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

Respiratory motion is a major concern in radiotherapy (RT) in liver cancer patients. Probability-based treatment planning is an evolving approach for tumor motion management. A major hurdle of this approach is that the dosimetric error is tightly linked to the reproducibility of the tumor motion probability density function (PDF). Previous studies in lung used single-slice dynamic MRI for PDF reproducibility evaluation that could only captured the 2D respiratory motion restricted by the MRI acquisition speed. Moreover, inter-subject and inter-fractional variability of time evolved PDF might be underestimated by using just two fractions. In this study, we aim to investigate the inter-fractional and inter-subject abdominal motion PDF and its reproducibility using an ultrafast volumetric 4D- MRI.

**Material and Methods: **

8 healthy volunteers (34.33±5.77years) were
recruited. Each underwent 5 scans of free-breathing 4D-MRI at 1.5T using 3D
spoiled-gradient-echo sequence, which (transversal, FOV=350(FE)x262.5(PE)mm,
thickness=4mm, matrix size=128x128x56, TE/TR=0.6/1.7ms, flip-angle=6^{o},
RBW=1250Hz/voxel, CAIPIRINHA factor=4, partial Fourier factor=6/8) yielded a
temporal resolution of 1s/volume (56 slices) and a reconstructed voxel-size of
2.2x2.2x4mm. 144 frames (totally 8,064 images) were obtained within ~144s. Organ
masks, including liver, left and right kidneys, and spleen were manually delineated
based on the 2nd frame images and served as reference. Following frames were
rigidly registered to the reference masks to calculate the mean position and
displacement from the mean position for each organ. The PDF(*δ, t, f*), a time-evolved probabilistic
organ position distribution, was estimated from fitting the organ respiratory displacement
(*δ*) histogram within the scan
duration (*t*) in a session (*f*) to a Gaussian function. The
time evolved inter-fractional PDF reproducibility function *R*(*t*), defined as:$$R(t) = 2{{PD{F_1} \cap PDF(\delta ,t,f)} \over {PD{F_1} \oplus PDF(\delta ,t,f)}} \tag{1}$$,was calculated at every
3-second. To simulate the real RT treatment, the PDF calculated from the first
scan was considered as the treatment planning reference.The mean PDF reproducibility was fitted to an
exponential function

$$\bar R(t) = {A_0}+{A_1}{e^{{\rm{ - }}{A_2}t}} \tag{2}$$ From the fitted curve, the mean initial PDF reproducibility, $$$[{\bar R_0} = \bar R(t=3s)]$$$, the mean ending PDF reproducibility,$$$[{\bar R_e} = \bar R(t=144s)]$$$, and the PDF reproducibility equilibrium time constant $$$T({R_{0.63}})$$$ (the time when PDF reproducibility curve reaches 63% of $$$({R_e}-{R_0})$$$ were determined. Inter-subject and intra-subject coefficients of variance (CVs) were determined. A Mann-Whitney U test was used to assess the differences between organs.

**Results**

**Discussion and Conclusion**

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.

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 Example of organs’ displacement histograms and the
fitted probability distribution functions of the reference 1st scan
fraction.

Figure 2 Different organs’ mean displacement probability
distribution functions (PDF) across all subjects of fractions relative to the
treatment planning reference plotted as a function of scan time.

Figure 3. Mean probability distribution function
(averaged over total of 8 subjects in 4 fractions) plotted as function of scan
time. Standard deviations plotted as error bars.

Table 1. Measurements of
*R*_{0} and *R*_{e} for all subjects