Brain cells don’t come and go. That’s why it’s so difficult to treat diseases like Alzheimer’s, Parkinson’s, Huntington’s, and even spinal cord injury (since the spinal cord is also part of your central nervous system, it also has non-renewable cells). Ordinary cell death leads to a general brain atrophy as you age, and pathological cell death as seen in the diseases I just mentioned facilitates this process leading to the cognitive deficits associated with them. The only areas of your brain that can produce new cells are the subventricular zone of the lateral ventricles and the subgranular zone in the dentate gyrus.