Aortic Shape Space Topology

The human aorta is the largest pressurized blood vessel in the body. Aortic pathology is inherently mechanical, ranging from through thickness fracture, aortic rupture, to intra-lamellar fracture, termed aortic dissection. While aortic rupture is immediately life-threatening, the stability of aortic dissections is poorly understood. Traditional metrics focus on singular scalar measurements of maximum aortic size. However these do not predict which dissected aortas are stable for observation versus require operative intervention. We have pioneered a differential geometry approach to classify the stability of aortic dissections. Using over 150 computed tomography scans from patients with normal and dissected aortas, we show that aortic classification is optimally performed in a scale space defined by topologic invariants rather than geometric ones. We prove that all aortas prior to rupture are globally topologically a 2-torus, T². However, dissected aortas separate from normal aortas by studying the gradients of the local aortic topology, which are calculated as spatial fluctuation of the Euler characteristic, χ. As aortic shapes become more distorted, δχ diverges with a characteristic power law, which is a hallmark of an impending topologic transition, mechanically rupture.