ESTIMATION OF MULTIMODAL ORIENTATION DISTRIBUTION FUNCTIONS FROM CARDIAC MRI FOR TRACKING PURKINJE FIBERS THROUGH BRANCHINGS H. Ertan C ¸ eting¨ ul † , Gernot Plank ‡ , Natalia Trayanova † and Ren´ e Vidal † † Department of Biomedical Engineering, Johns Hopkins University, Baltimore MD, USA ‡ Institute of Biophysics, Medical University Graz, Graz, Austria ABSTRACT The inclusion of the free-running Purkinje network in computational simulations provides a significant insight into understanding the mech- anisms of cardiac pathophysiologies. However, its automatic extrac- tion is challenging due to the presence of abundant local complexities. We thereby introduce a novel algorithm to track the Purkinje fibers in high resolution magnetic resonance (MR) images. Our formulation successively identifies local fiber orientations by using a nonlinear oriented filter. Specifically, the filter is used to compute several local profiles, from which one can estimate the orientation distribution function (ODF). The algorithm then determines the directions to be followed by detecting the modes of the local ODF using different spherical clustering methods. We quantitatively compare the accuracy of the tracked fibers with manually delineated anatomical structures. Index Terms— fiber tracking, nonlinear filters, spherical cluster- ing, cardiovascular systems, magnetic resonance imaging. 1. INTRODUCTION The extraction of fibrous structures is a well-studied problem in pat- tern recognition, which finds a wide range of applications in medical image analysis. A fibrous structure comprises a spatially coherent ap- pearance pattern, which can be quantified via different feature-based and/or model-based representations [1]. Furthermore, these repre- sentations have been used to develop computational tools that can improve current diagnostic and therapeutic approaches [1, 2, 3, 4]. Most of the existing fiber extraction methods can be categorized into three groups: i) region-based segmentation and curve thinning, ii) operator-based fiber detection and grouping, and iii) successive orien- tation estimation and fiber tracking. The first group uses region-based segmentation algorithms to find “fibrous” regions followed by curve thinning for centerline extraction. There exist a plethora of works which employ this top-down strategy (see [3] and references therein). The second group of methods employs a local operator for fiber detection and assigns a label to each pixel/voxel. These bottom-up ap- proaches often employ the image gradient/Hessian, the structure ten- sor, or linear/nonlinear/model-driven operators such as steerable and multiscale oriented filters (see [5] and references therein). However, these techniques require local detection/labeling at each pixel/voxel, which can be computationally expensive. The third group of methods estimates local orientations via a nonlinear operator and uses this in- formation to delineate the fiber by means of tracking. These methods are initiated at user-specified points and reduce the aforementioned computational load. Selected works employ intensity-based medial strength [6] and locally coherent appearance patterns [7]. This work has been funded by the grant NIH HL082729 and by startup funds from the JHU Whiting School of Engineering. Other tracking methods use diffusion weighted MR images (DW- MRI) to estimate the orientation distribution function (ODF), which is the radial projection of the probability density function (pdf) of particle displacements. Fiber directions are identified as the directions at which the corresponding ODF attains its peaks. However, the local displacement is often modeled with a Gaussian distribution. Consequently, the streamlining techniques that employ such unimodal representations do not solve partial volume effects [8]. Therefore, the state-of-the-art methods estimate local fiber orientations from multimodal representations (see [9, 10, 11] and references therein). In fact, any tractography technique employing ODFs could be applied on structural MRI if one could estimate the ODFs from intensity data. 1.1. Problem Statement and Algorithm Overview The Purkinje network (PN) comprises specialized fibers of the car- diac conduction system, which are responsible for the propagation of the electrical impulse initiating myofiber contraction. The PN is implicated in the generation and sustenance of arrhythmias, hence modeling this network in conduction simulations provides an un- derstanding of this pathophysiological mechanism. Novel ex vivo MRI techniques offer sufficient resolution to identify the free-running PN, which activates endocardial structures such as the papillary mus- cle (Fig. 1(a)). However, the automatic extraction of these fibers is difficult due to local complexities such as branchings (Fig. 1(b)). We thereby address the problem of tracking the free-running Purkinje fibers by employing a novel nonlinear filter for local ori- entation estimation. We represent a fibrous structure as a sequence of 3-D points (x0, x1,..., x l ) . = X , or equivalently as a sequence of vectors (s1, s2,..., s l ) with si = xi − xi−1. We initialize the algorithm by specifying {x0, x1}, which places the filter along the fiber of interest. We then compute the ODF at x1 and subsequently estimate the local orientations by detecting the modes of the ODF using two different spherical clustering techniques. We repeat the same procedure by shifting the filter to the newly identified locations and successively obtain the points x2, x3,... on the fiber. Our main contribution is the method to estimate the ODF from structural MRI. (a) (b) Fig. 1. Illustration of the cardiac PN: (a) 3-D rendering of the MR data, (b) A selected MR slice with manually extracted fibers (red).