Synopsis

A BHT model was introduced to modify the penalty term of hybrid method for monitoring microwave ablation. Simulation results demonstrate that the proposed method is robust with the BHT model and can reconstruct more accurate temperature maps with different regularization parameters. Ex vivo experiment shows that the proposed method can achieve improved performance for rapid background shifting.

Purpose

Recently, minimally invasive and noninvasive therapies like Radiofrequency (RF) and High Intensity Focused Ultrasound (HIFU) are gaining popularity rapidly. Several proton resonance frequency shift based thermometry techniques were developed to monitor the temperature during the treatment. According to a recent comparison study, the ability of hybrid thermometry to achieve superior performance was demonstrated.^1,2 However, the original hybrid algorithm suppresses the low-level temperature rise to zero, additionally, hybrid has difficulty correcting non-smooth background phase shift, which can arise from probe-induced perturbation in microwave ablation. To reduce the drawbacks, a self-adaptive bio-heat transfer (BHT) model is introduced to modify the penalty term of hybrid. The proposed method is more robust with the non-smooth background phase shift and can reserve the low-level temperature rise well.

Method

BHT Model:

The BHT model is based on the Pennes equation:

$$\rho C \frac{\partial T}{\partial t} = \lambda \Delta ^{2} T - \omega C (T - T_{blood}) + Q$$

where $$$\rho$$$ is the density of the tissue, $$$C$$$ is the specific heat of tissue, $$$T$$$ is the temperature distribution, $$$\lambda$$$ is the tissue thermal conductivity, $$$\omega$$$ is the perfusion rate and $$$Q$$$ is the heat source term.

Self-adaptive BHT Model Modifying Hybrid Penalty Term (BHT-hybrid):

In hybrid, the temperature induced phase shift $$$\theta$$$ is estimated by minimizing the cost function. Here BHT model is introduced and the cost function becomes:

$$\Psi(\omega, c, \theta) = \frac{1}{2} \sum_{j=1}^{N_s} \left| y_j-\left(\sum_{b=1}^{N_b}x_{b,j}\omega_b \right)e^{i(\{Ac\}_j + \theta_j)} \right|^2 + \lambda \Vert \theta - \theta_{bht}\Vert _0$$

where $$$y$$$ is the image phase, $$$x_{b}$$$ is the baseline library, $$$\omega$$$ is the weight vector of the baselines, $$$Ac$$$ is the background phase shift, $$$\theta$$$ is the temperature induced phase shift and $$$\theta_{bht}$$$ is the phase shift predicted by the BHT model.

Before the treatment, the baseline library is scanned and BHT parameters $$$\rho$$$, $$$c$$$, $$$\lambda$$$ are selected as experiential values. During the treatment, hybrid was applied for the first two time frames to estimate the source term $$$Q$$$ by temperature subtraction. Using the thermal parameters, temperature distribution in time t (t>=2) and the source term, $$$\theta_{bht}$$$ of time t+1 was predicted and BHT-hybrid method was performed to get the temperature distribution in time frame t+1, where thermal parameters and source term were updated with L-M method.³ Flowchart of the proposed method is illustrated by Fig 1.

Simulation Study:

A simulation experiment was performed to demonstrate the feasibility, accuracy and robustness of the proposed method.

A rectangle object with a random phase was generated on a 64$$$\times$$$64 grid, multibaseline library with 50 images was formed by shifting up and down the object. Then, a random polynomial background phase shift and a Gaussian hot spot were added into the image phase.¹ To validate the robustness of the proposed method, $$$\theta_{bht}$$$ was overestimated by 50%.

Ex Vivo Experiment:

A porcine tenderloin experiment was designed to demonstrate that the proposed method is insensitive to rapid background phase shift. The tenderloin was heated with a microwave probe under the power of 30 W for 300 seconds. Data was acquired on a 3T MR scanner (Philips Achieva, Philips Healthcare) with 2D gradient echo sequence (TE=10 ms, TR=50 ms, flip angle = 30°). Single baseline subtraction (SBS), hybrid and BHT-hybrid with $$$\lambda$$$=0.01 were performed, respectively.

Results

Simulation result is shown in Fig 2, as can be seen from the temperature curves, the proposed method can reconstruct the temperature induced phase with a 50% overestimated $$$\theta_{bht}$$$, and is robust with the BHT model error. The error maps show that the reconstruct results of proposed method are more accurate with different $$$\lambda$$$.

Ex vivo results are shown in Fig 3 and Fig 4. Fig 3 shows the temperature images reconstructed by SBS, hybrid and BHT-hybrid. It is shown that SBS is sensitive to background shifting, hybrid can reduce smooth background phase shift but suppresses the temperature to zero in rapid background shifting area. BHT-hybrid reduces the smooth background shifting and reserves the temperature rise in rapid shifting area.

In Fig 4, Temperature curves of point 1 show that hybrid has difficulty correcting rapid background phase shift. Temperature curves of point 2 show that both hybrid and BHT-hybrid reconstruct similar results and temperature curves of point 3 show that SBS is sensitive to background shifting, which can be reduced by hybrid and BHT-hybrid.

Discussion & Conclusion

Acknowledgements

References

1. Grissom, W. A., et al. Hybrid referenceless and multibaseline subtraction MR thermometry for monitoring thermal therapies in moving organs. Journal of Cardiovascular Magnetic Resonance 37.9(2010):5014.

2. Rieke, V, et al. Comparison of temperature processing methods for monitoring focused ultrasound ablation in the brain. Journal of Magnetic Resonance Imaging 38.6(2013):1462.

3. Ozisik, M. Necati, and Orlande, Helcio R. B. Inverse heat transfer : fundamentals and applications. (2000):37-57.