Figure1 01

Azeez Adebimpe

and 6 more

Human learning is a complex process in which future behavior is altered via the modulation of neural activity.   Yet, the degree to which such activity, and its resultant functional connectivity, is constrained across individual subjects and throughout learning remains unknown. Here, we measured brain activity and functional connectivity in a longitudinal experiment in which healthy adult human participants learned the values of novel objects over the course of four days. We assessed the presence of constraints on activity by calculating the Pearson correlation of a region's fMRI BOLD activity time series across pairs of subjects. Similarly, we assessed the presence of constraints on functional connectivity by calculating the Pearson correlation of the functional connectivity of a region across pairs of subjects. Together, these intersubject correlations in activity and connectivity were greater in magnitude than expected in a non-parametric permutation-based null model, particularly in primary sensory and motor systems, as well as in regions associated with the learning of value. Notably, intersubject correlations in activity and connectivity over the whole brain peaked in the early stages of learning, suggesting the presence of strong constraints on early, as opposed to late, skill acquisition. Intersubject correlations in activity were lower in magnitude than intersubject correlations in connectivity later in learning, suggesting that connectivity may be more highly constrained than activity in late skill acquisition. Finally, individual differences in performance accuracy tracked the degree to which a subject's connectivity, but not activity, tracked subject-general constraints. Taken together, our results support the notion that brain activity and connectivity are most constrained across subjects early in learning, with constraints on activity, but not connectivity, decreasing later in learning.
Figures1

Max Bertolero

and 2 more

Materials and Methods Brain network construction Generally, to perform network analyses one must define the two important elements of the network -- nodes and edges. These two elements are the building blocks of networks and their accurate definitions are very important for any network models (Butts 2009). The standard method of defining network nodes in the field of network neuroscience is to consider neuroimaging data such fMRI and apply a structural atlas or parcellation that separates the whole brain volume into different regions defined by known anatomical differences. Network nodes thus represent the collection of voxels within anatomically defined region. The network edges reflect statistical dependencies between the activity time series of two nodes. In this study, the brain is parcellated into 112 subcortical and cortical regions (see Supplementary Table 1) defined by the structural Harvard-Oxford atlas of the fMRIB (Smith et al. 2004; Woolrich et al. 2009). Each region's activity is given by the mean time series across all voxels within that region. The edge weights that link network nodes (brain regions) were defined as the wavelet transform coherence (WTC) (Torrence and Compo 1998), smoothed over time and frequency to avoid bias toward unity coherence. We use Morlet wavelets with coefficients given by\(:\) \(\begin{equation}w(t,f)=(\sigma_{t}\sqrt{(}\pi))^{-\frac{1}{2}}e^{-i2\pi ft}e^{-\frac{t^{2}}{2\sigma_{t}^{2}}}\nonumber \\ \end{equation}\) , where f is the centre frequency and \(\sigma_{t}\) is the temporal standard deviation. The time-frequency estimate, X(t,f) of time series x(t) was computed by a convolution with the wavelet coefficients: \(\begin{equation}X(t,f)=x(t)*w(t,f)\nonumber . \\ \end{equation}\)  We selected the central frequency of 1/12 Hz corresponding to a spectral width of 0.05 to 0.11 Hz for full width at half maximum. Then the wavelet transform coherence between two time series x(t) and y(t) is defined as follows (Torrence and Compo 1998; Cazelles et al. 2007; Grinsted, Moore, and Jevrejeva 2004)\(:\) \begin{equation} TC^{2}(f,t)=\frac{|S(s^{-1}X_{xy}(t,f)|^{2}}{S(s^{-1}|X_{x}(t,f)|^{2})\cdot S(s^{-1}|X_{y}(t,f)|^{2})}\nonumber \\ \end{equation} ,where \(X_{xy}\) is the cross-wavelet of \(X_{x}\) and \(X_{y}\), s is the scale which depends on the frequency (Cazelles et al. 2007; Grinsted, Moore, and Jevrejeva 2004), and S is the smoothing operator. This definition closely resembles that of a traditional coherence, with the marked difference that the wavelet coherence provides a localized correlation coefficient in both time and frequency. Higher scales are required for lower frequency signals (Cazelles et al. 2007; Grinsted, Moore, and Jevrejeva 2004) and in this study, we used s=32 for the smoothing operation. This procedure was repeated for all pair of regions yielding the 112 by 112 adjacency matrix, A , representing the functional connectivity between brain regions. Network modularity In neuroscience, the term network modularity can be used to refer to the concept that brain regions cluster into modules or communities. These communities can be identified computationally using machine learning techniques in the form of community detections algorithms (Girvan and Newman 2001). A community of nodes is a group of nodes that are tightly interconnected. In this study, we implemented a generalized Louvain community detection algorithm (De Meo et al. 2011; Mucha et al. 2010) which considers multiple adjacency matrices as slices of a multilayer network, and which then produces a partition of brain regions into modules that reflects each subject's community structure across the multiple stages of learning instantiated in the four days of task practice. The multilayer network was constructed by connecting the adjacency matrices of all scans and subjects with interlayer links. We then maximized a multilayer modularity quality function, Q , that seeks a partition of nodes into communities that maximizes intra-community connections (Mucha et al. 2010)\(:\) \(\begin{equation}Q=\frac{1}{2\mu}\sum_{ijs}[(A_{ijs}-\gamma_{s}V_{ijs})\delta_{sr}+\delta_{ij}\omega_{jsr}]\delta(g_{is},g_{jr})\nonumber ,\\ \end{equation}\) where \(A_{ijs}\) is the ijth element of the adjacency matrix of slice s, and element \(V_{ijs}\) is the component of the null model matrix tuned by the structural resolution parameter \(\gamma\). In this study, we set \(\gamma\)=1, which is the standard practice in the field when no a priori hypotheses exist to otherwise inform the choice of \(\gamma\). We employed the Newman-Girvan null model within each layer by using \(V_{ijs}=\frac{k_{is}k_{js}}{2m_{s}}\), where k is the total edge weight and \(m_{s}\) is the total edge weight in slice  s. The interslice coupling parameter, \(\omega_{jsr},\) is the connection strength of the interlayer link between node j in slice s and node j in slice r, and the total edge in the network is \(\mu=\frac{1}{2}\sum_{jr}\kappa_{jr}\). The node strength, \(\kappa_{jr}\), is the sum of the intraslice strength and interslice strength: \(\kappa_{jr}=k_{jr}+c_{jr}\), and \(c_{jr}=\sum_{s}\omega_{jrs}.\) In this study, we set  \(\omega=1,\) which is the standard practice in the field when no a priori hypotheses exist to otherwise inform the choice of \(\omega\). Finally, the indicator \(\delta(g_{i},g_{j})=1\) if nodes i and j are assigned to the same community, and is 0 otherwise. We obtained a partition of the brain into communities for each scan and subject, and from that ensemble of partitions we constructed a module allegiance matrix\cite{Bassett_2015} , whose elements correspond to the probability that two regions belong to the same community across all scans and subjects. The seven network communities generated with this procedure are shown in Table 1 in the main text. Edge strength In complementary analyses, we also investigated which regions of the brain were characterized by high strength within the network.  The edge strength of node i is defined as \(\begin{equation}S_{i}=\frac{1}{N-1}\sum_{j\epsilon N}a_{ij}\nonumber \\ \end{equation}\)  ,where  \(a_{ij}\) is the ijth element of the adjacency matrix with N nodes.
Figures1

Azeez Adebimpe

and 2 more

MATERIALS AND METHODS Brain network construction Generally, network analyses consist of two important elements - NODES and EDGES . These two elements are the building blocks of networks and their accurate definitions are very important for any network model and also applicable to network neuroscience. The standard method of defining nodes in neuroimaging, particularly for fMRI studies, is by a structural atlas or parcellation of brain structure into different regions. The nodes are usually represented by collection of voxels within the defined structure and the edges are the statistical dependences of the brain activity of the pair of nodes. In this study, the brain is parcellated into 112 subcortical and cortical regions (see supplementary Table 1) defines by structural Harvard-Oxford atlas of the fMRIB . Each region is represented by average of voxel time series within the region. The edge weights that link the brain nodes (regions) were calculated by the wavelet transform coherence (WTC) , smoothed over time and frequency to avoid bias toward unity coherence. We derived the spectral estimates of the time series using Morlet wavelets defined w(t,f) as : w(t,f)=(\sigma_t \sqrt(\pi))^{-{2}} e^{- i 2 \pi ft} e^{-{2^{2}}} Here, f is the centre frequency and σt is the temporal standard deviation. The time-frequency estimate, X(t,f) of time series x(t) was computed by the convolution with wavelet coefficients, w(t,f); X(t,f)=x(t)\ast w(t,f) We selected the central frequency of 1/12 Hz corresponding to spectral width of 0.05 to 0.11Hz for full width at half maximum(FWHM) . Therefore, the wavelet transform coherence between two regions x and y is defined as followed : WTC^2(f,t)=X_{xy}(t,f)|^2}{S(s^{-1}|X_x(t,f)|^2) \cdot S(s^{-1}|X_y(t,f)|^2) } Where Xxy is the cross-wavelet of Xx and Xy, s is the scale which depend on the frequency and S is the smoothing operator. This definition closely resembles that of a traditional coherence but the wavelet coherence is localized correlation coefficient in both time and frequency space. Higher scales are required for lower frequency signals and in this study, we used scale of s=32 for the smoothing operation. This procedure was repeated for all pair of regions yielding adjacency matrix, A, with 112 by 112 dimensions which is the representative of functional connectvity between the brain regions. Network modularity Network modularity the network neuroscience concept of that the brain’s nodes cluster into modules or _communities_ by using community detections algorithms . A community of nodes is group of nodes that are more connected not only by region but also by their functional similarity . The common method of community detection algorithms is the optimization of nodes partition into modules. In this study, we implemented a generalized Louvain detection algorithms which considers multiple adjacency matrices as slices of network. The multislice system was implemented by all adjacency matrices of all scans and subjects during the period of value learning task. The quality function, Q, which used intra-community and inter-community connections to identify a partition of networks nodes is defined as : Q={2 \mu}[(A_{ijs}-\gamma_s V_{ijs}) + ]\delta(g_{is},g_{jr}) Where Aijs is the components of adjacency matrix of slice, s, and element Vijs is the component of the null model matrix tuned by the structural resolution γ. In this study, the γ standard parameter of 1 is selected. We employed the Newman-Girvan null model within each layer by using $V_{ijs}=k_{js}}{2m_s}$, where k is the total edge weight and ms is the total edges weight in slice , s. The interslice coupling parameter, ωjsr is the connection strength between node j in slice s and node j in slice r and the total edge in the network is $\mu={2}$. The strength of the node, κjr is the sum of intraslice strength and interslice: κjr = kjr + cjr, and cjr = ∑sωjrs However, in our study we fixed this parameter to be ω = 1. The last part of the equation 4 is the community assignments and δ(gi, gj)=1 if gi and gj of nodes i and j are the same and 0 otherwise. We obtained partition of brain into network communities for each scan and subject with the standard parameter of γ = ω = 1. We obtained the module allegiance matrix , whose elements correspond to the probability that two regions belong to the same community across all the scans and subjects. The seven network communities generated with this procedure are as shown in Table 1 ( in the main text). Inter-subject correlation (ISC) and inter-subject functional connectivity (ISFC) We have shown in the main article how we obtained ISC and ISFC. ISC measured the reliability of stimulus driven responses across the subjects and allows the detection of all sensory cortical regions without assumptions or a priori knowledge of the temporal composition of exact cortical responses. However, we measures the reliability of ISC by computing the Pearson correlation between each subject three scans for each day to confirmed the ISC within subject. This was performed on bold time series signals on region-by-region. Each correlation value for each scan and subject was converted to Z score value to enable comparison with other scans and subjects. Similarly, we estimated the consistency of the FC by computing the edge persistence of the brain network across the three runs for each day to established the reliability of ISFC within subject . The edge persistence measures the topological overlap of the neighborhood from one scan to another by estimating the probability that nodes connected at a scan 1 will still be connected during scan 2 . For the three scans (s1,s2 and s3) in each day, the edge persistence is defined as: C_{i}(s_1,s_2,s_3)= a_{ij}(s_1)a_{ij}(s_2)a_{ij}(s_3)}{\sqrt([a_{ij}(s_1)][a_{ij}(s_2)][a_{ij}(s_3)])} Where aij is the edge strength between of node i and j from the adjacency functional matrix, A and Ci is the edge persistence for node i. Edge strength and Resistivity In order to determine the brain regions that mostly impact the brain network performance during the value learning task, we investigated the regions with high degree by computing the edge strength (or degree) and resistivity . A region with higher degree is said to be of very important for the system network performance. The edge strength is defined as S(i)={N-1} A_{ij} Where A is adjacency matrix with N total number of nodes in the network, and S(i) is the strength or degree of node .