The followings are English translations of quotations from one commentary, written by a Japanese brain expert. (Unfortunately, the commentary itself is written in Japanese)
By closely examining brain tissue samples from patients who died after taking anticancer drugs, researchers found that even in adult brains, neurons were nascent, at least in the dentate gyrus of the hippocampus.
On the other hand, a study using 14C as a tracer suggest that neurogenesis in the neocortex is very limited.
From the abstract of the first literature, you can achieve general understanding of how to prove neurogenesis. The following is a definitive statement of the first literature.
Human brain tissue was obtained postmortem from patients who had been treated with the thymidine analog, bromodeoxyuridine (BrdU), that labels DNA during the S phase.
The nature of the anticancer drug of first literature was such that it was only taken up into the DNA when the cells were dividing. The fact that these anticancer drug-incorporated nerve cells were located near the hippocampus seems to prove neurogenesis.
The second paper used 14C level in DNA as a date mark for when a cell was born based on following facts.
- Concentration of environmental 14C (these are produced in nuclear tests) has decreased exponentially since the 1963 Nuclear Test Ban Treaty.
- The DNA is stable after a cell has gone through its last cell division.
The key is to use substances having both of following properties; if we can prove that the substance was taken up at least after adulthood, then we can prove that the cells divided after adulthood.
- only taken up into the cell when the cell divides, and
- stay stably inside the cell after the cell divides.
For more information, read the references (written in English) cited above.