In our dental lab, we use an ultrasound machine to clean our teeth. I found it to be an effective non-abrasive way to keep them clean and to form. I've been wearing the fixer for years (a hawley), and I've used a microsonic machine to keep it clean. If you often use it to clean your fixator or appliance, you can buy a personal type of machine that should do well. Brushing can be proven to be abrasive, and odors cause bacteria to enter these tiny "little trees" that are formed on the surface of your fixator by brushing your teeth. Also, when you brush your teeth, there is a lot of wear and tear on your teeth, because there are a lot of bruises when you brush your teeth.
Note: some people's saliva will produce a large amount of calcium buildup, and these people will inevitably have some (or many) white blood accumulations. If your fixator is heavily overridden, you can consider sending them back to the dental lab for a deep professional cleaning, where they will be scraped off with special tools. A personal sonic can help slow down the process and reduce the severity of the deposition. When used with antibacterial cleansing agents, you can keep them fresh and clean for a long time.
Some ultra-luxurious personal sonic machines even have an ultraviolet ray that clearly doesn't require any extra detergent/tablet, but you'll probably see about $50 on the price. Many can be bought cheaper.