How does cancerous tissue break down radioisotopes faster than normal tissues?
Cancerous tissues break down glucose faster, not radioisotopes. Doctors use PET technique to detect breakdown of glucose, and "hot spots" are investigated as potential tumors.

Glucose can be labeled with radioisotope to show up on PET scan. Normal glucose is "invisible".

Hence, candidate for tumor will breakdown any glucose, but radioactive glucose will show up on scan.