Quantification and visualization of the 3D nonrigid motion of the left ventricle

The accurate and clinically useful estimation of the shape, motion and deformation of the heart's left ventricle (LV) is an important research problem. Recently, computer vision techniques for reconstructing the 3D shape and motion of the LV have been developed. However, the main drawback of these techniques is that the models are formulated in terms of either too many local parameters that require non-trivial processing to be useful for close-to-real-time diagnosis, or too few parameters to offer an adequate approximation to the LV motion. Method: To address the problem of a compact and accurate LV shape representation, we developed a new class of volumetric deformable models, whose parameters are functions rather than constants. These new models were based on the adaptation of the parametric definition of a superquadric whose parameters capture the radial and longitudinal contraction, the axial twisting, and the long-axis deformation. Using a physics-based approach and Lagrangian dynamics, we converted these volumetric geometric models into models that deform due to forces exerted from the datapoints. A novel algorithm to combine two orthogonal sets of planar motion was implemented to estimate the full 3D motion. We also developed a comprehensive method for visualizing the motion of the LV and for comparing normal and abnormal hearts in a way that is readily understood by a clinician. The methods included plotting parameter graphs, coloring techniques, tracking the motion paths of points on the LV, and video sequences displaying the nonrigid motion of the LV using standard SGI (Mountain View, CA) hardware. We applied our models to datasets obtained by a MR tagging method known as SPAMM (Spatial Modulation of Magnetization). In order to estimate the full 3D motion, datasets from short-axis and long-axis views of a heart were used during the model fitting procedure to compute 3D forces from the datapoints to the deformable model. The forces were then used to estimate the parameters which describe the 3D nonrigid motion of the LV. The extracted parameter functions were then displayed using our visualization methods. We also applied our models to datasets of patients with hypertrophic cardiomyopathy for a comparison with data from healthy volunteers. Results: By plotting the variation over time of the extracted LV model parameters, we were able to quantitatively analyze, localize, and compare the epicardial and endocardial motion. Based on the small number of parameters which vary from region to region, we were able to describe the complex volumetric shape and motion of the LV. Since each parameter function describes a clinically useful type of deformation in an intuitive way, it did not require any complex post-processing for a meaningful interpretation. The comparison study showed that the patients with hypertrophic cardiomyopathy had distinct and consistent differences in the extracted parameters as compared to the normal subjects. Conclusion: The results demonstrate that the proposed technique for estimating the 3D left ventricular wall motion provides useful visualization and quantitative motion analysis of the LV throughout its volume. Keywords: heart wall motion, left ventricle, MRI tagging, SPAMM, regional cardiac function, heart visualization, deformable model, parameter functions