Modelling the temperature evolution of bone under high intensity focused ultrasound.

Magnetic resonance-guided high intensity focused ultrasound (MR-HIFU) has been clinically shown to be effective for palliative pain management in patients suffering from skeletal metastasis. The underlying mechanism is supposed to be periosteal denervation caused by ablative temperatures reached through ultrasound heating of the cortex. The challenge is exact temperature control during sonication as MR-based thermometry approaches for bone tissue are currently not available. Thus, in contrast to the MR-HIFU ablation of soft tissue, a thermometry feedback to the HIFU is lacking, and the treatment of bone metastasis is entirely based on temperature information acquired in the soft tissue adjacent to the bone surface. However, heating of the adjacent tissue depends on the exact sonication protocol and requires extensive modelling to estimate the actual temperature of the cortex. Here we develop a computational model to calculate the spatial temperature evolution in bone and the adjacent tissue during sonication. First, a ray-tracing technique is used to compute the heat production in each spatial point serving as a source term for the second part, where the actual temperature is calculated as a function of space and time by solving the Pennes bio-heat equation. Importantly, our model includes shear waves that arise at the bone interface as well as all geometrical considerations of transducer and bone geometry. The model was compared with a theoretical approach based on the far field approximation and an MR-HIFU experiment using a bone phantom. Furthermore, we investigated the contribution of shear waves to the heat production and resulting temperatures in bone. The temperature evolution predicted by our model was in accordance with the far field approximation and agreed well with the experimental data obtained in phantoms. Our model allows the simulation of the HIFU treatments of bone metastasis in patients and can be extended to a planning tool prior to MR-HIFU treatments.