Investigation of tumor and vessel motion correlation in the liver

Abstract Intrafraction imaging‐based motion management systems for external beam radiotherapy can rely on internal surrogate structures when the target is not easily visualized. This work evaluated the validity of using liver vessels as internal surrogates for the estimation of liver tumor motion. Vessel and tumor motion were assessed using ten two‐dimensional sagittal MR cine datasets collected on the ViewRay MRIdian. For each case, a liver tumor and at least one vessel were tracked for 175 s. A tracking approach utilizing block matching and multiple simultaneous templates was applied. Accuracy of the tracked motion was calculated from the error between the tracked centroid position and manually defined ground truth annotations. The patient’s abdomen surface and diaphragm were manually annotated in all frames. The Pearson correlation coefficient (CC) was used to compare the motion of the features and tumor in the anterior–posterior (AP) and superior–inferior (SI) directions. The distance between the centroids of the features and the tumors was calculated to assess if feature proximity affects relative correlation, and the tumor range of motion was determined. Intra‐ and interfraction motion amplitude variabilities were evaluated to further assess the relationship between tumor and feature motion. The mean CC between the motion of the vessel and the tumor were 0.85 ± 0.11 (AP) and 0.92 ± 0.04 (SI), 0.83 ± 0.11 (AP) and −0.89 ± 0.06 (SI) for the surface and tumor, and 0.80 ± 0.17 (AP) and 0.94 ± 0.03 (SI) for the diaphragm and tumor. For intrafraction analysis, the average amplitude variability was 2.47 ± 0.77 mm (AP) and 3.14 ± 1.49 mm (SI) for the vessels, 2.70 ± 1.08 mm (AP) and 3.43 ± 1.73 mm (SI) for the surface, and 2.76 ± 1.41 mm (AP) and 2.91 ± 1.38 mm (SI) for the diaphragm. No relationship between distance and motion correlation was observed. The motion of liver tumors and liver vessels was well correlated, making vessels a suitable surrogate for tumor motion in the liver.


| INTRODUCTION
Intrafraction motion due to respiration can impact the accuracy of external beam radiation therapy. Managing intrafraction motion remains problematic especially in the thoracic and abdominal regions.
Tumor motion during treatment has been reported up to 20 mm in the lung, pancreas, and kidneys, and up to 30 mm in the liver. 1,2 Tumor motion cannot be predicted by tumor size or location, so direct or indirect tumor tracking is often utilized in the clinic when appropriate. 3 Tumor-tracking strategies are implemented to reduce margins placed around the tumor and further reduce absorbed dose to healthy tissue.
Most often, clinics employ systems that rely on external or internal surrogate fiducials as correlates of tumor motion. External motion tracking systems monitor the motion of the chest or abdomen through optical tracking whereas internal surrogate fiducials, such as implanted gold fiducial seeds, clips, or electromagnetic beacon transponders, are surgically implanted prior to treatment and subsequently monitored using x-ray fluoroscopy or electromagnetic arrays.
The accuracy of systems that use external or internal fiducials will depend on how well the motion of the fiducial(s) correlates with the motion of the tumor. In the case of external fiducials, reported correlations between internal fiducial implants and external markers have varied. Although good correlations were observed in thoracic 4 and abdominal regions, 5,6 others have concluded that external surrogates are not sensitive enough to capture breathing variability. [7][8][9][10][11] For these types of surrogates, issues with phase mismatch, internal drift, and deformation have been reported. [7][8][9][10] Correlations tend to improve for fiducials implanted close to tumors. 11 However, implanting fiducials is invasive and introduces additional risks to the patient.
Once implanted, fiducials only provide a point-wise estimate of the tumor volume location and may be subject to significant drift over the course of the treatment.
Internal tracking is possible with in-room or on-board imaging systems. The Cyberknife® Tracking System uses ceiling mounted kV x-ray sources to produce real-time digitally reconstructed radiographs (DRR).
However, this approach adds absorbed dose to the patient. Magnetic resonance (MR)-guided delivery systems such as MRIdian (ViewRay, Inc., Cleveland, OH, USA) and Unity (Elekta, Stockholm, Sweden) can image thoracic and abdominal tumor motion without exposing the patient to additional absorbed dose. However, even when these costly systems are available, there are situations when the tumor cannot be imaged directly due to poor MR contrast. In these scenarios, it may be desirable to use other anatomical features that provide better MR contrast. 12

2.A | 2D image data
Two-dimensional (2D) sagittal patient image datasets (n = 10) from the ViewRay MRIdian system were used in this study in accordance with an institutionally approved IRB protocol. This set includes seven unique patients, where two fractions from different days were used for three of the patients. All but one patient was coached to perform repeated breath-holds during the treatment.

2.B | Tumor and vessel tracking
A 2D tracking algorithm incorporating block matching and multiple simultaneous templates was utilized for efficient tracking of the tumor and vessels. 22 Vessels that persisted through the entire dataset and were sufficiently largeon the order of a few pixels or morewere chosen for tracking. For the patients analyzed over multiple fractions, the same vessel(s) were chosen for tracking in each fraction. Since this work aimed to determine the feature motion as accurately as possible and was not meant to serve as a test of the tracking robustness, tracking algorithm parameters were modified to achieve the most accurate tracking for each data set.

2.C | Abdomen surface and diaphragm annotations
The surface of the abdomen exhibits a stark contrast with the air in MR images; however, the tracking algorithm is written to cater to convex closed contours as opposed to a line or point. Therefore, the abdomen surface motion was quantified manually through the entire dataset. Only the anterior-posterior (AP) motion was considered as Similar to the abdomen surface, the diaphragm highly contrasts the lung in MR images. As the diaphragm does not provide a closed contour either, manual annotations were required. The peak point in the diaphragm was chosen to track manually in both AP and SI directions to pixel level resolution.

2.D | Assessment of motion correlation
Two calculations were performed to assess motion correlation between the tumor and feature of interest. To address phase correlation, the Pearson product moment correlation coefficient (CC) was utilized, following the correlation method used by similar studies. 15

2.E | Intra-and interfraction amplitude variabilities
To supplement the Pearson coefficient, the intra-and interfraction variabilities of the absolute difference between the motion ampli- For interfraction analysis, the mean of the absolute amplitude difference results for the three patients with two fractions each was extracted from the total dataset. The error between the mean amplitude differences for each fraction was calculated: where a 1 and a 2 are the earlier and later mean amplitude differences of the two fractions from a single patient. This calculation was com-

| RESULTS
We achieved mean tracking errors relative to manual annotations between 0.28 and 1.08 pixels (0.99-3.79 mm). Figure 2

3.A | Pearson correlation coefficients
The Pearson CCs for all datasets are shown in Fig. 3

3.B | Intra-and interfraction amplitude variabilities
Intrafraction amplitude variability results for all datasets are summarized in Table 1 as the mean and standard deviation (SD) for each feature and each direction of motion. Intrafraction amplitude variability for the vessel and patient surface is shown in Fig. 4(a) in the form of the standard deviation of the amplitude difference for each feature and direction of motion relative to the tumor. Generally, the feature to tumor intrafraction amplitude difference variability was comparable for each patient. The intrafraction amplitude variability for the breath-hold portions of the datasets is shown in Fig. 4(b).
Overall, the intrafraction variability decreased for all three features when only the breath-hold portions were analyzed.
Interfraction amplitude variability results for all datasets are summarized in Table 2

| DISCUSSION
Overall, the tumor motion was well correlated to the vessel, diaphragm, and abdomen surface motion. In six out of ten datasets, vessels that were tracked resulted in a higher correlation with the tumor than the abdomen surface for both AP and SI motion.  For all cases studied, the vessel and diaphragm were closer to the tumor than the abdomen surface. This may have contributed to the increase in motion correlation especially for deep-seated tumors.
Studies indicate that motion correlation for liver tumors may be negatively impacted by increasing distances between the features of interest. 5,13 Interestingly, for the vessel dataset as a whole, no trend or relationship was observed between the average distance between the vessel and tumor and the motion CC. It was also observed that the intrafraction amplitude variability between the tumor and feature was comparable between all features further indicating that the vessel and diaphragm mimics the tumor motion as well as the patient surface.
The Pearson product moment CC has been used in previous surrogate motion studies 15,18,21,31 ; however, the Pearson coefficient has its limitations. 33 Specifically, this metric is sensitive to outlier data since it is dependent on a mean. 33 The use of the tracking algorithm  there have been no studies reporting on the correlation between liver vessel and tumor motion with patient data until now. Additional work will explore the feasibility and reproducibility of imaging and tracking vessels in the liver with a simultaneous MR and ultrasound system. While the datasets available for this study did not provide the necessary information to assess the dosimetric impact of using vessels as motion surrogates, future work will assess this clinical impact.

| CONCLUSION S
The abdomen surface, liver vessel, and diaphragm motion relationship to liver tumor motion was successfully analyzed using multiple metrics to investigate the general phase and amplitudes of motion.
Tumor motion in the liver was well correlated to abdomen surface, vessel, and diaphragm motion. The tumor motion can be captured with a direct relationship with the vessel motion relatively well as indicated by the results of the intrafraction amplitude variability analysis. The results of this study suggest that the diaphragm and vessels in the liver are suitable surrogates for liver tumor motion.
While out of the scope of this work, an additional investigation into the dosimetric impact of utilizing liver vessels as surrogates of liver tumor motion is warranted. Finally, taking the results of this study forward, efforts to evaluate the practicality of tracking vessels in the clinic utilizing different motion management solutions such as MR and ultrasound are currently underway at our institution.

ACKNOWLEDG MENTS
This work was funded by NIH grant R01CA190298.