The shape of the mitral annulus: A hypothesis of mechanical morphogenesis

Abstract

This paper investigates the role of mechanics in the morphogenesis of the annulus of the mitral valve. We represent the annulus in its embryonic stage as an elastic ring and we perform a mechanical simulation of the development process applying a distributed torque on the rod: because of the mechanical action of the other growing cardiac chambers on the atrio-ventricular region, it departs from a planar circular shape. The numerical integration of the mathematical rod model subject to a bending load yields a shape very near to the one reported in the medical literature as anatomical reference for healthy patients. To make the comparison quantitative, we illustrate a numerical approach to match two curves in 3D defining their distance in a proper mathematical way. Such a methodology is first applied to compare the annular shape resulting from the mechanical model with an anatomical reference “master” shape and it is then applied to set to clinical data extracted from MRI for a cohort of healthy patients. The good agreement among anatomical master description, numerical mechanical model, and clinical data supports our speculation about a possible role of mechanics in determining the shape of the mitral valve.