Can I Wash My Ionic Breeze In The Dishwasher?

Can I wash some parts of my ionic breeze in the dishwasher, such as the collection grid/filter. I know from basic searches online, that I can wash the front and rear covers in the dishwasher, but there is some dirt on the grid that is really stubborn and doesn't want to come off.
I would call Sharper Image... but that doesn't really work considering they are out of business and I can't use the lifetime warranty if it breaks...