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Monday, July 20 • 6:00pm - 6:20pm
O13: Cortical integration and segregation explained by harmonic modes of functional connectivity

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Katharina Glomb, Gustavo Deco, Morten L. Kringelbach, Patric Hagmann, Joel Pearson, Selen Atasoy

The idea that harmonic modes - basis functions of the Laplace operator - are meaningful buildingblocks of brain function are gaining attention [1–3]. We extracted harmonic modes from the HumanConnectome Project’s (HCP) dense functional connectivity (dFC), an average over 812 participants’resting state fMRI dFC matrices. In this case, harmonic modes give rise tofunctional harmonics.Each functional harmonic is a connectivity gradient [4] that is associated with a different spatialfrequency, and thus, functional harmonics provide a frequency-ordered, multi-scale, multi-dimensionaldescription of cortical functional organization.

We propose functional harmonics as an underlying principle of integration and segregation. Figure 1a shows 2 functional harmonics on the cortical surface. In harmonic 11 (ψ11), the two functional regions that correspond to the two hands are on opposite ends of the gradient (different colors on thesurface) and are thus functionally segregated. In contrast, in harmonic 7 (ψ7), the two areas are onthe same end of the gradient, and are thus integrated. This way, functional harmonics explain howtwo brain regions can be both functionally integrated and segregated, depending on the context.

Figure 1a illustrates how specialized areas emerge from the smooth gradients of functional harmonics: the two hand areas occupy well-separated regions of the space spanned by ψ7and ψ11. Thus, functional harmonics unify two perspectives, a view where the brain is organized in discrete modules,and one in which function varies gradually [4].

The borders drawn on the cortex correspond to functional areas in the HCP’s multimodal parcellation [5]. In this example, the isolines of the gradients of the functional harmonics follow the borders. We quantified how well, in general, the first 11 functional harmonics follow the borders of corticalareas by comparing the variability of the functional harmonics within and between the areas given by the HCP parcellation; i.e. we computed the silhouette value (SH), averaged over all 360 cortical areas. The SH lies between 0 and 1, where 1 means perfect correspondence between isolines and parcels. We found average SHs between 0.65 (ψ10) and 0.85 (ψ1), indicating a very good correspondence. Thus, functional harmonics capture the “modular perspective” of brain function.

On the other hand, several functional harmonics are found to capture topographic maps and thus, gradually varying function. One important example is retinotopic organization of the visual cortex. Figure 1b shows functional harmonic 8 (ψ8) as an example in which both angular and eccentricity gradients are present [6]. Topographic organization is also found in the somatosensory/motor cor-tex, known as somatotopy. This is shown in Figure 1a, where several somatotopic body areas are reproduced.

Taken together, our results show that functional specialization, topographic maps, and the multi-scale, multi-dimensional nature of functional networks are captured by functional harmonics, thereby connecting these empirical observations to the general mathematical framework of harmonic eigenmodes.


1\. S. Atasoyet al.,Nature communications7(2016).

2\. P. A. Robinsonet al.,NeuroImage142, 79–98 (2016).1

3\. P. Tewarieet al.,NeuroImage186, 211–220 (2019).

4\. D. S. Margulieset al.,Proceedings of the National Academy of Sciences113, 12574–12579 (2016).

5\. M. F. Glasseret al.,Nature536, 171–178 (2016).

6\. N. C. Bensonet al.,Journal of vision18, 23–23 (2018).

avatar for Katharina Glomb

Katharina Glomb

Department of Radiology, Centre Hospitalier Universitaire Vaudois

Monday July 20, 2020 6:00pm - 6:20pm CEST
  Oral, Structural and Functional Connectivity
  • Moderator Sacha van Albada; Ingo Bojak