Introduction

Diffusion tensor magnetic resonance imaging (DT-MRI) [Basser et al. 1994] is a technique used to measure the anisotropic diffusion properties of biological tissues as a function of the spatial position within the sample. Diffusion properties allow the classification of different types of tissues and can be used for tissue segmentation and finding preferred directions in the tissue. Previously, DT-MRI data was successfully used to recover white matter fiber tracts in the brain [Basser et al. 2000,Poupon et al. 2001,Parker et al. 2001,Zhukov and Barr 2002]. Modeling of fiber orientation in the ventricular myocardium based on MR diffusion imaging was proposed by Tseng et al. Tseng99, Hsu and Henriquez Hsu01 and Sachse et al. Sachse01. In this paper we apply tensor visualization and fiber reconstruction methods to DT-MRI data to recover and demonstrate the 3D orientation and structure of the muscle fibers in the entire heart. In the brain, white matter fibers are detected by examining the largest eigenvalue and then ``growing'' the fiber along the principal eigenvector direction. This approach is effective, due to the microstructure of the white matter tissue. Heart muscle tissue has a different microstructure; as a result we have chosen to detect the fibers by examining the sum of the linear and planar tensor anisotropies (see Eq. 4), and then trace the fiber along the principal eigenvector direction as we did before. In this paper we use a moving least squares (MLS) fiber tracing algorithm from Zhukov and Barr Zhukov02 to recover heart muscle fibers. To our knowledge this is the first 3D reconstruction of the heart muscle fibers from DT-MRI data.