Question normal

As a cardiologist I routinely encounter patients post MI, who have severe segmental wall motion a kinesis, especially LV apex and have thrombus sitting on.
Despite of anticoagulation most of them still have thrombus even after 6 months.
Is there a method to determine that thrombus is organized and there is no longer risk of embolization? How long we can treat them?
Is there any role of noacs in patients with LV thrombus?