Sherrington-Kirkpatrick model analysis of fMRI-BOLD data from Alzheimer’s patients and healthy controls

Abstract

This thesis aimed to advance the understanding of Alzheimer’s disease (AD) using computational modelling tools rooted in statistical physics. Specifically, pseudo-likelihood maximisation of a spinglass model was employed to extract coupling matrices J from fMRI-BOLD data of elderly subjects diagnosed with AD and healthy controls (HC). Data was sourced from participants in the European Project Neurotwin’s clinical trial, where AD patients undergo brain stimulation as a potential treatment, and from the AD Neurological Initiative (ADNI) database for the healthy controls. The derived coupling matrices were then compared between conditions to identify differences in brain connectivity. The research also explored the criticality of these systems using Metropolis simulations to assess phase transitions and critical temperatures. First, the focus was on extracting and analysing the J matrices. It was found that the J homotopic connectivity decreased in the AD subjects compared to the healthy ones with weak statistical significance (p = 0.0496), a finding consistent with other studies on inter-hemispheric connectivity disruption in AD. Moreover, the J matrices’ standard deviation significantly differed between the HC and AD groups (p = 0.0039). Additionally, brain areas with the highest change in J across conditions aligned with regions previously identified in functional connectivity studies of AD. Then, the spin-glass systems — defined by the condition-specific J’s — were simulated with the Metropolis algorithm. The critical temperature was found to be lower in the AD spin lattice compared to the HC spin lattice, suggesting that the AD state is closer to a disordered (paramagnetic) phase, which aligns with the hypothesis that weaker inter-parcel connections in AD may lead to a state nearer to the paramagnetic phase transition. The research highlighted the potential of the J coupling matrix to capture structural features and homotopic connections, which can serve as a synthetic brain connectome when dMRI is unavailable. Future work will include using longer data and other type of data (e.g. new healthy controls, and pre- and post-stimulation data), and the optimisation of the sparsity value in the extraction of J. Also, the criticality analysis may be improved by building a theoretical phase diagram based on J characteristics.