Oi Lei Wong^{1}, Jing Yuan^{1}, Yihang Zhou^{1}, Siu Ki Yu^{1}, and Kin Yin Cheung^{1}

^{1}Medical Physics and Research Department, Hong Kong Sanatorium & Hospital, Hong Kong, Hong Kong

### Synopsis

Respiratory motion characterization and uncertainty estimation is important in radiotherapy treatment planning, and is hindered by the imaging capability of 4DCT or time-resolved single/multi-slice MRI (2D+t). In this study, characterization of the positional and orientation uncertainty of abdominal organ respiratory motion, extracted from the time-resolved volumetric 3D+t MRI, was done using bootstrapping and tensor analysis.

### Introduction

Radiotherapy (RT) treatment planning of the abdomen is often challenged by the pronounced respiratory motion. Probabilistic treatment planning provides a patient-specific motion management solution by including the respiratory-induced tumor motion in the treatment planning optimization processing [1]. Although a few preliminary studies showed limited dosimetric benefit by using probabilistic treatment planning [1], it was partially attributed to the limitations in respiratory motion characterization and its uncertainty estimation, restricted by the imaging capability of 4DCT or time-resolved single/multi-slice MRI (2D+t). Time-resolved volumetric MRI (3D+t MRI) has recently been proposed to overcome the limitations of 4DCT or 2D+t MRI by (1) its superior soft-tissue contrast [2,3], and (2) its prospective and simultaneous 3D motion capturing with sufficiently high temporal resolution. Moreover, respiratory motion uncertainty is postulated to be better estimated by motion tensor analysis and bootstrapping technique. We, thus, proposed to better characterize the positional and orientation uncertainty of abdominal organ motion during free-breathing using 3D+t MRI, bootstrapping and tensor analysis.###

Methods

Free-breathing upper abdominal 3D+t MR images were obtained on 9 healthy volunteers (age: 36±6) using a 3D-spoiled gradient-echo sequence (transversal, FOV=350(FE)x262.5(PE)mm, matrix size=128x128x56, thickness=4mm, TE/TR=0.53/1.57ms, flip-angle=5

^{o} , RBW=1400Hz/voxel, CAIPIRINHA factor=4, partial Fourier factor=6/8, 144 timeframes) at 1.63 frame-per-sec (fps) on a 1.5T MR-simulator with a 18-channel body matrix coil and spine coil. Liver, left kidney, right kidney and spleen were segmented on the first timeframe, and their motions were estimated by rigidly registering the image volumes to the chronologically first timeframe. For each image set, the estimated positional shift was subtracted by the mean positional shift prior to the generation of 1000 bootstrap samples through bootstrapping. For each bootstrap sample, the covariance matrix was calculated for the generation of the corresponding eigenvalues (λ

_{1}, λ

_{2}, λ

_{3}) and eigenvectors (

*v*_{1},

*v*_{2},

*v*_{3}) using single value decomposition (i.e. 1000 sets of eigenvalues and eigenvectors in total). The mean principle eigenvector was subsequently estimated using the mean dyadic tensor (i.e.$$$\frac{1}{1000} \sum_{i=1}^{1000} v_{1} v^{T}$$$ ). The uncertainty of the principle eigenvector orientation was evaluated using the apex angle of the cone of uncertainty (aCU, the angle between the mean principle eigenvector and each bootstrap estimate of principle eigenvector).

### Results

The mean eigenvectors(**v**_{1}, *v*_{2}, *v*_{3}) with the length of the corresponding mean eigenvalues (λ_{1}, λ_{2}, λ_{3}) of the respiratory organ position in a subject were illustrated in Figure 2. The mean and median of λ_{1}, λ_{2}, λ_{3} and aCU were shown in Table 1. For all organs, the mean aCU was small (< 0.01 radian (0.57^{o})). The largest mean λ_{1} and λ_{2} were obtained in the spleen (λ_{1} = 20.59±8.61mm, λ_{2} = 0.65±0.36mm) when compared with other organs (λ_{1} = 11.34±6.46mm (liver), 9.54±2.18mm (left kidney), 9.00±3.85mm (right kidney) , λ_{2} = 0.13±0.07mm (liver), 0.35±0.22mm (left kidney), 0.43±0.37mm (right kidney)).### Discussion

The stability of the probabilistic organ position distribution in the respiratory motion is mainly affected by the breathing irregularity, while could still subject to the imaging limitations in spatial and temporal resolution as well as registration error. The small aCU (<0.01 radian (0.57^{o})) obtained in this study suggests that the current 3D+t MRI protocol was fast enough for respiratory motion sampling, thus allowed a reliable estimation of the respiratory-induced organ motion. We believed that our estimation might better represent respiratory motion than the traditional methods by taking the advantage of the high temporal resolution of 3D+t MRI in that (1) our tensor-based estimation was rotationally invariant so, theoretically, independent of patient positioning and more reliable; (2) orientation uncertainty estimation, which was rarely investigated, might provide additional information on the respiratory motion for probabilistic treatment planning. For all organs, our estimated λ_{1} was much larger than λ_{2} and λ_{3}, which mainly reflected the expected largest positional shift along SI (Figure 2). The λ_{1} of the left (9.54±2.18mm) and right kidneys (9.00±3.85mm) were similar to the reported SI displacement (left kidney: 8.48±3.04mm; right kidney: 8.9±3.7mm) [4]. It was worth noting that a larger λ_{1} in liver than in spleen were observed, probably due to the large deformability of liver during respiration. As such, further study using non-linear registration is warrant. Other limitation of this study includes a small sample size and short scan time (relative to the typical radiotherapy treatment).### Acknowledgements

No acknowledgement found.### References

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