A medical apparatus comprising: - a heating system for heating a target zone of a subject , wherein the heating system is a high intensity focused ultrasound system ; - a processor for controlling the heating system ; - a memory containing machine executable instructions, wherein execution of the instructions causes the processor to receive a treatment plan, wherein execution of the instructions further causes the processor to repeatedly: - heat the target zone during alternating heating periods and cooling periods to create multiple differently positioned sonications by controlling the heating system using the treatment plan; - calculate a present energy density map in a predefined volume outside the target volume during each sonication using the treatment plan and a thermo acoustic model taking into account an estimated rate of tissue cooling, wherein the present energy density is repeatedly updated during the heating of the target zone ; - calculate a cumulative energy density map by using weighted averaging of the present energy density maps taking into account the estimated rate of tissue cooling between the sonications; - display the cumulative energy density map on a display; and - to modify the treatment plan in accordance with the cumulative energy density map taking into account a next heating event to limit the cumulative energy density in the predefined volume. - a heating system for heating a target zone of a subject , wherein the heating system is a high intensity focused ultrasound system ; - a processor for controlling the heating system ; - a memory containing machine executable instructions, wherein execution of the instructions causes the processor to receive a treatment plan, wherein execution of the instructions further causes the processor to repeatedly: - heat the target zone during alternating heating periods and cooling periods to create multiple differently positioned sonications by controlling the heating system using the treatment plan; - calculate a present energy density map in a predefined volume outside the target volume during each sonication using the treatment plan and a thermo acoustic model taking into account an estimated rate of tissue cooling, wherein the present energy density is repeatedly updated during the heating of the target zone ; - calculate a cumulative energy density map by using weighted averaging of the present energy density maps taking into account the estimated rate of tissue cooling between the sonications; - heat the target zone during alternating heating periods and cooling periods to create multiple differently positioned sonications by controlling the heating system using the treatment plan; - calculate a present energy density map in a predefined volume outside the target volume during each sonication using the treatment plan and a thermo acoustic model taking into account an estimated rate of tissue cooling, wherein the present energy density is repeatedly updated during the heating of the target zone ; - calculate a cumulative energy density map by using weighted averaging of the present energy density maps taking into account the estimated rate of tissue cooling between the sonications; - display the cumulative energy density map on a display; and - to modify the treatment plan in accordance with the cumulative energy density map taking into account a next heating event to limit the cumulative energy density in the predefined volume. <EOS>