Right off the bat, first issue, this is not attempted for one main reason: Gas exchange. Aquariums are usually longer width and lenght wise rather than height, because of this. There just has to be a large enough surface area for oxygen to dissolve in and CO2
The second thing is water flow, for filtres to work they must have the water available to pull it towards it self and filter it. With such caves you would need to study the water dynamics and install powerheads in strategic places to prevent water stagnation.
Third problem, cleaning the water, substrate or aquarium floor. For this usually syphoning vacuums are used in such a complex structure this would be a problem and a lot of waste would accumulate.
Fourth issue, adult fish size would have to be taken in consideration when stocking such a tank as the narrow curves and swimming space in general would influence the fish's quality of life.
Those are the main issues I can think of right now. Dont get me wrong everything is possible, check out my open bottom tank thread. I'm all for innovation, but this issues would have to be solved before attempting to put any fish in there. This has be done on large scale, in a café or bar, let me look up the link and I'll post it.