Fluorodeoxyglucose (18F-FDG^{18}\text{F}\text{-FDG}18F-FDG) is a radiotracer widely used in oncology and neurology. A patient undergoing a neurological study is administered 18F-FDG^{18}\text{F}\text{-FDG}18F-FDG, which concentrates in regions of the brain with high metabolic activity. The fluorine-18 isotope decays by emitting positrons (β+\beta^+β+ particles). Figure 1 shows a PET detector ring positioned around the patient's head, recording the resulting radiation.

Explain the physical process that occurs inside the patient's brain following positron emission, and how the PET scanner's detector ring and processing system use the resulting radiation to determine the exact location of high metabolic activity.