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

^{1}Medical 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 studies

^{1-3}
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-MRI

^{4}.

**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=6

^{o}, 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

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