Hybrid model¹ has been proposed to monitor temperature map in thermal ablation. However, it needs manual selection of regularization parameter λ and sometimes converges slowly. The proposed KalBHT hybrid algorithm is aimed to develop a self-adaptive, robust and real-time thermometry method by combining the original hybrid thermometry algorithm and the bio heat transfer equation (BHTE) model.

Algorithm We first use a BHTE model to calculate a predicted temperature map by the Fourier transform method². Then a regularization term with self-adaptive control parameter λ is introduced to the hybrid algorithm as$$ {\phi}(w,c,{\theta},{T})=\frac{1}{2}\sum\limits^{N_{c}}_{m=1}\sum\limits^{N_{s}}_{j=1}|y_{i,m}-(\sum\limits^{N_{b}}_{b=1}x_{b,j}w_{b})e^{i(\left\{Ac\right\}_{j,m}+\theta_{j,m})}|^2 +||{W(T)\theta}||_{0},$$where $$$\sum\limits^{N_{b}}_{b=1}x_{b,j}w_{b}$$$ gives the weighting of baseline images, $$$\left\{Ac\right\}_{j,m}$$$ presents the polynomial background phase and $$$\theta_{j,m}$$$ is the temperature induced phase of point j in coil m. The window W is a function of the predicted temperature map T, which has bigger value when the predicted temperature is higher and vice versa. However, the introduction of BHTE model will induce two more problems. The first is how to match the predicted temperature map with current image with the existence of motion and the second is the inaccuracy of BHTE model. Thus, we use a rough registration between the current frame and its previous frame to solve the motion problem. A Kalman filter is introduced to update the predicted temperature map to find a balance between prediction and real data when the BHTE model is inaccurate.

Experiment An agar phantom was heated with a microwave generator (10W, ECO healthcare, Nanjing, China) for ten minutes. Dynamic images were acquired on a 3T scanner (Philips Achieva, Philips Healthcare) during the heating with an 8-channel head coil (FFE, TE=10ms, TR=50ms). The phantom was simulated to move within ±8 pixels from left to right (Fig.1 left). In the proposed algorithm, the electric field power distribution produced by microwave was obtained from COMSOL (COMSOL Inc., Palo Alto, CA). Temperature maps were estimated and two points in the phantom were monitored with fiber optics （Foten, Canada) as golden standard. Additionally, healthy liver images were acquired dynamically by 32-channel cardiac coil (FFE, TE=10ms, TR=26ms, $$$N_{s}$$$=16384, $$$N_{b}$$$=50, $$$N_{c}$$$=8, FOV 240mm×307.5mm). A Gaussian hot spot with the highest temperature up to 40℃ was simulated on the image. Both the proposed KalBHT hybrid algorithm and the original hybrid algorithm at different λ were implemented to liver images. The computation time and RMSE of the hot spot region were calculated to illustrate the effect of the introduction of BHTE model. Furthermore, heating simulation was conducted in MATLAB to demonstrate the robustness of KalBHT hybrid algorithm to inaccuracy of BHTE model. The proposed algorithm was evaluated when the predicted temperature maps were +50% overestimated and −50% underestimated, respectively.

Fig.1 (right) shows the temperature curves of the two points (15mm and 20mm away from the hot spot center) estimated by hybrid and KalBHT hybrid algorithm and monitored by fiber optics. The proposed algorithm shows smoother and more accurate temperature change, especially for the outer point.

Fig.2 illustrates the heating simulation results on liver data. Compared to the original hybrid algorithm, the KalBHT hybrid algorithm converges faster in only 23 seconds and gives more accurate hot spot temperature estimation without tricky selection of regularization parameter λ.

Besides, since Kalman filter is used in the proposed algorithm to filter the predicted temperature map T, the estimated phase is still relatively accurate even when the BHTE model is underestimated or overestimated temperature by 50%, as shown in Fig.3.

The KalBHT hybrid algorithm introduces the BHTE model to the original hybrid MR thermometry algorithm as a prior knowledge of the hot spot. The proposed algorithm has a faster convergence rate and more accurate temperature estimation than the original hybrid algorithm. In addition, the BHTE model is able to interpolate temperature maps during the acquisition and reconstruction of the next frame of a MR temperature image, which makes real-time temperature monitoring possible.