Clustering-Based Approach for the Localization of Human Brain Nuclei

DEGREE PROJECT IN MEDICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2020

Clustering-based approach for the localization of Human Brain Nuclei

SAMEER MANICKAM

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES IN CHEMISTRY, BIOTECHNOLOGY AND HEALTH

Clustering-based approach for the localization of Human Brain Nuclei

Sameer Manickam

Master in Medical Engineering Supervisor: Benjamin Garzon Host Institute: Karolinska Institutet, Reviewer: Chunliang Wang School of Engineering Sciences in Chemistry, Biotechnology and Health

Klusterbaserat tillvägagångssätt för lokalisering av hjärnkärnor

Sameer Manickam

Dedicated to my Grandparents & my friend Ismael Faruqi

Acknowledgement:

I want to start by expressing my deepest gratitude to my supervisor Dr Benjamin Garzon who gave me this opportunity to work on such a challenging project. I want to thank him for all the support he showed to me whenever I needed to be it within the project or even in administrative activities. Without his support and guidance, it would have been an impossible job to get a project like this and complete it.

I want to thank my reviewer and group supervisor, Dr Chunliang Wang, for his guidance and support through all the supervision meetings. The feedbacks and ideas gave me many insights as to how to present the research problem at hand.

My sincerest thanks to Dr Anup Singh for introducing me to the world of MRI and Image processing. All my interest developed in this field is because of the opportunities he provided me to work on the challenges in MR.

I want to thank my friends Prashant, Tejas, Shruti, Mahima, Sakshi and Siddharth for their constant support and making my life filled with joy. I want to express my sincerest gratitude and love towards Ranjith, Maggi, Vijay and Swetha for making my stay in Stockholm comfortable as my home.

Lastly and most importantly, I thank my parents and my sister, without whom I am nothing. I want to thank them for the love and blessing they shine upon me. I cannot express how lucky to have them in my life.

Abstract:

The study of brain nuclei in neuroimaging poses challenges owing to its small size. Many neuroimaging studies have been reported for effectively locating these nuclei and characterizing their functional connectivity with other regions of the brain. Hypothalamus, Locus Coeruleus and Ventral Tegmental area are such nuclei found in the human brain, which are challenging to visualize owing to their size and lack of tissue contrast with surrounding regions.

Resting-state functional magnetic resonance imaging (rsfMRI) analysis on these nuclei enabled researchers to characterize their connectivity with other regions of the brain. An automated method to successfully isolate voxels belonging to these nuclei is still a great challenge in the field of neuroimaging. Atlas-based segmentation is the most common method used to study anatomy and functional connectivity of these brain nuclei. However, atlas-based segmentation has shown inconsistency due to variation in brain atlases owing to different population studies. Therefore, in this study, we try to address the research problem of brain nuclei imaging using a clustering-based approach.

Clustering-based methods separate of voxels utilizing their structural and functional homogeneity to each other. This type of method can help locate and cluster the voxels belonging to the nuclei. Elimination of erroneous voxels by the use of clustering methods would significantly improve the structural and functional analysis of the nuclei in the human brain. Since several clustering methods are available in neuroimaging studies, the goal of this study is to find a robust model that has less variability across different subjects.

Non-parametrical statistical analysis was performed as functional magnetic resonance imaging (fMRI) based studies are corrupted with noise and artefact. Statistical investigation on the fMRI data helps to assess the significant experimental effects.

Keywords: Neuroimaging, fMRI, Human Brain Nuclei, Clustering-based approach, Atlas-based segmentation

Sammanfattning:

Studien av hjärnkärnor vid neuroimaging utgör utmaningar på grund av dess lilla storlek. Många neuroimaging-studier har rapporterats för att effektivt lokalisera dessa kärnor och karakterisera deras funktionella koppling till andra hjärnregioner. Hypothalamus, locus coeruleus och ventralt tegmentalt område är sådana kärnor som finns i den mänskliga hjärnan som är svåra att visualisera på grund av deras storlek och felaktig framställning med omgivande regioner.

Resting-state functional magnetic resonance imaging (rsfMRI) analys av dessa kärnor gjorde det möjligt för forskare att karakterisera deras anslutning till andra hjärnregioner. En automatiserad metod för att framgångsrikt isolera voxels som tillhör dessa kärnor är fortfarande en stor utmaning inom området neuroavbildning. Atlasbaserad segmentering är den vanligaste metoden som används för att studera anatomi och funktionell anslutning av dessa hjärnkärnor. Atlasbaserad segmentering har dock visat inkonsekvens på grund av variation i hjärnatlas på grund av olika befolkningsstudier. Därför försöker denna studie att ta itu med forskningsproblemet med hjärnkärnavbildning med hjälp av ett klusterbaserat tillvägagångssätt.

Klusterbaserade metoder hjälper till att separera voxels med hjälp av deras strukturella och funktionella homogenitet med varandra. Denna typ av metod kan hjälpa till att lokalisera och kluster de voxels som tillhör kärnorna. Eliminering av felaktiga voxels genom användning av klustermetoder skulle avsevärt förbättra den strukturella och funktionella analysen av kärnorna i den mänskliga hjärnan. Eftersom flera klustermetoder finns tillgängliga i neuroimaging-studier är målet med denna studie att hitta en robust modell som har mindre variation mellan olika ämnen.

Icke-parametrisk statistisk analys utfördes eftersom funktionella magnetiska resonanstomografi (fMRI) baserade studier är skadade med brus och artefakt. Statistisk undersökning av fMRI-data hjälper till att bedöma de signifikanta experimentella effekterna.

Table of Contents 1. Introduction. 2. Materials and Methods. 2.1. Data 2.1.1. Midnight Scan Club Dataset 2.2. Atlas Based Segmentation 2.3. Clustering Methods 2.3.1. fMRI data preparation 2.3.2. Kmeans Clustering 2.3.3. Kmedoids Clustering 2.3.4. Spectral Clustering 2.3.5. Wards Clustering 2.4. Quantitative Analysis 2.4.1. Clustering Evaluation 2.4.1.1. Silhouette Coefficient 2.4.2. Dice Coefficient 2.4.3. Variance 2.5. Qualitative Analysis 2.5.1. Test for significance 2.5.2. FSL Randomise 3. Results. 3.1. Quantitative Analysis 3.1.1. Hypothalamus 3.1.2. Locus Coeruleus 3.1.3. Ventral Tegmental Area 3.2. Qualitative Analysis 3.2.1. Hypothalamus 3.2.2. Locus Coeruleus 3.2.3. Ventral Tegmental Area 4. Discussion. 5. Conclusion and Future Work. 6. References Appendix A. State of the Art

1. Introduction:

The recent advancement in Magnetic Resonance Imaging (MRI) such as the use of ultra-high field scanners (Stucht et al., 2015), data-processing techniques and data acquisition has opened the field of neuroimaging to study on Human Cognition and Behaviour. Recently, there has been considerable advancement in imaging of the nuclei in the human brain to determine the functional connectivity. These nuclei are challenging to image in an MRI because of their small size and their location in the human brain.

Nuclei such as Locus Coeruleus (LC) is studied extensively and has been involved in many imaging studies as it is the principal noradrenergic Nucleus of the brain (Samuels & Szabadi, 2008). Its functions include complex cognitive processing (like working, memory, learning and attention), emotion in adults, pathophysiology in neurodegenerative and neurodevelopmental disorders. LC has also shown its involvement in neurological disorders like dementia, Alzheimer's (Weinshenker, 2008), anxiety disorder (McCall et al., 2015), Parkinson (German et al., 1992), and depression (Weiss et al., 1994). Another critical nucleus is the Ventral Tegmental Area, and it is one of the significant dopaminergic nuclei alongside Substantia Nigra (SN) of the brain. The VTA is heavily linked with rewarding and reinforcing processes, being part of the Dopaminergic system its primary functions are reward-based and associate learning (MacInnes et al., 2016), motivation (Berridge & Kringelbach, 2013), memory (Kahn & Shohamy, 2013)and cognitive control in decision making (Goschke & Bolte, 2014). The other nuclei focused on this study is Hypothalamus (HTH) as it is small and functionally diverse. The HTH is known for its functions in controlling the vital functions of the body like Autonomic and endocrine functions, immune response, food homeostasis, sexual activity, stress, sleep, and thermoregulation. (Saper & Lowell, 2014).

The use of functional MRI (fMRI) in addition to the structural MR images to view the functional connectivity of each Nucleus may assist in locating the nuclei. The functional connectivity analysis of resting-state fMRI datasets is a powerful tool to visualize the neuronal design of the human brain (Cole et al., 2014), though the fMRI signal is very noisy. Blood Oxygen Level Dependent (BOLD) fMRI measures the neuronal activity of the brain by detecting the changes in relative levels of oxygenated and deoxygenated blood. The signal acquired using BOLD fMRI is corrupted with noises and artefacts resulting from neuronal and metabolic activities. Non-neural effects in the BOLD fMRI time series voxel comprises of multiple factors such as thermal noises from the electrical circuits used in MR signal reception, artefacts arising from hardware unreliability, changes in signal due to motion, and physiological changes of non-neural activity(e.g. breathing) (Caballero-Gaudes & Reynolds, 2017). Thus, the BOLD signal represents only a small fraction of the neuronal activities, and thus it hampers

8 the data analysis for any task-based or resting-state fMRI studies. With improved data preprocessing, especially non-linear image registration methods, the imaging of Brain Nuclei has been made possible.

Brain atlases are a significant resource for neuroanatomical definition and are often used for automated image analysis. The information derived based on functional, anatomical or connectivity of the brain structure one can form the brain atlas, which helps in distinguishing well-defined entities. However, the usefulness of existing brain atlases are limited in: a) inconsistent brain atlases from different sources (Bohland et al., 2009) and b) the atlas may not fit the data well. Inconsistent fitting of data can be due to the difference in the image characteristic or difference in processing strategies. The data misfit can also be because the data may consist of a population of subjects that are not well represented by the population used in the atlas creation. Unlike brain atlas, brain parcellations are performed using data supplied as information to define the regions of the brain and are carried out by the performing clustering algorithms.

Clustering algorithm has been extensively explored in recent times for the analysis and interpretation of neuroimaging data. The clustering algorithm is useful as it divides the brain into a specified number of non-overlapping regions or modules. Regions or modules are divided such that they show some homogeneity concerning some knowledge/information. Information can be delivered in the form of cytoarchitecture, functional connectivity, anatomical features, or task-related activity. These modules or regions or 'brain parcels' are acquired from particular clustering methods performed on the brain images. These efforts are highly useful in measuring at the level of a predefined/specified voxel, looking at the small brain region with many voxels (Thirion et al., 2014). While clustering algorithms or brain parcellations can be used in a different context, in this study, these algorithms are used to separate the voxels having a higher probability of belonging to a brain nucleus amongst other voxels that may be erroneous because of an acquisition artefact, motion artefact or even partial volume effect. Therefore, this study aims,

1) Evaluating the performance of the clustering-based approaches and atlas-based approaches to segmenting human brain nuclei. 2) Test the feasibility of clustering-based approaches to locate nuclei present in the brain and the brainstem.

2. Materials and Methods

2.1. Data:

The data were obtained from public repositories that were already preprocessed. The information of the dataset from the public repositories is given below.

2.1.1 Midnight scan club Dataset

The dataset available on OpenNeuro (Gordon et al., 2017, accession number ds000224) consisted of 10 subjects (5 Male, 5 Female, Mean age: 29.1, SD: 3.3). The images were primarily focused on understanding the functional brain organization by making use of Resting-State Functional Connectivity (RSFC), task-based fMRI and structural MRIs. The images of each subject were acquired on a Siemens TRIO 3T MRI scanner across 12 sessions. The functional images were acquired using a gradient echo EPI sequence (TE: 27ms, TR: 2.2s, flip angle: 90o, voxel size: 4mm x 4mm x 4mm, 36 slices ). From this dataset, the preprocessed RSFC data for ten subjects and five sessions each (Volumetric derivatives) were used for the functional analysis and segmentation in our study. The preprocessed data includes cross-session-averaged T1 and T2 images which were linearly registered to Talairach space (TALAIRACH & J., 1988), the resting state data was fully preprocessed, motion- censored, and confound regressed. For this study, only the resting-state functional connectivity MRI was analyzed for eight subjects across five sessions.

2.2 Atlas Based Segmentation:

The use of Priori anatomical information has been known to improve the segmentation task (Cabezas et al., 2011). The prior information is derived utilizing predefined rules based upon tissue properties, or as a set of manual expert annotations. The atlases were derived from available atlas repositories provided for MRI research.

Template (Space) Reference Additional Information Hypothalamus (HTH) MNI152 (Pauli et al., 2018) Resolution: 1mm per voxel, Voxel Size: 1x1x1 mm3. Locus Coeruleus (LC) MNI152 (Tona et al., 2017) Resolution: 2mm per voxel, Voxel Size: 0.5x0.5x0.5 mm3. Ventral Tegmental MNI152 (Pauli et al., 2018) Resolution: 1mm per Area (VTA) voxel, Voxel Size: 1x1x1 mm3. Table 1. This table provides the name and information of the nuclei used in this study.

Images below (Fig. 2-4) visually represent atlases of Nuclei overlaid on an MNI152 brain image template having a resolution of 1mm. As these atlases/masks were probabilistic, the images show higher intensity where the Nucleus's presence is most accurately located.

Fig 1: The probabilistic atlas of Hypothalamus mask overlaid on an MNI 152 T1 brain Image.

Fig 2: The probabilistic atlas of Locus Coeruleus Nuclei overlaid on MNI152 T1 brain image.

Fig Fig 3: The probabilistic atlas of Ventral Tegmental Area Nuclei overlaid on MNI152 T1 brain image.

Atlas-based functional connectivity maps were generated as a base model to evaluate the performance of clustering-based approaches on an fMRI dataset. This analysis was performed to study whether a clustering-based approach on functional data can be used to further accurately locate the nuclei in the brain. Mean signal from each of the subjects taking the Nucleus's atlas as the ROI was used to correlate with the signal from other parts of the brain. The resulting correlation map would highlight the regions where the nuclei had a positive and negative correlation with the other parts of the brain.

2.3 Clustering:

Five different clustering methods applied to the fMRI data were used to isolate the voxels that may correspond to the exact location of the Nucleus within the brain. Initially, the fMRI data was prepared to focus on the ROI, following which, the clustering methods were tested on the functional data to analyze the variability across the subject.

2.3.1 fMRI data preparation:

The following steps performed the initial preparation of the fMRI data. Firstly, the nuclei atlas was resampled to ensure that the different datasets had the same dimensions. They were then downsampled using 'Nearest Neighbour' as the metric system. The downsampling was performed by using the function from the Nilearn library (Abraham et al., 2014). After the resampling was performed, each atlas was binarized (thresholding at 0) using NumPy library(Van Der Walt et al., 2011) and dilated using from the SciPy library (Virtanen et al., 2020). Secondly, the fMRI data was metricized into 2D matrices before clustering approaches were applied. The first part of this step was to multiply the nuclei atlas on the fMRI data of a test subject and the resulting time series of the voxel that is particular to our ROI was saved in a 2D matrix format. Here, in this layout, the rows correspond to time, and the columns represent the voxels. Lastly, the 2D matrix was provided as an input to the clustering algorithm.

2.3.2 KMeans Clustering:

The algorithm works on the principle of separating samples/data into n groups of equal variances, the minimizing criterion on which the principle is based known as the inertia. The number of clusters has to be defined at the start of the algorithm. This method is widely applied for clustering technique having a wide range of applications. Given below is the mathematical formulation for the algorithm:

푛 2 ∑ min(‖푥푖 − 휇푗‖) 휇푗∈퐶 푖=0

The algorithm performs by progressively dividing the N samples X into K disjoint clusters C, the mean

µj, which defines each cluster of the samples. These means are known as the "centroids". The algorithm's goal is to choose centroids that minimize the inertia. Lloyd's algorithm is another name given to the K means. Steps involved in the algorithm are,

1). to initialize centroids by selecting the samples k from the dataset X,

2). following the initialization, a sample is assigned to the closest centroid then by taking the mean value of the samples assigned to specific centroids, and a new centroid is created.

3). lastly, the algorithm runs until the distance between the centroids is less than a given threshold.

2.3.3 KMedoids Clustering:

One of the main problems with clustering data using KMeans into a defined number of clusters is because of noise and outliers. This can be solved using another such analogous algorithm to K Mean known as the K Medoids algorithm. KMedoids is allied with the KMeans as it tries to minimize the sum of the distance between every data point and the medoid of its cluster, rather than minimizing the sum of squares within the cluster as in KMeans. The medoid can be defined as a data point having the least combined distance to the other members of its clusters. The use of a data point rather than a centroid allows any metric for the distance measurement of clustering. The complexity of K-medoids is O(N2KT), where N corresponds to the number of samples, T corresponds to the number of iterations, and K is the number of clusters.

The approach to performing this algorithm is as follows;

1) Initialize: Selection of the number of clusters for the dataset as the medoids to achieve through different approaches- Heuristic, random or k-medoids++,

2) Assignment: each element from the dataset is assigned to the closest medoid,

3) Update: Create new medoid for each cluster,

4) Loop over 'Assignment' and 'Update' steps while the medoids keep changing or till the maximum number of iterations is reached.

Kmedoids clustering was used in two different ways, i.e., distance metric as 'Euclidean Space' and the other 'Correlation'.

2.3.4 Spectral Clustering:

Another popular unsupervised machine learning algorithm is spectral clustering which has often shown the potential to outperform other approaches. The algorithm has a straightforward implementation of linear algebra methods. Points falling under specific clusters is computed by affinity, unlike the absolute location which is used in k-means. The absolute location can be used to address the problems where complicated shapes and structures in the data are involved.

Within the samples of the data, the program executes a low-dimension embedding of the affinity matrix. This is followed by clustering, e.g. by Kmeans, of the units of the eigenvectors placed in the space of

14 low dimension. The number of clusters has to be specified in advance, and as the algorithm works well with lesser number of clusters, it is well suited for this study. Similarity graphs having normalized cuts problem is solved by convex relaxation in spectral clustering of the two clusters. By cutting the graph in two, this makes the edges cut smaller compared to the edge weight inside the cluster. Spectral clustering is efficient while working on images as the pixels can be the graph vertices, and the similarity graph having the weights of the edge is computed using the function gradient of the image. To summarize the algorithm, we can look at the following steps:

✓ Similarity graph is established. ✓ Laplacian Matrix, degree matrix and the adjacency matrix are determined. ✓ Eigenvectors of the Laplacian matrix are computed. ✓ The input is the second smallest eigenvector for the Kmeans model to train and differentiate the clusters.

2.3.5 Wards Clustering:

Wards clustering is a type of linkage criteria that is used to find the metric for merging strategy in Hierarchical clustering. In hierarchical clustering, the nested clusters are built by merging or splitting them successively and is then depicted in the form of a tree or dendrogram. The unique cluster forms the root of the tree where all the samples have gathered a cluster having just one sample from the leaves. The ward algorithm in hierarchical clustering works in such a way that within all clusters, the sum of squared differences is minimized. It is similar to the Kmeans objective function as it also uses the variance-minimizing approach. Table 2 given below shows the details of the parameters for the different clustering Algorithms.

Cluster Metric Max_iter n_init Affinity Tolerance Range Kmeans 2-10 ‘Euclidean 1000 200 N/A 0.0001 distance’ Kmedoids 2-10 ‘Euclidean 1000 200 N/A N/A distance’ Kmedoids 2-10 ‘Correlation’ 1000 200 N/A N/A Spectral 2-10 ‘Euclidean N/A 200 ‘Nearest 0.01 distance’ Neighbors’ Wards 2-10 Eigen N/A N/A 'Euclidean' N/A Solver=’arpack.' Table 2. The clustering algorithms used in the study, along with the parameters used.

The cluster range is the number of clusters to be formed by the algorithm. As all the clustering algorithm require a defined number of cluster value to perform the clustering, a range of values was provided. Clustering evaluation was done on all the range of values to suggest the best number of clusters for each clustering algorithm. Metric is used to compute the distance matrix of the clusters with the centroids, medoids or within the clusters itself. Max_iter is for the number of iterations the algorithm will perform for a single run. n_init is specified for the number of times the algorithm will perform for different centroids or medoids. Tolerance is regarded with the inertia to declare convergence.

For the evaluation of the methods employed, the study includes quantitative and qualitative analysis of the results from the clustering algorithms. The details of the analysis are given in the following section.

2.4 Quantitative Analysis: 2.4.1 Clustering evaluation:

The performance of each clustering method applied to data has been evaluated. It is as significant to measure the number of errors /or the recall and precision of a supervised classification algorithm. Specifically, any metric used for evaluation should consider some defined separation of the data identical to some ground truth set of classes rather than considering the absolute values of the cluster labels. It may satisfy some supposition in a way that members belonging to similar class can be grouped as one cluster than the members of different class following similarity metric.

Since in this study, we do not know the actual ground truths; the performance evaluation of the clustering was performed by using the evaluation metric, which did not require any ground truth labels. These evaluation metrics were also used to find the best number of clusters. As stated earlier, a range of 'number of clusters' values was provided to each clustering algorithm. The evaluation metric suggested the best score, i.e., a score which suggested better similar densely packed cluster and better separation of different clusters.

2.4.1.1 Silhouette Coefficient:

The coefficient for a sample can be calculated by 푏 − 푎/max (푎, 푏) where a indicated the mean intra- cluster distance and b the mean nearest-cluster distance. It should be noted that b is the distance between the sample and the cluster the sample is not a part of. The function used in this study was silhouette_score from the scikit-learn library. This returned a mean silhouette coefficient over all the samples, where a score of +1 suggested best clustering and -1 worst clustering. Values near 0 were considered as overlapping, and negative values suggested samples assigned to the wrong cluster.

2.4.2 Dice Coefficient:

The Dice Coefficient or Sorensen-Dice index is used in statistics or statistical analysis of two sets of data measuring the similarity between them. It is known to be the most widely used statistical tool in the validation of segmentation of images. The formula for calculating the coefficient is given as follows:

|푋 ∩ 푌 | 퐷퐼퐶퐸 = (|푋| + |푌|)

Where X and Y are the two different sets of data, ∩ is the intersection of the two sets of the data.

2.4.3 Variance:

Another statistic metric used for the quantitative analysis in this study is the variance of the data. In statistics, the variance of a set of data tells us the spread of the data from its average value. Specifically, the variance tells us how the data deviates from its mean or median value. A low variance tells us the data is very closely clustered together, and a high value tells us there is high variability or spread in the data. Variance is the squared deviation of a variable from its mean.

2.5 Qualitative Analysis:

The Correlated images (Heat Maps) depicting how well the nuclei interact with other regions of the brain were computed. These heat maps visually show the brain regions with positive and negative correlations with the nuclei. Before the images are displayed, significance testing has to be performed. This will aid in the elimination of possibilities of regions appearing to show correlation because of the noises present in the data.

2.5.1 Test for significance:

When considering the variability across the subject, we have to consider where the correlations are different from zero. The test is used to understand that the higher values of correlation in the reported areas are unlikely to be produced by noise.

2.5.2 FSL Randomise:

When the null distribution is not known in a statistic map randomization methods (also known as Permutation methods) can be used as inference. This situation arises in two cases, either the noise in the data does not follow a simple distribution, or when non-standard statistics are used to summarize the data. The function used in this study is < randomize> (Winkler et al., 2014); it is an FSL's tool to be used on neuroimaging data for nonparametric permutation inference. In this study, One-Sample t- test is used to compare the average of each sample to a hypothesized value that is pre-determined in the null hypothesis. This test was used for every method individually.

Steps involved in this study:

1. Perform Atlas-based segmentation of each Nucleus on different subjects varying across sessions. 2. Mean signal from the segmented nuclei is used to find the correlation with the regions of the brain. 3. For clustering, first, the data was preprocessed using resampling function and dilating function on the nuclei atlas. 4. A time-series matrix was created for all the voxels present in the dilated region of the nuclei. 5. Clustering is performed on the time series matrix, based on the range of clusters and other intrinsic parameters of the algorithm. 6. The Silhouette coefficient is then used to decide the best number of clusters. 7. Now within the clusters, there might be 3 or 4 different clusters. To choose the best among them, the Dice coefficient was calculated (Dice calculated against the atlas-based segmentation). 8. The cluster having the best Dice score was chosen to produce the correlation map. 9. All the correlated images were averaged to generate correlation maps for all the different methods (With one-sample t-test, FWE corrected). 10. The Silhouette and Dice score along with its variance forms the basis for Quantitative analysis, while the heat maps provided the Qualitative analysis.

3 Results: 3.1 Quantitative Analysis: The performance of the clustering methods, Silhouette coefficient, and Dice Coefficient has been calculated for all the subjects. The Mean, standard deviation and the variance have been calculated across the subjects to understand the robustness of the clustering method. 3.1.1 Hypothalamus:

Mean Standard Mean Standard Variance Cluster DICE Deviation- Silhouette Deviation- (DICE) number DICE Silhouette Kmeans 0.59 0.08 0.39 0.15 0.007 3 Kmedoids 0.61 0.03 0.50 0.14 0.001 2 Kmedoids(Corr) 0.53 0.02 0.11 0.02 0.0004 2 Spectral 0.57 0.01 0.42 0.09 0.0003 2 Wards 0.61 0.02 0.53 0.14 0.0007 2

Table 3. The mean value of dice and silhouette with their standard deviation was calculated for Hypothalamus nuclei. Along with this, the table provides the variance of dice across the group and also the cluster number selected for correlation.

3.1.2 Locus Coeruleus

Mean Standard Mean Standard Variance Cluster Dice Deviation Silhouette Deviation number Dice (Silhouette) Kmeans 0.41 0.004 0.36 0.06 0.000016 3 Kmedoids 0.41 0.02 0.28 0.10 0.0006 3 Kmedoids(Corr) 0.36 0.01 0.09 0.02 0.0003 2 Spectral 0.40 0.01 0.08 0.02 0.0002 2 Wards 0.40 0.005 0.36 0.03 0.00003 2

Table 4. The mean value of dice and silhouette with their standard deviation was calculated for Locus Coeruleus nuclei. Along with this, the table provides the variance of dice across the group and also the cluster number selected for correlation.

3.1.3 Ventral Tegmental Area

Mean Standard Mean Standard Variance Cluster Dice Deviation Silhouette Deviation number Dice (Silhouette) Kmeans 0.44 0.02 0.47 0.06 0.0005 2 Kmedoids 0.44 0.02 0.47 0.07 0.0004 2 Kmedoids(Corr) 0.41 0.02 0.13 0.02 0.0008 2 Spectral 0.39 0.001 0.17 0.02 0.00001 2 Wards 0.39 0.03 0.37 0.01 0.0009 2

Table 5. The mean value of dice and silhouette with their standard deviation was calculated for Ventral Tegmental Area nuclei. Along with this, the table provides the variance of dice across the group and also the cluster number selected for correlation.

The dice coefficient was calculated against the base model, i.e., the atlas-based segmentation for all the different clustering methods. In the analysis of hypothalamus nuclei, we see larger dice values for the clustering methods as compared to the other two nuclei. Dice value can be a useful metric when we talk about the robustness of the method. The table also shows the silhouette coefficient and how the clustering algorithms scored with this evaluation of clusters. The silhouette coefficient metric is used in this study to understand how well the samples in the data are clustered, and it was used to choose the cluster number among the different clusters provided to the algorithm. The silhouette coefficient range for all the clustering method varied significantly. As seen from the table, Ventral Tegmental Area and Hypothalamus have higher values as compared to that of Locus Coeruleus. Since the atlas-based model is also subjected to variations and is not a robust method, thus, the variance of dice across the subject was also evaluated. The table shows that variance for Ventral Tegmental Area and Locus Coeruleus was lower to that of the Hypothalamus. The clustering method, with the least variance, showed that the model has less variability of measurement across the subjects. The cluster number preferentially chosen in each clustering method is also provided.

3.2 Qualitative Analysis:

The Functional connectivity map has been generated for each nuclei using atlas-based segmentation method and the five clustering methods. The averages have been taken for all the subjects, and the images were smoothened using a 5 mm Full width half maximum (FWHM) kernel. The goal has been to achieve similar connectivity patterns as reported in the previous neurological studies(Kullmann et al., 2014; Zhang et al., 2018; Liebe et al., 2020; Murty et al., 2014).

3.2.1 Hypothalamus:

Fig.4 The Averaged functional connectivity of Hypothalamus generated from 4 different methods A) Atlas Based Segmentation, B) Kmeans Clustering, C) Kmedoids Clustering D) Kmedoids Clustering using Correlation as Distance Metric. One-sample t-test, p<0.05, FWE corrected. Cool colours show negative correlation and warm colours show a positive correlation.

The Hypothalamus nuclei are known to have notable connections with temporal brain regions, middle and posterior cingulum, orbitofrontal cortex, brainstem, thalamus, striatum (Kullmann et al., 2014). Through the methods employed in this study, we have been focusing on visualizing the same connections.

From the correlation maps, our data shows that the atlas-based segmentation represents voxels other than that of the nuclei itself and thus gives a larger connectivity pattern than those in the previously reported studies (Kullmann et al., 2014). In the case with the different clustering methods, the current study has focussed on isolating the voxels that belong to the nuclei, and the results have been illustrated in Fig. 5. Kmedoids clustering, using both 'Euclidean' and' Correlation' metric, is the method that provides functional connectivity pattern (Kullmann et al., 2014; Zhang et al., 2018). Correlation maps of Spectral clustering and Wards clustering have not shown any significant correlation with the regions of the brain and thus have been omitted in the figure.

3.2.2 Locus Coeruleus:

Fig 5. The Averaged functional connectivity of Locus Coeruleus generated from 4 different methods A) Atlas Based Segmentation, B) Kmeans Clustering, C) Kmedoids Clustering D) Kmedoids Clustering using Correlation as Distance Metric E) Spectral Clustering One-sample t-test, p<0.05, FWE corrected. Cool colours show negative correlation and warm colours show a positive correlation.

The Locus Coeruleus (LC) is known to have significant neural connectivity with Anterior Cingulate Cortex (ACC), bilateral thalamus and bilateral cerebellum (Liebe et al., 2020). Another study reported that Locus coeruleus has a positive correlation with primary motor cortex, inferior temporal cortex, posterior insula, pallidum, inferior parietal cortex, ventrolateral thalamus, bilateral superior frontal gyrus, putamen, midbrain, anterior parahippocampal gyrus, and large areas of the cerebellum (Zhang et al., 2016). They have recorded that LC has negative connectivity to middle/superior temporal cortex, retrosplenial cortex, frontopolar cortex, a large region of bilateral visual cortex, posterior parahippocampal gyrus, precuneus, caudate Nucleus, and dorsal and medial thalamus. From the correlation maps, similar to the case with Hypothalamus Kmedoids clustering showed similar results as reported by (Zhang et al., 2016). In concurrence with the previous reports (Zhang et al., 2016), Atlas-based segmentation and the other clustering approaches have shown that there is significantly less correlation with the regions of the brain. Wards algorithm approach has failed to show any significant correlation and thus has been omitted from the figure in this case as well.

3.2.3 Ventral Tegmental Area (VTA):

Fig 6. The Averaged functional connectivity of Ventral Tegmental Area generated from 3 different methods A) Atlas Based Segmentation, B) Kmedoids Clustering C) Kmedoids Clustering using Correlation as Distance Metric. One-sample t-test, p<0.05, FWE corrected. Cool colours show negative correlation and warm colours show a positive correlation.

The VTA is very small and has no significant delineation with substantia nigra; thus, it is challenging to localize and generate the functional connectivity pattern. As seen in the figure (Fig. 6), the atlas- based segmentation has resulted in the connectivity patterns between VTA and SN together. The combined connectivity pattern of VTA and SN was previously shown by (Zhang et al., 2016.) While focussing on VTA, greater connectivity with the nucleus accumbens, cerebellum, posterior midbrain (encompassing the superior and inferior colliculi) and hippocampus has been observed (Murty et al., 2014). After the significant testing by other than the Kmedoids method, none of the clustering algorithms provided any significant correlation maps.

4 Discussion:

Clustering-based methods, when compared to atlas-based segmentation, can be complicated as there are many factors that one must consider before its application. The type of clustering method plays an important role, as with different applications and studies the clustering method may perform differently. When it comes to the localization of nuclei, it becomes more difficult as they are minimal in size. Analyzing the results of clustering-based methods over atlas-based segmentation is a demanding task and requires utmost focus as sometimes atlas-based segmentation do not provide the same connectivity pattern as known from previous studies. This is because of variations in scanning parameters or even because of the variation in the population of subjects. For the Hypothalamus nuclei, it is much easier to perform clustering as it is larger than the rest of the nuclei. Since there are more voxels because of the bigger size, it makes the clustering algorithm to work much more efficiently. From the Qualitative results, we can see that Kmedoids clustering method performs better than other clustering methods. The results from Kmedoids algorithm were almost similar to those presented with atlas-based segmentation and as reported with previous studies. The qualitative analysis can be supported by the quantitative analysis as the highest Dice score was achieved with this method, and we can also see that the variance and standard deviation is also minimized. Spectral and Wards algorithm shows a good quantitative score, but in qualitative analysis, there was not any significant correlation with the regions of the brain. For the Locus Coeruleus nuclei, it is much more challenging to perform the clustering as the nuclei are tiny and are embedded deep in the brain stem. Many artefacts like motion or partial blood volume effects can affect the functional assessment of this nuclei. Similar to the case of Hypothalamus, Kmedoids clustering performed better in LC than other clustering methods. The method did not have a significant advantage over other methods, and this can be seen in the qualitative analysis along with the atlas-based segmentation. In the case with locus coeruleus, the samples clustered has included noise or nearby regions because of which the results are not as good as with the hypothalamus nuclei. Wards algorithm failed to produce significant correlation maps as it may have clustered too much noise in the samples of the data provided to it.

In the last nuclei, the Ventral Tegmental Area which is the hardest to locate and segments owing to its small size and fusion with the substantia nigra. The Kmedoids clustering only provides some qualitative analysis when compared to the other methods, and in the quantitative analysis, the Kmedoids algorithm had better dice and silhouette score. Kmedoids clustering provided similar results in lower slices of the brain than the higher slices of the brain, when compared with atlas-based segmentation.

For increasing robustness, the clustering methods to be used on fMRI data should employ the linkage metric of the clusters as 'correlation' than using 'Euclidean' distance as seen in most of the cases. In

24 theory, fMRI data provides us with functional information from different parts of the brain. Thus, it makes sense to use 'correlation' in clustering approach where the creation of centroids or medoids is based on the distance metric. As seen in the study, the Kmedoids clustering when used with 'correlation' as the distance metric, sometimes provided a close similarity with that of the base model and the reported studies.

One other consideration, while using clustering-based segmentation or localization is the use of highly preprocessed data. As fMRI data is very noisy and is laden with different kinds of artefacts, one must be careful when applying the preprocessing steps. The nuclei present in the brain stem, such as LC and VTA, are prone to many noises. The noise present in the data because the brainstem is located close to major arteries and nearby pulsation of the cerebrospinal fluid, which increases the noise of the signals during functional MRI acquisition is recorded. This hampers the analysis of functional connectivity of the brain, as a set of voxels belonging to other regions may interfere and show different correlation pattern to that of the region of interest. The use of higher resolution data such as 7T fMRI data may improve the clustering-based approaches on the localization of the nuclei. As the resolution is much higher in this type of study, the nuclei's resolution will also be higher. The use of clustering-based methods on such data may provide better functional connectivity pattern than provided by atlas-based segmentation.

5 Conclusion and Future Work:

The current study focuses on the use of clustering-based methods to localize the nuclei in the human brain. The need for robust segmentation of nuclei continues to persist in the field of neurology as many diseases, human cognition, and human behaviour can be studied with better delineation of nuclei. Atlas- based segmentation and the functional connectivity derived from them for different nuclei of the brain are used in a lot of neurological studies. As these atlas-based investigations are not robust in fMRI based studies, clustering-based methods could serve as a complementary solution to this research problem. In this study, we tested different clustering methods applied after the atlas-based segmentation to help in localization of nuclei and their segmentation.

Our preliminary results show that clustering approaches further improve the performance of atlas-based segmentation. Clustering-based segmentation helps in eliminating erroneous voxels and allows interactive selection of voxels belonging to the human brain nuclei. Among the clustering algorithms used in this study, our preliminary conclusion was that Kmedoids should be preferred.

It is crucial to remember that finding functionally homogenous structures is rather challenging, as the signal to noise ratio (SNR) of the data is low, and even visual inspection is insufficient to outline parcels in the brain. The major limitation of this study was the proposed method was tested on 3T fMRI data which is quite noisy and has a lower resolution. For future work, applying the proposed method to 7T fMRI data would potentially increase the performance of these clustering algorithms.

The use of clustering-based algorithms can be helpful in a variety of neurological study where human brain nuclei are of primary focus. These neurological studies may focus on how the connectivity pattern and the volume of the nuclei change with age, gender, physiological disorders, psychological disorders and neurodegenerative diseases.

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Appendix A: State of the Art Table of Contents: A.1. Nucleus (Neuroanatomy) A.1.1 Locus Coeruleus A.1.2 Ventral Tegmental Area A.1.3 Nucleus Basalis of Meynert A.1.4 Raphe Nucleus A1.5 Hypothalamus A.2. FMRI A.3. Pre-Processing A.4. Segmentation A.4.1 Atlas-Based Segmentation A.5. Brain Atlas A.5.1 MNI 152 A.6. Clustering Algorithms A.6.1 K-means Algorithm A.6.2 Ward’s Algorithm A.6.3 Spectral Clustering A.7. Clustering Performance Evaluation A.7.1 Silhouette Coefficient A.7.2 Calinski-Harabasz Index A.7.3 Davies-Bouldin Index A.8. References

A.1. Nucleus (Neuroanatomy): A cluster of neurons occurring in the central nervous system is called a nucleus (Plural: Nuclei). These nuclei are located deep in the brainstem and the cerebral hemispheres. The neurons contained in a single nucleus have mostly the same functions and connections. There are many vital nuclei present in the brainstem of the human brain. Some of the nuclei which will be studied and analyzed in this project are Locus Coeruleus, Ventral Tegmental Area, Nucleus Basalis of Meynert, Hypothalamus and Raphe Nuclei. A.1.1 Locus Coeruleus: Locus Coeruleus (LC) has been increasingly studied upon as it has shown some early pathological changes in neurodegenerative conditions such as Parkinson's disease (PD and Alzheimer's disease (AD) [1]. Since its increased growth in the fields of neurology and psychiatry, studies are coming up to map the anatomical structure and the functional connectivity associated with it. LC is a hyperpigmented cylindrical nucleus located in the rostral pontine brainstem. It is a significant source of all the noradrenergic neurons, whose projections are spread till the cerebral cortex, the thalamic nuclei and hippocampus. The role of LC is the regulation of arousal and autonomic function, inflecting wakefulness, pupil control, blood pressure and temperature. While studying LC, particularly in humans, it has been a subject debate whether the Nucleus's neuron number decreases with age [2] or due to physiological diseases [3]. Optimal imaging of LC is required to evaluate its role in neurodegenerative conditions and also to evaluate its potential as a viable biomarker in neuroimaging. A.1.2 Ventral Tegmental Area: The Ventral Tegmental Area (VTA) is known for its dopaminergic neurons even though VTA is known to have different neurons. The neurons spread throughout the brain. The VTA is in the midbrain, adjacent to substantia nigra. The VTA is considered crucial for the reward system in the reinforcing behaviour. The VTA and the Substantia nigra are the two crucial dopaminergic areas in the brain. The major challenge VTA poses in its study is due to unclear anatomical boundaries with Substantia nigra. These areas are known to differ from one another when it comes to the neuron's projection. The difference in the destination of the neuron projection can be correlated with the difference in the functions associated with these regions. The VTA is primarily thought to be involved with the cognitive and emotional process, while substantia nigra is associated with movement [4]. A.1.3 Nucleus Basalis of Meynert: Nucleus Basalis of Meynert (NBM), like LC, is studied for its degeneration in neurodegenerative diseases like AD and PD. The NBM is the most significant source of cholinergic fibres in the brain. NBM was found to be located in the basal forebrain adjacent to the medial septum, vertical and horizontal limbs of the diagonal band of Broca [5]. NBM provides the primary origin of cholinergic innervation to the cortex. The basal forebrain's structural imaging containing the NBM has been studied as a biomarker for cognitive decline associated with the neurodegenerative diseases. The challenges of the imaging studies which hamper the utility of using it as a biomarker are because it is embedded in an area crowded by nuclei and concrete delineation of the anatomy is required [6].

A.1.4 Raphe Nuclei: Raphe Nuclei (RN) is named after the term "Raphe" which means a ridge that separates two symmetrical part of the body as this collection of nuclei is clustered around the midline of the brainstem. RN is the primary location in the brain that helps with the production of the neurotransmitter Serotonin. The Serotonin produced in the RN is sent throughout the central nervous system. It has to be noted that even though RN represents the most extensive collection of Serotonin neurons, RN does not only contain them alone. Since the RN is known to have its projection pervasive and carrying Serotonin throughout the Central Nervous System, the functions are also extensive and complex. Serotonin is studied for its various function like well- being and happiness, although its biological functions are even complex and multifaced like reward, cognition, learning, memory and others. This makes RN an exciting biomarker to study behaviour and neurodegenerative diseases in the central nervous system. [7] A.1.5 Hypothalamus: The primary function of the Hypothalamus is the link between the nervous and to the endocrine system via the pituitary gland. It contains a small number of nuclei that has a variety of function they are divided based on the regions: Anterior, middle and Posterior. Anterior part in itself contains a variety of nuclei but is mostly related to the function of releasing hormones. Middle region is known for its control for appetite and Growth hormone-releasing hormone. Lastly, the posterior helps in regulating the body temperature. The Hypothalamus is deeply interlinked with the central nervous system, especially the brainstem. A.2. FMRI After the long line of innovations like the Positron Emission Tomography (PET) and near- infrared spectroscopy which used blood flow and oxygen metabolism to infer brain activity, fMRI was developed in the 1990s. The FMRI is an imaging technique or method to measure and study brain activity. FMRI detects the changes in blood oxygenation and flows in response to the neural activity [8]. These changes, such as increased blood flow in a specific region, tell us which part is most active in the brain. FMRI is used today to produce activation maps that correlate the parts of the brain with a mental process. FMRI has a significant advantage over other imaging techniques as: 1. It does not involve radiation making it safe for the patients. 2. It is non-invasive. 3. It has a far greater spatial and temporal resolution than other methods. FMRI has grown popular both in clinical as well as in commercial settings. The exciting features that FMRI presents make it easier for researchers to study brain functionality rather than just structures like in the MRI. In the past decade, FMRI has helped researchers in understanding how memories are made, language, pain, motor learning and emotion to name but a few areas of research. Researchers study activity on a scan in voxels – or volume pixels which represents a single sample or data point in a three-dimensional image. Each voxel is studied over a time course; the correlation of each voxel regarding the time-course among one another tells us what score they achieve. Higher the correlation higher the score and vice-versa. These can thus be represented as activation maps.

A.3. Preprocessing: One of the essential steps in the studies involving FMRI data is the preprocessing step. It is vital to remove unwanted artefacts and to convert the data in a required format. The preprocessing identifies the erroneous sources and eliminates their effect on the data. Furthermore, reducing the image artefacts and localization of the signal anatomically. It is vital to extract the correct signal about the underlying neural activity to obtain the interpretability and accuracy of the results. Thus, one of the main goals of preprocessing is to decrease the causes of false-positive errors without producing false-negative ones. There are several preprocessing steps in neuroimaging available for use like SPM, FSL, AFNI, Freesurfer, FuNP and fMRIPrep. All this software differs in their preprocessing pipelines. Different MRI data would have different parameters with which the acquisition might have been done. These result in a wide range of intensity values, matrix size and orientations. Thus, a need for preprocessing step. The preprocessing in fMRI incorporates multiple steps to standardize and clean the data before the analysis is done. Usually, researchers produce their in-house workflows for each dataset, depending on the study and the acquisition parameters. Such workflows stack up much inventory of tools and make it complicated. Some of the steps performed in the preprocessing pipeline are: 1. Quality assurance: due to the difference in physiological sources such as patient motion, respiration, drowsiness, anxiety or drugs, the fMRI data acquisition usually suffers from random variations in signal intensities, data glitches, and noise. If ignored, these may hamper in the later part of the process like statistical or data analysis. 2. Distortion correction: Being sensitive to magnetic inhomogeneity (T2*) effect because of the acquisition of gradient echoes sequences, causes spatial distortion and signal dropout near the skull base in the fMRI data. These affect the anterior frontal and temporal lobes. Unwarping and Field mapping are some of the methods used to decrease these distortions. 3. Slice timing correction: Since most of the studies involving fMRI acquire slice by slice at a time, there may be an offset in time between two slices. Moreover, this gets even more complex as the acquisition can be sequential such as 1,2,3,4,5,6 or interleaved like 1,3,5…, 2,4,6 order and simultaneous multi-slice imaging can be utilized. Data shifting and model shifting are two strategies developed to correct the problems with slice timing. 4. Motion Correction: One of the most significant sources of error in FMRI studies is the head motion. Several strategies are available to reduce such errors. Even steps are taking during the acquisition, such as padding and straps to immobilize the Head. The most used strategy is the Rigid Body translation of the Head. A single functional volume is taken as the reference, and the others are aligned in relation with the reference. 5. Temporal Filtering: There are two types of problems that can be witnessed in an FMRI data one being noise (high frequency) and the other being the baseline signal shift (low frequency). Detrending is the removal of low-frequency drifts which can be achieved with the use of high pass filters. The noise is high pass is removed using low pass filters 6. Spatial smoothing: As we know that the neighbouring areas in the brain voxels are innately correlated in their blood supply and their functioning, spatial smoothing is employed to increase the signal-to-noise ratio (SNR). This is done by averaging the

signals from the adjacent voxels, the drawback being the blur in the image caused by the averaging. The standard method in FMRI is with the use of a 3D Gaussian kernel convolving over the FMRI data. In-plane resolution and slice thickness affect the optimal kernel size. Pre-processing of the data based on principal component analysis may help in estimation of confounds related to dimensionality reduction methods. Preprocessing pipelines such as fMRIPrep [9] houses all the tools used in neuroimaging and makes it simpler and more comfortable to perform the preprocessing. The developers of this tool stress on the fact that the software ensures reliability by the use of best software engineering principles. fMRIPrep is made to work best with "1) Robustness to data idiosyncrasies, 2) high quality and consistency of results, 3) maximal transparency, and 4) ease of use." The output from the fMRIPrep pipeline allows for a range of applications which includes intra-subject analysis, surface-based analysis, resting-state connectivity analysis, voxel-based analysis, task-based group analysis and others. fMRIPrep is the better choice as this pipeline automates the adaptation of the input dataset without having to compromise on the results. One limitation which the pipeline presents is the employment of semi-visual and visual examinations of the quality of the preprocessing steps. The method is designed in such a way that it permits assessment of various possible combinations of the processing steps and software tools. The design of the pipeline improves transparency and improves flexibility so that it is open for collaborators. A.4. Image Segmentation: Image segmentation is termed as the partitioning of an image into different regions for analysis and interpretation. Image segmentation can be differentiated based on the features and the type of technique used. The techniques are divided into three main groups: region-based, edged based or classification, which uses pixel intensity, gradient and texture features. The segmentation of images is one among the challenging task. In many studies, the outlines- contours of the object of analysis are not easy to segregate, even manually. The major problems are due to similar intensities, low contrast or fuzzy contours. Use of prior knowledge has proven to be useful in these segmentation problems. A widely used technique is the extraction of prior knowledge obtained from a reference image known as the atlas. As the image to be segmented resembles the map which would describe a geographical area, this technique is called 'Atlas Based Segmentation'. The use of spatial information saves enormous processing time localizing the objects to be extracted and permits to distinguish from the objects of interest with other comparable features. Also, the atlas can be used to gather information related to texture and shape. Another important tool of this technique is that the atlas points to the features of adjoining objects which allows to efficiently delineating the exciting objects of from their neighbouring regions. Till recently, a paper-based segmentation was in practice used. The recent advancements in processing the digital images resulted in developing digital atlases. With the use of atlas information, there has been an increased amount of details and its potential to be integrated with software-based and computer-based image analysis. Thus, in the studies with medical image, atlas-based segmentation is well suited.[19] A.5. Brain Atlases:

A brain template is a micrographic description of the anatomical details (example: fibre tracts, nuclei, cortical areas). Conventional brain atlases were a collection of micrographs and schematic drawing of different brain sections that may be from one or several brains. Digital or computerized brain atlases have begun to replace the conventional brain atlases. The advanced digital brain atlases have higher SNR and provide better contrast between the grey and white matter as they are made using several subjects [10]. Initially, the neuroimaging atlases were used to get higher resolution like in the MRI from aligning 2 D slices or transforming a 3D data. This transformation to an atlas space from one space (subject) provides us with the localization of structural, functional and physiological data. As the varying population is based on the phenotype, genetics, development, and environmental factors there is a need for population-specific templates that capture, quantifies and visualizes the brain anatomy so that it can be used for providing finer details in several structural, functional and physiological studies [11]. The template used in this project is MNI-152, and a short description of it is given below: A.5.1 MNI-152: In 2001 MNI-152 template was created from 3D brain MRI images of 152 normal subjects. The TT atlas was used as the reference system for the coordinate system. This template is used in various functional imaging analysis packages like the statistical parametric mapping (SPM) or FMRIB Software Library (FSL). The MNI-152 template was created after automated linear registration was applied to the brain images with the reference brain image. Following this, a non-linear registration was performed to overcome inter-subject 1) size, 2) shape, 3) orientation. The advantage of using the MNI-152 template is that it provides full coverage of the Head and better-detailed information of the top part of the brain to the lower part of the cerebellum. A table has been provided below with the details of all the available brain atlases that one can use in their study:

Size

same

is more is

templates

Larger than TT Larger

are are shorter than

305 but width is

Height is shorter is Height

than and MNI- IT

Length andLength height

Same as MNI-305 as Same

Smaller Smaller than other

Reduced voxel size Reduced size voxel

MNI-152 MNI-152 but width

ant

and

Less Less

white white

n gray n gray

signific

matter

betwee

Signific

Contra

l l

al al

of of

Lack Lack

detail

details

cortica

Cortic

Improv

l detail

and

Regions

Does notDoes

Excludes

Full head

the top of

brainstem brainstem

Coverage

fully cover fully cover

cerebellum

Deep Deep Brain

the head and

9 9

12 12

linear

Affine

mation

Spatial

transfor

parameter parameter

Parameter Parameter

ion

linear

Linear Linear

Linear

Manual

and non

procedur

Registrat

Non

atlas

Type Type

digital digital

Digital

Digital Digital

Digital

Yes Yes

Yes

n n specific

Populatio

type

Image Image

± ±

Age

1.76

19.4

44.6

23.4

± 4.1

24.49

M-49)

1 (F-1)

M-239)

1 (M-1)

subjects

78 (F-29,

452 (NA)

152 (NA)

56 (M-56)

305 (F-66,

Number Number of

[2010]

[2005]

[2003]

[2001]

[1998]

[1995]

Korean

MM-152

Colin-27

MNI 305MNI

Talairach

Tournoiix

ICBM-452

Chinese-56

(TT) (TT) [1988] French [2009]

A.6 Clustering Algorithms: In neuroimaging studies, it is often required to segregate the brain into several regions, or parcels, with homogenous features. The brain atlases talked about earlier do not adapt to the signal derived from individual subject images, parcellation approaches used by the activity brain and the clustering algorithms to define regions with some degree of signal homogeneity. Commonly used parcellation techniques are mixture models [12,13], variant of the k-means algorithm [14,15], hierarchical clustering [16], spectral clustering [17], and dense clustering [18]. Some of the models impose some spatial constraints and thus provides spatially connected spatial components. As there are many parcellation techniques available, showing great potential and applications in further analysis, it is crucial to assess their relative performance.

A.6.1 K-means algorithm: It is one of the most used clustering algorithms used for vector data. It is known for its alternative optimization of the allocation of uk-means of the samples to be clustered and the estimation of the centroid in the cluster

푗 ∀ 푗 ∈ [1, 푄], 푢푘−푚푒푎푛푠 ∗ 푗) = 푎푟푔푚푖푛푐 ∈ [1, … , 퐾]‖(푌)푐 − 푦 ‖

1 〈푌〉 ≜ ∑ 푦푗 푐 |푐| uk−means(j)=푐 It minimizes the sum of squared differences among the samples and their representative cluster centroid. It is crucial to understand that in FMRI k-means clustering is used without directly studying the spatial structure.

A.6.2 Ward's algorithm: This method is hierarchical agglomerative clustering. This is an alternative to the k-means clustering algorithm. The process starts with each voxel (xj) representing singleton clusters{j}, and after every iteration, pairs of clusters are combined into a single cluster according to the criterion discussed below. A binary tree 푇 is yielded, which represents the hierarchy of the clusters. Specifically, in Ward's algorithm when applied to our neuroimaging studies, usually two clusters are merged provided the resulting cluster minimizes the sum of squared differences derived from FMRI signal among clusters.

A.6.3 Spectral Clustering: This algorithm uses the k-means clustering on a representation of data preserving the spatial structure and yet represents the functional feature's similarities. The representation is typically obtained by the use of the first eigenvectors of the Laplacian matrix of the graph that encodes the spatial relationships weighted by the functional feature's similarity between adjacent locations. For all voxel pairs (i,j) ϵ [p1 …. Q]2, let

2 i j 2 Where σ f=meani-j‖y − y ‖ , averaging is performed using all pairs of the adjacent voxels, making mean squared differences among the data across the neighbouring pixels. W is the adjacency matrix, and ΔW is the diagonal matrix which has the sum of the rows of W.

The letting (ξ1, …, ξm) the first m solutions of Wξ = λΔWξ. The spectral clustering is defined as

Uspectral=k-means([ξ1, ……, ξm])

A.7 Clustering Performance Evaluation: After clustering the evaluation of its performance is not as trivial as counting total errors, the precision and the recall belonging to a supervised classification algorithm. In specific, an assessment metric must not include the absolute values of cluster labels. The only exception is when the clustering defines separations of data resembling some ground truth set of classes or satisfy a few expectations in a way that the members fit into the same class are similar to a greater extent than members belonging to different classes based on a similarity metric. The similarity metrics used in the project are:

A.7.1. Silhouette Coefficient: When the ground truth is not known, the evaluation is must be done using the model itself. The silhouette coefficient is the same type of assessment, where larger the coefficient scores to a model with better-specified clusters. For each sample, a silhouette coefficient is defined and is composed of two scores: • a: The mean distance between all points and the sample in the same class. • b: The mean distance between all points and the sample in the next nearest cluster. The Silhouette Coefficient s for a single sample is given by:

풃 − 풂 s = 풎풂풙(풂,풃) Advantages: the score is provided between -1 for incorrect clustering to +1 for highly dense clustering. If the score is close to zero, it shows overlapping clusters. Drawbacks: The score is high for clusters that are convex compare to any other concepts of clusters, for example, density-based clusters. [20]

A.7.2 Calinski-Harabasz Index: The index, alternatively known as the Variance Ratio Criterion may be used to examine the model when the ground truth labels are unknown. A higher score indicates the model resulting in defined clusters. An index is defined as the ratio of the sum or dispersion between-clusters and inter-cluster for all. Therefore, the dispersion is defined as the sum of distance squared. The Formulae is:

For set N of size mn which are clustered in k clusters, the score s is defined as the ratio of between clusters dispersion mean and the within-cluster dispersion: 풕풓 (푩 ) 풎 − 풌 풔 = 풌 × 풏 풕풓 (푾풌) 풌 − ퟏ

Where tr(Bk) is a trace between-group dispersion matrix and tr(Wk) is the trace within-cluster dispersion matrix:

푘 푇 푊푘 = ∑ ∑ (푥 − 푐푞) (푥 − 푐푞)

푞=1 푥∈푐푞

푘 푇 퐵푘 = ∑ 푛푞 (푐푞 − 푐퐸)(푐푞 − 푐퐸) 푞=1

With Cq, the set of points in cluster q, cq the centre of cluster q, CE the centre of E and nq the number of points in cluster q. Advantages: The score is higher for better dense clusters which relate to the concept of clusters and the index to get computed fast. Drawbacks: Same as the Silhouette Coefficient, it is usually high for convex clusters.[21]

A.7.3 Davies-Bouldin Index: Like the other evaluation metrics, the Davies-Bouldin Index can also be used when we do not have any ground truth labels. The lower Davies-Bouldin index states to a model which has better separation between clusters. The index tells us the mean 'similarity' among clusters, where similarity is defined as the measure which compares the distance between clusters with the cluster size. Zeros are the lowest score. A score close to zero indicates better partition.

Formulae:

The average similarity among every cluster Ci for i=1……k and its closest to Cj tells us the Davies-Bouldin index, and thus similarity is defined as a measure Rij:

• si, it is the average distance between every point of the cluster i and the centroid • dij, the distance between the cluster centroid i and j.

푠푖 + 푠푗 푅푖푗 = 푑푖푗 The index is thus defined as:

푘 1 퐷퐵 = ∑ 푚푎푥 푅 푘 푖≠푗 푖푗 푖=1

Advantages: The computation of this index is more accessible than to compute silhouette scores. Drawbacks: It is higher for convex clusters as the usage of centroid distance restricts the distance metric to Euclidean space. [22]

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2. Mann, D.A., 1983. The locus coeruleus and its possible role in aging and degenerative disease of the human central nervous system. 3. Mather, M., Harley, C.W., 2016. The locus coeruleus: essential for maintaining cognitive function and the aging brain. Trends Cogn. Sci. 20, 214–226. 4. Kalivas, P. (1993). Neurotransmitter regulation of dopamine neurons in the ventral tegmental area Brain Research Reviews, 18 (1), 75-113 DOI: 10.1016/0165-0173(93)90008-N. 5. Gratwicke, J., Kahan, J., Zrinzo, L., Hariz, M., Limousin, P., Foltynie, T. and Jahanshahi, M. (2013). The nucleus basalis of Meynert: A new target for deep brain stimulation in dementia?. Neuroscience & Biobehavioral Reviews, 37(10), pp.2676-2688. 6. James P Gratwicke, Thomas Foltynie, Early nucleus basalis of Meynert degeneration predicts cognitive decline in Parkinson's disease, Brain, Volume 141, Issue 1, January 2018, Pages 7–10, https://doi.org/10.1093/brain/awx333 7. Hornung, JP. Raphe Nuclei. In: Mai JK and Paxinos G, eds. The Human Nervous System. 3rd ed. New York: Elsevier; 2012. 8. Devlin, H. (2020). What is Functional Magnetic Resonance Imaging (fMRI)?. [online] Psych Central. Available at: https://psychcentral.com/lib/what-is- functional-magnetic-resonance-imaging-fmri/ [Accessed 3 Mar. 2020]. 9. Esteban, O., Markiewicz, C.J., Blair, R.W. et al. fMRIPrep: a robust preprocessing pipeline for functional MRI. Nat Methods 16, 111–116 (2019). https://doi.org/10.1038/s41592-018-0235-4 10. Mandal, P. K., Mahajan, R., & Dinov, I. D. (2012). Structural brain atlases: design, rationale, and applications in normal and pathological cohorts. Journal of Alzheimer's disease: JAD, 31 Suppl 3(0 3), S169–S188. https://doi.org/10.3233/JAD-2012-120412. 11. Mazziotta J, Toga A, Evans A, Fox P, Lancaster J, Zilles K, Woods R, Paus T, Simpson G, Pike B, Holmes C, Collins L, Thompson P, MacDonald D, Iacoboni M, Schormann T, Amunts K, Palomero-Gallagher N, Geyer S, Parsons L, Narr K, Kabani N, Le Goualher G, Boomsma D, Cannon T, Kawashima R, Mazoyer B. A probabilistic atlas and reference system for the human brain: International Consortium for Brain Mapping (ICBM) Philos Trans R Soc Lond B Biol Sci. 2001;356:1293–1322. 12. Golland P., Golland Y., Malach R. (2007). Detection of spatial activation patterns as unsupervised segmentation of fMRI data. Med. Image. Comput. Comput. Assist. Interv. 10(Pt 1), 110–118 10.1007/978-3-540-75757-3_14 13. Lashkari D., Sridharan R., Vul E., Hsieh P.-J., Kanwisher N., Golland P. (2012). Search for patterns of functional specificity in the brain: a nonparametric hierarchical bayesian model for group fMRI data. Neuroimage 59, 1348 10.1016/j.neuroimage.2011.08.031 14. Flandin G., Kherif F., Pennec X., Malandain G., Ayache N., Poline J.-B., et al. (2002). Improved detection sensitivity in functional MRI data using a brain parcelling technique. MICCAI 2488, 467–474 10.1007/3-540-45786-0_58 15. Kahnt T., Chang L. J., Park S. Q., Heinzle J., Haynes J.-D. (2012). Connectivity- based parcellation of the human orbitofrontal cortex. J. Neurosci. 32, 6240–6250 10.1523/JNEUROSCI.0257-12.2012

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TRITA TRITA-CBH-GRU-2020:110