Fig. 4

Theoretical and experimental performance of the predictive temperature controller. a Exponential projections calculated at each time point of observation. The average slope of the curve is used to estimate the asymptotic values \(T\left( {\delta, t \to \infty } \right)\), which are further used to adjust the new duty cycle of sonication. b Measured average temperature in a 13-pixel ROI inside the medullar cavity (axial PRFS thermometry) and the applied duty cycle versus time. Same experiment as shown in Figs. 2 and 6