Within biological systems water molecules undergo continuous stochastic Brownian motion. The rate of this diffusion can give clues to the structure of underlying tissues. In some tissues the rate is anisotropic - faster in some directions than others. Diffusion-rate images are second-order tensor fields and can be calculated from diffusion-weighted magnetic resonance images. A 2D diffusion tensor image (DTI) and an associated anatomical scalar field, created during the tensor calculation, define seven dependent values at each spatial location. Understanding the interrelationships among these values is necessary to understand the data. We present two new methods for visually representing DTIs. The first method displays an array of ellipsoids where the shape of each ellipsoid represents one tensor value. The novel aspect of this representation is that the ellipsoids are all normalized to approximately the same size so that they can be displayed in context. The second method uses concepts from oil painting to represent the seven-valued data with multiple layers of varying brush strokes. Both methods successfully display most or all of the information in DTIs and provide exploratory methods for understanding them. The ellipsoid method has a simpler interpretation and explanation than the painting-motivated method; the painting-motivated method displays more of the information and is easier to read quantitatively. We demonstrate the methods on images of the mouse spinal cord. The visualizations show significant differences between spinal cords from mice suffering from Experimental Allergic Encephalomyelitis (EAE) and spinal cords from wild-type mice. The differences are consistent with pathology differences shown histologically and suggest that our new non-invasive imaging methodology and visualization of the results could have early diagnostic value for neurodegenerative diseases.
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