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How long a 4D-MRI do we need for abdominal radiotherapy treatment planning? A time dependence analysis of abdominal motion probability distribution function using ultra-fast volumetric dynamic MRI
Yihang Zhou1, Jing Yuan1, Oi Lei Wong1, Kin Yin Cheung1, and Siu Ki Yu1

1Medical Physics and Research Department, Hong Kong Sanatorium & Hospital, Hong Kong, China

### Synopsis

Radiotherapy (RT) treatment planning (TP) based on probability distribution function (PDF) is an evolving approach for tumor motion management. In PDF-TP, the dose distribution is weighted by the probability of the tumor being in that location during the treatment, thus the determination of reliable tumor motion PDF from time resolved dynamic imaging, named 4D-imaging, is essential. Ideally, a 4D-MRI should be as long as or even longer than the real abdominal RT treatment to represent the real motion pattern and account for any motion irregularity in the treatment, but it is actually impractical. Thus, another unanswered question is how long a 4D-MRI scan is really needed in order to obtain a tumor motion PDF as reliable as possible but keep acquisition as short as possible. In this study, we aim to determine the optimal 4D-MRI duration for PDF-TP by analyzing the time dependency of different abdominal organs’ PDF using an ultrafast volumetric 4D-MRI.

### Purpose:

Radiotherapy (RT) treatment planning (TP) based on probability distribution function (PDF) is an evolving approach for tumor motion management. In PDF-TP, the dose distribution is weighted by the probability of the tumor being in that location during the treatment, thus the determination of reliable tumor motion PDF from time resolved dynamic imaging, named 4D-imaging, is essential. Previous studies1-3 used single-slice dynamic MRI, to determinate PDF and assess its reproducibility in lung. Single-slice MRI suffers from the incapability of the entire tumor volume motion capturing simultaneously in 3D, thus leads to potential errors in the estimation of tumor motion PDF. Ideally, a 4D-MRI should be as long as or even longer than the real abdominal RT treatment to represent the real motion pattern and account for any motion irregularity in the treatment, but it is actually impractical. Thus, another unanswered question is how long a 4D-MRI scan is really needed in order to obtain a tumor motion PDF as reliable as possible but keep acquisition as short as possible. In this study, we aim to determine the optimal 4D-MRI duration for PDF-TP by analyzing the time dependency of different abdominal organs’ PDF using an ultrafast volumetric 4D-MRI4.

### Material and Methods:

8 healthy volunteers (34.33±5.77years) underwent free-breathing 4D-MRI at 1.5T using 3D spoiled-gradient-echo sequence (transversal, FOV=350(FE)x262.5(PE)mm, thickness=4mm, matrix size=128x128x56, TE/TR=0.6/1.7ms, flip-angle=6o, RBW=1250Hz/voxel, CAIPIRINHA factor=4, partial Fourier factor=6/8). 720 frames (totally 103,680 images) were obtained within ~720s resulted in a temporal resolution of 1s-per-volume (56 slices) and a reconstructed voxel size of 2.2x2.2x4mm. Organ reference masks, including liver, left and right kidney, and spleen were manually delineated based on the 2nd frame images. Following frames were rigidly registered to the reference masks to calculate the mean position and the displacement from the mean position for each organ. The organ motion PDF, a time-evolved probabilistic organ position distribution, was extracted from fitting the organ respiratory displacement (δ) histogram within the scan duration (t) as PDF(δ,t). We hypothesized that the time-dependent organ motion PDF should approach the true PDF with time, but might establish an equilibrium state, sufficiently and reliably representing the true PDF for PDF-TP. To validate this, the calculated from the 720s scan was used as the ground truth, and the PDF reproducibility evolution function R(t) was calculated every 5 sec, and compared with the ground truth using $$R(t)=2{{PD{F_{ref}}\cap PDF(\delta ,t)}\over {PD{F_{ref}}\oplus PDF(\delta ,t)}}\tag{1}$$. The mean PDF across all subjects as a function of time $\bar R(t)$ was also calculated and fitted to an power function $$\bar R(t)=a{t^{{\rm{-}}b}}+c \tag{2}$$. From the fitted curve, the time for an organ to establish the equilibrium state, defined as the time when PDF reproducibility curve reaches 85%, named equilibrium time constant $T(R(t)=0.85)$ was recorded to determine the optimal 4D-MRI duration.

### Results:

Figure 1 demonstrates the reformatted 4D-MRI images of a volunteer in three orthogonal views acquired by the ultra-fast volumetric 4D MRI.Figure 2 shows an example of the displacement histogram of different organs in a subject.Figure 3 demonstrates the PDF reproducibility R(t) plotted as a function of scan time for each subject.All subjects showed an increasing PDF reproducibility with time and finally reach R(t)=1, equivalent to the ground truth, while with significant inter-subject difference (ranksum test p<0.001). Figure 4 presents the subject-averaged PDF reproducibility curve fitted by Eq.(2) in different organs.Different organs exhibited considerably different equilibrium time constant (Liver:111±70sec, 95%CI=[34,188]sec; Left Kidney:91±86sec, 95%CI=[13,204]sec; Right Kidney:90±78sec, 95%CI=[30,203]sec; Spleen:59±86sec, 95%CI=[0,185]sec). Considering the upper limit of the 95%CI as the criterion, the optimal 4D-MRI duration of 188sec, 204sec and 185sec was suggested for liver, kidneys and spleen, respectively. To characterize the entire abdomen respiratory motion including multiple organs, a 4D-MRI duration of approximately 200sec would be appropriate.

### Discussion and Conclusion:

In this study, we determined the optimal 4D-MRI duration for respiratory motion PDF estimation in abdominal organs by evaluating the time dependence of motion PDF reproducibility using a fast volumetric 4D MRI. Abdominal organ motion PDF contains critical temporal information for probability-based RT treatment planning, however, requires specific image techniques to extract confidently. With a high temporal resolution of 1s-per-volume, our volumetric 4D-MR was fast enough to capture the respiratory motion simultaneously in three dimensions, provided a reliable reference for motion PDF estimation. Furthermore, our study revealed the relationship between the abdominal organ motion PDF reproducibility and the scan time, and determined the optimal 4D-MRI duration for PDF-TP in different abdominal organs.The main limitation of this study is the recruitment of only a small number of healthy volunteers and the displacement approximation using rigid registration, neglecting the organ deformability during motion.The motion PDF of real patients might be substantially different from healthy volunteers.Respiration irregularity and its influence on motion PDF in patients should be further investigated.

### Acknowledgements

No acknowledgement found.

### References

1. Cai J, Read PW, Altes TA, Molloy JA, Brookeman JR, Sheng K. Evaluation of the reproducibility of lung motion probability distribution function (PDF) using dynamic MRI. Phys Med Biol 2007;52(2):365-373.

2. Cai J, Read PW, Larner JM, Jones DR, Benedict SH, Sheng K. Reproducibility of interfraction lung motion probability distribution function using dynamic MRI: statistical analysis. Int J Radiat Oncol Biol Phys 2008;72(4):1228-1235.

3. Zhang F, Hu J, Kelsey CR, Yoo D, Yin FF, Cai J. Reproducibility of tumor motion probability distribution function in stereotactic body radiation therapy of lung cancer. Int J Radiat Oncol Biol Phys 2012;84(3):861-866.

4. Yuan J, Zhou YH, Wong OL, Cheung KY,Yu SK. “Development of a fast 4D-MRI with sub-second volumetric frame rate for respiratory motion tracking in abdominal radiotherapy”, ISMRM, Paris, Jun 2018.

### Figures

Figure.1 The reformatted 4D-MRI images of a volunteer in three orthogonal views acquired by 3D gradient echo sequence based 4D-MRI (56 slices, voxel size= 2.2x2.2x4mm, 1s/frame).

Figure. 2 An example of the displacement histogram of different abdominal organs in a subject during the 720 sec scan.

Figure. 3 The PDF reproducibility R(t) plotted as a function of scan time for each subject.

Figure. 4 The subject-averaged PDF reproducibility curve fitted by a power function for different abdominal organs.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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