Non-rigid cardiac motion quantification from 2D image sequences based on wavelet synthesis

Abstract

Motion quantification from 2D sequential cardiac images has been performed on axial images of the left ventricle (LV) obtained from two different imaging modalities (MRI and Echocardiography images). The detail point wise motion vectors were evaluated by establishing shape correspondence between the consecutive contours after reconstructing curvature information by wavelet synthesis filters at multiple levels. We present a simple approach that optimizes the shape correspondence taking the non-uniform contour variation in to account. The shape matching is done by maximizing the correlation between the approximation coefficient vectors at certain levels. The algorithm has been tested over sets of 2D images and the results are compared with that obtained from a bending energy model. Some experimental results have also been presented for validation of the algorithm.

Introduction

The study of the endocardial wall motion of left ventricle (LV) has become an area of focus in recent years. Primary importance has been given to the study of the dynamic features of LV as it is the powerful biological pump for the systemic circulation. Quantitative evaluation of endocardial wall motions are done conventionally by analyzing sequential images to study the degree of infracted muscles and other coronary artery diseases. In this work we have tried to quantify LV motion point wise in a cardiac cycle for an accurate assessment and interpretation of cardiac motion required in clinical diagnosis of cardiac pathology, related to coronary circulation deficiency and myocardial artifacts.

A good volume of work has been done in the field of sequential image processing using differential and correlation methods mostly to analyze the motion of rigid bodies. The results of the above approaches depend on gray value changes and adequate selection of the correct discriminatory features. However, in case of non-rigid objects, an accurate determination of displacement velocity field is more difficult when it involves temporal and spatial shape changes in image frames. The active contour model, or snakes, originally proposed by Kass et al. [1] has become an important tool for segmentation and contour propagation in recent literature for the study of cardiac motion using verity of imaging modalities [2], [3], [4], [5]. A physical description of the model in the above work need information regarding the stiffness and mass characteristics, which is difficult to be parameterized and often not available. The final optimization is done iteratively to propagate contours in to future frames. The measure drawback of the process lies with the initial approximation to the solution when the temporal resolution is poor and it is impossible to get point wise trajectory of the motion field.

Considerable attention has been given to non-rigid motion estimation since the early 1990s. Shape correspondence technique based on curvature information that optimizes a cost functional in the contour space has been presented by Cohen et al. [6]. The minimization being highly non-linear, it is difficult to get a smooth shape based correspondence in the Euclidean space. A possible 3D expandability is suggested taking similar considerations in to account [7]. Similar approach in the work of M. Demi et al. [8] implements regularization of the flow vectors using an interpolation scheme to estimate the shape correspondence between sub sampled shape features. Experimental methods have been proposed using physically implanted markers to quantify the motion in animal heart [9] where the markers are corresponded and tracked in an external co-ordinate system. This approach possesses its inherent disadvantage of invasiveness and limitation on implanting markers to track motion at all locations of interest. Few other methods have been developed to analyze and evaluate the overall cardiac motion [10], [11], [12], [13]. Many of them could not justify satisfactory clinical assessment because of the model considerations.

Significant contribution on point wise motion quantification has been reported in recent work of McEachen and Duncan [14] based on bending energy models. Correspondence between samples on two sequential contours are found by matching the shape properties of contour segments surrounding each of the points [15], [16]. The model based on bending energy was made adaptable to the contour data by considering it as a thin flexible rod. The local curvature difference between the contour under consideration and the mean normal contour is found out at a number of equidistant sample points. The weighted square of these differences added over a set of points is found to be the regional bending energy. The flexibility and success of the approach depends on the meaningful curvature information of the boundary, which may not lead to a better correspondence in the presence of high frequency noise. Hence the discrete contour data requires preprocessing, low pass filtering or smoothing to reduce the effect of noise and inter observer variation in tracing the boundaries (in case of manually contouring). The final flow field evaluation is an optimization problem by adding a smoothness constraint to the flow vectors weighted by two uniquely defined functions (i.e. closeness and uniqueness) in both Euclidean and contour space.

Section 2 describes the problem formulation. In Section 3 we present a brief overview of wavelet analysis filters. Detail procedure for shape matching is explained in Section 4 using the bending energy method and wavelet based approach. Section 5 discusses the experimental results using MRI and echocardiographic image sequences for motion estimation.