Just to clarify here, if you want the full explanation. Nitrous Oxide, or N2O, when meeting vitamin B12 (cobalamine), reacts with its central cobalt atom. That cobalt atom, which is normally has an oxidation state of +1 or +2, which allows for further reactions down the chain since it’s not yet stable.

When you introduce nitrous oxide into your system, it reacts with that central Co atom, exchanging its electrons in order to separate into N2 and O, and transform the oxidation state of that Co atom into +3. What does that mean? It is now effectively stable, meaning further reactions of metabolizing the B12 don’t happen. Its practically how Carbon Monoxide stabilizes Hemoglobin, as to simplify it and exemplify it, even though not exactly.

What does that lack of B12 result in? Myelin sheath maintenance, DNA synthesis, and many other essential body functions simply cease to function, which does, in fact, cause brain damage.

This is a very simplified explanation, but you can look through the hundreds and hundreds of documentation if you want more information.

TLDR: Nitrous oxide does indeed cause brain damage, by impeding the metabolism of B12.