An ultrasound exposure safety processor is configured for spatially relating respective definitions of an imaging zone, and an extended dead-tissue zone that includes both a dead-tissue zone and a surrounding margin. Based on whether a push pulse focus is to be within the extended dead-tissue zone, the processor automatically decides a level of acoustic power with which the pulse is to be produced. If the pulse focus is to be within the extended dead-tissue zone, the pulse may be produced with a mechanical index (MI), a thermal index (TI), and/or a spatial-peak-temporal-average intensity (IspTA) that exceeds respectively 1.9, 6.0 and 720 milliwatts per square centimeter. The imaging zone may be definable interactively to dynamically trigger the deciding and the producing, with push pulse settings being dynamically derived automatically. A display of multiple push pulse sites allows user manipulation of spatial definition indicia to dynamically control displacement tracking.