Brain Network Modelling

Abstract

Den menneskelige hjerne består af et gigantisk netværk af forbundne neuroner, der i samarbejde former vores eksistens og lader os agere ud fra sanseindtryk. Hjerneaktivitet kan måles med funktionel magnetisk resonans skanninger (fMRI) og ved at bruge matematiske netværksmodeller kan hjerneområder grupperes ud fra hvordan de arbejder sammen. I denne afhandling bliver forskellige modeller, der kan danne disse grupperinger, testet for deres stabilitet og prædiktionsevne. Resultatet viser at en model, der favoriserer community struktur, klarer sig bedst. Community struktur er karakteriseret ved høj link-tæthed indenfor en gruppe og lav link-tætheder til andre grupper og findes ofte i fx sociale netværk. Ydermere bliver en model, der kan finde fælles grupperinger i forskellige netværks typer, udviklet. Modellen anvendes på funktionelle og strukturelle hjernenetværk. Resultatet viser dog en beskeden fælles struktur mellem de to typer netværk, hvilket dog reflekterer begrænsninger i optagelsen af data. Brugen af disse netværksmodeller til analyse af hjernenetværk er relativ ny, men modellerne har et stort potentiale til bl.a. at finde forskelle i hjernens kommunikation mellem raske og syge.I et andet studie inkluderet i afhandlingen undersøges lokale netværksegenskaber i funktionelle netværk. Den lokale konnektivitet, som er et mål for hvor godt et lille område af hjernen er funktionelt forbundet med de omkringliggende hjerneomr åder, bliver sammenlignet mellem patienter med multipel sklerose (MS) og raske personer. Resultatet viser en nedsat lokal konnektivitet i lillehjernen hos MS, og ydermere at konnektiviteten bliver lavere ved højere sygdomsgrad. Det tyder på at dette skyldes læsioner i hjerneområdet, der rummer forbindelserne til lillehjernen.Det sidste område som berøres i afhandlingen er vedrørende fjernelse af støj fra data. Kernel Principal Component Analysis (KPCA) kan bruges til støjfjernelse men resultatet afhænger af valg af parametre. Vi har udviklet en metode hvorved udvælgelsen af disse parametre sker automatisk og vi viser at metoden klarer sig bedre end andre heuristikker til parametervalg.Three main topics are presented in this thesis. The first and largest topic concerns network modelling of functional Magnetic Resonance Imaging (fMRI) and Diffusion Weighted Imaging (DWI). In particular nonparametric Bayesian methods are used to model brain networks derived from resting state fMRI data. The models used are the Infinite Relational Model (IRM), Bayesian Community Detection (BCD), and Infinite Diagonal Model (IDM). The models have different constraints on how they cluster nodes. IRM is flexible in the sense that it allows for complex interactions between clusters of nodes. BCD conforms to the definition of community structure in the sense that it forces clusters of nodes to have larger density of internal connections than external connections. IDM models only the linking within a cluster and treats linking between clusters as background noise. The models are evaluated for their ability to reproduce node clustering and predict unseen data. Comparing the models on whole brain networks, BCD and IRM showed better reproducibility and predictability than IDM, suggesting that resting state networks exhibit community structure. This also points to the importance of using models, which allow for complex interactions between all pairs of clusters. In addition, it is demonstrated how the IRM can be used for segmenting brain structures into functionally coherent clusters.A new nonparametric Bayesian network model is presented. The model builds upon the IRM and can be used to infer shared clustering structure across different types of networks. The model is used to jointly model fMRI and DWI networks. However, results show only a limited amount of sharing across fMRI and DWI networks. Using the model within the same modality can reveal the clustering consistency across scans. A high consistency was found between DWI networks and an intermediate level of consistency was found between fMRI networks. The model is of interest for other applications, for instance in finding dissimilarity between network structure in case-control studies. The second topic of the thesis concerns local functional connectivity. In particular the local functional connectivity is studied in patients with multiple sclerosis (MS). The functional connectivity in a small neighborhood was estimated using Kendall’s Coefficient of Concordance (KCC). By generating voxelwise KCC maps, MS patients were compared with healthy controls. MS patients had reduced KCC in cerebellum and KCC correlated negatively with disease progression. Lesion load of the left cerebellar peduncles correlated negatively with KCC suggesting that the reduced local connectivity in MS is caused by disrupted inputs to the cerebellum.The final topic of this thesis concerns model selection for Gaussian Kernel Principal Component Analysis (KPCA) denoising. KPCA can be used for non-linear denoising by mapping data to feature space using a non-linear map. By projecting data onto a subspace in feature space and mapping this projection back to input space noise in data is (hopefully) removed. However, two important parameters must be set, namely the scale of the Gaussian kernel and the subspace dimensionality. A principled method for selecting these two parameters is presented. The method is based on maximizing the signal energy in feature space. When testing on synthetic and real data, the method outperformed a number of other heuristics in terms of signal to noise ratio of the denoised data