**2. Focused ultrasound principles**

FUS surgery was first reported in 1942 after being applied to cat and dog brain tissue [34, 35] and more elaborate neurological studies later followed [36, 37]. MRgHIFU integrates a FUS transducer into a MRI system with near real-time imaging feedback; capable of temporal resolution less than 1.0 seconds, in-plane resolution less than 1.0 mm, and temperature resolution less than 1.0°C [34]. Thermal tissue ablation results from rapid temperature change of greater than 55°C during heating or −20 to −50°C during cooling [38]. Adequate ablation for coagulative necrosis requires about 10 seconds, with intermittent cooling periods to avoid skin burning [34]. More recent developments enable various feedback methods to regulate temperature, optimize speed, and automate the scanning procedure [39].

FUS works via constructive wave interference. The waves are generated by powering piezoelectric elements with an alternating current [40]. Most modern transducers are phase-array types, composed of hundreds of elements that can be individually controlled, each emitting a low amplitude ultrasonic wave at the focus [40]. Each wave is low enough in amplitude to pass through the tissue without causing significant heating, interfering constructively at the focus. The phase lag of each transducer element is adjusted so the waves are in-phase at the focal region, capable of performing beam steering and refocusing phase aberrations from bone or tissue inhomogeneities. When the waves form a large amplitude oscillation, the heating increases substantially and allows ablation and coagulative necrosis. The wave amplitude and frequency can be controlled by the operator as well as other factors like position, applied power, and pulse modulation. Lower frequencies are better for deep sites like transcranial applications, while high frequencies are used for surface sites [41].

Tissue has an inherent property to absorb ultrasonic energy. The acoustic absorption coefficient measures a tissue's ability to absorb ultrasound. In tissue at 1 MHz, the beam attenuates to about 50% at a depth of about 7 cm [38]. Beam reflection is significant at interfaces with large differences in acoustic absorption coefficient, causing high amounts of reflection at tissue-gas interfaces and tissue-bone interfaces [38]. At large FUS powers, strong rarefactional pressures exist. If this is coupled with lower frequency ultrasound waves, the conditions are favorable to induce tissue nucleation [34, 42]. This results in cavitational heating that can cause detrimental tissue damage or be utilized in techniques like lithotripsy [43, 44] and histotripsy [45, 46]. Low temperature therapies expose cells to about 43–45°C for long time periods. High temperature thermal therapy uses temperature between 50°C and 80°C for short time periods to ablate tissue, cause coagulation, and induce necrosis [47]. The tissue damage is estimated by the equivalent number of thermal doses at 43°C, with necrosis induced after about 240 min at 43°C [48, 49].
