Repairing a Cane Back Chair?

I have a beautiful cane backed chair from the 50s or 60s. it has a lovely curved back, with caning in 3 sections. The middle section has broken. It had been in California since purchased by the original owner (beach side).

I purchased it from her estate and after about a year moved it to Las Vegas. My husband sat in it and leaned back kind of hard. The caning had dried and tore apart and not in a way it could be glued back. I can't find any place to repair it. The chair has a cushion seat and I had it redone in a retro fabric. It looks great, but now back is broken. Help please.