Virtually every engineering field can be applied to biological or medical questions, including not only chemical, electrical and mechanical engineering but also materials science and other engineering specialties. My own training is in mechanical engineering, and I now work in orthopaedic biomechanics, which applies the concepts of mechanics to orthopaedic problems such as osteoporosis and fracture healing. For an idea of the breadth of biomechanics problems that are currently being researched, you can view the program of the recent World Congress of Biomechanics:
For chemical or electrical engineering, you can find similar information by searching on "bioelectrical engineering" and "biochemical engineering." As you will see, these areas are broad and can encompass many systems, more than I can possibly present here. Remember that you also may have elective courses in your curriculum that will allow you to take further courses beyond the specific track you select and that allow you to further diversify. There are many interesting engineering applications in medicine, I'm sure you will enjoy your decision!