Introduction

Safe and time-efficient MRI scans remain challenging as radiofrequency heating notably depends on patients’ anatomy^1-3. We propose a non-invasive and precision approach to temperature, supported by deep learning^4,5 and tested on two different brains. Our goal is to accurately predict internal body temperature based on patient-specific parameters such as tissue distribution and surface temperature. The principle behind our Non-Invasive Temperature Estimation (NITE) method is as follows: consider a brain slice inside which the temperature distribution is unknown (N points). Let us now consider N_s surface temperature sensors. Each internal point N_p is linked to each surface sensor by an imaginary line divided in q segments, to take into account the tissue distribution and parameters - permittivity, conductivity, density ($$$\epsilon$$$, $$$\sigma$$$, $$$\rho$$$) - along this line. The temperature profile for the N_p point can be written as: $$$P_N{{_p-}}{_N}_{{_S}{_1}} = [\epsilon(\overrightarrow{r}),\sigma(\overrightarrow{r}),\rho(\overrightarrow{r}),\parallel N{{_p-}}N_{{_S}{_1}} \parallel_2, N_{{_S}{_1}}(\overrightarrow{r},T{_{N}}_{{_S}{_1}})]$$$. Finally, we can describe the mapping of internal temperature as an inverse problem. We consider a neural network classification problem with a defined precision of 0.1°C, train a neural network on one brain slice using the features mentioned above, and then test this model on other slices to predict the unknown internal temperatures.

Methods

Using the CST Studio Suite software (Dassault Systèmes, France), a 4T TEM head coil was modeled and two different numerical human models (Visible Human Male HUGO and Visible Human Female NELLY) were imported in this coil with a 0.8 mm resolution. An electromagnetic and thermal co-simulation was performed and temperature maps were obtained for both brains, on 9 axial slices (5 HUGO’s, 4 NELLY’s). The slices were manually segmented in CST with different tissue types (White Matter, Gray Matter, CerebroSpinal Fluid, Bone, Muscle, Fat, Skin, Blood, Air) as seen in Figure 1a (HUGO) and Figure 1b (NELLY). They were then imported in Matlab to map the tissue properties to each slice: permittivity, conductivity, density. The thermal maps obtained from CST were imported in Matlab for data preparation for the deep learning training (Figure 2). An array of 35 features for each point was the input: 33 tissue properties (11 segments having 3 properties each), 1 norm distance to each of the four surface sensors, 1 surface temperature value. The output was the internal temperature for each point. The neural network was implemented in TensorFlow with 3 layers, a total of 270 nodes, a ReLU (Rectified Linear Unit) activation function, a learning rate of 0.0001 and 800 epochs (Figure 3a). Random dropout was implemented to prevent overfitting and improve the generalization to unseen slices. The training was done on one slice from the HUGO model: after the training was completed, testing was performed on the other slices from both HUGO and NELLY. The generated temperature maps were then compared with the temperature maps obtained from CST (Figure 3b). Additionally, the time necessary to run the full CST simulation and NITE was examined.

Results

The cost at the final epoch was 0.18, the training and testing accuracy were 93% and validation loss was 0.19. The solution converged as the validation loss reached a minimum. Simulated and predicted temperature maps are visible in Figure 4a (HUGO) and Figure 4b (NELLY). Figure 5 shows the quantitative comparison between the same simulated and predicted temperature maps both for HUGO (Figure 5a) and NELLY (Figure 5b). The left picture shows the correlation between CST and NITE. The right picture shows the temperature difference between CST and NITE: positive and negative values respectively show where NITE is overestimating and underestimating temperature compared to CST. The CST full simulation was in the order of magnitude of hours, whereas once the training was done (in less than an hour) the thermal map prediction was done in milliseconds.

Discussion

The closer (anatomically) a test slice is from the training slice, the more accurate the prediction is. Intra-brain results obtained with the first HUGO test slice (Figure 4a – upper row) show comparable results between CST and NITE, which is consistent with the similarities existing between the training and test slice. In NELLY’s test slices, some tissue types who were present in the training slice are not present in NELLY’s slices (Blood and Air): this has an influence on inter-brain testing performance and the ability to generalize. However, hotspots predictions are encouraging especially when considering Figure 5: NITE tends to overestimate rather than underestimating temperature, while still accurately locating major hotspots. Finally, the time comparison is in favor of NITE which generates temperature maps in milliseconds compared to the hours needed for CST. One challenge to overcome is to use several brain slices to train the network. Nevertheless, deep learning has shown promising capabilities in other safety estimation methods (SAR-wise)⁶, and our current work also supports the use of artificial intelligence to tackle RF safety problems. Finally, this work is an in silico study, however we plan to test our method in vivo using MRI images acquisition.

Conclusion

This study demonstrates the potential of this deep learning-based temperature estimation method to generalize to different brains, while keeping the computational cost low compared to traditional numerical simulations: in vivo experiments will allow to definitely conclude on the potential of the method.

Acknowledgements

No acknowledgement found.

References

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