James, you might want to use mild soap/detergents; if you think it needs washing because of contamination with excessive oily road grime or grease you should clean the brush as soon as possible. The use of any solvents is up to you; depending on the type of brush and the level of damage to the filaments/bristles it may be better to replace the brush stock only, all the other brush parts can be re-used many times over.
Usually though I remove the brush from the pole give it a through rinse with pure water wipe it over including the filaments then let it completely air dry for a few days (or sometimes weeks in my case). Once its bone dry I remove any build up of grime at the base then clean the brush and rinse well with pure.
You can test the brush by holding it in your hand and go over clean pane of glass, (don’t rinse) check the results when it’s dry.
The Aerial brushes can last many years and can come up almost like new, scuffs marks aside. Even so filaments do wear and once a brush has lost it edge - by that I mean its ability to maintain its cleaning speed; it is more practical to replace the stock.