Cartan frames for heart wall fiber motion

Current understanding of heart wall fiber geometry is based on ex vivo static data obtained through diffusion imaging or histology. Thus, little is known about the manner in which fibers rotate as the heart beats. Yet, the geometric organization of moving fibers in the heart wall is key to its mechanical function and to the distribution of forces in it to effect efficient, repetitive pumping. We develop a moving frame method to address this problem, with a spatio-temporal formulation of the associated Cartan matrix. We apply our construction to simulated (canine) data obtained from a left ventricular mechanics challenge, and to in vivo human left ventricular data. The method shows promise in providing Cartan connection parameters to describe spatio-temporal rotations of fibers, which in turn could benefit subsequent analyses or be used for diagnostic purposes.