An Introduction to Visualization of Diffusion Tensor Imaging and Its Applications A. Vilanova 1 , S. Zhang 2 , G. Kindlmann 3 , and D. Laidlaw 2 1 Department of Biomedical Engineering Eindhoven University of Technology, Eindhoven a.vilanova@tue.nl 2 Department of Computer Science Brown University, Providence {dhl,sz}@cs.brown.edu 3 School of Computing University of Utah, Salt Lake City gk@cs.utah.edu Summary. Water diffusion is anisotropic in organized tissues such as white matter and muscle. Diffusion tensor imaging (DTI), a non-invasive MR technique, mea- sures water self-diffusion rates and thus gives an indication of the underlying tissue microstructure. The diffusion rate is often expressed by a second-order tensor. In- sightful DTI visualization is challenging because of the multivariate nature and the complex spatial relationships in a diffusion tensor field. This chapter surveys the different visualization techniques that have been developed for DTI and compares their main characteristics and drawbacks. We also discuss some of the many biomed- ical applications in which DTI helps extend our understanding or improve clinical procedures. We conclude with an overview of open problems and research directions. 1 Introduction Diffusion tensor imaging (DTI) is a medical imaging modality that can reveal directional information in vivo in fibrous structures such as white matter or muscles. Although barely a decade old, DTI has become an important tool in studying white matter anatomy and pathology. Many hospitals, universi- ties, and research centers have MRI scanners and diffusion imaging capability, allowing widespread DTI applications. However, DTI data require interpretation before they can be useful. Vi- sualization methods are needed to bridge the gap between the DTI data sets and understanding of the underlying tissue microstructure. A diffusion tensor measures a 3D diffusion process and has six interrelated tensor components. A volumetric DTI data set is a 3D grid of these diffusion tensors that form complicated patterns. The multivariate nature of the diffusion tensor and the