The Analysis of Cardiac Velocity MR Images Using Fuzzy Clustering

1 ABSTRACT Velocity Magnetic Resonance (MR) images are a novel form of medical images. A special gradient-modulation technique is utilised to capture motion velocity of tissue and blood. As well as the tissue density image, there are also other images that depict the velocity components along axes deened relative to the plane of imaging. The images are of the cardiac region and are aligned with the short-axis of the left ventricle. We present the results of clustering cardiac image sequences using the Fuzzy c-Means (FCM) algorithm. Our paper demonstrates how the application of clustering to one frame in the cine sequence of images can be utilised in order to track reasonably well the contraction and relaxation of the Left Ventricle. Our paper shows that this imaging technique is generally accurate and certainly adds to the information already contained in the tissue density images. 2 INTRODUCTION Magnetic Resonance (MR) images picture anatomic detail by registering tissue density in the plane of imaging. Every pixel in an MR image carries a value that is proportional to the average tissue density registered by the MR scanner at the corresponding approximate location in the plane of imaging. Our application consists of analysing image cine sequences acquired at the mid-ventricular plane of the heart. The cine sequence of images is aligned with the short-axis of the left ventricle (LV). The number of images in the sequence is 16. For each of the density images, velocity images of the same anatomic plane of the ventricle are produced using a phase-sensitive MRI technique. The velocity data is rendered as 3 images, v x , v y and v z , corresponding to the cartesian components of the velocity vector eld V. The reference coordinate system we use has the x-y plane lying on the plane of imaging (aligned with the short-axis of the left ventricle) and the z axis perpendicular to it (aligned with the LV long-axis). In this paper, we describe our use of the fuzzy c-means clustering algorithm to analyse the image sequence. The fuzzy c-means (FCM) algorithm is also sometimes called fuzzy k-means and fuzzy ISODATA. The monograph by James Bezdek 1] is the most widely cited reference for FCM. Using clustering algorithms for image analysis, particularly segmentation, probably goes back to the early seventies. The motivation behind its use is that image intensity values tend to cluster in ways that correspond to the …