Spline Based Microstructural Mapping for Soft Biological Tissues: Application to Aortic Valves

Splines are the standard tools in computer aided design for geometric representations and have been recently integrated into the finite element analysis of structures and fluids [1]. As the biomedical engineering is making progress, there is a need for an integrated tool for expanding the geometrical representation to include the microstructural details specific to soft tissue, e.g. fiber alignment, orientation, crimp and stiffness. In this work, a spline-based method is presented for aortic valves which facilitates mapping of the fiber structure from any aortic valve specimen to any other aortic valve geometry through a common parameter space. This techniques also has the ability to calculate mean tissue microstructure of representative population. Also strain and pre-strain from in-vivo state to the in-vitro state, where all the mechanical tests are done, are calculated for forward and inverse modeling of aortic valves.