Purpose

Proton resonance frequency (PRF) shift imaging is one of the most accurate temperature imaging methods currently on MRI, and has many important applications, such as measuring MR heating due to RF pulses, and monitoring temperature increase for MR-guided high intensity focused ultrasound (MRgHIFU) intervention. Currently PRF imaging is limited by its acquisition speed to cover large region-of-interest with high temporal resolution. Developing methods to accelerate the PRF could potentially enable monitoring RF heating of a human subject directly using the MRI scanner, instead of relying on EM field calculation with human tissue models that do not match reality. By accelerating the PRF imaging, MRgHIFU can also get higher temporal resolution to ensure better treatment quality. Among many other efforts on accelerating PRF through non-linear reconstruction methods, such as applying temporal constraint on standard CS reconstruction (1), or fitting a k-space model (2), this work presents a novel reconstruction method based on complex difference (CD) based compressed sensing (CS) (3) and low rank plus sparse (L+S) separation (4).

Theory & Methods

Based on previous work (3) in which complex difference was effective in approximating PRF phase shift, and CD based cost function was effective for CS reconstruction for PRF, this work further explores the benefit of using low rank and sparse separation on CD, and demonstrates the feasibility of using singular value thresholding (SVT) to regularize the low rank temperature-related component (L) of CD, as temperature change over time is typically smooth, and using soft-thresholding to regularize the non-temperature related sparse component (S) of CD, such as water motion in water-bathed brain HIFU intervention. A CS based reconstruction method can be formulated as min(||L||_* + u||TS||₁), s.t. E(L+S) = d-d₀ (Eqn 1), where ||L||_* is the nuclear norm or sum of singular values of the matrix L, ||S|| the l₁ norm or sum of the absolute values of the entries of S, T the sparsifying transform and the temporal FFT in this study, E the multichannel encoding operator with undersampled data d and fully-sampled baseline data d₀, and u a tuning parameter. An algorithm to solve the constrained minimization problem is in Table 1. The validation of the method is demonstrated in three representative applications at 3T: Fig 1, ex vivo heating of beef for RF heating monitoring at (TE/TR = 10/100 ms, 300 x 300 mm2 FOV, 128 x 128 matrix size, 8 mm slice thickness); Fig 2, in vivo HIFU in the human leg muscle (TE/TR = 12/25 ms, 280 x 280 mm2 FOV, 256 x 256 matrix size, 5 mm slice thickness); and Fig 3, HIFU intervention of human brain phantom in water-bath (TE/TR = 13/28 ms, 280 x 280 mm2 FOV, 256 x 256 matrix size, 3 mm slice thickness). For all three cases, spatial-temporal single channel data were collected with full-sampling, and the corresponding image domain data were weighted with simulated receive field patterns from an eight channel circular array to obtain multichannel k-space data. The data, except for the baseline, were then undersampled in cartesian with 1D variable density (R=4) within each time frame to exploit image domain incoherence, and the undersampling patterns are different in temporal dimension to exploit temporal incoherence. Because CD-only based method was shown with better accuracy than standard TCR (3), in this report, the proposed L+S CD based CS reconstruction is mainly compared to 1) CD-only based CS method, and 2) direct implementation of L+S to TCR.

Results

In all three cases (Fig 1,2,3), the proposed L+S CD based CS reconstruction demonstrates better accuracy than the CD-only based CS reconstruction and direct implementation of L+S to TCR. The method is also demonstrated to be robust and accurate throughout different time frames. Especially for water-bathed HIFU heating (Fig 3) in which undersampling artifacts due to water motion is a major challenge to reconstruction, the proposed method, by separating apart the water motion (S) and temperature change (L) components of the CD (Fig 4) and applying different l-norm metric and sparsifying transformations to each component, delivered the least artifact to date to the best knowledge of the authors.

Discussion & Conclusions

This study validated using the low rank feature of temperature evolution for PRF acceleration. Compared to previous study, this study provides a CS algorithm that can benefit from using an receive array, and re-validated that using CD to approximate and constrain PRF-induced phase change is effective for CS reconstruction, especially for HIFU applications that have not been presented previously. The results here further imply a potentially new direction that high field RF safety is monitored and regulated.

Acknowledgements

The authors thank Kim Butts Pauly from Stanford in providing leg muscle HIFU dataset, and Pooja Gaur for helpful discussion.