Locally Linear Embedding for the Construction of the Purkinje System

Locally linear embedding (LLE), recently proposed unsupervised procedure for mapping high-dimensional data nonlinearly to a lower-dimensional space, is shown to yield remarkable good results in exploratory analysis and visualization. LLE is able to learn the global structure of nonlinear manifolds, and it maps its inputs into a single global coordinate system of lower dimensionality, which takes good advantage of remaining points close to each other in the computed low-dimensional space when they are close to each other in the high-dimensional space. However, the application to the closed geometry is consequently limited. The purkinje system is a very important conduction system in the endocardial surface of the ventricle that is a semi-closed organ. Traditional construction of the purkinje system is mostly relevant to the fractal tree or something similar, which is based of supposed theory and is an approximation to the actuality. In this paper, a novel method for the construction of the purkinje system in the canine left ventricle by applying LLE algorithm is proposed. The results show that the construction of the purkinje system approaches the one in real structure of the left ventricle better than ever reconstructed.