afni.nimh.nih.gov

As Paul said, the Jacobian determinant is a measurement at each location of the expansion or contraction of the volume in that location. To measure the overall expansion or contraction of the brain, the simplest method that comes to my brain at this second would be to create brain-only masks of the before and after brain volumes, and then add up the volume of these masks.

Jacobian (and other) values can be computed from a warp in AFNI using the 3dNwarpFuncs program.