I recently came across a study which looked at blood flow with people with stutter and people who do not. The results were people who stuttered have less blood flowing to their brain. Exercise may increase the blood flow to the brain. I do not know if this is the case here as I am not an expert. From my experience I have seen an improvement in my speech when I have not thought about my stutter or when I have accepted my stutter and did not think about people's reactions to my stutter.