Accuracy of deformable image registration on magnetic resonance images in digital and physical phantoms

Abstract

Purpose

Accurate deformable image registration is necessary for longitudinal studies. The error associated with commercial systems has been evaluated using computed tomography (CT). Several in‐house algorithms have been evaluated for use with magnetic resonance imaging (MRI), but there is still relatively little information about MRI deformable image registration. This work presents an evaluation of two deformable image registration systems, one commercial (Velocity) and one in‐house (demons‐based algorithm), with MRI using two different metrics to quantify the registration error.

Methods

The registration error was analyzed with synthetic MR images. These images were generated from interpatient and intrapatient variation models trained on 28 patients. Four synthetic post‐treatment images were generated for each of four synthetic pretreatment images, resulting in 16 image registrations for both the T1‐ and T2‐weighted images. The synthetic post‐treatment images were registered to their corresponding synthetic pretreatment image. The registration error was calculated between the known deformation vector field and the generated deformation vector field from the image registration system. The registration error was also analyzed using a porcine phantom with ten implanted 0.35‐mm diameter gold markers. The markers were visible on CT but not MRI. CT, T1‐weighted MR, and T2‐weighted MR images were taken in four different positions. The markers were contoured on the CT images and rigidly registered to their corresponding MR images. The MR images were deformably registered and the distance between the projected marker location and true marker location was measured as the registration error.

Results

The synthetic images were evaluated only on Velocity. Root mean square errors (RMSEs) of 0.76 mm in the left‐right (LR) direction, 0.76 mm in the anteroposterior (AP) direction, and 0.69 mm in the superior‐inferior (SI) direction were observed for the T1‐weighted MR images. RMSEs of 1.1 mm in the LR direction, 0.75 mm in the AP direction, and 0.81 mm in the SI direction were observed for the T2‐weighted MR images. The porcine phantom MR images, when evaluated with Velocity, had RMSEs of 1.8, 1.5, and 2.7 mm in the LR, AP, and SI directions for the T1‐weighted images and 1.3, 1.2, and 1.6 mm in the LR, AP, and SI directions for the T2‐weighted images. When the porcine phantom images were evaluated with the in‐house demons‐based algorithm, RMSEs were 1.2, 1.5, and 2.1 mm in the LR, AP, and SI directions for the T1‐weighted images and 0.81, 1.1, and 1.1 mm in the LR, AP, and SI directions for the T2‐weighted images.

Conclusions

The MRI registration error was low for both Velocity and the in‐house demons‐based algorithm according to both image evaluation methods, with all RMSEs below 3 mm. This implies that both image registration systems can be used for longitudinal studies using MRI.

1. Introduction

The use of magnetic resonance imaging (MRI) has increased because it allows for noninvasive evaluation of patients without ionizing radiation and provides superior soft tissue contrast in comparison with computed tomography (CT). With these attributes, MRI has great potential for use in longitudinal studies.^{1, 2, 3, 4, 5} A longitudinal study is when data is acquired for the same subjects over a period of time and may have different designs based on the type of study, such as prospective or retrospective.⁶ An example of a prospective longitudinal study is the recent DCE‐MRI study evaluating mandible changes in patients that were scanned before chemoradiotherapy treatment started, 3–4 weeks after initiation of treatment, and 6–8 weeks after treatment concluded.⁷ An example of a retrospective longitudinal study is the recent delta radiomics study on nonsmall cell lung cancer patient outcome predictions.⁸ However, for MRI to be useful in the setting of longitudinal studies, accurate deformable image registration is needed.

Many commercial and in‐house image registration systems have been benchmarked using CT.^{9, 10, 11, 12, 13, 14} For MRI, various in‐house algorithms have been validated for different anatomic sites, including the liver,^{15, 16} prostate,^{17, 18, 19} and breast.^{20, 21} However, image registration error on commercial software using MRI has not been widely reported. A B‐spline‐based commercial software, Velocity (Velocity AI version 3.0.1, Varian Medical Systems, Palo Alto, CA, USA), has been evaluated for CT‐based image registration and shown to have an average registration error below 5 mm.^{10, 22, 23, 24, 25, 26} In addition, our in‐house demons‐based algorithm has been validated for CT with registration error below 2 mm.^{11, 12, 27} Both systems are used for MRI applications, but have not been validated for this use.

This study aimed to evaluate two registration systems, Velocity commercial deformable image registration software and an in‐house demons‐based algorithm, for MRI. This was accomplished using synthetic images derived from patient longitudinal deformations and a phantom with implanted markers.

2. Materials and methods

The deformable image registration uncertainty of the two registration systems was evaluated using two methods: synthetic images and a porcine phantom.

2.A. Porcine phantom

Porcine meat was implanted with ten 0.35 mm gold markers. These markers are currently the smallest commercially available gold markers and therefore do not appear in the MR images for the imaging protocol used. This allowed for accurate assessment of the imaging registration error. If the markers appeared on the image they could bias the registration at those points leading to inaccurate registration error estimates.

The porcine tissue was placed in a plastic container with movable dividers (United States Plastic Company, Lima, OH, USA) to secure it in place. The porcine tissue was imaged using T1‐weighted and T2‐weighted MRI sequences where the markers were not visible and then imaged using CT where the markers were identifiable. The porcine tissue was then deformed by changing the placement of the dividers (as shown in Fig. 1) and re‐imaged. This process was repeated three times for a total of four sets of T1‐weighted, T2‐weighted, and CT images. The container is 27.6 cm × 21.0 cm × 12.7 cm with five notches in the short direction and seven notches in the long direction. The notches are spaced 3.25 cm apart, and the first and last notches are 1.6 cm from the edge in the short direction and 1.8 cm in the long direction. Long dividers are placed using the notches in the short direction and short dividers are placed using the notches in the long direction. The four different positions were as follows: (a) no dividers in the short direction, one divider in the first notch in the long direction; (b) one divider in the first notch in the short direction, one divider in the first notch in the long direction, (c) one divider in the first notch and one divider in the last notch in the short direction, one divider in the first notch in the long direction; and (d) one divider in the first notch and one divider in the last notch in the short direction, one divider in the first notch and one divider in the last notch in the long direction.

Figure 1.

Porcine Phantom Representative Deformation. A deformation was applied to the porcine phantom by moving the dividers. The red box represents the container with the grooves for the movable dividers and the position of the dividers is shown in blue. The original position is shown on the left and a deformed position using more movable dividers to secure the phantom in place is shown on the right. [Color figure can be viewed at wileyonlinelibrary.com]

The images were imported into the registration system where the MR images were rigidly registered to the CT image for each divider position and then deformably registered to the MR images at different divider positions. The gold markers were contoured for each divider position on the CT images and their center location was extracted. The markers were propagated through the registrations to determine the virtual location, and the error was measured by the distance between the virtual location and the known location. For example, the gold markers were transferred from CT‐1 to MR‐1 through rigid registration, then from MR‐1 to MR‐2 through deformable registration, then from MR‐2 to CT‐2 through rigid registration, and the error was measured as the distance between the propagated marker location on CT‐2 and the actual marker location in CT‐2. This method was applied to both registration systems.

2.B. Synthetic images

The image registration methodology from Yu et al.²⁸ was followed for 28 patients with human papillomavirus‐positive oropharyngeal squamous cell carcinoma who were treated with definitive chemoradiotherapy. The patients were selected from a prospective trial under a protocol approved by the institutional review board at MD Anderson Cancer Center with study‐specific informed consent. The first 28 patients to complete the three MRI scans were included. Patients underwent MRI scans from December 2013 to October 2015. Patient median age was 57 (range 46–70), with 26 men and two women. The median left parotid volume was 30.9 cm³ (range 22.4–47.1 cm³), median right parotid volume was 33.5 cm³ (range 18.0–46.7 cm³), median left submandibular volume was 9.6 cm³ (range 5.7–19.7 cm³), median right submandibular volume was 9.4 cm³ (range 4.3–17.5 cm³), and median sublingual volume was 4.8 cm³ (range 1.6–9.4 cm³).

Patients underwent T1‐weighted and T2‐weighted MRI scans before treatment (within 1 week prior to treatment), during treatment (3–4 weeks after the start of treatment), and after treatment (6–8 weeks after completion of treatment). This methodology has been described previously²⁸; briefly, models were trained on the patient images using an in‐house demons‐based algorithm. An intrapatient variation model was created by deforming each patient's midtreatment and post‐treatment images to the pretreatment image. One patient was selected to be the template for the synthetic images based on being the median age and having salivary glands with volumes near the median volume for all glands. An interpatient variation model was created by deforming each patient's pretreatment image to the selected patient's pretreatment image. Ninety‐five percent of the variation was included in the intra‐ and interpatient variation models. This was done separately for T1‐weighted and T2‐weighted images.

Synthetic pretreatment images were created by deforming the selected patient's pretreatment image using the interpatient variation model. Synthetic post‐treatment images were created by deforming the synthetic pretreatment image using the intrapatient variation model. For each synthetic pretreatment image, four synthetic post‐treatment images were created. Four synthetic pretreatment images were created, resulting in 16 image registrations for both T1‐ and T2‐weighted images. This process is demonstrated in Fig. 2. An example of the applied deformation is shown in Fig. 3.

Figure 2.

Workflow of Synthetic Image Generation. The generation of synthetic images is represented visually. The selected patient's pretreatment image is deformed by the interpatient variation model to generate the synthetic pretreatment images (highlighted in pink). For each of the synthetic pretreatment images, four synthetic post‐treatment images (highlighted in blue) are generated by deforming the synthetic pretreatment image using the intrapatient variation model. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 3.

Parotid Deformation in Synthetic Image Generation. An example of one of the deformations applied to the T1‐weighted synthetic pretreatment image left parotid to generate a synthetic post‐treatment image. The arrows show the direction of the left‐right and anteroposterior deformation and the size shows the magnitude of the deformation for that voxel. [Color figure can be viewed at wileyonlinelibrary.com]

The synthetic post‐treatment images were registered to the synthetic pretreatment images in the image registration system and the deformation vector field for each registration was exported. The difference between the registration system's deformation vector field and the applied deformation from the intrapatient variation model was evaluated within the salivary glands (left/right parotid, left/right submandibular, and sublingual). This method was not applied to the in‐house demons‐based algorithm because the algorithm was used to generate the inter‐ and intrapatient variation models used to generate the synthetic images for this method, and this would cause bias.

2.C. Imaging

2.C.1. Porcine MRI protocol

The T1‐weighted MRI sequence was a three‐dimensional spoiled gradient recalled echo sequence with flip angle 12°, repetition time 4.96 ms, echo time 2.1 ms, effective number of excitations 2, pixel bandwidth 325 Hz, field of view 25.6 cm, slice thickness 1 mm, and pixel size 1 mm × 1 mm. The T2‐weighted MRI sequence was a two‐dimensional fast spin echo sequence with flip angle 90°, repetition time 5884 ms, echo time 98 ms, effective number of excitations 2, pixel bandwidth 325 Hz, field of view 25.6 cm, slice thickness 2.5 mm, gap 1.5 mm, and acquisition pixel size 1 mm × 1 mm, and zero filling interpolation × 2. The MRI sequences were executed on the same 3.0 T GE machine as the patient scans using an 8US TORSOPA coil (GE Healthcare, Waukesha, WI, USA). The CT images were acquired on a GE Discovery CT 750HD (GE Healthcare) in helical mode at 120 kVp, 150 mA, 0.516 pitch, 0.8‐s rotation time, 0.625‐mm slice thickness, 0.625‐mm spacing between slices, pixel size 0.39 mm × 0.39 mm, and CTDIvol 41.07 mGy.

2.C.2. Patient MRI protocol

MRI scans were performed using a 3.0 T Discovery 750 MRI scanner (GE Healthcare) with 6‐element flex coils and a flat insert table (GE Healthcare). Thirty slices with an axial field of view of 25.6 cm and slice direction in the superior‐inferior direction (slice thickness of 4 mm) were selected to cover the spatial region encompassing the palatine process region cranially to the cricoid cartilage caudally for all scans. The T1‐weighted MRI sequence was a three‐dimensional spoiled gradient recalled echo sequence with flip angle 15°, repetition time 3.6 ms, echo time 1 ms, effective number of excitations 0.7, pixel bandwidth 325 Hz, acquisition pixel size 2 mm × 2 mm (matrix size 128 × 128), and zero filling interpolation × 2. This resulted in reconstructed voxel sizes of 1 mm × 1 mm × 4 mm. The T2‐weighted MRI sequence was a two‐dimensional fast spin echo multislice sequence with flip angle 90°, repetition time ~3600 ms, echo time ~100 ms, effective number of excitations 1, pixel bandwidth 195 Hz, slice thickness 2.5 mm, gap 1.5 mm, acquisition pixel size 1 mm × 1 mm, and zero filling interpolation × 2.

2.D. Registration techniques

2.D.1. Velocity

The images were first registered using manual alignment by shifting and rotating the secondary image. Then a region of interest that encompassed the whole porcine phantom or patient anatomy was drawn. Within this region of interest, the images were aligned first using Rigid 3 Passes. The Velocity rigid registration uses mutual information to align anatomy. Then MR Corrected Deformable was used to deformably align the images. Velocity's deformable image registration uses a cubic B‐spline algorithm with a uniform knot vector and a steepest gradient descent optimizer. Mattes Mutual Information is used as the “goodness of match” driver for the registration. The MR correction applies a fade correction to the image to correct for shading artifacts typically caused by inhomogeneities in the magnetic field and then proceeds with the deformable image registration.

2.D.2. In‐house demons‐based algorithm

The in‐house deformable image registration is a dual‐force Demons algorithm.¹² Before performing the deformable registration, we performed histogram equalization to match the contrast of the two images. The histogram equalization was performed locally by separating the images into small blocks. A multiresolution scheme was used to accelerate the registration and improve the robustness of the registration. The parameter settings for the deformable registration are specified in Table 1. These parameters were chosen based on our experience in optimizing the algorithm for the MR–MR registration. Refer to Wang et al.¹² for details about this deformable registration algorithm.

Table 1.

Parameter settings for the dual‐force Demons deformable image registration

Parameter	Value
Number of bins for histogram equalization	256
Block size for histogram equalization	20
Multiresolution levels	6
Number of iterations	200
Upper bound of step size	1.25
Gaussian variance for regularization	1.5

2.E. Statistical methods

The applied deformation for the synthetic images was obtained from the deformation vector field used to generate the synthetic post‐treatment image from the synthetic pretreatment image. The applied deformation for the porcine phantom was calculated from the difference in marker location on the CT images. The applied deformation was summarized using the root mean square (RMSD) and maximum. The registration error was calculated as described above and was also summarized using the root mean square (RMSE) and maximum.

3. Results

3.A. Porcine phantom

The four image sets were registered producing six different pairs of images. In our analysis using Velocity one of the gold markers was not mapped to a voxel. For the T1‐weighted MR image registrations using the in‐house demons‐based algorithm, one of the gold markers was mapped to the registered image for only one of the registrations. For the T2‐weighted MR image registrations using the in‐house demons‐based algorithm, one of the gold markers was not mapped to the registered image in two of the registrations. The markers in our study are represented by regions of interest (ROIs). Some markers have very small volume. The deformable mapping of these small ROIs could not produce a reasonable volume so the software treated the deformed ROIs as noise and removed them. To avoid the confusion, we take out these small ROIs from our results.

For both the T1‐ and T2‐weighted MR images, the RMSD was 5.0 mm in the left‐right (LR) direction, 9.0 mm in the anteroposterior (AP) direction, and 6.1 mm in the superior‐inferior (SI) direction. The T1‐weighted MR images registered using Velocity had RMSEs of 1.8 mm in the LR direction, 1.5 mm in the AP direction, and 2.7 mm in the SI direction. The T1‐weighted MR images registered using the in‐house demons‐based algorithm had RMSEs of 1.2 mm in the LR direction, 1.5 mm in the AP direction, and 2.1 mm in the SI direction. The T2‐weighted MR images registered using Velocity had RMSEs of 1.3 mm in the LR direction, 1.2 mm in the AP direction, and 1.6 mm in the SI direction. The T2‐weighted MR images registered using the in‐house demons‐based algorithm had RMSEs of 0.81 mm in the LR direction, 1.1 mm in the AP direction, and 1.1 mm in the SI direction. Boxplots of the RMSE and RMSD in the LR, AP, and SI directions from Velocity are shown in Fig. 4. The maximum registration errors from both registration systems are summarized in Table 2.

Figure 4.

Porcine Phantom Registration Error. The registration error using the T1‐weighted MR images is shown in red, the registration error using the T2‐weighted MR images is shown in green, and the applied deformation is shown in blue. Values are shown for the left‐right (LR) direction, anteroposterior (AP) direction, superior‐inferior (SI) direction, and magnitude. [Color figure can be viewed at wileyonlinelibrary.com]

Table 2.

Maximum registration error from synthetic images and the porcine phantom

Source	T1‐weighted images, mm			T2‐weighted images, mm
	LR	AP	SI	LR	AP	SI
Left parotid gland	3.37	2.65	4.62	4.51	3.25	2.60
Right parotid gland	2.77	1.99	4.38	5.97	4.27	3.40
Left submandibular gland	4.90	3.80	10.2	3.66	1.95	2.04
Right submandibular gland	5.72	1.94	2.44	2.31	1.78	2.37
Sublingual gland	1.09	1.34	1.71	1.87	1.52	2.84
Porcine phantom, Velocity	6.5	5.9	12.9	3.7	2.9	4.3
Porcine phantom, in‐house algorithm	2.9	5.1	10.8	2.4	3.8	2.4

LR, left‐right; AP, anteroposterior; SI, superior‐inferior.

3.B. Synthetic images

For the T1‐weighted MR images, the RMSD was 1.5 mm in the LR direction, 2.1 mm in the AP direction, and 0.79 mm in the SI direction. The RMSE was 0.76 mm in the LR direction, 0.76 mm in the AP direction, and 0.69 mm in the SI direction. RMSD and RMSE for each gland can be found in Fig. 5. The maximum registration error was 1.1–5.7 mm in the LR direction, 1.3–3.8 mm in the AP direction, and 1.7–10 mm in the SI direction for the five salivary glands. The applied deformation is larger for the left parotid than the right parotid for these synthetic images. This was a result of the patients included in this study. A larger sample size would likely not have seen this effect.

Figure 5.

Root Mean Square (RMS) Applied Deformation and Registration Error in T1‐Weighted Synthetic Images. RMS registration error is shown in red and RMS applied deformation is shown in blue for the left‐right (LR) direction, anteroposterior (AP) direction, superior‐inferior (SI) direction, and magnitude. Each boxplot shows RMS registration error and applied deformation for the left parotid (Lt Par), right parotid (Rt Par), left submandibular (Lt Sub), right submandibular (Rt Sub), and sublingual (Subl) glands. In each plot, the RMS registration error is shown to the right of the RMS applied deformation for each gland. [Color figure can be viewed at wileyonlinelibrary.com]

For the T2‐weighted MR images, the RMSD was 1.1 mm in the LR direction, 3.4 mm in the AP direction, and 1.4 mm in the SI direction. The RMSE was 1.1 mm, 0.75 mm, and 0.81 mm in the LR, AP, and SI directions, respectively. RMSD and RMSE for each gland can be found in Fig. 6. The maximum registration error was 1.9–6.0 mm in the LR direction, 1.5–4.3 mm in the AP direction, and 2.0–3.4 mm in the SI direction for the five salivary glands. The maximum registration error for each salivary gland is shown in Table 2.

Figure 6.

Root Mean Square (RMS) Applied Deformation and Registration Error in T2‐Weighted Synthetic Images. RMS registration error is shown in red and RMS applied deformation is shown in blue for the left‐right (LR) direction, anteroposterior (AP) direction, superior‐inferior (SI) direction, and magnitude. Each boxplot shows RMS registration error and RMS applied deformation for the left parotid (Lt Par), right parotid (Rt Par), left submandibular (Lt Sub), right submandibular (Rt Sub), and sublingual (Subl) glands. In each plot, the RMS registration error is shown to the right of the RMS applied deformation for each gland. [Color figure can be viewed at wileyonlinelibrary.com]

4. Discussion

MRI use in the United States has increased more than threefold over the past 20 yr according to the Organisation for Economic Co‐Operation and Development database.²⁹ This increased use includes longitudinal studies that require deformable image registration. This study evaluated the performance of two image registration systems for MRI deformable image registration. The porcine phantom validated both image registration systems, Velocity and the in‐house demons‐based algorithm. Then in order to validate Velocity further, the in‐house demons‐based algorithm was used to generate synthetic images. The use of synthetic images relies on the accuracy of the in‐house demons‐based algorithm to create the inter‐ and intrapatient variation models. This system has been previously validated using CT.^{11, 12, 27} The porcine phantom results demonstrated that this validation is also applicable to MRI. These evaluation measures, the porcine phantom and synthetic images, showed that both Velocity and the in‐house demons‐based image registration system performed well, with all RMSEs below 3 mm.

The RMSE was relatively stable, as shown by the increase in the applied deformation in the AP direction compared with the LR and SI direction for the synthetic images, even though the registration error stayed around the same values for the LR, AP, and SI directions. Furthermore, when applied deformations were pushed past physiological bounds in the porcine phantom, the registration errors were similar to the registration errors from the synthetic images.

The generally low RMSEs for both image registration systems are consistent with average registration errors reported in the literature when evaluated using CT.^{10, 11, 12, 22, 23, 24, 25, 26, 27} However, we did find occurrences of registration errors greater than 10 mm in both image registration systems. The maximum registration errors of 10.2 mm for the SI direction of the left submandibular gland on the T1‐weighted synthetic images and 12.9 mm for the SI direction of the porcine phantom T1‐weighted MR images in Velocity were higher than the maximum registration errors measured in CT‐based registration with Velocity.^{10, 22, 23, 24, 25, 26} These large registration errors may be due to the type of surrounding tissue. Both of these points were in the vicinity of bone but at least 3 cm away. Singhrao et al. used a head and neck phantom that included representative bony anatomy, and found maximum errors between 6.5 and 8.3 mm for Velocity's deformable image registration with CT images.²³ This maximum error is closer to the error we found in this study than are the maximum errors found in studies of anatomical regions outside the head and neck.^{24, 25}

The porcine phantom results showed that the maximum registration errors for both the T1‐weighted and T2‐weighted MR images were lower than those observed for CT using the in‐house demons‐based algorithm.¹¹ This system has been previously validated and subsequently used for a variety of CT studies.^{30, 31, 32} Results from this study presented here imply that the in‐house demons‐based algorithm can be used reliably for MRI as well as CT.

However, there is a limitation with the use of a porcine phantom in this setup because we were only able to deform and not shrink the phantom. The synthetic images included shrinkage as part of the intrapatient variation model. The lack of shrinking in the porcine model limits its applicability in regions of interest that shrink or grow over time. Nevertheless, this study expands on other studies that have evaluated deformable image registration using only a few markers.^{17, 18} Our study design is similar to that used by Lian et al.¹⁹ who used 10–15 markers, but the phantom in this study was meat rather than tissue‐equivalent bolus material, so that it included muscle, bone, and fat. Another limitation of this porcine phantom is the size of deformations that were applied. The deformations applied are directly linked to the spacing of the notches for the movable dividers in the container which was larger than the typical deformation seen in the synthetic images. Therefore, these deformations provide an extreme scenario. The low RMSE by both registration systems in this extreme case shows the good performance of these two systems for MRI deformable image registration.

Both studies utilized consistent imaging parameters and did not investigate the influence of acquisition parameters, such as coil placement, on the MRI deformable image registration. Therefore, these results demonstrate a controlled study which may not fully represent what is seen within clinics. Additionally, image noise and artifacts can impact deformable image registration accuracy — high image noise would degrade accuracy as would the presence of artifacts — and their impacts were not evaluated in this study. However, it is not unreasonable to assume that these error estimates are applicable when imaging parameters are controlled, such as using a repeatable setup in a thermoplastic mask. Setup in a head and shoulder thermoplastic mask with dental stent and coils centered on the base of tongue region showed significantly improved image quality and reproducibility³³ and has consequently been used in a DCE‐MRI longitudinal study for radiotherapy‐induced mandibular changes.⁷

The synthetic images experiment produced SI RMSDs that were typically less than the slice thickness, 4 mm. This is due to the patient population that was used to create the inter‐ and intrapatient variation models. Therefore, extending the results to different patient populations that have larger SI displacement must be done with caution. The porcine phantom results have larger SI displacement and demonstrated similar registration error. However, these larger SI displacements should be verified with patient data, such as synthetic images derived from patients with larger displacements, for full confidence in the registration error in different patient populations.

Additionally, the synthetic images experiment was limited to the salivary glands as these are often analyzed in normal tissue studies. However, the porcine phantom experiment is not site limited. While it was used in this study to support the synthetic image data, the results from this experiment are applicable to other body sites. Therefore, with similar synthetic image experiments, the results can be applied to other locations within the body.

5. Conclusions

Both Velocity and the in‐house demons‐based algorithm demonstrated low registration errors, with all RMSEs below 3 mm for RMSDs between 0.79 and 9.0 mm, indicating that these deformable image registration systems can be used for MRI longitudinal studies.

Conflicts of interest

The authors have no conflicts of interest to disclose.