Apparent diffusion tensor maps of the human brain were acquired with a magnetic resonance imaging sequence (Gudbjartsson, H., Maier, S.E., Mulkern, R.V., M6rocz, I.A., Patz, S., Jolesz, F.A., Magn. Reson. Med. 36 (1996) 509-519). It was shown that the geometric nature of the apparent diffusion tensors can quantitatively characterize the tissue structure. Display of the orientation and directional uniformity of the water diffusion in the brain demonstrated most of the known major anatomical constituents of human white matter. A comparison of corresponding anatomic regions in the white matter of both hemispheres in 24 healthy volunteers revealed that fiber tracts within the anterior limb of the internal capsule have a significantly higher (P < 0.01) measure of alignment in the right hemisphere. This method offers a unique tool for the in vivo demonstration of neural connectivity in healthy and diseased brain.