Kalman Filtered Bio Heat Transfer Model Based Self-adaptive Hybrid Magnetic Resonance Thermometry

Yuxin Zhang^{1}, Kexin Deng^{1}, Shuo Chen^{2}, Bingyao Chen^{3}, Xing Wei^{3}, Jiafei Yang^{3}, Shi Wang^{2}, and Kui Ying^{2}

** Algorithm** We first use a BHTE model to calculate a predicted
temperature map by the Fourier transform method

** 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.

[1] WA. Grissom, V. Rieke, AB. Holbrook, Y. Medan, M. Lustig, J. Santos, et al. Hybrid referenceless and multibaseline subtraction MR thermometry for monitoring thermal therapies in moving organs. Med. Phys. 2010, 37(9): 5014-5026.

[2] S. Roujol, De Senneville BD, S. Hey, C. Moonen, M. Ries, Robust adaptive extended kalman filtering for real time MR-thermometry guided HIFU interventions. IEEE Trans. Med. Imag. 2012, 31(3): 533-542.

Fig.1 An agar phantom was scanned with microwave heating. The phantom was moved
manually within ±8 pixels from left to right. Two points of the phantom were
monitored by fiber optics, (i)
1.5cm and (ii) 2cm away from the hot spot center. The temperature curves of the
two points estimated by two algorithms were compared with the golden standard measured by fiber optics.

Fig.2 Image of liver and the simulated temperature map are illustrated in
the
first row.
Temperature maps of both hybrid and KalBHT
hybrid algorithm were estimated, with their error maps, calculation time and
RMSE of the hot spot region shown.

Fig.3 Effect of inaccurate BHTE model on the KalBHT hybrid algorithm. The predicted temperature maps were overestimated (bottom row) and underestimated (upper row) by 50%, respectively in simulation with Gaussian noise. The estimated phase under these two situations is still relatively accurate.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

2108