Modeling intra-fractional abdominal configuration changes using breathing motion-corrected radial MRI

Abstract

Abdominal organ motions introduce geometric uncertainties to gastrointestinal radiotherapy. This study investigated slow drifting motion induced by changes of internal anatomic organ arrangements using a 3D radial MRI sequence with a scan length of 20 min. Breathing motion and cyclic GI motion were first removed through multi-temporal resolution image reconstruction. Slow drifting motion analysis was performed using an image time series consisting of 72 image volumes with a temporal sampling rate of 17 s. B-spline deformable registration was performed to align image volumes of the time series to a reference volume. The resulting deformation fields were used for motion velocity evaluation and patient-specific motion model construction through principal component analysis (PCA). Geometric uncertainties introduced by slow drifting motion were assessed by Hausdorff distances between unions of organs at risk (OARs) at different motion states and reference OAR contours as well as probabilistic distributions of OARs predicted using the PCA model. Thirteen examinations from 11 patients were included in this study. The averaged motion velocities ranged from 0.8 to 1.9 mm min⁻¹, 0.7 to 1.6 mm min⁻¹, 0.6 to 2.0 mm min⁻¹ and 0.7 to 1.4 mm min⁻¹ for the small bowel, colon, duodenum and stomach respectively; the averaged Hausdorff distances were 5.6 mm, 5.3 mm, 5.1 mm and 4.6 mm. On average, a margin larger than 4.5 mm was needed to cover a space with OAR occupancy probability higher than 55%. Temporal variations of geometric uncertainties were evaluated by comparing across four 5 min sub-scans extracted from the full scan. Standard deviations of Hausdorff distances across sub-scans were less than 1 mm for most examinations, indicating stability of relative margin estimates from separate time windows. These results suggested slow drifting motion of GI organs is significant and geometric uncertainties introduced by such motion should be accounted for during radiotherapy planning and delivery.

1. Introduction

Radiotherapy for gastrointestinal (GI) cancers has been challenged by complex motions in the abdomen (Wysocka et al 2010, Abbas et al 2014). Displacements and deformations of abdominal organs introduce geometric uncertainties to the delivery of radiation treatment. Such uncertainties, if not properly accounted for may result in under dosage to the target volume and/or over dosage to organs at risk (OARs) (Balter et al 1996, Aruga et al 2000, Jayachandran et al 2010). The recent advent of MR-guided radiation therapy invites higher precision of GI treatments due to the availability of monitoring and gating based on tumor and/or nearby surrogate tissue positions during treatment delivery (Wojcieszynski et al 2016). Several studies have demonstrated the ability of adapting abdominal radiotherapy treatments to day-to-day variations based on imaging immediately prior to treatments (Balter et al 2002, Acharya et al 2016, Henke et al 2016, Fischer-Valuck et al 2017, Henke et al 2018), with promising initial results for pancreatic cancer (Bohoudi et al 2017, Jiang et al 2017, Rudra et al 2017, Weiner et al 2017, Mittauer et al 2018), suggesting the potential of imaging-based GI motion quantification and modeling for improved radiation treatment outcomes.

GI motion is influenced by multiple factors, including respiration, change of organ filling status and change of internal anatomic organ arrangements (Abbas et al 2014). Although respiration-induced motion has been extensively studied (Korin et al 1992, Singh et al 2006, Feng et al 2009), other types of GI motion and their impact on radiotherapy require further investigation. Studies using 4D-CT (Kumagai et al 2009, Lischalk et al 2016, Magallon-Baro et al 2019) and fluoroscopy (Watanabe et al 2008) observed significant intra and inter fractional GI motions and suggested these factors may lead to violating OAR dose constraints (Magallon-Baro et al 2019), although it was not clear how different types of GI motion contributed to the observations. While cine-MRI has been used for GI motion assessment (Ajaj et al 2004, Baba et al 2009, Menys et al 2014, Mostafaei et al 2018, Nonaka et al 2019), sampling of one or two 2D planes limits its ability to provide 3D motion information. Differentiating impacts of different motions has also been challenging. Several studies adopt a breath-hold protocol, which requires patient cooperation and limits the length of scanning. Such short scan times may be insufficient to evaluate the impact of GI motions on radiotherapy treatment delivery, a process usually lasts several minutes. A limited number of studies have attempted to separate different motions presented in free-breathing data, including Mostafaei et al (Mostafaei et al 2018) where breathing motion was excluded by subtracting the centroid motion of liver from that of gallbladder, and Menys et al (Menys et al 2014) where breathing and peristalsis were identified as different components of low-rank decomposition results.

In this study, we investigated internal abdominal configuration changes using a dynamic 3D radial MRI sequence and a scan time comparable to the length of radiotherapy delivery. Multi-temporal resolution images were reconstructed to correct breathing motion prior to analysis of GI motion induced by changes of internal anatomic organ arrangements, which happened at a much slower rate than respiratory motion. We evaluated the impact of such ‘slow drifting’ motion for multiple OARs including small bowel, colon, duodenum and stomach. A motion model was also constructed using principal component analysis to further analyze geometric uncertainties introduced by slow drifting motion.

2. Methods and materials

2.1. Image acquisition

Under an institution review board approved protocol, 13 MRI examinations of 11 patients were investigated. Two out of the 11 patients received repeated MRI scans that were more than 1 month apart which were treated as independent examinations for analysis. All MR images were acquired using an in-house 3 Tesla scanner (Skyra, Siemens Medical Systems, Erlangen, Germany) with an 18-channel flexible surface coil (BodyMatrix) placed anteriorly and 2-5 4-coil elements of a posterior coil inserted in the scanner table (SpineMatrix). Each examination consisted of two consecutive 10 min scans acquired using a golden-angle stack-of-stars spoiled gradient echo sequence (Chandarana et al 2014, Feng et al 2016) with fat suppression, as part of a scan protocol designed to assess liver function using Dynamic Contrast-Enhanced (DCE)-MRI (Cao et al 2013, Wang et al 2016, Simeth et al 2018). The field of view covered the liver, stomach and a large portion of the intestines. The imaging parameters ranged from 1.14 to 1.21 ms for echo time, 2.71–4.51 ms for repetition time, 10° to 14° for flip angle, 2–2.45 mm for in-plane voxel size and 3–4 mm for slice thickness. The size of the imaging matrix was 192 × 192 and the number of slices was 64. The 7000 raw k-space radial stacks of spokes were collected from each examination for analysis.

2.2. Breathing-motion corrected image time series reconstruction

Each k-space radial stack of spokes was first corrected for breathing motion using a previously described technique (Johansson et al 2018a, Johansson et al 2018b). Briefly, radial spokes from one examination were sorted into 21 breathing motion states from exhale to inhale based on a respiratory signal extracted from high temporal resolution image reconstructions using a view-sharing filter (Barger et al 2002). The temporal resolution of the view sharing filter was 340 ms at the center and 850 ms at the periphery of k-space. Deformable registration was then performed to align all states to the exhale state. The resulting deformation fields were used to deform back-projections of each spoke to correct breathing motions between spokes. A time series of 72 image volumes with an equal time interval of 17 s was then reconstructed by combining the breathing-motion corrected spokes using temporal view sharing. The temporal resolution of the view-sharing filter was 34 s at the center and 85 s at the periphery of k-space. By reconstructing images at a low temporal resolution, cyclic GI motions that occur at a higher frequency (2—3 cycles min ⁻¹) were to first order blurred out, with remaining changes primarily due to slow drifting motions of GI structures.

2.3. Modeling slow drifting motion of gastrointestinal structures

2.3.1. Registration across different motion states

To model slow drifting motion in the abdomen, registrations between image volumes reconstructed at different time points were first performed. For all examinations, the last of the 72 images volumes was chosen as the reference. To account for potential patient position changes during the 20 min scan, a rigid registration of the entire field of view was first performed to align all images to the reference. A mask that covers the GI region but excludes liver, heart and lungs was manually contoured on the reference. Cubic B-spline registration was performed within the mask to match GI structures of the reference to other images using an open source alignment tool NiftyReg (Modat et al 2010) with normalized mutual information as the metric. The B-spline grid spacing was 2 × 2 × 1 voxels and penalties on the log of Jacobian determinant and the bending energy were 0.8 and 0.001 respectively. The image sample that represents the motion state closest to the reference state, in our case the image volume that is temporally closest to the reference volume, was aligned to the reference first. The resulting deformation field was used to initialize deformable registration between the second closest image sample and the reference. This deformable registration process produced a time series of 71 deformation fields D = [D₁, D₂, ⋯, D₇₁] ∈ R^{192×192×64×3×71} for each examination, where deformation field D_i, represents the change of abdomen configuration from the reference state to motion state i.

2.3.2. Motion model construction via principal component analysis

A patient-specific slow drifting motion model was constructed by performing principal component analysis (PCA) on the deformation field series D = [D₁, D₂, ⋯, D₇₁]. Each deformation field D_i ∈ R^{192×192×64×3} was organized into a vector d_i. PCA was performed on the matrix M = [d₁, d₂, ⋯, d₇₁] which yields a series of orthonormal PCA modes m₁, m₂, ⋯, m₇₁. A model describing potential GI motion states s was constructed by linearly combining the leading k PCA modes

$$\mathit{s}={\mathit{m}}_0+{\alpha }_1{\mathit{m}}_1+{\alpha }_2{\mathit{m}}_2+\mathrm{\cdots }+{\alpha }_k{\mathit{m}}_k,$$ (1)

where m₀ is the mean deformation vector of M and α_i is the linear coefficient of mode m_i.

One important model parameter to consider for motion modeling is the number of PC modes k that will be used. Including more PC modes, while increasing the model complexity, may incorporate deformable registration errors into the model. The use of too few PC modes, while both reducing complexity as well as increasing robustness to alignment errors, may not be sufficient to describe potential GI motion states. In this study, we determined the number of PC modes needed by comparing the source deformation vector d_i and the reconstruction of d_i using the leading k PC modes

$${\widehat{\mathit{d}}}_i={\mathit{m}}_0+\sum _{l=1}^k{\mathit{m}}_k{\mathit{m}}_k^T({\mathit{d}}_i-{\mathit{m}}_0).$$ (2)

Contours of GI organs were deformed using both d_i and ${\widehat{\mathit{d}}}_i$. Convergence of 95-percentile Hausdorff distances between deformed contours with increasing number of PC modes was evaluated and we chose the number of PC modes so that averaged 95-percentile Hausdorff distance across GI organs was less than 1 mm.

2.4. Gastrointestinal motion analysis

2.4.1. Motions of organs at risk

We investigated slow drifting motion of multiple GI organs at risk (OARs) including the small bowel, colon, duodenum and stomach. Clinically-defined OAR contours delineated on CT images acquired and used for treatment planning were transferred to the reference MRI to define a rough space wherein the relevant anatomic structures are expected to lie on the MRI. This was done by first aligning the whole volume of CT images to MRI rigidly followed by B-spline deformable registration within space encompassed by each OAR volume separately. Both rigid and deformable registrations were implemented in NiftyReg (Modat et al 2010) with configuration parameters for deformable registration the same as the ones used for alignment between MR images of different GI motion states. Alignment between abdominal CT and MR images acquired on different days is a challenging task and the accuracy is limited. However, given that B-spline deformation fields between different GI motion states were regularized to be spatially smooth, we assumed that displacements of neighboring voxels were similar and delineation errors would not have a significant impact on OAR motion analysis. Figure 1 shows example clinically defined OAR contours overlaid on planning CT images and corresponding OAR space defined on MR images.

Figure 1.

Example OAR contours of small bowel (yellow), colon (red), duodenum (magenta) and stomach (green) overlaid with planning CT images (top) and reference MRI (bottom). As the contours were generated originally for liver tumor patients, coverage of inferior bowel structures was limited. Contouring of bowel structures was done for treatment planning purposes and did not follow the tissue interfaces strictly. Instead a loose bag that contained the relevant OAR was defined.

We estimated the velocity of slow drifting motion from the deformation field series D = [D₁, D₂, ⋯, D₇₁] associated with each examination by assuming a uniform motion within the 17 s inter-image time interval, and calculating the averaged displacements of voxels within each OAR volume between two successive deformation fields in anterior–posterior (AP), lateral and superior–inferior (SI) directions. The mean and maximum velocities during the 20 min examination were calculated by the displacements divided by the time intervals. The magnitude of motion velocity was calculated as the rooted sum of square of velocities in the 3 directions. Motion traces of OAR centroids were also calculated by deforming OAR volumes defined on reference MRI with each of the deformation fields D₁, D₂, ⋯, D₇₁ and calculating the centroids of deformed OAR volumes.

2.4.2. Geometric uncertainties introduced by slow motion

The composite OAR spatial occupancy was generated by superimposing binary masks encompassing OAR image volumes deformed by each of the 71 deformation field D_i. The external contour of the union of binary masks represented an envelope that encompassed the observed composite OAR motions. The 95-percentile Hausdorff distance between the envelope and the reference OAR contour was calculated. Probabilistic distributions of OARs were generated by simulating 5000 motion states using the PCA-based motion model. PC coefficients for each simulated motion state were sampled from a kernel distribution, obtained by fitting a non-parameterized kernel model to the observed PC coefficients associated with the 71 motion states. Both kernel model fitting and sampling process was performed using built-in functions in MATLAB (Natick, MA). The resulting 5000 deformation fields were applied to binary OAR image volumes, and probabilistic distributions of OARs were calculated by averaging over the 5000 deformed OAR image volumes. We referred to such probabilistic distributions of OARs as ‘probabilistic Planning Organ at Risk Volumes’ (pPRVs). Similar with PRV studies using CT data (Hysing et al 2006), we compared pPRVs to PRVs generated by adding isotropic margins to OARs. PRV margins required to cover 99% of pPRV voxels of different probability levels (⩾5%, ⩾55% and ⩾95%) were calculated. The specificity of PRVs was also evaluated by fractions of PRV volumes that covered voxels that an OAR will not occupy.

Slow drifting motion may be irregular and non-periodic. To evaluate whether intra-fractional geometric uncertainties introduced by slow drifting motion change over time, we divided the 20 min scan evenly into four 5 min sub-scans and compared geometric uncertainties associated with different sub-scans. For each sub-time series, the last volume was treated as the reference. Temporal variations of geometric uncertainties were evaluated by standard deviations of both Hausdorff distances between reference OAR contour/OAR motion envelope pairs, and PRV margins required to cover pPRVs of a certain probability level. Geometric uncertainties estimated from sub-scans were also compared to those estimated from the full 20 min scan.

3. Results

3.1. Registration across different motion states

Rigid alignment transforms of the entire field of view of images showed an averaged rotation less than 1.2° across different reconstruction time points for all examinations. Averaged translations from these transforms were less than 1 mm for 10 out of the 13 examinations, and 1.1 mm, 1.7 mm and 3.4 mm for the remaining 3 examinations respectively. The rigid registration results suggested gross patient position changes were small for most of the examinations. Figure 2 shows example reference and target image volumes from reconstructed slow motion image time series. Regions of interest (ROI) within the GI tract were delineated on reference volumes and target volumes independently. GI structures showed visible changes between reference and target volumes, while reference volumes after deformable registration showed improved agreement with target volumes in the abdomen, as demonstrated by overlaying target volume ROIs with deformed reference volume. To demonstrate the efficacy of breathing motion correction, respiratory signal associated with each time series was also plotted and ROIs of liver were delineated on reference volumes and overlaid with other volumes. Despite of irregular breathing motion patterns, position and shape of the liver were consistent across different image volumes after berating motion correction.

Figure 2.

Example volumes of (a) reference motion states, (b) target motion states from slow motion time series reconstructed after breathing motion correction and (c) deformed reference motion states. Respiratory signal used for breathing motion correction was also plotted. ROIs within the abdomen were drawn on reference volumes (green) and target volumes (red) independently. Overlaying target ROIs with deformed reference volumes shows agreements between deformed reference volumes and target volumes. Liver ROIs (yellow) were contoured on reference states and overlaid with both target states and deformed reference states.

The accuracy of registration was also evaluated by 95-percentile Hausdorff distances between OAR contours on deformed and target image volumes. For each patient, a sub-scan of 3 image volumes was evenly sampled from the image time series (the 1st, the 36th and the 71st image volume out of the 72 image volumes). Contours of the stomach were manually drawn on the 3 image volumes, as well as the reference volume deformed to match each of the 3 image volumes. To quantify the uncertainty in manual contouring, stomach was also contoured on the reference image volume twice with 95-percentile Hausdorff distances calculated between the two contours. All contours were independently reviewed by a board-certified medical physicist. Across the 13 examinations investigated, the averaged registration uncertainty equaled in-plane voxel resolution which was 2.2 mm, while the averaged registration accuracy was 2.3 mm. The consistency between registration accuracy and registration uncertainty suggested the discrepancy between deformed and target contours were mainly due to the uncertainty of manual contouring and limited voxel resolutions. The averaged 95-percentile distance between contours drawn on target volumes and the reference volume without deformations other hand was 5.4 mm. To evaluate the smoothness of the deformation fields, standard deviations of displacement vectors around each voxel location within the GI tract were calculated using a sliding window of 5 × 5 × 3 voxels, which corresponds to a neighborhood of about 1 × 1 × 1 cm³. The averaged local standard deviations of displacement vectors in AP, lateral and SI directions were 0.9 ± 0.2 mm, 0.9 ± 0.2 mm and 1.4 ± 0.4 mm across examinations.

3.2. Principal component analysis of deformation fields

Across the 13 PCA models constructed, the first principal mode explained an average of 25.8% of the total variance, with a standard deviation of 4.5%. Figure 3 plots averaged 95-percentile Hausdorff distances between OAR contours deformed by target deformation fields d_i and PCA-reconstructed deformation fields ${\widehat{\mathit{d}}}_i$ with different numbers of PC modes. Including the leading 4 PC modes in the model resulted in an averaged Hausdorff distances less than 1 mm for all 4 OARs and thus we chose to use 4 modes for all models constructed in this study. Figure 4 shows example histograms of PC coefficients associated with the observed 71 motion states. The histogram shapes vary across patients, which warrant non-parametric kernels to characterize PC coefficients distributions. Histograms of the 5000 PC coefficients simulated from fitted kernel distributions were overlaid with histograms of observed PC coefficients. All histograms were normalized to have an integral count of 1. Shapes of distributions were similar between observed and simulated PC coefficients, while some PC coefficients outside of the range of observations were also sampled by the fitted kernel distributions.

Figure 3.

Averaged 95-percentile Hausdorff distances between OAR contours deformed by target deformation fields and PCA-reconstructed deformation fields across patients.

Figure 4.

Example histograms of PC coefficients of the 71 observed motion states (blue) and 5000 simulated motion states (red). All histograms were normalized to an integral count of 1.

The motion pattern described by the first leading PCA mode was investigated by constructing deformation fields with the leading PCA mode coefficient varied ±2 standard deviations (SD) of observations about their mean values. Comparing deformation fields constructed with PCA mode coefficients of +2 SD and −2 SD, the averaged displacements of voxels within the GI region ranged from 1.4 to 3.8 mm, 1.3 to 3.5 mm and 2.2 to 5.1 mm with mean/standard deviations of 2.8/0.6 mm, 2.7/0.5 mm and 3.9/0.8 mm in AP, lateral and SI directions respectively across the 13 models. The displacement induced by the leading PCA mode was the largest in SI direction for 12 out of the 13 models constructed, except for one model where the largest displacement was in the AP direction. Figure 5 shows example coronal and sagittal views of image volumes deformed by the leading PC modes that induce the largest displacement in lateral, SI and AP directions respectively.

Figure 5.

Example motion patterns of the 1st leading PC modes across the 13 PCA models that induce the largest displacement in lateral (top), SI (middle) and AP (bottom) directions respectively. The reference image was deformed by transforms generated using the leading PCA mode with mode coefficients of mean ± 2 SD. Example abdominal structures were contoured on the two deformed images (red and green) and overlaid on the reference image.

3.3. Motions of organs at risk

Table 1 summarizes statistics of OAR motion velocities in AP, lateral and SI directions respectively. Motion of the stomach is slower than the other 3 OARs, in terms of both averaged velocity and maximum velocity observed during the 20 min examination. The averaged velocity magnitude, calculated as the rooted sum of square of velocities in the 3 directions during the 20 min examination ranged from 0.8 to 1.9 mm min⁻¹, 0.7 to 1.6 mm min⁻¹, 0.6 to 2 mm min⁻¹ and 0.7 to 1.4 mm min⁻¹ for small bowel, colon, duodenum and stomach respectively with mean/standard deviations of 1.3/0.4 mm min⁻¹, 1.1/0.2 mm min⁻¹, 1.2/0.4 mm min⁻¹ and 0.9/0.2 mm min⁻¹ across the 13 examinations evaluated. Figure 6 shows motion traces of OAR centroids in the SI direction of example patients. The motion traces are irregular across time and variable across patients.

Table 1.

(a). Averaged velocity (mm min−1) during the 20 min scan time interval across 13 examinations.
	AP	Lateral	SI
Small bowel	0.6 ± 0.2	0.6 ± 0.1	0.8 ± 0.3
	range: 0.3–0.8	range: 0.3–0.8	range: 0.5–1.2
Colon	0.5 ± 0.1	0.5 ± 0.1	0.7 ± 0.2
	range: 0.3–0.6	range: 0.3–0.6	range: 0.4–1.1
Duodenum	0.5 ± 0.2	0.5 ± 0.2	0.8 ± 0.3
	range: 0.2–0.8	range: 0.3–0.8	range: 0.3–1.4
Stomach	0.4 ± 0.1	0.4 ± 0.1	0.6 ± 0.2
	range: 0.3–0.6	range: 0.4–0.6	range: 0.4–0.9
(b). Maximum velocity (mm min−1) during the 20 min scan time interval across 13 examinations.
Small bowel	1.4 ± 0.4	1.3 ± 0.3	2.2 ± 1.1
	range: 0.9–4.1	range: 0.7–1.8	range: 1.0–3.1
Colon	1.2 ± 0.4	1.2 ± 0.4	1.8 ± 1.0
	range: 0.6–2.1	range: 0.6–1.8	range: 0.9–3.4
Duodenum	1.3 ± 0.5	1.2 ± 0.4	2.7 ± 1.1
	range: 0.7–2.2	range: 0.7–2.1	range: 1.1–2.9
Stomach	1.0 ± 0.3	1.0 ± 0.3	2.3 ± 1.2
	range: 0.7–1.7	range: 0.7–1.6	range: 1.0–2.5

Figure 6.

Motion traces of OAR centroids in SI direction over the 20 min examination of example patients. The trace of each OAR centroid was shifted to have a mean position at 0 mm.

3.4. Geometric uncertainties introduced by slow motion

The 95-percentile Hausdorff distances between OAR motion envelopes generated from the 71 motion states and reference OAR contours for small bowel, colon, duodenum and stomach ranged from 4.1 to 7.4 mm, 4.1 to 6.8 mm, 3.5 to 7.0 mm and 3.1 to 6.3 mm across examinations, with mean/standard deviations of 5.6/1.1 mm, 5.3/0.8 mm, 5.1/1.1 mm and 4.6/0.8 mm. Figure 7 shows example motion envelopes of OARs overlaid with PCA model-predicted probabilistic distributions of OARs (i.e. pPRVs).Table 2 summarizes isotropic PRV margins required to cover pPRV voxels with different probability levels. The PRV margin required to cover 99% of a space that an OAR is highly likely to occupy (probability ⩾95%) was about 3 mm, while a margin about 10 mm was required to cover the entire space an OAR may occupy (probability ⩾5%). With such generous margin, the PRV was not very specific and covered a large portion of volumes (>15% on average) an OAR will not occupy.

Figure 7.

Example OAR motion envelopes (white lines) overlaid with pPRVs (color wash). Top and bottom rows show examinations that demonstrated the largest and smallest Hausdorff distances between motion envelopes and reference OAR contours respectively. The color bar corresponds to the probability scale of pPRVs.

Table 2.

Isotropic PRV margins (mm) required to cover pPRV volumes with different probability levels and the fractions of PRVs (%) that covered voxels that an OAR will not occupy.

	Probability level ⩾5%	Probability level ⩾55%	Probability level ⩾95%
Small bowel	10.9 ± 4.6 mm	5.3 ± 1.2 mm	3.5 ± 0.5 mm
	25.0 ± 17.0%	5.0 ± 5.0%	0.5% ± 0.5%
Colon	10.2 ± 3.4 mm	5.1 ± 0.9 mm	3.6 ± 0.7 mm
	22.9 ± 9.1%	4.5 ± 3.0%	0.9% ± 1.1%
Duodenum	11.2 ± 4.6 mm	5.5 ± 1.2 mm	3.5 ± 0.7 mm
	37.4 ± 16.5%	9.7 ± 6.0%	1.6% ± 1.9%
Stomach	8.2 ± 2.9 mm	4.8 ± 0.7 mm	2.8 ± 1.3 mm
	17.3 ± 11.0%	4.2 ± 2.9%	0.6% ± 0.7%

Standard deviations of 95-percentile Hausdorff distances between motion envelopes and reference OAR contours across the four 5 min sub-scans were less than 1 mm for all examinations/OARs, except for one examination where the standard deviation was 1 mm for bowel structures (small bowel, colon and duodenum). The maximum Hausdorff distances obtained from the four sub-scans for small bowel, colon, duodenum and stomach were 3.4 ± 0.8 mm, 3.0 ± 0.8 mm, 2.8 ± 0.9 mm and 2.6 ± 0.6 mm across examinations, which were smaller than those obtained from full 20 min scans. A two-sample Kolmogorov-Smirnov test showed that maximum Hausdorff distances obtained from sub-scans were significantly different from those obtained from the full scan (p < 0.01). Standard deviation of isotropic PRV margins required to cover pPRV voxels with medium probability threshold (⩾55%) was the smallest among the three probability levels evaluated and was less than 1 mm on average across patients. Standard deviations of isotropic PRV margins required to cover pPRV voxels with high probability threshold (⩾95%) and low probability threshold (⩾5%) were larger but less than 2 mm on average across patients. No statistically significant difference was found between the maximum PRV margins estimated from sub-scans and PRV margins estimated from full scans.

4. Discussion

This study investigated slow drifting motion of GI organs in subjects over a 20 min time window. Using a 3D radial MRI sequence that covers a volume much larger than reported in prior studies using Cine-MRI, we were able to assess motions of multiple GI organs simultaneously in 3 dimensions. The radial sampling pattern of the MRI sequence allows image reconstructions at multiple temporal resolutions, thus allowing analysis to account for GI motions that occur at different time scales. The prior removal of breathing motion as well as temporal blurring of stomach contractions in the reconstructions permitted clear visualization of slow drifting motion and its impact on GI organs. Such multi-temporal resolution reconstruction scheme provides a framework to study different components of GI motion independently and has the potential of building a comprehensive model that assembles all motion components to evaluate the overall impact of GI motion on radiotherapy planning and delivery.

Our results suggested that the magnitude of slow drifting motion is not negligible for precise radiotherapy delivery. Assuming a short delivery time of 5 min, displacements of GI organs in the SI direction could be more than 5 mm for bowel structures and 4 mm for the stomach, according to averaged motion velocities observed during examinations. Motion magnitudes in the AP and lateral directions were smaller but could still exceed 3 mm. Extra OAR margins induced by slow drifting motion, as evaluated by 95-percentile Hausdorff distances between OAR motion envelopes and OAR contours, were more than 4 mm on average. It is worth noting though slow drifting motion is non-periodic over at least 20 min and OARs may occupy a certain space within the motion envelope only for a limited amount of time during radiation treatment delivery. Adding isotropic PRV margins derived from observed motion states, which is commonly used in clinical practice (Hysing et al 2006, Suzuki et al 2006) may therefore overestimate the margin required to spare OARs during radiotherapy delivery and result in difficulty in achieving desired dose-volume histogram constrains due to the large margin added. A PCA-based motion model was constructed to reduce the uncertainty during organ contouring and image registration process, as well as to obtain probabilistic distributions of OARs which may better guide radiotherapy planning than PRV margins. Such probabilistic PRVs may permit sparing of OARs with different levels, by thresholding probabilistic PRVs with different probability levels. Comparing PRVs with isotropic margins to probabilistic PRVs showed that a generous margin of about 10 mm is required to generate PRV volumes that cover the entire space an OAR will likely to occupy (with probability >= 5%) while the specificity of such PRV is not ideal with more than 15% of the volume covers voxels that an OAR will not occupy. Such results are consistent with previous studies of intestine PRV margins using daily CT images (Hysing et al 2006) and suggested model-based probabilistic OAR distributions, or probabilistic PRVs may be a better approach to account for geometric uncertainties introduced by slow drifting motion. Different from previous PCA-based methods for geometric uncertainty modeling, the proposed PCA model described intra-fractional variations induced by involuntary GI motion instead of inter-fractional variations (Budiarto et al 2011, Magallon-Baro et al 2019) or breathing motion-induced variations (Fayad et al 2018, Ranjbar et al 2019). The large number of image samples associated with each patient permitted the construction of patient-specific instead of population-based models, thus avoided the degradation of model accuracy caused by heterogeneity of motion patterns among patients.

Different from breathing motion, slow drifting motion is irregular and non-periodic over times comparable to typical radiation treatment. Our primary results showed limited temporal variations of geometric uncertainties introduced by such motion, as indicated by comparisons across sub-scans. Most examinations/OARs showed standard deviations less than 1 mm for Hausdorff distances between motion envelopes and reference OAR contours. Similar results were observed for PRV margins required to cover pPRVs with medium probability levels. Hausdorff distance analysis showed a significantly larger margin between motion envelopes and reference OAR contours when using a 20 min full scan versus a 5 min sub-scan. Analysis of PRV margins for pPRV coverage between sub-cans and full scans however, did not show such difference, which may be due to the capability of the PCA model to extrapolate to unseen motion states. The length of examination that is required to fully represent geometric uncertainties during treatment delivery requires further investigation. With our limited sample size of 71 motion states, it is difficult to characterize the PC coefficient distributions using any parametrized statistical models. A non-parametrized kernel distribution was therefore used to simulate potential motion states. Future study will evaluate distributions of PC coefficients more thoroughly. Spatial and temporal variations of slow drifting motion will also be evaluated further to better characterize motion-induced geometric uncertainties for radiotherapy. Although motions of each GI organ were evaluated separately in the current study, organ displacements are not independent of each other. Taking spatial correlations of organ motions into account may further reduce the impact of errors during deformable registration and model fitting, and thus improve the accuracy of geometric uncertainty characterization. Our current study evaluated temporal changes of GI motion by comparing across short time windows extracted from a long examination. Comparing examinations acquired a few days apart will provide further insights about correlations of geometric variations presented during a pre-treatment simulation and subsequent treatments.

One limitation of this study is the motion analysis of OARs was preformed within a rough space defined by transforming OAR contours from CT images to MR images. The accuracy of OAR space definition was limited by both the precision of initial contouring, which was for treatment planning purpose only, and the challenge of deformable alignment between MR and CT images. However, since we were evaluating slow configuration changes in the abdomen rather than cyclic motion or change of filling status for a specific organ, motions of OARs and surrounding tissues were assumed to be correlated. Such correlation was also enforced by performing B-spline deformable registration over the entire GI region, instead over each OAR separately. The spatial smoothness of B-spline coefficients ensured similarities between motions of neighboring voxels, and thus reduced the impact of OAR definition errors on our analysis. Future studies will delineate OAR contours directly on MR images. Other registration techniques, such as the Thin-Plate Spline Robust Point Matching (TPS-RPM) algorithm used by Magallon-Baro et al (2019) may also be evaluated in the future to further improve image registration accuracy.

5. Conclusion

This study investigated 3D slow drifting motion of GI organs induced by changes of internal anatomic organ arrangements without confounding respiratory motion and cyclic GI motion, using a volumetric radial MRI sequence and multi-temporal resolution image reconstructions. Motion analysis for multiple OARs suggested slow drifting motion is non-negligible and should be taken into account during radiotherapy planning and delivery. A patient-specific motion model was also constructed and used to predict probabilistic distributions of OARs. Such probabilistic maps may be used to better account for geometric uncertainties introduced by slow drifting motion.