However, when I export the segmentation as a model and save it as a PolyData (.VTK) file, the 3D model is hollow and only shows the outer surface of the segmentation. (shown below)
VTK polydata is a polygonal surface mesh: the volume is defined by the enclosing surface. There is no need for elements inside.
What would you like to do with your model? Use it for finite-element analysis? In that case you can use Segment Mesher extension, which creates volumetric mesh (tetrahedral mesh, stored in a VTK unstructured grid) directly from segmentation.