Sorry, I probably should have more more specific. What I should really say is 'how important the unique fine-grained structure of white matter is.'
If the structure is relatively generic between brains, and doesn't encode identity-crucial info in its microstructure, we may be able to fill it in using data from other brains in the future.
http://www.technologyreview.com/view/541311/the-false-science-of-cryonics/
Michael Hendricks is a neuroscientist and assistant professor of biology at McGill University.