Is it common for physical illness (unrelated to the brain) to cause mental changes? What have been your or your loved ones' experiences with this?

For example, my grandma was sharp as a tack until she got a stomach ulcer. She was around 80 and she developed dementia. Even after she was all healed up physically, she never regained the mental acuity she had before.

My other grandma is about the same age, and whenever she gets a UTI she gets really confused for a while, but she bounces back after it gets cleared up.

How common is this? Does it happen to people other than the elderly? Has it ever happened to you or someone you love?