Fractal dimension of an aortic heart valve leaflet

The complexity of nature can often be observed in the geometry of biological structure. The aortic valve model of Peskin and McQueen can be used to study the apparently fractal character of the valve's fiber architecture. The branching and braiding of the model fibers is similar to that seen in the real aortic valve. In this study, we compute the fractal dimension of the leaflets of the model aortic valve. We find a fractal dimension of 2.21. The computation of the aortic valve leaflet at the most refined level in the fractal dimension calculation requires the computation of over 6.5 billion points (5.1 million aortic valve fibers with 1280 points/fiber). A high-performance variant of the grid-based box counting method is developed, based on a recursive, octal-tree data structure.