How do I clean up unintended mesh inside a mesh? I'm a novice Blender user and I could use some advice on cleaning up some unintended mesh. 

I'm working on a 3D model that I extracted from microscopy data. For this purpose the volumes are extracted from the raw data using a program called AVIZO. Then I exported the volumes to blender for smoothing and animation etc. 
I've been working on the model for a couple of months and I was adding the finishing touches when I found out that there was a lot of unintended mesh inside of the model. I think that I must have been sloppy with the "fill holes" or "fill" functions in an earlier version of the model. 

I've deleted part of the unintended mesh by hand but it takes a lot of time.  I'm wondering if you know a faster way of cleaning it up? Due to the pending deadline I don't have enough time to go back to an earlier version. I can provide some screenshots of the mesh if that helps.

I hope it's okay for me to ask such a question on this forum. 

Thanks!

Edit: 

This is the screenshot of my mesh. As you can see there is a lot of stuff going on in the centerpart.


Edit: 

I've uploaded the most troublesome part of the mesh
Your mesh is really a mess. 

I think the method I show here can help you with it.

In Edit mode, wireframe view, use the border select to select the up and bottom parts.

Hide them or invert the selection.

In case you use HIDE: Select all the rest and separate it (do not delete it because you can need it later ).

Now the interior is a separated mesh.

See the image below.