After brain tumor is resected and going thru radiation and chemo how is it determined if the cancer is gone? Just if tumor doesn't grow back?

CT and MRI. After treatment patients come for regular neurological exams and imaging with ct or mri. Often the patient develops neurological symptoms which signals a recurrence. On imaging you hope to achieve either no tumor or at least no growth.
Yes. Since cancer is basically defined by inappropriate cell growth that continues beyond normal cellular regulation, one could say the cancer is gone when a tumor does not recur/regrow after treatments as above. A pet scan can determine possible tumor activity in the body. I truly wish you the best in your treatments for your astrocytoma.
Brain tumor f/u. The best way is by examination and history. How is the patient doing? Are they stable, are they improving, or are they getting worse? The other important aspect of monitoring is imaging studies, usually MRI is best, but ct, or pet may be used as well.
Yes. Imaging and clinical exams are the best way to determine if the cancer is coming back, short of going back in and doing another biopsy (which is not recommended).
Brain tumor. It's almost entirely based on follow-up MRI scans to see if there is any evidence of re-growth, along with tracking and evaluating any symptoms, along with physical exams.
Yes and MRI. The best evidence for cure is the fact that the cancer has not grown back. This fact is not only verified by how you feel but also by periodic imaging, particularly MRI scans (magnetic resonance imaging) for anaplastic astrocytomas at periodic intervals to be determined by your physicians.