This DICOM result comes with many connections between the exterior and interior surface. These connections happen on the "ends" of the veins (which is correct) but also due to errors while meshing.
Basic workflow:
You need to break ALL those connections so you'll get the interior and exterior as non connected surfaces. After that you can EDIT/Separate both surfaces as separate objects. Now you need to SelectAll of the interior object, do Edit/FlipNormals and fix the holes using ANALYSIS/Inspector.
Best way to get rid of the exterior surface is to sample different SelectVisibles:
Go to SELECT.
Select some "seed" selection. Which selection doesn't matter - just to get access to selection based tools.
Navigate to a view where you do not see the interior surface through the outlet of the veins and run Modify/SelectVisible. Now navigate to a different view (again where you don't see the interior) and with Shift pressed do Modify/SelectVisible again. This adds the new aspect to the previous selection. Repeat until you got the exterior selected.
When you selected most of the exterior without selecting the interior you might use the selection brush to add missed surfaces manually (or deselect while pressing CTRL (Cmd on Mac)).
Now hit Y to separate the exterior and hide it via ObjectBrowser's eye icon (against deleting the surface this gives the chance to transfer regions back if you didn't select properly)
With the interior object being active hit Ctrl+A (Cmd+A on Mac) to SelectAll and run Edit/FlipNormals.
Now fix the holes via ANALYSIS/Inspector:

This result is attached below.