How does a vampire ... you know? [read details-NSFW!]?

I’d like to know how a vampire gets an erection.
For example, in Twilight, Bella has sex with Edward, the vampire.
a VAMPIRE.
He has no blood flow, no circulation; he is not alive. He is dead. He is cold. How on earth did he manage an erection when he and Bella had intercourse?
I mean, she mentions how hard he is all the time, but I doubt he has a permanent erection…