Do tick regenerate from the head?

My cat had a tick on her shoulder last night and my boyfriend pulled it off with tweezers, but half of the head ripped off with the blood sac and the other half stayed. He thinks that ticks can regenerate from the head, but can they regenerate from half of their head? Or is the sucker dead? By the way, she is on flea and tick preventive. (Frontline) For some reason it's becoming more and more ineffective. Any brands ya'll might suggest?