You would want to do it by talking about your feelings perhaps, but I don't think you need to go into any detail regarding any particular patient. Talk about what the experience was like for you, not about the patient.
For example: I came to learn X about myself when working in close proximity to patients who were struggling with the aftermath of diffuse axonal injuries. I came to realize that I was fascinated with why some injuries were more severe despite having less pronounced visible damage... etc... I want to study X because of my experience in working with patients who were working hard to overcome the effects of Y. It was this struggle that resonated with me on an emotional level and I knew that I found an area of work that I could really dedicate my efforts to.
It's more important to focus on why you want to be there than the impact a particular patient had on you.
Mark