The temporal, multilayer, controllable brain network

In order to show the starting point of synergizing between the three subfields of temporal network theory, multilayer network theory, and control theory, I will first illustrate how I approach them separately.

Temporal brain networks 

The temporal brain network is marked by variation in connectivity strength and network topology across the span of seconds to minutes, schematically depicted below (Van Geest, …, Douw (2018) Brain and Behavior):

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I have investigated these dynamics in both resting-state functional magnetic resonance imaging (rsfMRI) and magnetoencephalography (MEG), showing that these dynamics indeed relate to and may even predict future changes in individual cognitive performance (Douw et al (2015) PLoS ONE; Douw et al (2016) Neuroscience; Carbo, …, Douw (2017) Scientific Reports; Van Geest, …, Douw (2018) Brain and Behavior).

Multilayer brain networks 

To illustrate how powerful multilayer network theory is, let us consider the European flight network. Each airport is a node, while connections between airports represent the average number of daily direct flights between them. Although this average network may give useful information on European coverage and airport importance, understanding its dynamics is problematic: suppose that a flight from Schiphol Airport to Frankfurt is delayed. Modeling the spread of delay based on the average network may predict delays across the entire continent and even the rest of the world, because of Frankfurt’s hub properties. However, flights are not all equal: some are operated by the Royal Dutch Airlines (KLM), others by Iberia or Lufthansa (see figure on the right). The delay of a Frankfurt-headed KLM flight will not have direct consequences for all Lufthansa flights departing from Frankfurt, but will first impact other KLM flights. Then it may spread to other airlines through interlayer connectivity (indicated in grey dotted lines), e.g. delayed ground personnel or a queue of airplanes forming to use a landing strip. Multilayer network algorithms take both intralayer and interlayer connections into account to accurately explain these flight delays, predict its dynamics, and ultimately manipulate the network to prevent further delays. Importantly, dynamics of the multilayer network supersede properties of individual layers: reducing the network to its separate layers yields misleading results. It is therefore essential to unify layers and implement mathematical analyses able to capture intra- and interlayer processes, as has been increasingly recognized in the field of complex networks.

In order to illustrate the aimed implementation of multilayer networks in neuroscience, I explain a pilot study that we performed to merge different modalities ánd the temporal dynamics of the functional brain network in individual subjects in two movies:


Controllable brain networks

Many measures reflecting network behavior and hypothetically cognition and mood have been introduced (e.g. efficiency, clustering, modularity). However, these measures are largely descriptive, and have only limited power when trying to explain behavior of the network in terms of individual cognitive functioning and mood. Control theory, which stems from electrical engineering, regards not just an instance, but the entire range of connectivity states that can be reached by nodes in the multilayer brain network. Thus, controllability refers to the possibility of manipulating particular interactions to steer a global system along a particular trajectory, and has only recently been mathematically defined for networks. In the context of the brain, let us view ‘a particular trajectory’ as intact cognitive functioning (for instance cognitive profile y in highly schematic figure on the right, which occupies a particular state space trajectory according to three dimensions), and consider ‘interactions’ as all multilayer connections of a node (as indicated in figure). Control theory can now determine how this specific interaction enables the entire network dynamics to reach (and maintain) the network state associated with cognitive profile y. More importantly, control theory also allows us to determine which input should be delivered in order to manipulate the trajectory of the system to a desired state associated with this cognitive profile, thereby overcoming the current limitation of many studies merely associating network topologies to cognitive (dys)functioning. Recent studies have indeed shown that controllability of the unilayer brain network may accurately describe brain functionality in general, and cognitive functioning specifically, although time has not been incorporated into these studies. Mathematical definitions of multilayer network controllability, even across differently time-scaled layers, have only recently been formulated, and have not been investigated in multilayer brain networks.

Modeling brain dynamics in brain tumor patients using The Virtual Brain

By Shanna Kulik, Tianne Numan, Linda Douw

With great interest we read the recent BioRxiv contribution by Aerts and colleagues (2018). We would here like to informally offer some of our thoughts and suggestions on this piece of work. In this simulation study, Aerts and colleagues aimed to bridge the gap between pre-surgical planning for brain tumor resection and post-surgical functional outcome in terms of cognition. The Virtual Brain (VB) was used to simulate large-scale brain dynamics based on the structural connectome of individual patients. A global scaling factor was individually optimized by comparing the VB model with the individual patients’ functional connectome based on fMRI. Aerts and colleagues showed that the accuracy of simulated functional connectivity in reflecting the empirical data was significantly improved by individualized VB models. Moreover, the individualized model parameters correlated with cognition.

Gaining insight into mechanisms describing how tumor(-related) processes influence network topology and cognition is very important to obtain new insights into the disease and its symptomatology. Particularly predicting the cognitive outcome of a resection, one of the future directions of this work, is highly relevant to brain tumor patients from a clinical point of view: a better understanding of how post-surgical cognitive complaints come about will improve decision making in treatment strategy in this patient group. The relevance of this work can therefore not be underestimated.

Our thoughts primarily relate to the (details of) the methodology used and some of the results. We were surprised to see that the individually tuned model parameters in combination with the individual structural connectivity matrices did not result in better predictions of the individual functional connectivity patterns compared to individually tuned model parameters and the control average structural connectivity matrix. Although this finding is in line with previous work by Jirsa and colleagues (2017), it would be interesting to hear the authors’ own (speculative) explanations for this result after working with the model.

Furthermore, it is not completely clear why an average firing rate of ~3 Hz was applied. This is also not evident to us when reading the paper by Deco and colleagues (2014), who mention that in a large-scale model of interconnected brain areas, a range of 2.63-3.55 Hz should be applied. Therefore, we were wondering why only one firing rate has been applied instead of using a range of values, particularly as it is known that brain tumors may impact neurotransmitter levels around the tumor and possibly neuronal firing rates.

Finally, the relationship of the model parameters with cognitive functioning suggests a major step forward in getting a grip on explaining cognitive symptoms in brain tumor patients. We would like to suggest that it is also interesting to relate the available cognitive measures to the already calculated empirical functional network measures, to be able to assess how much variance in cognitive functioning can be explained by ‘simply’ using the model versus empirical data. Of course prospectively, it would be very interesting to relate the pre-surgical model parameters to post-surgical cognitive status, once longitudinal measurements are available as the authors imply. We are therefore looking forward see the prediction accuracy of the VB model using longitudinal cognitive data!

Quirien Oort

Quirien Oort is no stranger in neuro-oncological research: coming from a neuropsychological background, she is been working on her dissertation on quality of life in brain tumor patients with Martin Taphoorn (LUMC), Linda Dirven (LUMC), and Jaap Reijneveld (VUmc). She now joins the lab to explore MRI and network analysis. Welcome Quirien!


Spotlight on Neurology paper

The paper on hub-rich networks in MS by Kim Meijer was put in the spotlight by the editors of Neurology. In this study, cognitive impairment in multiple sclerosis was related to altered communication of hub-rich networks. The default mode and frontoparietal networks showed increased functional connectivity, but only with more peripheral regions (i.e., non-hubs), in cognitively impaired patients. This seemingly negative shift in network balance potentially underlies cognitive dysfunction in multiple sclerosis.

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OHBM 2017

We will be going to Vancouver, and will present the following posters:

  • Tuesday, #2019: the microscopic substrates of macro-scale graph theoretical properties of the brain, first author Svenja Kiljan (more info here)
  • Thursday, #3057: the (dynamic) connectivity profile of the cerebellum in MS, and its cognitive correlates, first author Menno Schoonheim (more info here)
  • Thursday, #3061: the dynamic connectivity mechanisms underlying content-specific memory functioning in MS, first author Quinten van Geest (more info here)

Hope to have some great discussions over these investigations!

Tianne Numan

I am trained as technFoto Tianneical physician and have a specific interest in the brain. During my PhD project in the UMC Utrecht at the intensive care unit (ICU) I did several projects on EEG based delirium monitoring and EEG based network analyses during delirium and sedation. I really enjoyed the combination of performing analyses and interpretation of these complex analyses, as well as the cooperation with a broad range of people, from highly experienced researchers to students doing their first internship.

I hope I can use my experience in this new opportunity to join the research lab of Linda Douw. I will participate in the complex network analyses on MEG and MRI data of patients with brain tumors to improve understanding of the pathophysiology and aim for better treatments.