Design of optimal nonlinear network controllers for Alzheimer's disease

Abstract

Brain stimulation can modulate the activity of neural circuits impaired by Alzheimer’s disease (AD), having promising clinical benefit. However, all individuals with the same condition currently receive identical brain stimulation, with limited theoretical basis for this generic approach. In this study, we introduce a control theory framework for obtaining exogenous signals that revert pathological electroencephalographic activity in AD at a minimal energetic cost, while reflecting patients’ biological variability. We used anatomical networks obtained from diffusion magnetic resonance images acquired by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) as mediators for the interaction between Duffing oscillators. The nonlinear nature of the brain dynamics is preserved, given that we extend the so-called state-dependent Riccati equation control to reflect the stimulation objective in the high-dimensional neural system. By considering nonlinearities in our model, we identified regions for which control inputs fail to correct abnormal activity. There are changes to the way stimulated regions are ranked in terms of the energetic cost of controlling the entire network, from a linear to a nonlinear approach. We also found that limbic system and basal ganglia structures constitute the top target locations for stimulation in AD. Patients with highly integrated anatomical networks–namely, networks having low average shortest path length, high global efficiency–are the most suitable candidates for the propagation of stimuli and consequent success on the control task. Other diseases associated with alterations in brain dynamics and the self-control mechanisms of the brain can be addressed through our framework.

Diffusion MRI Indices and their Relation to Cognitive Impairment in Brain Aging: The updated multi-protocol approach in ADNI3

“…dMRI has since been used in numerous studies to understand the effects of AD on white matter (WM) microstructure and brain connectivity (Daianu et al, 2013a,b;Nir et al, 2013;Prasad et al, 2013). Some of these approaches assess dMRI indices in normal appearing WM (Giulietti et al, 2018), while others use tractography and graph-theoretic analysis to study abnormalities in structural brain networks (Nir et al, 2015;Hu et al, 2016;Maggipinto et al, 2017;Sulaimany et al, 2017;Powell et al, 2018;Sanchez-Rodriguez et al, 2018). In aggregate, these studies point to WM abnormalities in AD, which may play a key role in early pathogenesis and diagnosis (Sachdev et al, 2013).…”

Detecting brain network communities: considering the role of information flow and its different temporal scales

“…This is shown in Fig. S10 where the probability of finding a node between zero-crossings is represented as a function of the strength ("weighted degree") of the connections that such a node has (Rubinov & Sporns, 2010;Sanchez-Rodriguez et al, 2018) On the other hand, the IMFs per se represent the frequencies at which the information flow inside those communities occurs. Since these can be somewhat irregular signals (see Fig.…”

“…The tracking parameters were imposed as follows: a maximum of 500 mm trace length and a curvature threshold of ±90º. The anatomical regions were defined following the labeling procedure by Klein & Tourville (Klein & Tourville, 2012), from which 78 regions were considered -see (Y Iturria-Medina et al, 2016;Sanchez-Rodriguez et al, 2018) for more details. Based on the resulting voxel-region connectivity maps, the anatomical connection probability between any pair of regions and (0 ≤ ≤ 1, = ) was calculated as the maximum voxel region connectivity value between both regions.…”

“…To clarify these issues, we considered all the real networks herein studied, their hierarchical patterns, and the IMFs at which these meaningful (see above) communities appeared. Then, for each of the reported communities, we calculated the (within-community) characteristic path length(Rubinov & Sporns, 2010;Sanchez-Rodriguez et al, 2018), i.e. the mean shortest path length between all pairs of nodes belonging to that community.…”

Cross-Frequency Interactions During Information Flow in Complex Brain Networks Are Facilitated by Scale-Free Properties

“…For this, freely available (http://adni.loni.usc.edu) images from the Alzheimer's disease neuroimaging initiative (ADNI) were utilized. In a first stage, structural magnetic resonance images (MRI) and DWMRI obtained for 51 healthy control (HC) subjects were used to estimate anatomical connectivity matrices for each subject 24,25 (see Materials and Methods). A network backbone containing the dominant connections in the average network was computed using a minimum-spanning tree based algorithm 26 .…”