Computational Complexity Reduction for Volumetric Cardiac Deformation Recovery

Abstract

Cardiac deformation recovery is to estimate displacements and thus strains of the myocardium from patient’s medical measurements, which can then be used to locate possible areas of cardiac diseases such as infarction. In order to properly couple a priori cardiac physiological models with measurements from medical images, different state-space based filtering algorithms have been proposed for physically meaningful and statistically optimal estimations with promising results demonstrated. Nevertheless, as the filtering procedures include matrix multiplications and inversions of dense matrices which sizes increase exponentially with the number of nodes representing the heart, the computational complexities of these algorithms are very large and thus their scalability and practicability are limited. In order to alleviate the computational requirements while minimizing the loss of accuracy, the mode superposition approach is adopted in this paper. Mode superposition transforms the origin cardiac system dynamics into a mathematically equivalent space spanned by shape vectors of different modes, with each mode representing a particular frequency of the displacements. As only relatively few frequencies are required for a good approximation of the system, many shape vectors can be discarded and results in a space of much lower dimension. With the proper transformations of the filtering components derived in this paper, the filtering procedures can then be performed in this space with largely reduced computational complexity. Experiments have been performed on synthetic data to show the benefits and costs of using the proposed framework, and also on a magnetic resonance image sequence to show its effects and performance on real data.