Unfortunately there is no public api that will allow you to execute the Apply logic. The Apply method is executed when the Mappings are modified (add, remove, clear), when the LayoutStrategies are modified (add, remove, clear) and when a property of the TreeMapData changes.
I think that it would be much easier if you could implement this PropertyChanged logic in your DataTemplate and have the image reload when the property in mind changes. Let us know how it goes.
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