To date, there is no study showing a link between unforgiveness and Alzheimers, but there are indications that this could be the case in an indirect sense. Consider this article, “The Healing Power of Forgiveness,” written by a board-certified psychiatrist and neurologist, from the Fortanasce-Barton Neurology Center in California.
The article presents evidence that high levels of anger can lead to more toxins going to the brain (the study was done on mice and so we must be careful in extrapolating this to humans). In this same article above, a study on humans showed that when presented with very disturbing stimuli, the research participants’ brains showed signs of agitation “and exhaustion of the neurons, therefore increasing their stress and cortisol levels that will interfere with good neuronal transmission.”
So, your intuition of a link between unforgiveness (agitation, anger) and brain function has merit as a hypothesis.
In closing, I want to mention one prevalent issue on the Internet between forgiveness and Alzheimers and that is the need for caretakers to forgive the patient and to forgive the self.
Here is one article on forgiving the one with the disease: “Forgiveness Toward an Alzheimer’s Victim.”
Here is one from the Mayo Clinic on forgiving the self when caring for someone with the disease: “Forgive yourself as a caregiver, and relieve anger.”