Biomimetic Canopy

Hi, This is my first post here. I am looking for any suggestions on how to best model a biomimetic canopy that replicates the structure of capillaries (smallest of the body's blood vessels). I have had little success. It seems like a combination of brancing and weaving. 

As of now all I can think of is setting two curves on each end for the main structure, then dividing each and connecting with lines in between and piping it all at the end but the results are not that great. 

Here is an image of what I wish to replicate.

Any suggestions?