens and closes simply due to changes in pressure. Though originally developed in the 1800s, these equations are still the basis for calculations and mathematical modelling [4] of flow in the left ventricular tract and across the aortic valve, and subsequently for echocardiographic measurement and quantification of the size and haemodynamic parameters of the native and prosthetic valves as well as for computational fluid dynamics modelling during the design, development and testing of valve prostheses. However, this Euclidean pattern of anatomy and flow does not explain the age-old phenomenon of the ‘pulse’ [5], where vascular structures undergo regular change in geometry in response to the travelling bolus of blood during the systolic phase of the cardiac cycle. Observed since antiquity, described in exquisite detail by Da Vinci and still seen in every operating room, these cyclic changes in cardiovascular geometry argue against a perfectly cylindrical, axisymmetric flow inside a rigid conduit. The important findings from this study add to the growing body of evidence [6] pointing to a different, complex, 3-dimensional helical vorticial flow pattern across the left ventricular tract and aortic root. This helical flow may be an extension or propagation of the well-documented intraventricular vortex. Further research into understanding and modelling of this unique pattern of flow is needed for the improved understanding of the process of mechanotransduction, i.e. the effects of mechanical loading on the signalling and homoeostasis of the vascular wall and its impact on cardiovascular health. Such understanding is necessary for the identification and development of diagnostic and therapeutic targets and modalities for cardiovascular disease. In addition, a more up-to-date and realistic understanding of the functional anatomy and fluid dynamics in the ventriculo-arterial junction is essential for a better understanding of the propulsive function of the heart and improved design of valve prostheses, with implications on the management of heart failure as well. In light of the rapidly expanding body of scientific knowledge in each discipline, improved communication and collaboration between the medical, surgical and biomedical engineering communities are called upon achieve these goals.