Synopsis

MR image-guided radiotherapy (IGRT) holds potentials on outcome improvement in the head-and-neck (HN) radiotherapy. Patients receiving MR-guided multi-fractional HN IGRT are immobilized in each treatment fraction and set up to the exact position as of the treatment planning scan. Inter-fractional MR images are supposed to show highly correlated anatomy structure and edge information which can be incorporated into compressed sensing (CS) based MR reconstruction to shorten the scan time while preserve image quality in multiple fractions. In this study, we investigated the feasibility of accelerating high spatial resolution 3D MRI using CS with structure-guided total variation for multi-fractional HN radiotherapy.

Introduction

Method

Image Acquisition under Radiotherapy Setup

Eleven healthy volunteers were recruited and informed consent was obtained. MR images were acquired on a 1.5-Tesla MR scanner (Aera, Siemens Healthineers, Erlangen, Germany) dedicated for radiotherapy applications. Each volunteer received a series of scans (4-40 times) in an immobilized RT treatment position to simulate the HN-RT treatment fractions. All volunteers were immobilized using a personalized 5-point thermoplastic mask, and carefully aligned using a well-calibrated 3-dimensional external laser system. T1-weighted SPACE images were acquired with: FOV = 470mm×470mm×269mm and matrix size = 448×448×256 (PE×FE×SE); TR/TE = 420/7.2 ms, echo train length (ETL) = 40, bandwidth = 657Hz/pixel, yielding an isotropic voxel size of 1.05mm. The k-space was retrospectively undersampled along the phase-slice encoding direction using a 2D Poisson Disc sampling pattern with a reduction factor of 8. Images from the first scan were used as the anatomical prior.

Image Reconstruction

Following the conventional CS framework, the reconstruction of the i-th scan session images can be formulated as $$\mathop {\arg \min }\limits_{\bf{x}} \left\| {{\bf{Fx}} - {\bf{y}}} \right\|_2^2 + \lambda R({\bf{x}})\tag{1},$$ where $$${\bf{F}}$$$ is the undersampled Fourier transform, $$${\bf{y}}$$$ represents the acquired undersampled k-space data, $$$R({\bf{x}})$$$ is the regularization function, and $$$\lambda $$$ is the regularization parameter.

In multi-fractional radiotherapy, as the patient is scanned in the immobilized treatment position using the same imaging protocol, images acquired from multiple sessions are expected to show high correlation on anatomical structures and edges to the first scan session image. To exploit such inherent structural correlation, we proposed to use the three-dimensional structure-guided total variation as the penalty function to aid the reconstruction process. Specifically, instead of blindly and uniformly enforcing local smoothness on an image itself, the structure-guided total variation enforces the parallelity between the reconstructed image $$${\bf{x}}$$$ and the first scan reference image $$${\bf{I}}$$$’s gradients, or mathematically as $$R({\bf{x}}|{\bf{I}}) = \sum\limits_{n = 1}^N {{{\left( {{{\left| {\nabla {{\bf{x}}_n}} \right|}^2} - {{\left\langle {\nabla {{\bf{x}}_n},{{\bf{\xi }}_n}} \right\rangle }^2}} \right)}^{1/2}}} \tag{2},$$ where $$$N$$$represents the total number of pixels, $$$n$$$ is the pixel index, $$$\nabla $$$ denotes the three dimensional discrete gradient operation to compute the image gradient along three orthogonal directions, $$${{\bf{\xi }}_n} = \nabla {{\bf{I}}_n}/{\left| {\nabla {{\bf{I}}_n}} \right|_\tau }$$$ with $$${\left| {\nabla {{\bf{I}}_n}} \right|_\tau } = {({\left| {\nabla {{\bf{I}}_n}} \right|^2} + {\tau ^2})^{1/2}}$$$ denotes the normalized spatially varying gradient field obtained from $$${\bf{I}}$$$, and parameter $$$\tau $$$ penalizes the influence of noise. Such measure of structure similarity using the parallelism of paired images’ gradients is also known as a special case of asymmetric parallel level sets⁶ and has been proven to be convex that allows the employment of any smooth minimization methods.

Based on the abovementioned model, the compressed sensing reconstruction with the structure-guided total variation regularization can be formulated as $$\mathop {\arg \min }\limits_{\bf{x}} \left\| {{\bf{Fx}} - {\bf{y}}} \right\|_2^2 + \lambda R({\bf{x}}|{\bf{I}})\tag{3}.$$ The underlying convex optimization problem was solved using alternating direction method of multipliers (ADMM).

Results

Conclusion

Acknowledgements

References

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