Caused injury?

How much of an injury? Any medical bills? If not, get some. Then make a claim against him, in writing, for your bills and pain and suffering. Follow up with a lawsuit if you get no response. If he gets his homeowners insurance involved he will be in a world of hurt when his insurance company either makes him take the fence down or cancels his policy.

I don't think there is any doubt about negligence here. He knows damned well that a barbed wire fence is dangerous and not necessary in a residential area.

Also check your city and county ordinances to see if it's a violation.