Our 3D medical image segmentation software ITK-SNAP makes it pretty easy to extract structures from 3D scans and save them as STL files for 3D printing. Structures can be labeled manually or extracted semi-automatically.
The software is open-source, and available for major platforms from itksnap.org
Unfortunately, it will not read proprietary .vol files - but if you convert to standard DICOM, NIFTI or other common 3D image format, it works.