Original ArticleOn the use of low-dimensional temporal subspace constraints to reduce reconstruction time and improve image quality of accelerated 4D-MRI
Introduction
In stereotactic body radiotherapy (SBRT), ablative radiation doses are delivered to tumor targets over one to five fractions. With this technique, accurate daily delineations are critical to ensure precise delivery to the target while minimizing dose to nearby organs at risk (OARs). MR-guided online adaptive radiotherapy (MRgOART) on hybrid MRI/treatment machines, such as the Elekta Unity MR-Linac [1], permit treatment plan adaptations incorporating daily changes in geometry or motion prior to delivery of each treatment fraction. However, obtaining high quality daily reference images on which the adaptive plans are based can be challenging due to significant respiratory induced motion in the abdomen and thorax.
Recently, we detailed the implementation and initial clinical use of a 4D-MRI driven workflow for free-breathing abdominal SBRT on an Elekta Unity MR-Linac [2]. Currently, only free-breathing treatment deliveries are supported on Unity. The implementation of 4D-MRI was performed to eliminate systematic offsets between daily reference images and free-breathing treatment deliveries. Our approach employed a 3D golden angle radial [3] stack-of-stars [4] (GAR SoS) acquisition that is inherently robust against motion [5] and has favorable point spread function properties for recovery of artifact-free images from highly accelerated data acquisition periods [6], [7].
The use of iterative algorithms is necessary for image recovery of highly accelerated data [8], which always come with a heavy computational burden. Using high performance computing helps to alleviate some of these issues [9], but trade offs between scan duration, reconstruction time, and image quality must be carefully made.
Most 4D methods consider the 4D-MRI reconstruction process as resolving completely separate images of the same anatomy in several motion states. An alternative approach considers 4D-MRI reconstruction as resolving the changes in each voxel’s image intensity as a function of respiratory phase. The latter approach presents some interesting reconstruction possibilities. Over the average respiratory cycle, the image intensity within any given voxel will change slowly, or minimally in large homogeneous structures. This concept lends itself to a low-dimensional subspace representation of each voxel’s signal evolution over respiratory phases. Constraining the reconstructed images to span a low-dimensional subspace with a rank less than the number of desired respiratory phases offers a lower computational complexity through the need for fewer 2D fast Fourier transform operations. The accuracy of the images, however, is dependent on an accurate selection of the basis functions. In the case of subspace-constrained reconstruction for resolving MR signal dynamics, basis functions are estimated by principal component analysis (PCA) of a dictionary of signal evolutions that were simulated via the Bloch equation [10], [11], [12]. In the case of resolving respiratory or cardiac motion, however, no analytical model exists for generation of subspace basis functions applicable to all patients. Rather, a low-resolution image navigator is acquired, from which the basis functions can be estimated via similar PCA methods [13], [14], [15]. Recent work by Feng et al. demonstrated that, for radial k-space coverage, the low-resolution navigator can be extracted directly from the full-resolution dataset to be reconstructed, thus eliminating any uncertainty between the acquisition of the navigator and imaging data [16], [17]. This method was found to be profoundly successful for dynamic contrast-enhanced MRI applications. Here we assess the applicability of such methods for use in 4D-MRgOART.
The primary motivation for incorporating subspace constraints into the 4D-MRgOART workflow is reduced computational burden and, therefore, reconstruction time. The iterative methods necessary to reconstruct highly accelerated data require the use of many forward and adjoint Fourier transform operations. By approximating each voxel’s signal evolution over respiratory phases as a low-dimensional subspace of rank K, the number of Fourier transform operations in each iteration reduces to K instead of the number of respiratory phases . Further, subspace constraints improve the conditioning of the inverse problem provided the sampling of k-space produces incoherent artifacts over respiratory phases. This often results in improved image quality with the use of subspace-constrained reconstructions in addition to the computational efficiency benefits [18], [10], [15].
Section snippets
Image reconstruction
Raw k-space data from each 4D-MRI acquisition were transferred to an offline server (96 core Intel Xenon Platinum 2.7 GHz, 512 GB RAM) on the local Unity machine network where custom code written in MATLAB (The MathWorks, Natick, MA) automatically queues and processes each dataset. The data were pre-whitened to de-correlate inter-RF-coil noise [8], [19], corrected for delays between gradients and data acquisition objects [20], brought to a hybrid image-k-space with an inverse Fourier transform
Results
The image reconstruction time comparisons are summarized in Fig. 1. For each reconstruction type, a total of 12 data points were included (i.e. four contrasts for five subjects). The mean reconstruction time (“4D Recon. Time”) includes the iterative reconstruction time spent performing the ADMM algorithm for each 4D-MRI reconstruction. For the subspace-constrained reconstructions, the time to calculate the subspace basis functions is also shown. The mean 4D reconstruction time of 3.25 min for
Discussion
Temporal subspace-constrained image reconstruction was implemented and tested in the context of 4D-MRgOART. A subspace-constrained reconstruction with two or three basis functions yielded lower reconstruction times, fewer image artifacts, sharper mid-position images, and similar motion estimates compared with conventional bin-by-bin 4D-MRI reconstructions. Subspace constraints provided all of these benefits for five patients across four different image contrasts. These results demonstrate the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors would like to thank Cathy Marszalkowski for her efforts with IRB protocol submission and consenting patients.
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