Evolution of Aortic Geometry Modeled with Morphoelastic Growth

While growth is normal during development, it is often a hallmark of or response to disease in adults. We study the evolution of the largest blood vessel in the human body, the aorta. Geometrically the aorta is a curved cylinder with the first portion being toroidal attached to a second cylindrical segment. Looking at a cohort of 150 normal people ranging from 1 years to 93 years old, we calculate the shape operator on the aortic surface and perform a Gauss mapping of each surface to the unit sphere. This allows us to study changes in shape independently of changes in size. Using constant rate isotropic growth, where the volume of all finite elements increases proportionally to the growth tensor, we can trace out the trajectory of normal aortic growth. A second cohort of patients, with diseased aneurysmal or dissected aortas, was shown to geometrically diverge from the shape-preserving normal growth. Diseased aortic shape evolution is highly sensitive to the initial geometry. Furthermore, the correct shape evolution cannot be captured with a single growth law. Globally the shape evolution of diseased aortas is shown to be similar to the development of amplitude fluctuations on a sphere that can be modeled using spatially heterogenous growth. Aortic surfaces are sub-divided into patches of relatively constant Gaussian curvature. Each individual patch grows with a varying growth rate coupled to the mean Gaussian curavtrue within the patch, this strategy allows us to reproduce shape evolution of diseased aortas.