Neuroinform DOI 10.1007/s12021-013-9216-z

ORIGINAL ARTICLE

Intensity Based Methods for Brain MRI Longitudinal Registration. A Study on Multiple Sclerosis Patients Yago Diez · Arnau Oliver · Mariano Cabezas · Sergi Valverde · Robert Mart´ı · Joan Carles Vilanova · ` Llu´ıs Rami´o-Torrent`a · Alex Rovira · Xavier Llad´o

© Springer Science+Business Media New York 2013

Abstract Registration is a key step in many automatic brain Magnetic Resonance Imaging (MRI) applications. In this work we focus on longitudinal registration of brain MRI for Multiple Sclerosis (MS) patients. First of all, we analyze the effect that MS lesions have on registration by synthetically eliminating some of the lesions. Our results show how a widely used method for longitudinal registration such as rigid registration is practically unconcerned by the presence of MS lesions while several non-rigid registration methods produce outputs that are significantly different. We then

focus on assessing which is the best registration method for longitudinal MRI images of MS patients. In order to analyze the results obtained for all studied criteria, we use both descriptive statistics and statistical inference: one way ANOVA, pairwise t-tests and permutation tests. Keywords Brain MRI · Longitudinal analysis · Multiple sclerosis · Registration

Introduction Y. Diez · A. Oliver () · M. Cabezas · S. Valverde · R. Mart´ı · X. Llad´o Computer Vision and Robotics Group, University of Girona, Campus Montilivi, Ed. P-IV, 17071 Girona, Spain e-mail: [email protected] Y. Diez e-mail: [email protected] M. Cabezas e-mail: [email protected] S. Valverde e-mail: [email protected] R. Mart´ı e-mail: [email protected] X. Llad´o e-mail: [email protected] J. C. Vilanova Girona Magnetic Resonance Center, Girona, Spain L. Rami´o-Torrent`a Multiple Sclerosis and Neuroimmunology Unit, Dr. Josep Trueta University Hospital, Institut d’Investigaci´o Biom`edica de Girona, Girona, Spain ` Rovira A. Magnetic Resonance Unit, Department of Radiology, Vall d’Hebron University Hospital, Barcelona, Spain

Computer vision and machine learning techniques are becoming more and more important in the analysis of Magnetic Resonance Imaging (MRI) images (Wang and Summers 2012). Within these techniques, image registration is a necessary step in brain segmentation algorithms (Liu et al. 2013) or fiber tracking (Prados et al. 2012) and can also be used as a stand-alone tool in applications such as lesion monitoring (Moraal et al. 2010). Historically, rigid methods have been used for longitudinal registration of MRI in clinical practice. While these methods are fast and produce images almost without registration artifacts, their global nature renders them unable to account for smaller, local variations. In many applications, as for example Multiple Sclerosis (MS) lesions (Shah et al. 2011; Llad´o et al. 2012b; Garc´ıa-Lorenzo et al. 2013), these variations are quite frequent. Non-rigid registration methods have been used for MRI registration and are becoming increasingly popular. Examples of these methods are B-splines (Rueckert et al. 2006; Modat et al. 2010) or Diffeomorphic Demons (Vercauteren et al. 2009), which are commonly used for atlas or inter-patient registration or algorithms that consider a group-wise approach such as

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SPM Dartel (Ashburner 2007). The use of non-rigid registration is, however, far from being a closed issue and methods with potential for application still appear (Parisot et al. 2012; Shi et al. 2012). Concerning the state of the art on brain MRI registration methods, Klein et al. (2009) presented a very thorough study that detailed the performances of 14 different registration strategies for brain MRI atlas registration. Although longitudinal and atlas registration of brain MRI images might seem closely related problems, the best strategies to solve them do not actually coincide. The present paper contains a comparative study that includes the methods that performed best in Klein et al. (2009). Concerning the use of computer vision techniques for MS imaging, Llad´o et al. (2012a) presented a comprehensive survey on MS lesion change detection methods that showed how most approaches are based on rigid longitudinal registration. On the other hand, Sdika and Pelletier (2009) studied the effects of White Matter (WM) lesions on atlas registration for MS patients. They identified the issue as a problem when non-rigid registration is used and only one of the images (target or source) contains the lesions as is the case for atlas registration. This is the first paper where a comparison on state-of-the-art methods for longitudinal brain MRI registration of MS patients is presented. We also provide insight on the potential of application of non-rigid registration methods for MS lesion detection and monitoring. Registration of brain images is still a challenging problem. As opposed to other registration scenarios where the two objects being registered are essentially the same and suffer only from noise or occlusion problems, in brain registration the two images to be registered may actually be very different. The clearest example of this occurs when one of the images being used is actually an atlas, but even in longitudinal registration important differences may appear. In this case, although all images are taken from the same brain, noticeable changes might appear. These changes may be due to morphological reasons, appearing lesions, the presence of atrophy or the use of varying scanning protocols. In this sense, the brain registration problem is “ill posed”, as the goal is to find correspondences between images that may differ significantly. On the other hand, evaluating the quality of a proposed solution is also challenging. First of all, different methods might fulfil different goals. For example, rigid registration will provide images with deformation that are less strange to observers but methods that allow local deformations will be able to accommodate variations that are both smaller and localized. Second, the apparently simple issue of telling which between two images bears a closer resemblance to a third one is also controversial. Although image metrics exist, having a best result according to one of them (most methods optimize a single measure) does not always mean that result corresponds to what can be

intuitively considered a better solution (Rohlfing 2012). For all these reasons the use of several criteria that target different aspects of registration and the attention to the particular application being considered is mandatory. The main contributions of this work are: –





First, we present a study on the effect that MS lesions have on longitudinal/temporal registration by analyzing the results of several registration methods for three different data sets. The first one is a clinical data set including 37 MS patients with two studies each (basal and 12M). The second one is built by synthetically eliminating MS lesions from both studies (Chard et al. 2010). The aim of this data set is to simulate patients that do not present MS lesions while being as similar as possible to the original patients. The third data set is constructed by eliminating lesions only from the basal study and puts the stress on how new lesions affect registration. We also present a study on registration algorithms for longitudinal brain MRI images. We follow some of the ideas presented in Klein et al. (2009): use of metrics and statistical tools to analyze results. The main differences with this paper are that 1) we focus on longitudinal registration of MS patients, and 2) we analyze mono-modal registration for T1 and PD channels. We also propose application-specific criteria focused on MS lesions. In order to see whether or not registration brings MS lesions into closer alignment, we compare lesion masks before and after registration using lesion overlap Dice coefficient.

The rest of the paper is organized as follows: section “Materials and Methods” provides details on the methodology used (including tested methods and evaluation criteria). Section “Results and Discussion” provides experimental discussion on the findings of the work. Finally, these findings are summarized and contextualized in section “Conclusions”.

Materials and Methods This section provides details on the methodology used. First, the data set used in this work is described in section “Data Used”. Afterwards, the registration pipeline used is summarized in section “Registration Pipeline”. We then briefly describe the registration methods studied (section “Methods Tested”). Finally, the criteria used to evaluate the results are presented in section “Evaluation Criteria”.

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Data Used Our database consists of data from 37 patients with clinically confirmed MS from three different hospitals. For each patient we have two studies conducted one year apart in time (basal and 12M studies respectively). Each patient underwent MR imaging by using the same protocol, although a different scanning machine was used in each hospital. Namely, the first scanner was a 1.5T Philips Intera (R12) with 2D conventional spin-echo T1-w (TR 653 ms, TE 14 ms) and dual echo PD (TR 2800 ms, TE 16 / 80 ms). The second scanner was a 1.5T Siemens Simphony Quantum, with 2D conventional spin-echo T1-w (TR 450 ms, TE 17 ms) and dual echo PD (TR 3750 ms, TE 14 / 86 ms). The last scanner used was a 1.5T GE Signa HDxt with 3D fast spoiled gradient T1-w (TR 30 ms, TE 9 ms) and PD-w (TR 2700 ms, TE 11.9 ms). All images were acquired in axial-view with slice thickness of 3 mm. The database contained patients with different white matter lesion load. For all patients, all the lesions were accurately annotated by a trained technician and confirmed by expert radiologists. All the people conforming the team responsible for these annotations had more than ten years experience in annotation of brain MS images. All annotations were done on the PD-w images and semiautomatically delineated using JIM© software.1 Figure 1 presents the lesion loads in mm3 . We observe how patients in different stages of MS are present in the database, as indicated by the varying lesion load. Moreover, changes in lesion load range from almost undetectable to very high. This allows us to present a realistic comparison of the performance of longitudinal registration methods in section “Experiment 2: Longitudinal Registration of MS Patients” providing examples of different registration scenarios. On the other hand, we also see how, from the point of view of image processing, it is important to remember that the total lesion load is small compared to the whole of the brain volume: the biggest lesion load in the database, although very high in terms of MS, amounts to less than 4 % of image volume. This suggests that registration methods need to be able to account for small image variations. We back this claim up in section “Experiment 1: Effect of MS Lesions in Longitudinal Registration of MS Patients” and see how rigid registration methods are unfit for this purpose. Concerning atrophy, the two studies for each patient were collected only one year apart, therefore the influence of atrophy is small. In order to assess the impact of lesions in registration, and following the ideas presented in Sdika and Pelletier (2009), we used lesion inpainting in order to obtain lesion 1 Xinapse Systems, JIM software webpage, http://www.xinapse.com/ home.php.

free images that are as similar as possible to our original images. Lesions were inpainted by substituting the intensity values of the pixels that had been identified as belonging to lesions by intensities corresponding to white matter. For this process we used the method described in Chard et al. (2010). As the code was developed for T1 images, we used this channel for our two alternative data sets: –



NOLES data set, where all lesions in both studies were inpainted. The aim behind this data set was to decrease as much as possible the importance of MS lesions in registration and produce patients that looked as much as possible like healthy patients. MAXLES data set, where only lesions in the basal study were inpainted by using the same method. The intention for this data set was to maximize the effect of lesions in registration by mimicking the effect of appearing lesions while still working with a realistic database.

Figure 2 shows an example of the three different data sets used. First column shows the original images with highlighted lesions. The second column shows the same images after lesion inpainting (NOLES data set). The third column shows the data set where the lesions have been inpainted only in the basal control (MAXLES data set). Registration Pipeline Bearing in mind the potential applications in MS lesion monitoring, we considered the following registration scenario. Each of the 37 patients was considered independently. Two longitudinal registrations were performed for each patient corresponding to two separate image modalities (T1, PD). Concerning the choice of the modalities in the study, T1 images are widely used in clinical practice and are also the most frequently used images in registration papers. On the other hand, using PD images, where MS lesions are more clearly visible allowed us to focus on the changes that lesions underwent during the registration process. Furthermore, PD images were used by the experts to make the annotations of MS lesions. Each registration was performed with all registration methods and results were studied using the criteria described in section “Evaluation Criteria”. Figure 3 illustrates this registration pipeline. The only step not present in the pipeline was the usual co-registration between the different channels performed for every acquisition. Specifically, T1 images needed to be translated to PD space. The effect of this is that T1 images experienced one interpolation step more than PD. This coregistration step is not in itself free from error but its effects do not compromise the results obtained: first, T1 images might be smoother due to the extra interpolation step, but this affects all images in the same way. Second, when applying registration transformations computed for one channel

Neuroinform Fig. 1 Lesion volume in the basal study of the original database, in mm3 (up) and change in lesion load between basal and 12M studies (down). Patients are sorted according to lesion volume in basal scans

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to images from another channel the registration error might alter the results (this would be a case of inter-modality and inter-subject registration). The registration scenarios in this paper are all within one modality so this situation does not appear. Methods Tested Our study includes representative examples of the best state-of-the-art MRI registration methods, with a variety of implementations, as summarized in the central table of Fig. 3. In order to make it easier to reproduce the experiments presented in this work we have included all the code used along with the links to publicly available methods and installation instructions at: http://atc.udg.edu/salem/ mriToolbox/. This webpage also includes execution scripts for all methods with details on the parameters used for each method. Specifically, we have tested 12 fundamentally different methods. First of all, we considered rigid and affine registration. These two methods were considered mainly as an initialization step for a posterior non-rigid registration. Best

results were obtained with the combination of both methods, therefore all methods were tested with rigid plus affine initialization. Given its widespread use in clinical practice, results for stand-alone rigid registration are also included. Both methods were implemented using the Insight Toolkit (ITK) libraries.2 We studied three B-spline-based methods: the first one is Nifty Reg,3 which provides faster convergence as well as the possibility of improved running time by running in the GPU (Modat et al. 2010). The second one is the IRTK cubicspline-based method4 (Rueckert et al. 1999; Denton et al. 1999; Schnabel et al. 2001). Finally, we also tested the Bspline implementation of (Rueckert et al. 2006) provided by ITK. Notice how methods using the same working principle might differ greatly in their implementation details, initialization parameters or even optimization functions, so they do not always produce similar results. 2 Insight

Segmentation and Registration Toolkit webpage, http://www. itk.org/. 3 Nifty Reg download at sourceforge, http://sourceforge.net/projects/ niftyreg/. 4 Image Registration Toolkit, http://www.doc.ic.ac.uk/∼dr/software/ index.html.

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Fig. 2 Example of the data used. First row corresponds to basal study and second row to 12M study, while each column corresponds to Original Data (with highlighted lesions), NOLES database, and MAXLES database respectively. In the NOLES database the lesions are inpainted in both controls, while in the MAXLES only the basal control is inpainted. The aim of these processed images is to obtain the maximum similarity between both controls in the NOLES database and the maximum difference (only due to lesions) in the MAXLES one

We also included the DRAMMS5 method (Ou et al. 2011). This is a general-purpose non-rigid registration algorithm that, as opposed to all the other algorithms studied is not solely based on intensity values. To be fully precise, some of the methods studied (as, for example, SyN), allow landmark based registration in addition to the intensity based registration that we used in this study. This registration modality requires, however, the (usually manual) placement of landmarks, so in order to keep the registration process as free from user intervention as possible, we have not used it. As its authors claim, DRAMMS bridges the gap between intensity and landmark-based methods. This is achieved by assigning a rich set of Gabor attributes to each voxel and then computing a non-parametric transformation. The correspondences between voxels in this transformation are determined by a function named “mutual saliency” that aims at giving more weight in the transformation to more distinctive voxels. These two concepts, attribute matching and mutual saliency, play the role that similarity metrics do for most registration methods.

5 DRAMMS can be downloaded at: http://www.rad.upenn.edu/sbia/ software/dramms/download.html

In addition to the already mentioned IRTK, this study includes most of the methods that obtained good results in Klein et al. (2009): ART, SPM8 DARTEL, SyN and Diffeomorphic Demons. ART registration (Ardekani et al. 2005) a non-parametric method that is part of the NITRC: Automatic Registration Toolbox.6 The Statistical Parametric Mapping software package (SPM).7 is widely used in clinical practice and is often regarded as the standard tool for some tasks such as segmentation. Taking the good results obtained by the SPM8 DARTEL toolbox in Klein et al. (2009) into account, we decided to also include it in this study. This toolbox, based in Ashburner (2007), uses a finite difference model to estimate a flow that can then be used to generate diffeomorphic transformations. We have also used SPM8’s High Dimensional Warping (HDW) toolbox (Ashburner and Friston 2004), which, although primarily designed for group-wise registration, presents a focus closer to longitudinal registration. In this case, a high dimensional model is used, whereby a finite element approach is employed to estimate translations at the location of each voxel in the template image. Bayesian statistics are used to obtain a maximum a posteriori (MAP) estimate of the deformation field. SyN registration, is part of the Advanced Normalization Tools (ANTs) package8 and uses bi-directional diffeomorphism (Avants et al. 2008).These bidirectional diffeomorphisms (as is also the case for diffeomorphic demons) do not need to distinguish between target and source images, enhancing, thus, their application scenarios. Finally, a well-established method for brain MRI registration is the Diffeomorphic Demons algorithm (Vercauteren et al. 2009). This method was originally based on Thirion’s demons9 (Thirion 1996). This paper reformulated the original idea by formalizing the original demons optimization (identified from now on as “DEM”) as an optimization procedure over the space of displacement fields. This reformulation allowed the authors to show how Thirion’s formulation, although apparently very different to the classical registration pipeline based on an interpolator, an optimizer and a measure to be optimised,

6 NITRC

Automatic Registration Toolbox webpage, http://www.nitrc. org/projects/art/. 7 Statistical Parameter Mapping webpage, http://www.fil.ion.ucl.ac.uk/ spm/ For the computations related to this paper we used the SPM8 version. 8 Advanced Normalization Tools webpage, http://www.picsl.upenn. edu/ANTS/download.php. 9 We used ITK implementation for both Demons and Diffeomorphic Demons. Specifically, the Diffeomorphic demons implementation can be downloaded at http://www.insight-journal.org/browse/publication/ 154/. See “the itk programming guide” for details on how to download the code for classical itk demons.

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Fig. 3 Registration pipeline overview. Longitudinal registration for all the patients in the database is performed using all studied methods and evaluated with all described criteria. Experiments focus on two aspects: the effect that lesions produce in registration algorithms and the comparison of registration methods for longitudinal registration of MS patients. The registration methods, their physical basis, the acronyms used throughout the paper and the measure optimised by

each method are also included in the central table. Legend: NMI: Normalized Mutual Information, MI: Mutual Information, BE: Bending Energy, AM: Attribute Matching, MS: Mutual Saliency, Mult. Mod.: Multinomial Model, Post. Pot.: Posterior Potential, NCC: Normalized Cross Correlation, CC: Cross Correlation, SSD: Sum of Squared Differences

could be fit to a similar schema based on SSD minimization. Furthermore, the authors provided different variants corresponding to the operation allowed in the space of deformation field: exponentiation and composition, which stands for standard diffeomorphic demons (identified from now on as “DD0”), additive demons (identified from now on as “DD1”), and compositive demons (identified from now on as “DD2”). In this work we extend the study of these methods respect to Klein et al. (2009) by including the three diffeomorphic variants as well as the classical formulation. For each patient, longitudinal single-channel registrations for both channels (T1 and PD) were performed. Basal control was used as Target and 12M control was used as source. Registration was performed with all methods described. Figure 4 presents an example of one of the central slices for some of the registration output 3D volumes. With this we intend to present the nature of the deformations obtained but in order to visually assess how much a particular registration output resembles the target volumes (or differs from the source), inspection of all the slices of the 3D volume would be necessary. All computations performed were run in a Linux machine with 8 Gbyte RAM and 8 dual core Intel i5 processors.

Evaluation Criteria Evaluating the results of registration is a very challenging problem. In this section we describe the criteria aimed at evaluating different aspects that characterize a good registration. Throughout the paper we will consider the evaluation of registration as a sum of factors and provide insights on the potential applications of the method tested in light of their combined values. Similarity Metric Measuring similarity between images or regions is a crucial component in image registration along with the selection of the transformation function. In addition to using a similarity metric to drive the optimization process of registration, these metrics are also used to evaluate the performance of image registration. This is done under the assumption that an improvement in the similarity metric between images after registration means better alignment. The measure used to guide the minimization processes for each method can be found in Fig. 3. We feel, however, that presenting alternative metrics helps separate two concepts: a) how well did the optimizer do, and b) how similar the images really are.

Neuroinform Fig. 4 Registration example. a target and b source images. Output images using: c Rigid, d Nifty Reg, e IRTK, f ITK B-splines, g Dramms, h Art, i SPM8 DARTEL, j SPM8 HDW, k SyN, l ITK Demons, and m Diffeom. Demons algorithms

With this in mind, we present data on Normalized Mutual Information (NMI) and Sum of Squared Differences (SSD). MI and NMI are based on information theory and provide a more “global” approach to image similarity while SSD is more sensible to localized changes. Although metrics provide an objective way of computing similarity between images, they present some important limitations. Specifically, Diez et al. (2011) showed how some images, although providing better results in terms of MI metrics, were deemed by experts as “unrealistic” and containing many image artifacts. On the other hand, Rohlfing (2012) showed how a method could be designed so that it obtained the best results in terms of measures (and tissue overlap) while making absolutely no sense in medical terms. Consequently, metric values cannot be considered as the only way to evaluate registration and must be combined with measures that make up for their limitations.

Consequently, and following the conclusions presented in Rohlfing (2012), we will also use lesion overlap measures as detailed in the following section. MS Lesions Overlap One of the conclusions presented in Rohlfing (2012), was that only overlap of sufficiently local labeled ROIs could distinguish reasonable from poor registrations. Following this idea, we used a measure that focuses on widely distributed but small regions of interest that correspond to MS lesions. In addition to not being affected by the limitations concerning image metrics, this measure is also application oriented. An important point in any registration method is quantifying how useful it can potentially be for clinical tasks. In this case, we focus on assessing whether each particular registration method is able to bring MS lesions into

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closer alignment after registration. In order to measure this, we used voxel-wise Dice coefficient. Statistical Analysis We use boxplots as a compact way to describe large sets of data. Specifically, throughout section “Results and Discussion” we will present several multiple boxplots where each box will group the data resulting from a registration method. Although boxplots present a convenient way to visualize data, statistical inference is necessary in order to provide objective backup to observations. In this paper we generally compare the performance of several methods, hence ANOVA analysis is a natural option to use. There is however, one problem. In some cases, the alternative hypothesis of ANOVA tests (i.e., “not all the means of all the methods coincide”) is too general as a single under-performing method might hide the fact that two or more methods present similar performances. In these cases, pairwise t-tests are the natural option, but given the high number of methods studied, their use is impractical and will only be used momentarily in order to highlight particular differences. In order to present pairwise comparisons between methods in a compact way, we use permutation tests (Klein et al. 2009; Menke and Martinez 2004). These tests choose small sets of independent values obtained by the different registration methods, choose pairs of methods, and performs permutation tests that are regarded in Menke and Martinez (2004) to compute the p-value more exactly than usual t-tests. Finally, the number of times when p < 0.05 is stored. All these steps are repeated and what we present is the mean and standard deviation (μ, σ ) of the fraction of times when each method produced significant p-values. Consequently, methods with higher means have passed a higher number of pairwise comparisons with other methods using randomly chosen subsets of values. Following Klein et al. (2009), methods are presented in ranks determined by the mean and standard deviation of the method with highest mean: (μ0 , σ0 ). Only methods with positive mean are presented. Ranks are decided in terms of the distance of the mean of each method to the best mean observed. Specifically, rank 1 methods are those in (μ0 − σ0 , μ0 ], rank 2 methods fall in (μ0 − 2σ0 , μ0 − σ0 ], and finally rank 3 methods are those in the interval (μ0 − 3σ0 , μ0 − 2σ0 ].

Results and Discussion This section is split in two main experiments. In section “Experiment 1: Effect of MS Lesions in Longitudinal Registration of MS Patients” we assess the effect of MS

lesions in registration while in section “Experiment 2: Longitudinal Registration of MS Patients” the goal is to study which the best method is for the registration of the images in our database. Experiment 1: Effect of MS Lesions in Longitudinal Registration of MS Patients In this section we aim at studying the effect of MS white matter lesions in longitudinal studies, where the lesions might appear in both images. To this end, registration was performed for all methods described in section “Methods Tested” for the NOLES and MAXLES data sets independently (see section “Data Used”). In both cases, the basal studies were considered the target images and the 12M studies were used as the reference images. Consequently, for each method, two different output images were obtained (corresponding to registration within NOLES and MAXLES data sets). In order to assess how much the presence of lesions affected registration, we compared the registration output Out for each specific registration method j and patient i using MI, NMI, and SSD metrics: MI (OutjNOLES (i), OutjMAXLES (i)) NMI (OutjNOLES (i), OutjMAXLES (i)) SSD(OutjNOLES (i), OutjMAXLES (i)) Additionally, we also computed the voxel-wise difference image (diff) between both output images: diffjNOLES−MAXLES(i) = OutjNOLES(i)−OutjMAXLES(i) With these measures we expect to see bigger differences in registration methods that are influenced by the presence of lesions. Alternatively, methods not influenced by lesions should produce two output images that are much more similar. Figure 5a, b, and c, shows the metric comparison, while Fig. 5d shows the entropy of the difference image (E(diffjNOLES−MAXLES (i))). Results depicted in Fig. 5 show how rigid and rigid plus affine registration produce very similar images regardless of the data set used. On the other hand, according to all criteria studied, non-rigid registration methods produce output images that are much less similar to those of other data sets. We studied MI, SSD, and NMI values obtaining similar trends although for the sake of clarity we present only results on methods that are representative of the most extreme tendencies. For example, for the SSD measure, the average difference between the original and NOLES data sets was of 0.05 % for rigid registration while for Nifty reg it reached 3.94 %. Notice that this amount of difference is very important, especially if we take into account the amount of lesions in the image. As mentioned in section “Data Used”,

Neuroinform Fig. 5 Similarity between output for NOLES and MAXLES data sets (T1). Three metrics are presented between output images: a NMI, b MI, c SSD. Finally d presents entropy of difference images between output images. For NMI and MI, higher values represent higher similarity, conversely, for SSD and entropy of difference images, lower values represent higher similarity

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biggest lesions take up to 4 % of the brain volume and for most patients, lesion volume is under 0.01 % of it. Table 1 presents the correlation between lesion load and the metrics between the output for the NOLES and MAXLES data sets. The reason for computing this data was to see whether the changes observed in registration were contained purely in the regions of the image containing the lesions or if changes due to lesion inpainting affected the rest of the output image too. A perfect correlation means that only the inpainted voxels change while a low correlation shows that the changes in lesion voxels spread to other regions of the image. Concerning the correlation between SSD distance and lesion load, we observe a very strong direct linear correlation for rigid methods. Consequently, for these methods, a bigger difference between output images is observed for patients with more lesion load. Bearing in mind that these methods are the ones that vary less between both data sets (Fig. 5), variations seem to be circumscribed mostly to the areas changed by lesion inpainting. Visual inspection of the

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two sets of output images confirmed this suspicion. On the other hand, non-rigid registration methods are able to produce images that differ much more between data sets. This yields a smaller correlation between lesion load and SSD distance as the effect of lesions ripple to other parts of the images and are not only localized in the lesions area. Mutual information metrics are less sensitive to local changes such as those produced by MS lesions. Consequently, when we consider the NMI metric the correlation between lesion load and image difference is much lower for all methods. To sum up, we have observed how rigid registration methods produce the most similar images even when lesions are inpainted while lesion inpainting changes the output much more for non-rigid methods. We have also been able to correlate differences with lesion load mostly for rigid registration. Once it has been established that rigid and non-rigid registration behave differently in the presence of MS lesions, it remains to be seen which behavior is better. On the one hand, having a method that is unaffected by lesions might come in handy for example in situations

Neuroinform Table 1 Correlation between lesion load and metric values between output images for the NOLES and MAXLES data sets (Pearson correlation coefficient) METRIC

RIG

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SSD NMI

0.89 0.45

0.89 0.37

−0.08 −0.48

0.45 0.28

−0.07 −0.04

−0.09 −0.20

−0.03 −0.03

0.64 0.52

Correlation coefficients higher than 0.7 are usually regarded as indicators of strong relation between the variables being studied

where what is desirable is to have registration guided by global (as opposed to local) image similarity. This is the case, for example, for lesion monitoring in absence of atrophy and with small (or non-existent) global anatomical changes (Moraal et al. 2009, 2010; Llad´o et al. 2012a). On the other hand, that non-rigid methods show a higher degree of variation looks like a better fit in applications where local changes might be important enough to affect registration or whenever localized changes need to be accounted for (Elliott et al. 2013). In the following section we study this question.

Metric Measurement Boxplots Metrics provide objective values relating to how successful a particular method was in terms of optimization and how similar two images are. Unfortunately, a metric that is able to express exactly what medical experts perceive as a “better” registration does not yet exist, therefore other criteria are also necessary. In Figs. 6 and 7 we present metric measurements for SSD and NMI. We omit the results for MI here for the sake of brevity though the conclusions drawn for the other measures presented also stand for it. We provide NMI and SSD to focus not only on the success of the optimization process but also on image similarity as expressed by other metrics. Additionally, we provide the information separated according to the two image modalities considered in this study (T1 and PD). The first column “BEF”, stands for metric values prior to registration and is included in order to provide better context for the differences observed between registration methods. We observe how, as expected, all methods improve the metric measurements taken prior to registration. Rigid registration does worse than most methods according to both distances. The method that obtains best results is ITK Demons, with SyN and IRTK performing a little worse. DRAMMS registration obtains very good results for the NMI metric, reaching a performance very close to that of

Experiment 2: Longitudinal Registration of MS Patients In this section we use real MS patient data (original database) to study the performances of registration methods according to a variety of criteria. Additionally, we also compare the results of all methods in order to provide insight on the strengths and weaknesses of every particular method. An important point is that we do not include evaluation by expert observers. Although we consider this to be a valid criterion, it is necessarily subjective. Taking our intention to make a purely objective evaluation into account as well as the large volume of data (37 patients ×2 image modalities × 12 methods = 888 registrations) we do not include this criterion in the present study.

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ITK Demons. For the SSD distance it performs a little worse but still similarly to SyN and IRTK. Concerning the values obtained for the two separate channels, T1 obtains slightly better results than PD. This is clearer for NMI. The relative performances of the methods are similar in both channels. Variances in data are slightly larger for PD images, especially for the NMI measure. Notice however, that T1 images might present slightly smaller variances due to the extra smoothing step they experienced during the initial step performed when building the database. To further support the conclusions presented, we performed a series of one way ANOVA tests. The following corresponds to NMI data, although the conclusions are the same for MI and SSD. First, we performed tests with all data (including all methods and the measures before registration) in order to ensure statistical significance of the claim that registration helps improve metric values. As is usual practice, the null hypothesis (H0 ) can be stated as “all mean values coincide”, hence in order to obtain statistical backup for the proposed claims and reject H0 the obtained p-values should be as low as possible. These obtained p-values for the two channels were always in the range 10−4 − 10−9 rejecting, thus, the hypothesis that all the means involved are equal. Furthermore, in order to see if the observation that some non-rigid methods improved the performance of rigid registration, we performed another one way ANOVA test including only data by the following methods: rigid, Nifty reg, SyN, ITK B-splines, and all demons variants. In this case, p-values ranged in 10−4 − 10−7 backing up our claim. Finally, we aimed at checking whether or not the different variants of diffeomorphic demons (DDi) could be shown to perform differently in a statistically significant way. To achieve this, we performed a series of pairwise t-tests. The p-values obtained were bigger than 0.1, not allowing us to statistically support this assertion.

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MS Lesion Overlap An important issue concerning MS lesions is how they affect registration. So far we have seen how rigid methods are much less affected by the presence of lesions than nonrigid methods (this was also claimed in Sdika and Pelletier (2009)). The second, and perhaps more important issue is the effect that is desirable for registration methods to have in the presence of lesions. This depends on many factors such as patient-related factors (MS stage or treatment applied) or the particular goal of registration (monitoring Moraal et al. (2010), atlas construction Cabezas et al. (2011) or groupwise registration Liao et al. (2012)). A first scenario (contemplated in Sdika and Pelletier 2009) is the registration of a MS patient to a healthy brain or to an atlas. Any method that is able to “see” a lesion will be unable to morph it into any region of the target image (because no corresponding landmark exists) and might produce undesirable distortions. The fact that a method (such as rigid) is impervious to the presence of lesions is often considered positive in this scenario. We feel that the approach taken by the authors in Sdika and Pelletier (2009), where lesions are inpainted to take them out of the registration process, is sounder in the sense that it can also accommodate small anatomical variations. A second scenario takes into account the monitoring of patients in a fairly stable MS stage in short periods of time (Llad´o et al. 2012a, b). In this case, both target and source images belong to the same patient and contain similar lesions. Therefore, rigid registration is generally considered a valid, fast option. It is generally used in combination with the analysis of difference images to track small lesion variations (Llad´o et al. 2012a). To the best of our knowledge, no study on the compared performance of non-rigid registration methods exists for this scenario.

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Furthermore, the study of lesion overlap before and after registration is an indicator on the quality of registration that is deemed by later studies as more reliable than classical metric values as they represent small regions that are distributed in different regions of the brain (Rohlfing 2012). Figure 8 shows Dice coefficient for lesions in basal and follow-up images before and after registration. Again, the first column “BEF”, stands for values prior to registration. Concerning channels, better results are obtained for PD than for T1. This observation coincides with clinical practice, where T2 and PD channels are generally used to visualize and manually annotate lesions (Llad´o et al. 2012b). Most methods obtain their best values for PD (Demons methods being perhaps the clearest example). The only exception is Nifty reg, whose performance is slightly better for T1 images (although still good for PD images). Concerning methods, most of them manage to improve the results obtained before registration. Best results are obtained by Nifty reg and SyN, registration with SMP8 HDW and IRTK obtained good results for one of the two image modalities. In this case, rigid registration seems to do quite well and be not too far from the best methods. We feel, however, that this is mainly an artifice produced by data variability inside the results observed for each method. As can be seen in Fig. 1, lesion load (at most 4 % of image volume, as seen in section “Data Used”) varies a lot between the patients in our database and produces variations between methods to be hidden by the differences between patients in the same method. In terms of boxplots, the length of the boxes “hides” the differences in relative position. In order to separate these two phenomena, we grouped the patients in three groups according to their lesion load (< 0.5mm3 , [0.5 − 2.5)mm3 , and ≥ 2.5mm3 ). The average values for Dice coefficient, PD images and rigid

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registration were of (0.40, 0.49, 0.66) for the three groups respectively. Values for SyN registration were: (0.44, 0.53, 0.82). The difference between rigid registration and SyN for the patients for higher lesion load exceed data variance inside the group. These differences are also similar to those measured between rigid and the values obtained prior to registration. Although these values show a better performance for SyN in all groups, the differences in values from one group to the other tend to make it difficult to visualize these differences in the boxplot. Specifically, the differences in average and in the positions of boxes appear small when compared to the lengths of the boxes. These differences were found to be statistically significant by using pairwise t-tests inside each group (after checking normality in data using Kolmogorov normality test). Further insight can be gained by counting the number of times a method does better than another: SyN registration outperforms rigid registration in all 37 cases. A similar trend is observed for Nifty registration (outperforming rigid in 36 of the 37 cases with group means (0.42, 0.52, 0.70) and, to a lesser extent, with other methods such as IRTK, HDW or ART. For example, IRTK obtains values of (0.40, 0.51, 0.68) and performs better than rigid in 27 out of 37 cases. The remaining 10 cases correspond mainly to those with smaller lesion load. We believe that these numbers provide a more detailed explanation of what is really happening than the boxplots alone. Concerning the statistical significance of data, t-tests using all studied values did not allow us to affirm that the differences observed were statistically significantly. Once again, we believe the main reason for this is intra-data variability. A possibility to back this claim up would be to perform pairwise difference-of-mean tests using smaller groups of data with minor intra-data variability such as was

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presented for SyN and Rigid. The problem is that additional normality tests are needed in order to use t-tests for difference of means and it is impractical to convey all the details of all the tests in this discussion. In order to summarize this type of discussion, Table 2 shows the permutation test performed over results on lesion Dice coefficient. Essentially, each method is compared against all others using randomly selected subsets of data using statistical difference-of-mean test that do not require data to follow the normality condition. Notice that the data variability is still present in the fact that mean values obtained by all methods are not too high (best methods obtain μ = 0.60). It is, however, possible to see how some methods do better than other in pairwise comparisons that bear statistical significance. Nifty reg and SyN consistently outrank the other methods and are the only ones that always appear in the first rank. SPM8 HDW achieves rank 2 for T1-w images and rank 3 for PD images and is the only other method that outranks Rigid registration in both categories. IRTK achieves rank 3 for T1-w and rank 2 for PD and is, in the later modality, the method that comes closer to SyN and Nifty reg. Rigid registration obtains its best results for T1, where it achieves rank 2, but is clearly far away from the best two methods. For PD images it achieves rank 3. Finally, ART registration appears in rank 3 for both image modalities. We conclude that non-rigid registration methods are more suited for bringing MS lesions into closer alignment in a general scenario. This happens especially for SyN and Nifty reg and, to a lesser extent for spm8 HDW and even IRTK. In accordance with clinical practice (Llad´o et al. 2012b), best overall results were obtained for registration of PD images.

Table 2 Permutation test for lesion overlap. Rank 1: (μ0 − σ0 , μ0 ], rank 2: (μ0 − 2σ0 , μ0 − σ0 ], rank 3: (μ0 − 3σ0 , μ0 − 2σ0 ] T1 METHOD Rank 1 NIFTY SYN Rank 2 HDW RIG Rank 3 ART IRTK

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Conclusions In this paper we have provided insight on several aspects of longitudinal registration of MRI images corresponding to MS patients. Not only have we compared the performances of 12 different methods but also provided details on application specific aspects concerning MS. Such aspects include quantifying the effect of MS lesion in registration and quantifying and comparing how good methods are at increasing lesion overlap. All the claims to be made in this section have been found to be statistically significant throughout the paper by using permutation tests, pairwise t-tests, or ANOVA analysis. First of all, we have shown how non-rigid registration methods are much more sensitive to the presence of MS lesions. Not only do output images vary much more for non-rigid registration methods when MS lesions are inpainted but the variation observed in rigid registration can be strongly correlated to lesion load. This shows how changes in rigid registration due to inpainting lesions are mostly localized to the regions being inpainted. We claim that this shows non-rigid registration methods to be more adequate for registration of images from MS patients, as rigid registration is much less able to react to the presence of lesions. Furthermore, we have addressed the issue of what methods provide better registration. As the registration problem is very complex, we have provided data concerning different aspects of registration and have evaluated it using different indicators and statistical methodologies. We have shown how most non-rigid registration methods outperform rigid registration in all the studied criteria. We have also provided insight on some of the specific strengths and weaknesses of the studied methods. Our main criterion concerning registration quality was lesion overlap Dice coefficient. SyN and Nifty reg provided especially good values for this criteria. IRTK and SPM8 HDW obtained remarkable performances for one of the image types. Rigid registration is a convenient method and, although it was not generally amongst the better methods (SyN, Nifty reg and SPM8 HDW performed better for the two image types), the fact that it is less perturbed by lesions may also be a strong point for particular applications. ART registration also managed to obtain noticeably good results in the proposed permutation test. Concerning image modalities, best results were obtained for PD, which is in accordance to common clinical considerations that deem PD image more adequate for the annotation of lesions. We also studied image metric values as a complimentary criterion for registration quality. Demons based methods, especially ITK Demons, showed very good performance in terms of this criteria, but did worse for lesion overlap measures. The best methods in terms of lesion overlap (SyN and

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Nifty reg) also obtained good values both for NMI and SSD metrics. DRAMMS registration obtained very good results for this criteria, specially for the NMI metric. We also gained some insight in some general aspects of MRI longitudinal registration of MS patients. The registration methods studied can be grouped in terms of the approach they use (B-splines, demons...) their performances fail to fall in the same groups. For example, ITK demons ranked first in terms of MI metric but Diffeomorphic Demons approaches were outperformed by some B-splines approaches such as IRTK. This shows how the specific implementation of every approach and the details of the optimization process followed constrain the final result of each method to a larger extent than its theoretical foundation.

Information Sharing Statement The code and links to external registration libraries are found in the webpage http://atc.udg.edu/salem/mriToolbox/. The toolbox code is distributed for free, and developed using the Insight Segmentation and Registration Toolkit (ITK) which is also an open-source software system. Some routines and libraries may need to be compiled for your specific OS. For further information on how to use the software, please consult the manual available in the webpage.

Acknowledgments We would like to thank to all the authors that have provided public registration algorithms. Moreover, we would like to specially thank the collaborators from University College London that provided us with the MS lesion filling software. This work has been supported by the Instituto de Salud Carlos III Grant PI09/91018, Grant VALTEC09-1-0025 from the Generalitat de Catalunya, and Grant CEM-Cat 2011 from the Fundaci´o Esclerosi M´ultiple. S. Valverde holds a FI-DGR2013 Grant from the Generalitat de Catalunya.

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Intensity based methods for brain MRI longitudinal registration. A study on multiple sclerosis patients.

Registration is a key step in many automatic brain Magnetic Resonance Imaging (MRI) applications. In this work we focus on longitudinal registration o...
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