Kilian Hett

Vinh-Thong Ta

José V Manjón

Pierrick Coupé

Adaptive fusion of texture-based grading for Alzheimer's disease classication

Keywords: Patch-based grading fusion, multi-features, Alzheimer's disease classication, Mild Cognitive Impairment

Alzheimer's disease is a neurodegenerative process leading to irreversible mental dysfunctions. To date, diagnosis is established after incurable brain structure alterations. The development of new biomarkers is crucial to perform an early detection of this disease. With the recent improvement of magnetic resonance imaging, numerous methods were proposed to improve computer-aided detection. Among these methods, patch-based grading framework demonstrated state-of-the-art performance. Usually, methods based on this framework use intensity or grey matter maps. However, it has been shown that texture lters improve classication performance in many cases. The aim of this work is to improve performance of patch-based grading framework with the development of a novel texture-based grading method. In this paper, we study the potential of multi-directional texture maps extracted with 3D Gabor lters to improve patch-based grading method. We also proposed a novel patch-based fusion scheme to eciently combine multiple grading maps. To validate our approach, we study the optimal set of lters and compare the proposed method with dierent fusion schemes. In addition, we also compare our new texture-based grading biomarker with state-of-the-art methods. Experiments show an improvement of AD detection and prediction accuracy. Moreover, our method obtains competitive performance with 91.3% of accuracy and 94.6% of area under a curve for AD detection.

Introduction

Alzheimer's disease (AD) is the most prevalent dementia [START_REF] Petrella | Neuroimaging and early diagnosis of Alzheimer disease: a look to the future[END_REF] that is characterized by an irreversible neurodegeneration leading to mental dysfunctions. Patients with AD have a memory lost with diculty of remembering newly learned information that disrupts daily life [START_REF] Alzheimer | 's. 2015 Alzheimer's disease facts and gures. Alzheimer's & dementia: the journal of the Alzheimer[END_REF]. Subjects with Mild Cognitive Impairment (MCI) present higher risk to develop AD [START_REF] Petersen | Current concepts in mild cognitive impairment[END_REF]. However, before rst clinical symptoms brain changes occur such as synaptic and neuronal loses. To date, diagnosis of AD is established after advanced brain structure alterations. This motivates the development of new imaging biomarkers able to detect the early stages of the disease. Furthermore, the early detection of AD can accelerate the development of new therapies by making easier the design of clinical trials.

During the last decades, the improvement of medical imaging like magnetic resonance imaging (MRI) led to the development of new biomarkers with competitive performance for AD diagnosis and prognosis [START_REF] Bron | Standardized evaluation of algorithms for computer-aided diagnosis of dementia based on structural MRI: The CADDementia challenge[END_REF]. Most of the proposed methods have been based on specic regions of interest (ROI). Among structures impacted by AD, previous investigations mainly focused on medial temporal lobe and especially on hippocampus (HIPP). Alterations on this structure are usually estimated using volume [START_REF] Jack | Hypothetical model of dynamic biomarkers of the Alzheimer's pathological cascade[END_REF], shape [START_REF] Achterberg | Hippocampal shape is predictive for the development of dementia in a normal, elderly population[END_REF] or cortical thickness measurements [START_REF] Eskildsen | Prediction of Alzheimer's disease in subjects with mild cognitive impairment from the ADNI cohort using patterns of cortical thinning[END_REF] (see [START_REF] Wolz | Multi-method analysis of MRI images in early diagnostics of Alzheimer's disease[END_REF] for a review). Besides ROI-based methods, whole brain analysis performed on anatomical MRI have also been proposed to detect areas impacted by AD. These methods are usually based on voxel-based morphometry (VBM) or tensor based morphometry (TBM) frameworks [START_REF] Ashburner | Voxel-based morphometrythe methods[END_REF]. It is interesting to note that both VBM and ROI-based studies conrmed that medial temporal lobe is a key area to detect the rst signs of AD [START_REF] Wolz | Multi-method analysis of MRI images in early diagnostics of Alzheimer's disease[END_REF]. In the medial temporal lobe, the HIPP is one of the earliest region altered by AD [START_REF] Braak | Staging of Alzheimer's disease-related neurobrillary changes[END_REF]. Recently, advanced methods were proposed to capture structural alterations of the HIPP [START_REF] Bron | Standardized evaluation of algorithms for computer-aided diagnosis of dementia based on structural MRI: The CADDementia challenge[END_REF]. Those techniques demonstrated their eciency to detect the dierent stages of AD [START_REF] Sørensen | Dierential diagnosis of mild cognitive impairment and Alzheimer's disease using structural MRI cortical thickness, hippocampal shape, hippocampal texture, and volumetry[END_REF]. Among them, patch-based methods obtained competitive results to detect the earliest stages of AD [21; 9; 32]. Moreover, it has been shown that patch-based methods could detect AD more than seven years before conversion to dementia [START_REF] Coupé | Detection of Alzheimer's disease signature in MR images seven years before conversion to dementia: Toward an early individual prognosis[END_REF] or can be used for dierential diagnosis [START_REF] Koikkalainen | Dierential diagnosis of neurodegenerative diseases using structural MRI data[END_REF]. Therefore, such advanced image analysis methods seem promising candidates to perform AD prediction.

Patch-based methods are usually based on intensities [9; 33] or grey matter density maps [START_REF] Komlagan | Anatomically constrained weak classier fusion for early detection of Alzheimer's disease[END_REF]. However, it is has been demonstrated that HIPP texture improves the detection of early stages of AD [START_REF] Sørensen | Dierential diagnosis of mild cognitive impairment and Alzheimer's disease using structural MRI cortical thickness, hippocampal shape, hippocampal texture, and volumetry[END_REF]. A VBM method using several textural lter on medial temporal lobe area demonstrated the reliability of texture information in AD detection [START_REF] Chincarini | Local MRI analysis approach in the diagnosis of early and prodromal Alzheimer's disease[END_REF]. Moreover, HIPP texture enables to improve AD detection compared to HIPP volume [START_REF] Sørensen | Early detection of Alzheimer's disease using MRI hippocampal texture[END_REF]. This method could potentially capture MRI signal alterations related to neurobrillary tangles and beta-amyloid plaque deposition, although such alterations are not directly detectable with MRI at current resolution. Besides, a recent study recently showed the eciency of using edge detection lters to improve of patch-based segmentation [START_REF]An optimized patchmatch for multi-scale and multi-feature label fusion[END_REF]. This result highlights that patch-based grading methods could be improved by estimating patterns similarity on derivative image features. Therefore, we propose to perform patch-based grading on multiple texture maps obtained with Gabor lters. Gabor lters are designed to detect salient features at specic resolution and direction. These lters were widely used for texture classication [25; 12; 14]. The proposed strategy enables to better capture texture modications occurring at the rst stages of the pathology by improving patch comparison.

The rst contribution of this work is to propose a new texture-based grading framework to better capture structural alterations caused by AD. This new framework proposes multi-directional texture grading based on 3D Gabor lters. Secondly, in order to combine all the grading maps estimated on texture maps, we propose an innovative adaptive patch-based fusion strategy based on a local condence criterion. This fusion framework can be applied to any patch-based processing to combine dierent features or modalities. Moreover, contrary to usual grading-based methods using the average grading values over the considered ROI, we propose a classication step based on a nonparametric grading values distribution representation to better discriminate pathologies stages. In our experiments, we rst study the optimal number of Gabor lter directions for AD detection. In addition, we compare dierent texture lers such as local variance or entropy. We also compare our new adaptive fusion method with dierent fusion schemes. Finally, to highlight the improvement of classication performances provided by our new framework, we compare our new method with the state-of-the-art approaches and demonstrate its eciency. Data used in this work were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset 1 . ADNI is a North American campaign launched in 2003 with aims to provide MRI, positron emission tomography scans, clinical neurological measures and other biomarkers. The data used in this study are all the baseline T1-weighted (T1w) MRI of the ADNI1 phase. This dataset includes AD patients, MCI and cognitive normal (CN) subjects.

Materials

Dataset

The group of MCI is composed of subjects who have abnormal memory dysfunctions and embed two groups, the rst one is composed with patients having stable MCI (sMCI) and the second one is composed with patients with progressive MCI (pMCI), such patients converted to AD during the following 48 months from the baseline [START_REF] Wolz | Multi-method analysis of MRI images in early diagnostics of Alzheimer's disease[END_REF]. The information of the dataset used in our work is summarized in Table 1.

Preprocessing

All the T1w images were processed using the volBrain system [START_REF] Manjón | volbrain: An online MRI brain volumetry system[END_REF] 4 . This system is based on an advanced pipeline providing automatic segmentation of dierent brain structures from T1w MRI. However, in this work, only hippocampus segmentations were used. The preprocessing is based on: (a) a denoising step with an adaptive non-local means lter [START_REF] Manjón | Adaptive non-local means denoising of MR images with spatially varying noise levels[END_REF], (b) an ane registration in the MNI space [START_REF] Avants | A reproducible evaluation of ANTs similarity metric performance in brain image registration[END_REF], (c) a correction of the image inhomogeneities [START_REF] Tustison | N4ITK: improved N3 bias correction[END_REF] and (d) an intensity normalization [START_REF] Manjón | NICE: non-local intracranial cavity extraction[END_REF]. Afterwards, MRI were segmented in the MNI space using non-local patch-based multi-atlas methods [START_REF] Coupé | Patch-based segmentation using expert priors: Application to hippocampus and ventricle segmentation[END_REF]. The obtained hippocampus were segmented according to the EADC protocol [START_REF] Boccardi | Training labels for hippocampal segmentation based on the eadc-ADNI harmonized hippocampal protocol[END_REF] designed for AD studies.

Methods

In this section, we describe the dierent steps of the proposed texture-based grading framework as illustrated in Figure 1. First, we use multi-directional Gabor lters to extract texture in dierent directions. Second, a patch-based grading method is applied within each texture map computed. Afterwards, all the texture grading maps are merged with our novel adaptive fusion method. Finally, the input of classication method is a histogram representation of texture grading values in each hippocampus.

Texture maps estimation

The estimation of patch similarities could be improved by using texture representation instead of using raw intensities. Indeed, it was demonstrated that the use of edge detectors improves patch-based segmentation accuracy [START_REF]An optimized patchmatch for multi-scale and multi-feature label fusion[END_REF]. Moreover, it was also demonstrated that HIPP textural information plays an important role in AD detection [START_REF] Sørensen | Dierential diagnosis of mild cognitive impairment and Alzheimer's disease using structural MRI cortical thickness, hippocampal shape, hippocampal texture, and volumetry[END_REF]. Hence, we propose a new texture-based grading framework that simultaneously captures HIPP texture alterations and improves patches similarity estimation. In this work, texture information is extracted from MRI using a bank of 3D Gabor lters (see Figure 2). We used Gabor lters since they are designed to detect texture patterns at dierent scales and directions [START_REF] Manjunath | Texture features for browsing and retrieval of image data[END_REF]. Impulse response of the 3D Gabor lter is given by the following equation:

h(X, σ, F, θ, φ) = 1 (2π) 3/2 σ 3 exp - x 2 + y 2 + z 2 2σ 2 ĥ(X, F, θ, φ) (1)
where X = (x, y, z), σ represents the standard deviation of the Gaussian function. (θ, φ) are the orientation angles. F represents the central frequency of the frequency response. Finally, ĥ(X, F, θ, φ) is given by: ĥ(X, F, θ, φ) = exp j2πF (x sin θ cos φ + y sin θ sin φ + z cos θ)

In our method, the texture maps are the magnitude of the signal resulting from the convolution of our Gabor lters bank with the MRI. In the proposed pipeline (see Fig. 1), the preprocessed MRI of the subject under study is ltered with a bank of Gabor lters to obtain multiple texture maps. All the training library is also ltered with the same lters bank. Therefore, for each texture map, a texture-based grading map can be estimated.

Patch-based grading

Grading framework uses patch-based techniques to capture signal modications related to anatomical degradations caused by AD [START_REF] Coupé | Scoring by nonlocal image patch estimator for early detection of Alzheimer's disease[END_REF]. To date, patch-based grading methods demonstrate state-of-the-art performances to detect the earliest stages of AD [20; 33]. To determine the pathological status of a subject, Figure 2: Sample of absolute value of complex number computed by Gabor lters. The hippocampal area is ltered with gabor at dierent directions. From left: Original image, textural maps provided by our Gabor lters bank given by the parameter set {(θ = 0; φ = 0), (π/2; π/2), (0; π/2), (0; π/4), (0; -π/4), (-π/4, π/4), (π/4, π/4)}. It can be noticed that for each direction, dierent textures are extracted.

. grading-based methods estimate at each voxel the state of cerebral tissues using anatomical patterns extracted from a training library T composed of two datasets, one with images from CN subjects and one with AD patients. Next, for each voxel of the considered subject, the patch-based grading method produces weak classiers denoted g. This weak classier is based on the similarity between the patch surrounding the voxel under study x i and a set K i of similar patches extracted from T . In this work, we used an approximative nearest neighbor method to nd similar patches in the training library in order to drastically reduce the required computational time [START_REF] Hett | Patch-based DTI grading: Application to Alzheimer's disease classication[END_REF]. The grading value g at x i is dened as:

g xi = tj ∈Ki w(P xi , P tj )p t tj ∈Ki w(P xi , P tj ) , (3)
where t j is the voxel j belonging to the training template t ∈ T , P xi and P tj are the patches surrounding x i and t j , respectively. The function w(P xi , P tj ) is the weight assigned to the pathological status p t of t. We estimate w such as:

w(P xi , P tj ) = exp - ||P xi -P tj || 2 2 h 2 + (4)
where h = min tj ||P xi -P tj || 2 2 with → 0, p t is set to -1 for patches extracted from AD patient and to 1 for those extracted from CN subject. The L2-norm is used to estimate the similarly between patches. Thus, our patch-based grading method provides at each voxel a score representing an estimation of the alterations caused by AD.

Adaptive fusion

In this work, we propose a novel framework to fuse the multiple texturebased grading maps obtained from the estimated texture maps. Our fusion strategy assumes that all the estimated grading maps may not have the same relevance, but more importantly all local weak classiers g xi in these maps do not have the same quality. Hence, at each location, we propose to combine weak classiers derived from multiple texture maps according to a condence criterion. Therefore, the grading value g xi,n at voxel x i,n of a texture-based grading map n , is weighted by:

α xi,n = tj ∈Ki,n w(P xi,n , P tj,n ) (5)
that reects the condence of g xi,n for the texture-based grading map n, here t j is the voxel j belonging to the training template t ∈ T and K i,n is the set of similar patches extracted from the training library T at the voxel x i of the texture map n. Thus, each texture-based grading map provides a weak classier at each voxel that is weighted with its degree of condence α xi,n . The nal grading value g xi is given by:

g xi = n∈N α xi,n g xi,n n∈N α xi,n . (6)
The proposed fusion framework is spatially adaptive and take advantage of having access to a local degree of condence α xi,n for each grading map n.

Basically, the condence α xi,n gives more weight to a weak classier estimated with a well-matched set of patches. This adaptive fusion strategy can applied to any patch-based processing to combine multiple feature or modalities.

Weak classiers aggregation

In previous works on patch-based grading, the weak classier aggregation was performed using a simple averaging [9; 17]. While using a strategy based on averaging enables to be robust to noise, this may remove relevant information on weak classiers distribution. Therefore, in this paper we propose to approximate weak classiers distribution using histogram. Consequently, we classify histogram bins instead of classifying mean grading value over the segmentation mask. Here, histograms were separately estimated for right and left hippocampus and concatenate into a single feature vector. The number of bins are set following Sturge's formula that intends to nd the optimum number of bin for a certain size of sample [START_REF] Sturges | The choice of a class interval[END_REF]. Finally, to prevent bias introduced by structure alterations related to aging, all the grading values are age corrected with a linear regression based on the CN group [START_REF] Dukart | Age correction in dementiamatching to a healthy brain[END_REF]. This correction is done by removing the test CN subjects into a cross-validation procedure.

Implementation

During our experiments, texture maps were obtained using one scale and 11 dierent directions. The texture-based grading maps were estimated using patches of 5 × 5 × 5 voxels. The grading step based on an optimized Patch-Match [START_REF] Hett | Patch-based DTI grading: Application to Alzheimer's disease classication[END_REF] was performed using K = 50. The required computational time was 3s per texture maps, thus the global grading step required 15 seconds with our setup. A support vector machine (SVM) with a linear kernel was used to classify each test subject. We used the Matlab function provided by the Statistics and Machine Learning In our experiments, the soft margin parameter C was optimized with a Bayesian optimization method. The results of each experiment were compared in terms of accuracy (ACC) and area under the ROC curve (AUC), specicity (SPE), and sensitivity (SEN). The AUC is estimated with the a posteriori probabilities provided by the SVM classier. We carried out several experiments: CN versus AD, CN versus pMCI, AD versus sMCI and sMCI versus pMCI. A t-test were performed to study the signicance of the results provided by adaptive fusion scheme compared to mean of textural maps and late fusion into SVM classier. Finally, our new texture-based grading framework was validated within a repeated stratied 10-fold cross-validation procedure iterated 50 times for CN versus AD, CN versus pMCI and AD versus sMCI comparisons. The mean ACC, AUC, SPE, and SEN over these 50 iterations are provided as results. As demonstrated in [START_REF] Tong | A novel grading biomarker for the prediction of conversion from mild cognitive impairment to Alzheimer's disease[END_REF], training the classier with CN and AD enables to discriminate sMCI and pMCI subjects better. Moreover, it enables to perform classication without cross-validation procedure and to limit bias and over-tting problem. Therefore, only one run was performed for sMCI versus pMCI comparison. First, the optimal number of lter directions were investigated. Figure 3 shows the evolution of accuracy related to the number of directions. This experiment demonstrates that 5 dierent directions are enough to obtain the best results for CN versus AD comparison. Indeed, the accuracy does not increase using more directions. The best accuracy is reached with 5 dierent directions for sMCI versus pMCI. A fusion of Gabor lters at dierent scales was also performed. However, this experiment shown that lters at the full image resolution is enough to obtain the best results. The experiments showed that the optimal set of lters directions is {(θ = 0; φ = 0), (π/2; π/2), (0; π/2), (π/4; π/4), (π/4; -π/4)}. Therefore, in the rest of the experiments, comparisons were performed with Gabor lters in these 5 dierent directions and at the full images resolution. To estimate the improvement provided by texture-based approach, we compare results obtained with our framework using intensities of the images in the MNI space (i.e., intensity-based grading) and texture maps. For this comparisons, intensity and texture-based grading were estimated using exactly the same pipeline involving adaptive fusion and histogram-based weak classiers aggregation. Table 2 summarizes the results of intensity-based grading and the proposed texture-based grading obtained with 5 Gabor lters. Results are expressed with area under the curve (AUC), sensibility (SEN) and specicity (SPE) measures.

Results

Accuracy

As it is shown, texture-based grading improves classication performances in all experiments using mean or histogram-based grading. Indeed, the comparisons conducted with histogram-based representation show that texture-based grading obtains 94.6% of AUC for CN versus AD, 92.0% of AUC for CN versus pMCI, and 82.6% of AUC for AD versus sMCI comparisons while intensitybased grading obtains 93.5% of AUC for CN versus AD, 90.0% of AUC for CN versus pMCI, and 81.1% of AUC for AD versus sMCI comparisons. Finally, with histogram representation, texture-based grading obtains 76.1% of AUC for sMCI versus pMCI comparisons and intensity-based grading obtains 74.9%. As results based on histogram representation, the average grading aggregation follows the same tendency. These results demonstrate that texture maps enable to better capture structural alterations.

Comparison average grading vs. histogram-based grading

In this section, we compare our proposed histogram-based weak-classier aggregation of texture-based grading values with a straightforward average that is usually used in patch-based grading framework. As presented in Table 3 and 2, the results show that histogram representation of weak classiers distribution provides similar or better classications results for all comparisons. Histogrambased aggregation obtains 94.6% and 92.0% of AUC while the average obtains 94.7% and 92.3% of AUC for CN versus AD and CN versus pMCI comparisons, respectively. Moreover, histogram-based aggregation obtains better results for AD versus sMCI and sMCI versus pMCI comparisons with 82.6%, and 76.1% of AUC compare to the average that obtains 82.2% and 75.1% of AUC for the same comparisons, respectively.

Comparison of dierent fusion schemes

Our fusion scheme was compared with a fusion based on the mean of texturebased grading maps (i.e., fusion of the dierent grading maps provided at each direction with a straightforward average) and a SVM fusion of our texture-based grading features (i.e., concatenation of the histogram features at the dierent considered directions into the SVM classier). Results are summarized in Fig- ure 4. During the experiments, adaptive fusion obtained an accuracy of 91.3% for CN versus AD comparison, the fusion using SVM classier obtained 90.1% and the mean fusion obtained 89.1%. Moreover, for sMCI versus pMCI comparison adaptive fusion obtains 72.2% of accuracy while SVM fusion obtains 68.3% and mean fusion obtains 69.1%. Thus, adaptive fusion obtained the best results. Indeed, the results obtained by adaptive fusion is 1.2 percentage point higher than SVM fusion and 2.1 percentage point higher than mean fusion for CN versus AD comparison and 3.8 percentage point higher than SVM fusion and 3.1 percentage point higher than mean fusion. In order to study the signicance of the accuracy dierences between each fusion method, p-values were This comparison shows that adaptive fusion provides best results for both AD detection and prediction (i.e., CN versus AD and sMCI versus pMCI). P-values were estimated with a t-test to compare adaptive fusion with other fusion methods.

estimated with a t-test. These experiments showed that adaptive fusion provides signicantly better results for CN versus AD comparisons.

Comparison of dierent texture-based lters

Figure 5 shows comparison of classication results for dierent texture lters. This comparison was conducted with standard deviation (STD), entropy, gradient, and Gabor lters. Entropy and STD lters were computed into a window size of 5×5×5 voxels. Patch-based grading maps from gradient and Gabor lters were merged with our novel adaptive fusion scheme. STD lters obtained 89.1% of accuracy for CN versus AD comparison and 67.1% for sMCI versus pMCI comparison. Entropy lter obtained an accuracy of 90.5% for CN versus AD comparison and 68.1% for sMCI versus pMCI comparison. Gradient lter obtained 90.8% for CN versus AD and 70.1% for sMCI versus pMCI. This exper- iment shows that only gradient and Gabor lters obtain better results for both, AD detection and prediction compared to intensity-based grading with 91.3% and 72.2% of ACC for CN versus AD and sMCI versus pMCI comparisons, respectively. Thus, patch-based grading applied on an optimal set of Gabor lters provides better results than others texture lters for both considered comparison. Gabor lters improve by 3.2 and 2.1 percent points of accuracy for CN versus AD and sMCI versus pMCI, respectively, compared to gradient lter.

STD

Comparison to state-of-the-art methods

In addition, a comparison with state-of-the-art methods are provided in Table 4. The results of this comparison are expressed in accuracy. On one hand, to compare classication results using the same structure, the proposed framework is compared with grading methods based on HIPP (see the upper part of Table 4). Thus, our proposed texture-based grading method is compared with the original patch-based grading method [START_REF] Coupé | Scoring by nonlocal image patch estimator for early detection of Alzheimer's disease[END_REF], a grading based on multiple instance learning method [START_REF] Tong | Multiple instance learning for classication of dementia in brain MRI[END_REF], and a patch-based grading based on a sparse representation using two dierent registration strategies [START_REF] Tong | A novel grading biomarker for the prediction of conversion from mild cognitive impairment to Alzheimer's disease[END_REF]. This comparison shows that our method provides best results among HIPP-based grading methods. It reaches 91.3% of accuracy for CN versus AD, and 72.2% of accuracy for sMCI versus pMCI comparisons. On the other hand, our proposed method applied into hippocampus is compared with methods based on a whole brain analysis using similar dataset (see the lower part of Table 4). Indeed, we compare our texture-based grading approach applied on HIPP with an ensemble grading that proposed to extend the original patch-based grading to a whole brain analysis based on grey matter maps [START_REF] Komlagan | Anatomically constrained weak classier fusion for early detection of Alzheimer's disease[END_REF], the patch-based grading method based on a sparse representation applied on the whole brain [START_REF] Tong | A novel grading biomarker for the prediction of conversion from mild cognitive impairment to Alzheimer's disease[END_REF], a sparse ensemble grading method that analyzes the whole brain [START_REF] Liu | Ensemble sparse classication of Alzheimer's disease[END_REF], and a Deep Learning (DL) method based a whole brain analysis [START_REF]Deep ensemble learning of sparse regression models for brain disease diagnosis[END_REF]. The results show that our method obtains the best accuracy for AD versus CN. This result is similar to classication results obtained with a DL and sparse ensemble grading method [31; 21]. However, methods based on a whole brain analysis and using non linear registration obtain more accurate classication results for sMCI versus pMCI.

Discussion

In this work, to improve patch-based grading framework, we proposed to capture texture information with a bank of Gabor lters. Our experiments showed that using more than 5 directions does not improve the results while increasing computational time (see Figure 3). Moreover, we also investigated a multi-scale texture approach. However, the experiments carried out showed that only one scale, at the full image resolution, is enough and the use of multiscale texture did not improve classication performances. Therefore, we propose a multi-directional texture-based grading framework based on 1 scale and 5 directions.

A new grading values aggregation method based on histogram was also proposed. During our experiments, histogram representation of grading values distribution did not provide improvement for CN versus AD comparison compared to use a simple average value. That could be explained by the fact that CN and AD distributions are well separated and a parametric representation of their distributions is enough to discriminate these two groups. However, for sMCI versus pMCI case, the two distributions are less separable and histogram representation lead to better classication performances with in average a gain of 1 percentage point of AUC compared to a simple average value.

In order to fuse eciently the dierent texture-based grading maps, we proposed a novel patch-based grading fusion scheme. This method is based on a condence value estimated at each voxel. The comparison with dierent fusion schemes demonstrated the eciency of our method. Indeed, compared to a straight average of the texture-based grading maps and a SVM fusion of the nal histogram features with the classier, our proposed method obtained best accuracy for AD detection and prediction. Moreover, the obtained improvement was signicant. This improvement can be explained by the fact that our proposed adaptive fusion method weights the grading values of each texture map according to their relevances while the fusion into SVM classier and the average of texture maps considers each grading value as having the same importance. Our work hypothesis is also that directional texture lters enable to improve patch comparison, and thus increase AD detection and prediction accuracy. To validate this hypothesis, our novel texture-based grading using an optimal set of Gabor lters were compared with others texture lters as done for segmentation in [START_REF] Wachinger | Ecient descriptor-based segmentation of parotid glands with nonlocal means[END_REF] (see Figure 5). STD, entropy, gradient and Gabor lters were compared for AD detection and prediction. This experiment showed that STD and entropy does not enable to improve patch comparison compare to intensity. The limitation of these lters might be to perform feature estimation within a window. Thus, only gradient and Gabor lters improve classication performances for AD detection and prediction. Moreover, Gabor lters obtain best results for both comparisons. This improvement is related to the use of additional texture directions compared to the three texture directions provided by gradient lter. Table 4 summarizes the comparison of our proposed method with other grading methods proposed in the literature. These results demonstrate that Gabor lters enable to better capture structural alterations than method based on intensity or grey matter data. Indeed, texture maps provide enhance information leading to a better grading process. Thus, our method outperforms other grading methods using intensity when applied on the same structure [9; 32; 33]. At the lower part of Table 4, we compare the performance of our HIPP-based grading method with methods using the whole brain. First, for AD versus CN, the proposed method obtained similar or better results than methods applied over the whole brain. It is important to note that these methods require non linear registration [21; 20; 33; 31] while our method only requires ane registration and proposes a fast grading step. Second, for sMCI versus pMCI, our method obtained better results than all the methods involving a simple ane registration, including whole brain method proposed in [START_REF] Tong | A novel grading biomarker for the prediction of conversion from mild cognitive impairment to Alzheimer's disease[END_REF]. On the other hand, the best results for sMCI versus pMCI are produced by whole brain grading [20; 33] using non linear registration. The improvement when using non linear registration is observed for HIPP-based and whole brain methods [START_REF] Tong | A novel grading biomarker for the prediction of conversion from mild cognitive impairment to Alzheimer's disease[END_REF]. However, this improvement is obtained at the expense of using non linear registration, which is subject to failure and requires high computational time. Our method also demonstrated competitive performances for AD versus CN classication compared to advanced DL methods using whole brain and non linear registration [START_REF]Deep ensemble learning of sparse regression models for brain disease diagnosis[END_REF]. Finally, this comparison shows that patch-based grading methods [20; 33] obtain similar or better results than recent deep learning methods [START_REF]Deep ensemble learning of sparse regression models for brain disease diagnosis[END_REF] when applied over the entire brain after non linear registration.

Conclusion

In this work, we have proposed a new texture-based grading framework to better capture structural alterations caused by AD. Moreover, to combine grading maps estimated on texture maps, we have presented a new adaptive fusion scheme. We also have proposed an histogram-based weak classiers aggregation step to better discriminate early stages of AD. We have studied the optimal set of texture directions and compare to others fusion schemes. Experiments conducted in this work demonstrated the relevance of using textural information in combination with with our novel locally adaptive fusion method. Finally, we have demonstrated the competitive performances of our new texture-based grading framework compared to several state-of-the-art approaches. In future works, we will investigate the extension of our texture-based grading framework to a whole brain analysis.

Figure 1 :

 1 Figure 1: Proposed adaptive fusion of texture-based grading framework: from left to right, the T1w input data, the texture maps for dierent directions, the intermediate texture-based grading maps, the nal fused grading map and the histogram-based weak classiers aggregation.

Figure 3 :

 3 Figure 3: Evolution of the accuracy and AUC for CN versus AD and sMCI versus pMCI comparisons according to the number of Gabor lters. Red and green doted line represented the accuracy and the AUC of intensity-based grading.

Figure 4 :

 4 Figure 4: Comparison of dierent fusion schemes: mean of textural-grading maps, adaptive fusion of textural-grading maps and fusion into a SVM classier (i.e., concatenation of the histogram representing the grading of each texture direction as the input of SVM method).This comparison shows that adaptive fusion provides best results for both AD detection and prediction (i.e., CN versus AD and sMCI versus pMCI). P-values were estimated with a t-test to compare adaptive fusion with other fusion methods.

Figure 5 :

 5 Figure 5: Comparison of classication performances for dierent texture lters. From left to right, we compare standard deviation (STD), entropy, gradient and Gabor lters. Entropy and STD lters were computed with a window size of 5×5×5 voxels. The results shows that only gradient and Gabor lters enable to improve performances for both AD detection and prediction. P-values were estimated with a t-test to compare Gabor lters to other texture lters.

  been carried out with nancial support from the French State, managed by the French National Research Agency (ANR) in the frame of the Investments for the future Program IdEx Bordeaux (HL-MRI ANR-10-IDEX-03-02), Cluster of excellence CPU and TRAIL (BigDataBrain ANR-10-LABX-57).

Table 1 :

 1 Description of the dataset used in this work. Data are provided by ADNI.

	Characteristic / Group	CN	sMCI	pMCI	AD
	Number of subjects	226	223	165	186
	Ages (years)	76.0 ± 5.0 75.1 ± 7.5 74.5 ± 7.2 75.3 ± 7.4
	Sex (M/F)	117/109	150/73	101/64	98/88
	MMSE	29.05 ± 0.9 27.1 ± 2.5 26.3 ± 2.0 22.8 ± 2.9

Table 2 :

 2 Comparison of grading features based on histogram representation of the probability distribution of grading values. This table presents a comparison of intensity-based grading and texture-based grading. These results show that texture-based grading improves AUC of all comparisons. Moreover, these results show that histogram representation provides similar or better results for all comparisons than using average value (see Table3). All the results are expressed in percentage of AUC, SEN, and SPE.

		Intensity-based grading histo. Texture-based grading histo.
		(AUC/SEN/SPE in %)	(AUC/SEN/SPE in %)
	CN vs. AD	93.5/95.5/82.7	94.6/94.2/86.6
	CN vs. pMCI	90.0/81.8/81.4	92.0/92.5/81.2
	AD vs. sMCI	81.1/78.5/68.3	82.6/77.6/72.6
	sMCI vs. pMCI	74.9/77.6/67.2	76.1/74.9/70.2
	4.1. Optimal number of directions

Table 3 :

 3 Comparison of grading features based on mean of the grading values within the HIPP structure. This table presents a comparison of intensity-based grading and texture-based grading. These results show that texture-based grading improves AUC of all comparisons. All the results are expressed in percentage of AUC, SEN, and SPE.

		Intensity-based grading mean Texture-based grading mean
		(AUC/SEN/SPE in %)	(AUC/SEN/SPE in %)
	CN vs. AD	92.6/86.7/83.3	94.7/93.4/87.6
	CN vs. pMCI	89.9/78.2/85.4	92.3/91.6/83.0
	AD vs. sMCI	80.8/76.2/69.9	82.2/77.6/71.0
	sMCI vs. pMCI	73.2/76.4/65.0	75.1/77.0/64.1
	4.2. Comparison grading based on intensity vs. texture

Table 4 :

 4 Comparison with state-of-the-art methods, all the results are expressed in accuracy. The upper part of this table presents results of results of methods applied on the HIPP structure. Texture-based grading improves CN versus AD classication by 2.3 percent points and sMCI versus pMCI classication by 1.2 percent points of accuracy compared to grading approaches based on the same HIPP structure. The lower part presents results of methods that propose a whole brain analysis. Compared to these approaches, our method obtains similar results than advanced methods based on whole brain analysis for CN versus AD classication. However, such methods obtain better performances for sMCI versus pMCI classication. In this table, we provide the type of registration (Reg.) involved in the methods and the type of features (Feat.).

	Methods	Reg.	Feat. CN vs. AD sMCI vs. pMCI
				(ACC in %) (ACC in %)
	Hippocampus
	Original Grading [9]	Ane Intensity	88.0	71.0
	Multiple Instance Grading [32] Ane Intensity	89.0	70.0
	Sparse-based Grading [33]	Ane Intensity	-	66.0
	Sparse-based Grading [33]	NL Intensity	-	69.0
	Proposed Method	Ane Texture	91.3	72.2
	Whole Brain
	Ensemble Grading [20]	NL	GM	-	75.6
	Sparse-based Grading [33]	Ane Intensity	-	66.7
	Sparse-based Grading [33]	NL Intensity	-	75.0
	Sparse Ensemble Grading [21] NL	GM	90.8	-
	Deep Ensemble Learning [31]	NL	GM	91.0	74.8
	GM = Grey matter
	NL = Non linear

http://adni.loni.ucla.edu

http://volbrain.upv.es


Kilian Hett

Vinh-Thong Ta

José V Manjón

Pierrick Coupé

Graph of hippocampal subfields grading for Alzheimer's disease prediction

Keywords: Hippocampal subfields, Patch-based grading, Graph-based method, Alzheimer's disease classification, Mild Cognitive Impairment

Numerous methods have been proposed to capture early hippocampus alterations caused by Alzheimer's disease. Among them, patch-based grading approach showed its capability to capture subtle structural alterations. This framework applied on hippocampus obtains state-of-the-art results for AD detection but is limited for its prediction compared to the same approaches based on whole-brain analysis. We assume that this limitation could come from the fact that hippocampus is a complex structure divided into different subfields. Indeed, it has been shown that AD does not equally impact hippocampal subfields. In this work, we propose a graph-based representation of the hippocampal subfields alterations based on patch-based grading feature. The strength of this approach comes from better modeling of the inter-related alterations through the different hippocampal subfields. Thus, we show that our novel method obtains similar results than state-of-the-art approaches based on whole-brain analysis with improving by 4 percent points of accuracy patch-based grading methods based on hippocampus.

Introduction

Alzheimer's disease (AD) is the most prevalent dementia for the older adults. This disease leads to an irreversible form of neurodegenerative process causing mental dysfunctions. Neuroimaging studies performed on AD patients has revealed that AD causes structural brain changes. These changes are characterized by an accelerated neural and synapse losses, which are advanced when the diagnosis is established. A presymptomatic phase of AD is named mild cognitive Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf.

impairment (MCI). Patients having MCI suffer from amnesia and light mental issues that do not impact their daily life. Moreover, MCI patients can return to a cognitive normal status or progress to dementia. Predicting this conversion is a challenging task but can make easier the design of clinical trials and accelerate the development of new therapies.

It has long been known that in-vivo imaging with magnetic resonance imaging (MRI) can detect structural alterations such as atrophy of grey matter volume. Thus, several methods were proposed. On the one hand, voxel-based morphometry (VBM) methods were designed to detect the most discriminant regions at a voxel scale [START_REF] Wolz | Multi-method analysis of MRI images in early diagnostics of Alzheimer's disease[END_REF]. On the other hand, region-based methods were proposed to analyze specific brain structures. These analysis are usually conducted with volume, shape or thickness measurements [START_REF] Wolz | Multi-method analysis of MRI images in early diagnostics of Alzheimer's disease[END_REF]. It is interesting to note that both of VBM and region-based approaches have demonstrated that the medial temporal lobe especially the hippocampus is the area having the earliest alterations. However, although the hippocampus volume is one of the criterion that can be used to confirm the diagnosis of AD in clinical routines, it does not provide acceptable performance for the prediction of AD conversion. Recently, more advanced methods were proposed to detect subtler structural modifications of the hippocampus [START_REF] Sørensen | Differential diagnosis of mild cognitive impairment and Alzheimer's disease using structural MRI cortical thickness, hippocampal shape, hippocampal texture, and volumetry[END_REF]. Among them, patch-based grading (PBG) framework was proposed to better capture subtle brain alterations caused by AD [START_REF] Coupé | Scoring by nonlocal image patch estimator for early detection of Alzheimer's disease[END_REF]. The main idea of PBG methods is to detect modifications in a cubic fixed-size area named patch. PBG methods applied to the hippocampus have demonstrated state-of-the-art performances for AD detection and prediction compared to others methods based on the hippocampus [START_REF] Coupé | Scoring by nonlocal image patch estimator for early detection of Alzheimer's disease[END_REF][START_REF] Tong | A novel grading biomarker for the prediction of conversion from mild cognitive impairment to Alzheimer's disease[END_REF][START_REF] Hett | Adaptive fusion of texture-based grading: Application to alzheimer's disease detection[END_REF].

However, the hippocampus is not a heterogeneous structure. Indeed, the hippocampus is composed of different subfields having distinct characteristics. A common definition of hippocampal subfields [START_REF] Winterburn | A novel in vivo atlas of human hippocampal subfields using high-resolution 3T magnetic resonance imaging[END_REF] divided them into the subiculum, the cornu ammonis (CA), and the dentrate gyrus (DG). The CA represents the most prominent area. It is usually divided into four regions: CA1, CA2, CA3, and CA4. The CA1 is also composed of several layers, such as the stratum pyramidale (SP), stratum radiatum (SR), stratum molecular (SM), and stratum lacunosum (SL). Moreover, postmortem and animal-based studies showed that hippocampal subfields are not impacted equally. Those studies showed that CA1 and subiculum are the most impacted at the last stages of AD [START_REF] Kerchner | Hippocampal CA1 apical neuropil atrophy and memory performance in Alzheimer's disease[END_REF][START_REF] Trujillo-Estrada | Early neuronal loss and axonal/presynaptic damage is associated with accelerated amyloid-β accumulation in aβpp/ps1 Alzheimer's disease mice subiculum[END_REF]. Consequently, we assume that a straightforward whole hippocampus analysis could limit the prediction performances. An analysis of the hippocampus at a finner scale such as hippocampal subfields may improve prediction.

To confirm this assumption, we propose a novel method to better capture AD signature within hippocampal subfields. Our method integrates patch-based grading features into a new graph-based model that provides efficient representation of the inter-related alterations through the hippocampus. We demonstrate that our novel approach improves patch-based grading method applied into the hippocampus by 4 percent points of accuracy and obtains state-of-the-art results compared to last advanced methods based on whole brain analysis for AD prediction.

Materials and Methods

Dataset Data used in this work were obtained from Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset1 . ADNI is a North American campaign launched in 2003 with aims to provide MRI, positron emission tomography scans, clinical neurological measures and other biomarkers. The data used in this study are all the baseline T1-weighted (T1-w) MRI of the ADNI1 phase. This dataset includes AD patients, MCI and cognitive normal (CN) subjects. The group of MCI is composed of subjects who have abnormal memory dysfunctions and embed two groups; the first one is composed with patients having stable MCI (sMCI) and the second one with patients having progressive MCI (pMCI) who converted in the following 36 months after the baseline. The information of the dataset used in our work is summarized in Table 1. Preprocessing First, each image was preprocessed with a method based on an advanced pipeline providing: (a) a denoising step with an adaptive non-local mean filter [START_REF] Manjón | Adaptive non-local means denoising of MR images with spatially varying noise levels[END_REF], (b) an affine registration in the MNI space [START_REF] Avants | A reproducible evaluation of ANTs similarity metric performance in brain image registration[END_REF], (c) a correction of the image inhomogeneities [START_REF] Tustison | N4ITK: improved N3 bias correction[END_REF] and (d) an intensity normalization. Second, segmentation of hippocampal subfields was performed with HIPS. This method is based on a combination of non-linear registration and patch-based label fusion [START_REF] Romero | Hips: A new hippocampus subfield segmentation method[END_REF]. This method uses a training library based on a dataset composed of high resolution T1w images manually labeled according to the protocol proposed by [START_REF] Winterburn | A novel in vivo atlas of human hippocampal subfields using high-resolution 3T magnetic resonance imaging[END_REF]. Consequently, to perform the segmentation, the ADNI images are upsampled with a local adaptive super resolution method to fit in the training image resolution [START_REF] Coupé | Collaborative patch-based super-resolution for diffusion-weighted images[END_REF]. The method provides automatic segmentation of hippocampal subfields gathered into 5 regions: Subiculum, CA1SP, CA1SR-L-M, CA2-3 and CA4/DG. Finally, visual quality control was conducted to remove all wrong segmentations from the dataset. Moreover, to prevent any bias in the dataset, the quality control was performed without the pathological status of each subject.

Computation of patch-based grading biomarkers

To capture anatomical similarities of alterations caused by AD, we use the patch-based grading framework [START_REF] Coupé | Scoring by nonlocal image patch estimator for early detection of Alzheimer's disease[END_REF]. PBG framework provides at each voxel a score between -1 and 1 related to the alteration severity. The patch-based grading value g at x i is defined as: Graph construction First, the grading process is carried out over the whole hippocampus. Afterwards, the corresponding hippocampal subfield segmentations is used to fuse grading values and to built our graph (see Fig. 1). An undirected graph is defined as G = (V, E, Γ, ω), where V = {v 1 , ..., v N } is the set of vertices for the N considered hippocampal regions (i.e., the whole hippocampus and each on its hippocampal subfields) and E = V × V is the set of edges. Thus, in our model the vertices represents the mean of the grading values for a given hippocampus region while the edges are based on grading distribution distances between two hippocampal regions.

g xi = tj
The probability distributions of PBG values are estimated with a histogram H v for each hippocampus region v. The number of bins is set following the Sturge's rule. For each vertex we assign a function Γ : V → R defined as Γ (v) = µ Hv , where µ Hv is the mean of H v . For each edge we assign a weight given by the function ω : E → R defined as ω(v i , v j ) = exp(-d(H vi , H vj ) 2 /σ 2 ) where d is the Wasserstein distance with L 1 norm that showed best performance during our experiments.

In this work, we used the Elastic Net regression (EN) method that provides a sparse representation of the most discriminative edges and vertices, and thus enables to reduce the feature dimensionality by capturing the key regions and the key relationships between the different hippocampus regions (see Fig. 1). Finally, after z-score normalization, a concatenation of the two feature vectors is given as input of EN feature selection method.

Details of implementation

The most similar patches were extracted with a patch-match method [START_REF]An optimized patchmatch for multi-scale and multi-feature label fusion[END_REF]. We used the parameters proposed in [START_REF] Hett | Adaptive fusion of texture-based grading: Application to alzheimer's disease detection[END_REF] for the sizes of the patches and K i . This results in a hippocampus grading computation in about 1 second. Next, the age effect is corrected using linear regression estimated on CN population. The EN method is computed with the SLEP package [START_REF] Liu | Slep: Sparse learning with efficient projections[END_REF]. The classifications were obtained with the random forest method (RF) 5 . All features were normalized using z-score before selection and classification methods. In our experiments, we performed sMCI versus pMCI classification. The EN features selection and the classifier were trained with CN and AD. Indeed, as shown in [START_REF] Tong | A novel grading biomarker for the prediction of conversion from mild cognitive impairment to Alzheimer's disease[END_REF], using CN and AD to train the feature selection method and the classifier enables to better discriminate sMCI and pMCI subjects. Furthermore, it also enables to limit bias and over-fitting problem without cross-validation step. However, 100 runs were performed to decrease the inner variability of RF. Mean area under curve (AUC), accuracy (ACC), balanced accuracy (BACC), sensibility (SEN), and specificity (SPE) are provided as results in Tables 2 and3.

Results and Discussions

First, a comparison of the prediction performances was conducted with PBG applied into the whole hippocampus as proposed in [START_REF] Coupé | Scoring by nonlocal image patch estimator for early detection of Alzheimer's disease[END_REF], the hippocampal subfields with EN selection, and our proposed method (see Table 2). The average of PBG values into each region (i.e., whole hippocampus and hippocampal subfields) were used. For hippocampal subfields features, the most relevant subfields selected are the subiculum, and the two definitions of CA1 (i.e., CA1-SP and CA1-SRLM, see Figure 2). It is very interesting that hippocampal subfields selected by EN method are in line with previous studies which have shown CA1 and subiculum are the subfields having the most significant atrophy in late stages of AD [START_REF] Kerchner | Hippocampal CA1 apical neuropil atrophy and memory performance in Alzheimer's disease[END_REF][START_REF] Trujillo-Estrada | Early neuronal loss and axonal/presynaptic damage is associated with accelerated amyloid-β accumulation in aβpp/ps1 Alzheimer's disease mice subiculum[END_REF]. PBG based on the whole hippocampus structure obtains 76.8% of Fig. 2. Graphic representing the coefficients estimated by EN method from the vector of features computed by our graph-based method after z-score normalization. The first six labels represent hippocampal regions and the others represents relationships of these regions. It is interesting to note that selected structures are in line with previous hippocampal subfields investigations.

Table 2. Comparison of different hippocampal PBG approaches is presented. First, PBG applied within the whole hippocampus is provided as the baseline. Second, the best hippocampal subfield features selected by EN method. Finally, results provided by our graph-based of hippocampal subfields grading. This comparison shows that our proposed method improves AUC, ACC, BACC, and SEN compared to other approaches. All results are given in percentage. AUC, 70.3% of ACC and is more specific than sensitive. The averages of PBG values within subiculum, CA1-SP, and CA1-SRLM obtain 77.1% of AUC, 71.1% of ACC and improve specificity compare to the hippocampus. Thus, the concatenation of mean grading values based on each hippocampal subfields selected with a EN method slightly increases the prediction performances of AD. However, our proposed graph-based method improves by 1.4 percent points with AUC and 4.4 percent points of ACC compared to the hippocampus. Our graph-based method also improves by 1.1 percent points with AUC and 3.6 percent points with ACC compared to the use of the most discriminant hippocampal subfields. Moreover, in both cases, our proposed method increases the sensibility of AD conversion.

Second, a comparison of our novel graph-based method based on hippocampal subfields and state-of-the-art methods based on the hippocampus, using similar ADNI1 dataset, is provided in the upper part of Table 3. In this comparison, we included the original PBG method [START_REF] Coupé | Scoring by nonlocal image patch estimator for early detection of Alzheimer's disease[END_REF], a method based on multiple instance learning [START_REF] Tong | Multiple instance learning for classification of dementia in brain MRI[END_REF], and an advanced PBG method based on a sparse representation [START_REF] Tong | A novel grading biomarker for the prediction of conversion from mild cognitive impairment to Alzheimer's disease[END_REF]. The results demonstrate that our novel graph-based method obtains better results than all compared methods applied to the hippocampus. Indeed, to the Table 3. Comparison with state-of-the-art methods based on the hippocampus region and approaches based on a whole brain analysis using similar ADNI1 dataset and the same definition of sMCI/pMCI. These results show that our proposed method obtains best results compared to methods applied within the hippocampus. Moreover, compared to approaches based on a whole brain analysis, our method obtains competitive results. All results are given in percentage. Finally, in the lower part of Table 3 a comparison with state-of-the-art methods applied on the whole brain is provided. Our method is compared with a VBM approach [START_REF] Moradi | Machine learning framework for early MRI-based Alzheimer's conversion prediction in MCI subjects[END_REF], the advanced PBG method based on a sparse representation [START_REF] Tong | A novel grading biomarker for the prediction of conversion from mild cognitive impairment to Alzheimer's disease[END_REF] and a recent deep ensemble learning method [START_REF]Deep ensemble learning of sparse regression models for brain disease diagnosis[END_REF]. This comparison shows that our novel graph of hippocampal subfields grading obtains comparable ACC and AUC than the last advanced approaches.

Methods

Registration

Conclusions

In this work, we proposed a new approach to better capture AD signature into the hippocampus. Our method is based on a graph-based representation of inter-related hippocampal subfields alterations. Alterations were captured with a patch-based grading framework while the relationships of alterations between the different subfields are based on histogram distances. We demonstrate that our method improves patch-based grading method based on hippocampus by 4 percent points for sMCI versus pMCI classification. Moreover, our novel approach obtains competitive results compared to state-of-the-art methods based on a whole brain analysis.

Acknowledgement This study has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) within the project DeepVolbrain and in the frame of the investments for the future program IdEx Bordeaux (HL-MRI ANR-10-IDEX-03-02), Cluster of excellence CPU, TRAIL (BigDataBrain ANR-10-LABX-57) and the Spanish DPI2017-87743-R grant from the Ministerio de Economia, Industria y Competitividad of Spain.

Fig. 1 .

 1 Fig. 1. Illustration of the graph construction. From left to right, for each hippocampal region an estimation of the density probability of PBG values is computed. Next, histograms are used to built our graph of hippocampal subfields grading. Graph edges represent the distances between structure grading distribution while vertices represents the mean grading value for a given hippocampal regions (i.e., hippocampus, subiculum, CA1-SP, etc.)

  .2 70.3±0.0 70.6±0.0 69.0±0.0 72.2±0.0 Hipp. subfields EN 77.1±0.2 71.1±0.4 71.4±0.4 69.5±0.6 73.2±0.5 Proposed method 78.2±0.2 74.7±0.4 74.3±0.5 77.1±0.5 71.4 ± 0.9

Table 1 .

 1 Description of the dataset used in this work. Data are provided by ADNI.

	Characteristic / Group	CN	sMCI	pMCI	AD
	Number of subjects	213	90	126	130
	Ages (years)
	Sex (M/F)	108/105	58/32	68/58	64/66

75.7 ± 5.0 74.9 ± 7.5 73.7 ± 7.0 74.1 ± 7.7 MMSE 29.1 ± 1.0 27.6 ± 1.7 26.5 ± 1.6 23.5 ± 1.9

  best of our knowledge, state-of-the-art methods applied on hippocampus have obtained 71% of ACC for sMCI versus pMCI classification while our graph-based of hippocampal subfields grading obtains 74.7% of ACC.

			AUC	ACC	SEN	SPE
	Hippocampus
	Original grading [2]	Affine	-	71.0	70.0	71.0
	Multiple instance grading [13]	Affine	-	70.4	66.5	73.1
	Sparse-based grading [14]	Non Linear	-	69.0	-	-
	Proposed method	Affine	78.2	74.7	77.1	71.4
	Whole brain
	Voxel-based [9]	Non Linear	76.6	74.7	88.8	51.6
	Sparse-based grading [14]	Non Linear	-	75.0	-	-
	Deep ensemble learning [12]	Non Linear	75.4	74.8	70.9	78.8

http://adni.loni.ucla.edu

http://code.google.com/p/randomforest-matlab