This Is Your Brain on Psychedelic Drugs (via Discover)

Dr. David Nutt and a team of researchers have published a study on the psychoactive substance in mushrooms, psilocybin, and how it impacts the brain circuits. As you can see in the picture below, the effect of psilocybin is a much more interconnected brain (which suggests some other circuits that limit activity are inactive under the influence of psilocybin).

Interesting stuff.

The summary below is from Discover, then the whole article, which is open access, is also included below.

This Is Your Brain on Psychedelic Drugs

By Ben Thomas | October 29, 2014 4:16 pm


Left, the stable brain activity in a normal brain. Right, under the influence of psilocybin, diverse brain regions not normally in communication become strongly linked.
Psychedelic substances can change a user’s mindset in profound ways — a fact that’s relevant even to those who’ve never touched the stuff, because such altered states of consciousness give scientists a window into how our brains give rise to our normal mental states. But neuroscientists are only beginning to understand how and why those mental changes occur.

Now some mathematicians have jumped into the fray, using a new mathematical technique to analyze the brains of people on magic mushrooms.

Psychedelic Puzzles

Scientists have known for decades that many of psychedelic drugs’ most famous effects — visual hallucinations, heightened sensory and emotional sensitivity, etc. — are linked to elevated levels of the neurotransmitter serotonin.

But increasingly neuroscience researchers are interested not just in single chemicals but also in overall brain activity, because the most complicated brain functions arise from lots of different regions working together. Over the last several years, a branch of mathematics known as network theory has been applied to study this phenomenon.

Paul Expert, a complexity researcher at the Imperial College London, and his team took this approach to analyzing fMRI data from people who’d taken psilocybin, the psychedelic chemical in magic mushrooms. The team had recently been working on a new technique for network modeling — one designed to highlight small but unusual patterns in network connectivity.

Brains on Drugs

The team used fMRI data from a previous study, in which 15 healthy people rested inside an fMRI scanner for 12 minutes on two separate occasions. The volunteers received a placebo in one of those sessions, and a mild dose of psilocybin during the other, but they weren’t told which was which.

The investigators crunched the data, specifically studying the brain’s functional connectivity — the amount of active communication among different brain areas.

They found two main effects of the psilocybin. First, most brain connections were fleeting. New connectivity patterns tended to disperse more quickly under the influence of psilocybin than under placebo. But, intriguingly, the second effect was in the opposite direction: a few select connectivity patterns were surprisingly stable, and very different from the normal brain’s stable connections.

This indicates “that the brain does not simply become a random system after psilocybin injection, but instead retains some organizational features, albeit different from the normal state,” the authors write in their paper in the Journal of the Royal Society Interface.

Far Out
The findings seem to explain some of the psychological experiences of a psilocybin trip. Linear thinking and planning become extremely difficult, but nonlinear “out of the box” thinking explodes in all directions. By the same token, it can become difficult to tell fantasy apart from reality during a psilocybin trip; but focusing on a certain thought or image — real or imagined — often greatly amplifies that thought’s intensity and vividness.

The authors suggest that effects like these may be rooted in the two connectivity traits they spotted, since the connectivity patterns that rapidly disperse may reflect unorganized thinking, while the stable inter-regional connections may reflect information from one sensory domain “bleeding” into other areas of sensory experience. In fact, the researchers also suggest that synesthesia — the sensory blurring that causes users of psychedelics to experience sounds as colors, for example — may be a result of these connectivity changes too.

The researchers hope that the patterns they’ve found will provide neuroscientists with new approaches for studying the brain on psychedelic drugs, and therefore better understand the strange psychological effects their users report.

* * * * *

Full Citation:
Petri, G, Expert, P,  Turkheimer, F, Carhart-Harris, R, Nutt, D, Hellyer, PJ, and Vaccarino, F. (2014, Oct 29). Homological scaffolds of brain functional networks. J. R. Soc. Interface; 11(101). doi: 10.1098/​rsif.2014.0873 [Print: 6 December 2014] 

Homological scaffolds of brain functional networks

G. Petri [1], P. Expert [2], F. Turkheimer [2], R. Carhart-Harris [3], D. Nutt [3], P. J. Hellyer [4] and
F. Vaccarino [1,5]

1. ISI Foundation, Via Alassio 11/c, 10126 Torino, Italy
2. Centre for Neuroimaging Sciences, Institute of Psychiatry, Kings College London, De Crespigny Park, London SE5 8AF, UK
3. Centre for Neuropsychopharmacology, Imperial College London, London W12 0NN, UK
4. Computational, Cognitive and Clinical Neuroimaging Laboratory, Division of Brain Sciences, Imperial College London, London W12 0NN, UK
5. Dipartimento di Scienze Matematiche, Politecnico di Torino, C.so Duca degli Abruzzi no 24, Torino 10129, Italy

Abstract

Networks, as efficient representations of complex systems, have appealed to scientists for a long time and now permeate many areas of science, including neuroimaging (Bullmore and Sporns 2009 Nat. Rev. Neurosci. 10, 186–198. (doi:10.1038/nrn2618)). Traditionally, the structure of complex networks has been studied through their statistical properties and metrics concerned with node and link properties, e.g. degree-distribution, node centrality and modularity. Here, we study the characteristics of functional brain networks at the mesoscopic level from a novel perspective that highlights the role of inhomogeneities in the fabric of functional connections. This can be done by focusing on the features of a set of topological objects—homological cycles—associated with the weighted functional network. We leverage the detected topological information to define the homological scaffolds, a new set of objects designed to represent compactly the homological features of the correlation network and simultaneously make their homological properties amenable to networks theoretical methods. As a proof of principle, we apply these tools to compare resting-state functional brain activity in 15 healthy volunteers after intravenous infusion of placebo and psilocybin—the main psychoactive component of magic mushrooms. The results show that the homological structure of the brain's functional patterns undergoes a dramatic change post-psilocybin, characterized by the appearance of many transient structures of low stability and of a small number of persistent ones that are not observed in the case of placebo.

1. Motivation

The understanding of global brain organization and its large-scale integration remains a challenge for modern neurosciences. Network theory is an elegant framework to approach these questions, thanks to its simplicity and versatility [1]. Indeed, in recent years, networks have become a prominent tool to analyse and understand neuroimaging data coming from very diverse sources, such as functional magnetic resonance imaging (fMRI), electroencephalography and magnetoencephalography [2,3], also showing potential for clinical applications [4,5]. 

A natural way of approaching these datasets is to devise a measure of dynamical similarity between the microscopic constituents and interpret it as the strength of the link between those elements. In the case of brain functional activity, this often implies the use of similarity measures such as (partial) correlations or coherence [6–8], which generally yield fully connected, weighted and possibly signed adjacency matrices. Despite the fact that most network metrics can be extended to the weighted case [9–13], the combined effect of complete connectedness and edge weights makes the interpretation of functional networks significantly harder and motivates the widespread use of ad hoc thresholding methods [7,14–18]. However, neglecting weak links incurs the dangers of a trade-off between information completeness and clarity. In fact, it risks overlooking the role that weak links might have, as shown for example in the cases of resting-state dynamics [19,20], cognitive control [21] and correlated network states [22]. 

In order to overcome these limits, Rubinov & Sporn [13,23,24] recently introduced a set of generalized network and community metrics for functional networks that among others were used to uncover the contrasting dynamics underlying recollection [25] and the physiology of functional hubs [26]. 

In this paper, we present an alternative route to the analysis of brain functional networks. We focus on the combined structure of connections and weights as captured by the homology of the network. A summary of all the keywords and concepts introduced in this paper can be found in table 1.

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Table 1. List of notations.

2. From networks to topological spaces and homology

Homology is a topological invariant that characterizes a topological space X by counting its holes and their dimensions. By hole, we mean a hollow region bounded by the parts of that space. The dimension of a hole is directly related to the dimension of its boundary. The boundary of a two-dimensional hole is a one-dimensional loop; the three-dimensional inner part of a doughnut, where the filling goes, is bounded by two-dimensional surface; for dimensions higher than 2, it becomes difficult to have a mental representation of a hole, but k-dimensional holes are still bounded by (k − 1) dimensional faces. In our work, we start with a network and from it construct a topological space. We now use figure 1 to show how we proceed and make rigorous what we mean by boundaries and holes. 

Figure 1. Panels (a,b) display an unweighted network and its clique complex, obtained by promoting cliques to simplices. Simplices can be intuitively thought as higher-dimensional interactions between vertices, e.g. as a simplex the clique (b,c,i) corresponds to a filled triangle and not just its sides. The same principle applies to cliques—thus simplices—of higher order. (Online version in colour.) 

In a network like that of figure 1a, we want the ring of nodes (a,b,c,d) to be a good candidate for a one-dimensional boundary, whereas the other rings of three nodes should not constitute interesting holes. The reason for this choice comes from the formalization of the notion of hole. One way to formalize this is by opposition that is we define what we mean by a dense subnetwork in order to highlight regions of reduced connectivity, i.e. holes. The most natural and conservative definition we can adopt for a dense subnetwork is that of clique, a completely connected subgraph [27]. Moreover, cliques have the crucial property, which will be important later, of being nested, i.e. a clique of dimension k (k-clique) contains all the m-cliques defined by its nodes with m < k. Using this definition and filling in all the maximal cliques, the network in figure 1a can be represented as in figure 1b: 3-cliques are filled in, becoming tiles, and the only interesting structure left is the square (a,b,c,d). It is important at this point to note that a k-clique can be seen as a k − 1 simplex, i.e. as the convex hull of k-points. Our representation of a network can thus be seen as a topological space formed by a finite set of simplices that by construction satisfy the condition that defines the type of topological spaces called abstract simplicial complexes [28]: each element of the space is a simplex, and each of its faces (or subset in the case of cliques) is also a simplex. 

This condition is satisfied, because each clique is a simplex, and subsets of cliques are cliques themselves, and the intersection of two cliques is still a clique. 

The situation with weighted networks becomes more complicated. In the context of a weighted network, the holes can be thought of as representing regions of reduced connectivity with respect to the surrounding structure. 

Consider, for example, the case depicted in figure 2a: the network is almost the same as figure 1 with the two exceptions that it now has weighted edges and has an additional very weak edge between nodes a and c. The edges in the cycle [a,b,c,d] are all much stronger than the link (a,c) that closes the hole by making (a,b,d) and (b,c,d) cliques and therefore fills them. The loop (e,f,g,h,i) has a similar situation, but the difference in edge weights between the links along the cycle and those crossing, is not as large as in the previous case. It would be therefore useful to be able to generalize the approach exposed earlier for binary networks to the case of weighted networks in such a way as to be able to measure the difference between the two cases (a,b,c,d) and (e,f,g,h,i). As shown by figure 2b, this problem can be intuitively thought of as a stratigraphy in the link-weight fabric of the network, where the aim is to detect the holes, measure their depth and when they appear as we scan across the weights' range. 

Figure 2. Panels (a­–c) display a weighted network (a), its intuitive representation in terms of a stratigraphy in the weight structure according the weight filtration described in the main text (b) and the persistence diagram for H₁ associated with the network shown (c). By promoting cliques to simplices, we identify network connectivity with relations between the vertices defining the simplicial complex. By producing a sequence of networks through the filtration, we can study the emergence and relative significance of specific features along the filtration. In this example, the hole defined by (a,b,c,d) has a longer persistence (vertical solid green bars) implying that the boundary of the cycle are much heavier than the internal links that eventually close it. The other hole instead has a much shorter persistence, surviving only for one step and is therefore considered less important in the description of the network homological properties. Note that the births and deaths are defined along the sequence of descending edge weights in the network, not in time. (Online version in colour.) 

From figure 2b, it becomes clear that the added value of this method over conventional network techniques lies in its capability to describe mesoscopic patterns that coexist over different intensity scales, and hence to complement the information about the community structure of brain functional networks. A way to quantify the relevance of holes is given by persistent homology. We describe it and its application to the case of weighted networks in full detail in §3.

3. A persistent homology of weighted networks

The method that we adopt was introduced in references [29,30] and relies on an extension of the metrical persistent homology theory originally introduced by references [31,32]. Technical details about the theory of persistent homology and how the computation is performed can be found in the works of Carlsson, Zomorodian and Edelsbrunner [28,31–35]. Persistent homology is a recent technique in computational topology developed for shape recognition and the analysis of high dimensional datasets [36,37]. It has been used in very diverse fields, ranging from biology [38,39] and sensor network coverage [40] to cosmology [41]. Similar approaches to brain data [42,43], collaboration data [44] and network structure [45] also exist. The central idea is the construction of a sequence of successive approximations of the original dataset seen as a topological space X. This sequence of topological spaces X₀, X₁, … , X_N = X is such that whenever i < j and is called the filtration. Choosing how to construct a filtration from the data is equivalent to choosing the type of goggles one wears to analyse the data. 

In our case, we sort the edge weights in descending order and use the ranks as indices for the subspaces. More specifically, denote by the functional network with vertices V, edges E and weights . We then consider the family of binary graphs G_ω = (V, E_ω), where an edge e ∈ E is also included in G_ω if its weight ω_e is larger than ω (). 

To each of the G_ω, we associate its clique, or flag complex K_ω, that is the simplicial complex that contains the k-simplex [n₀, n₁, n₂, … n_{k − 1}] whenever the nodes n₀, n₁, n₂, … n_{k −1} define a clique in G_ω [27]. As subsets of cliques and intersections of cliques are cliques themselves, as we pointed out in §2, our clique complex is thus a particular case of a simplicial complex. 

The family of complexes {K_ω} defines a filtration, because we have for ω > ω′. At each step, the simplices in K_ω inherit their configuration from the underlying network structure and, because the filtration swipes across all weight scales in descending order, the holes among these units constitute mesoscopic regions of reduced functional connectivity.

Moreover, this approach also highlights how network properties evolve along the filtration, providing insights about where and when lower connectivity regions emerge. This information is available, because it is possible to keep track of each k-dimensional cycle in the homology group H_k. A generator uniquely identifies a hole by its constituting elements at each step of the filtration process. The importance of a hole is encoded in the form of ‘time-stamps' recording its birth β_g and death δ_g along the filtration {K_ω} [31]. These two time-stamps can be combined to define the persistence π_g = δ_g − β_g of a hole, which gives a notion of its importance in terms of it lifespan. Continuing the analogy with stratigraphy, β_g and δ_g correspond, respectively, to the top and the bottom of a hole and π_g would be its depth. As we said above, a generator , or hole, of the kth homology group H_k is identified by its birth and death along the filtration. Therefore, is described by the point . A standard way to summarize the information about the whole kth persistent homology group is then to consider the diagram obtained plotting the points corresponding to the set of generators. The (multi)set {(β_g,δ_g} is called the persistence diagram of H_k. In figure 2c, we show the persistence diagram for the network shown in figure 2a for H₁. Axes are labelled by weights in decreasing order. It is easy to check that the coordinates correspond exactly to the appearance and disappearance of generators. The green vertical bars highlight the persistence of a generator along the filtration. The further a point is from the diagonal (vertically), the more persistent the generator is. In §4, we introduce two objects, the persistence and the frequency homological scaffolds, designed to summarize the topological information about the system. 

4. Homological scaffolds

Once one has calculated the generators of the kth persistent homology group H_k, the corresponding persistence diagram contains a wealth of information that can be used, for example, to highlight differences between two datasets. It would be instructive to obtain a synthetic description of the uncovered topological features in order to interpret the observed differences in terms of the microscopic components, at least for low dimensions k. Here, we present a scheme to obtain such a description by using the information associated with the generators during the filtration process. As each generator, is associated with a whole equivalence class, rather than to a single chain of simplices, we need to choose a representative for each class, we use the representative that is returned by the javaplex implementation [46] of the persistent homology algorithm [47]. For the sake of simplicity in the following, we use the same symbol to refer to a generator and its representative cycle. 

We exploit this to define two new objects, the persistence and the frequency homological scaffolds and of a graph G. The persistence homological scaffold is the network composed of all the cycle paths corresponding to generators weighted by their persistence. If an edge e belongs to multiple cycles g₀,g₁, … ,g_s, its weight is defined as the sum of the generators' persistence:

4.1

Similarly, we define the frequency homological scaffold as the network composed of all the cycle paths corresponding to generators, where this time, an edge e is weighted by the number of different cycles it belongs to

4.2

where is the indicator function for the set of edges composing g_i. By definition, the two scaffolds have the same edge set, although differently weighted. 

The construction of these two scaffolds therefore highlights the role of links which are part of many and/or long persistence cycles, isolating the different roles of edges within the functional connectivity network. The persistence scaffolds encodes the overall persistence of a link through the filtration process: the weight in the persistence scaffold of a link belonging to a certain set of generators is equal to the sum of the persistence of those cycles. The frequency scaffold instead highlights the number of cycles to which a link belongs, thus giving another measure of the importance of that edge during the filtration. The combined information given by the two scaffolds then enables us to decipher the nature of the role different links have regarding the homological properties of the system. A large total persistence for a link in the persistence scaffold implies that the local structure around that link is very weak when compared with the weight of the link, highlighting the link as a locally strong bridge. We remark that the definition of scaffolds we gave depends on the choice of a specific basis of the homology group, and the choice of a consistent basis is an open problem in itself, therefore the scaffolds are not topological invariants. Moreover, it is possible for an edge to be added to a cycle shortly after the cycle's birth in such a way that it creates a triangle with the two edges composing the cycle. In this way, the new edge would be part of the shortest cycle, but the scaffold persistence value would be misattributed to the two other edges. This can be checked, for example, by monitoring the clustering coefficient of the cycle's subgraph as edges are added to it. We checked for this effect and found that in over 80% of the cases the edges do not create triangles that would imply the error, but instead new cycles are created, whose contribution to the scaffold is then accounted for by the new cycle. Finally, we note also that, when a new triangle inside the cycle is created, the two choices of generator differ for a path through a third strongly connected node, owing to the properties of boundary operators. Despite this ambiguity, we show in the following that they can be useful to gain an understanding of what the topological differences detected by the persistent homology actually mean in terms of the system under study.

5. Results from fMRI networks

We start from the processed fMRI time series (see Methods for details). The linear correlations between regional time series were calculated after covarying out the variance owing to all other regions and the residual motion variance represented by the 24 rigid motion parameters obtained from the pre-processing, yielding a partial-correlation matrix χ^α for each subject. The matrices χ^α were then analysed with the algorithm described in the previous sections. We calculated the generators of the first homological group H₁ along the filtration. As mentioned before, each of these generators identifies a lack of mesoscopic connectivity in the form of a one-dimensional cycle and can be represented in a persistence diagram. We aggregate together the persistence diagrams of subjects belonging to each group and compute an associated persistence probability density (figure 3). These probability density functions constitute the statistical signature of the groups' H₁ features. 

Figure 3. Probability densities for the H₁ generators. Panel (a) reports the (log-)probability density for the placebo group, whereas panel (b) refers to the psilocybin group. The placebo displays a uniform broad distribution of values for the births–deaths of H₁ generators, whereas the plot for the psilocybin condition is very peaked at small values with a fatter tail. These heterogeneities are evident also in the persistence distribution and find explanation in the different functional integration schemes in placebo and drugged brains. (Online version in colour.) 

We find that, although the number of cycles in the groups are comparable, the two probability densities strongly differ (Kolmogorov–Smirnov statistics: 0.22, p-value less than 10⁻¹⁰). 

The placebo group displays generators appearing and persisting over a limited interval of the filtration. On the contrary, most of the generators for the psilocybin group are situated in a well-defined peak at small birth indices, indicating a shorter average cycle persistence. However, the psilocybin distribution is also endowed with a longer tail implying the existence of a few cycles that are longer-lived compared with the placebo condition and that influences the weight distribution of the psilocybin persistence scaffold. The difference in behaviour of the two groups is made explicit when looking at the probability distribution functions for the persistence and the birth of generators (figure 4), which are both found to be significantly different (Kolmogorov–Smirnov statistics: 0.13, p-value < 10⁻³⁰ for persistence and Kolmogorov–Smirnov statistics: 0.14, p-value < 10⁻³⁵ for births). In order to better interpret and understand the differences between the two groups, we use the two secondary networks described in §4, and for the placebo group and and for the psilocybin group. The weight of the edges in these secondary networks is proportional to the total number of cycles an edge is part of, and the total persistence of those cycles, respectively. They complement the information given by the persistence density distribution, where the focus is on the entire cycle's behaviour, with information on single links. In fact, individual edges belonging to many and long persistence cycles represent functionally stable ‘hub’ links. As with the persistence density distribution, the scaffolds are obtained at a group level by aggregating the information about all subjects in each group. These networks are slightly sparser than the original complete χ^α networks

5.1 

and 5.2 

and have comparable densities. A first difference between the two groups becomes evident when we look at the distributions for the edge weights (figure 5a). In particular, the weights of display a cut-off for large weights, whereas the weights of have a broader tail (Kolmogorov–Smirnov statistics: 0.06, p-value < 10⁻²⁰; figure 5a). Interestingly, the frequency scaffold weights probability density functions cannot be distinguished from each other figure 5a (inset) (Kolmogorov–Smirnov statistics: 0.008, p-value = 0.72). Taken together, these two results imply that while edges statistically belong to the same number of cycles, in the psilocybin scaffold, there exist very strong, persistent links. 

Figure 4. Comparison of persistence π and birth β distributions. Panel (a) reports the H₁ generators' persistence distributions for the placebo group (blue line) and psilocybin group (red line). Panel (b) reports the distributions of births with the same colour scheme. It is very easy to see that the generators in the psilocybin condition have persistence peaked at shorter values and a wider range of birth times when compared with the placebo condition. (Online version in colour.) 

Figure 5. Statistical features of group homological scaffolds. Panel (a) reports the (log-binned) probability distributions for the edge weights in the persistence homological scaffolds (main plot) and the frequency homological scaffolds (inset). While the weights in the frequency scaffold are not significantly different, the weight distributions for the persistence scaffold display clearly a broader tail. Panel (b) shows instead the scatter plot of the edge frequency versus total persistence. In both cases, there is a clear linear relationship between the two, with a large slope in the psilocybin case. Moreover, the psilocybin scaffold has a larger spread in the frequency and total persistence of individual edges, hinting to a different local functional structure within the functional network of the drugged brains. (Online version in colour.) 

The difference between the two sets of homological scaffolds for the two groups becomes even more evident when one compares the weights between the frequency and persistence scaffolds of the same group. Figure 5b is a scatter plot of between the weights of edges from both scaffolds for the two groups. The placebo group has a linear relationship between the two quantities meaning that edges that are persistent also belongs to many cycles (R² = 0.95, slope = 0.23). Although the linear relationship is still a reasonable fit for the psilocybin group (R² = 0.9, slope = 0.3), the data in this case display a larger dispersion. In particular, it shows that edges in can be much more persistent/longer-lived than in but still appear in the same number of cycles, i.e. the frequency of a link is not predictive of its persistence or simply put: some connections are much more persistent in the psychedelic state. Moreover, the slopes of linear fits of the two clouds are statistically different (p-value < 10⁻²⁰, n_pla = 13 200 and n_psi = 13 275 [48]) pointing to a starkly different local functional structure in the two conditions. 

The results from the persistent homology analysis and the insights provided by the homological scaffolds imply that although the mesoscopic structures, i.e. cycles, in the psilocybin condition are less stable than in the placebo group, their constituent edges are more stable.

6. Discussion

In this paper, we first described a variation of persistent homology that allows us to deal with weighted and signed networks. We then introduced two new objects, the homological scaffolds, to go beyond the picture given by persistent homology to represent and summarize information about individual links. The homological scaffolds represent a new measure of topological importance of edges in the original system in terms of how frequently they are part of the generators of the persistent homology groups and how persistent are the generators to which they belong to. We applied this method to an fMRI dataset comprising a group of subjects injected with a placebo and another injected with psilocybin. 

By focusing on the second homology group H₁, we found that the stability of mesoscopic association cycles is reduced by the action of psilocybin, as shown by the difference in the probability density function of the generators of H₁ (figure 3). 

It is here that the importance of the insight given by the homological scaffolds in the persistent homology procedure becomes apparent. A simple reading of this result would be that the effect of psilocybin is to relax the constraints on brain function, ascribing cognition a more flexible quality, but when looking at the edge level, the picture becomes more complex. The analysis of the homological scaffolds reveals the existence of a set of edges that are predominant in terms of their persistence although they are statistically part of the same number of cycles in the two conditions (figure 5). In other words, these functional connections support cycles that are especially stable and are only present in the psychedelic state. This further implies that the brain does not simply become a random system after psilocybin injection, but instead retains some organizational features, albeit different from the normal state, as suggested by the first part of the analysis. Further work is required to identify the exact functional significance of these edges. Nonetheless, it is interesting to look at the community structure of the persistence homological scaffolds in figure 6. The two pictures are simplified cartoons of the placebo (figure 6a) and psilocybin (figure 6b) scaffolds. In figure 6a,b, the nodes are organized and coloured according to their community membership in the placebo scaffold (obtained with the Louvain algorithm for maximal modularity and resolution 1 [50]). This is done in order to highlight the striking difference in connectivity structure in the two cases. When considering the edges in the tail of the distribution, weight greater than or equal to 80, in figure 5a, only 29 of the 374 edges present in the truncated psilocybin scaffold are shared with the truncated placebo scaffold (165 edges). Of these 374 edges, 217 are between placebo communities and are observed to mostly connect cortical regions. This supports our idea that psilocybin disrupts the normal organization of the brain with the emergence of strong, topologically long-range functional connections that are not present in a normal state. 

Figure 6. Simplified visualization of the persistence homological scaffolds. The persistence homological scaffolds (a) and (b) are shown for comparison. For ease of visualization, only the links heavier than 80 (the weight at which the distributions in figure 5a bifurcate) are shown. This value is slightly smaller than the bifurcation point of the weights distributions in figure 5a. In both networks, colours represent communities obtained by modularity [49] optimization on the placebo persistence scaffold using the Louvain method [50] and are used to show the departure of the psilocybin connectivity structure from the placebo baseline. The width of the links is proportional to their weight and the size of the nodes is proportional to their strength. Note that the proportion of heavy links between communities is much higher (and very different) in the psilocybin group, suggesting greater integration. A labelled version of the two scaffolds is available as GEXF graph files as the electronic supplementary material. (Online version in colour.)

The two key results of the analysis of the homological scaffolds can therefore be summarized as follows (i) there is an increased integration between cortical regions in the psilocybin state and (ii) this integration is supported by a persistent scaffold of a set of edges that support cross modular connectivity probably as a result of the stimulation of the 5HT2A receptors in the cortex [51]. 

We can speculate on the implications of such an organization. One possible by-product of this greater communication across the whole brain is the phenomenon of synaesthesia which is often reported in conjunction with the psychedelic state. Synaesthesia is described as an inducer-concurrent pairing, where the inducer could be a grapheme or a visual stimulus that generates a secondary sensory output—like a colour for example. Drug-induced synaesthesia often leads to chain of associations, pointing to dynamic causes rather than fixed structural ones as may be the case for acquired synaesthesia [52]. Broadly consistent with this, it has been reported that subjects under the influence of psilocybin have objectively worse colour perception performance despite subjectively intensified colour experience [53]. 

To summarize, we presented a new method to analyse fully connected, weighted and signed networks and applied it to a unique fMRI dataset of subjects under the influence of mushrooms. We find that the psychedelic state is associated with a less constrained and more intercommunicative mode of brain function, which is consistent with descriptions of the nature of consciousness in the psychedelic state.

7. Methods

7.1. Dataset

A pharmacological MRI dataset of 15 healthy controls was used for a proof-of-principle test of the methodology [54]. Each subject was scanned on two separate occasions, 14 days apart. Each scan consisted of a structural MRI image (T1-weighted), followed by a 12 min eyes-close resting-state blood oxygen-level-dependent (BOLD) fMRI scan which lasted for 12 min. Placebo (10 ml saline, intravenous injection) was given on one occasion and psilocybin (2 mg dissolved in 10 ml saline) on the other. Injections were given manually by a study doctor situated within the scanning suite. Injections began exactly 6 min after the start of the 12-min scans, and continued for 60 s. 

7.1.1. Scanning parameters

The BOLD fMRI data were acquired using standard gradient-echo EPI sequences, reported in detail in reference [54]. The volume repetition time was 3000 ms, resulting in a total of 240 volumes acquired during each 12 min resting-state scan (120 pre- and 120 post-injection of placebo/psilocybin). 

7.1.2. Image pre-processing

fMRI images were corrected for subject motion within individual resting-state acquisitions, by registering all volumes of the functional data to the middle volume of the acquisition using the FMRIB linear registration motion correction tool, generating a six-dimension parameter time course [55]. Recent work demonstrates that the six parameter motion model is insufficient to correct for motion-induced artefact within functional data, instead a Volterra expansion of these parameters to form a 24 parameter model is favoured as a trade-off between artefact correction and lost degrees of freedom as a result of regressing motion away from functional time courses [56]. fMRI data were pre-processed according to standard protocols using a high-pass filter with a cut-off of 300 s.

Structural MRI images were segmented into n = 194 cortical and subcortical regions, including white matter cerebrospinal fluid (CSF) compartments, using Freesurfer (http://surfer.nmr.mgh.harvard.edu/), according to the Destrieux anatomical atlas [57]. In order to extract mean-functional time courses from the BOLD fMRI, segmented T1 images were registered to the middle volume of the motion-corrected fMRI data, using boundary-based registration [58], once in functional space mean time-courses were extracted for each of the n = 194 regions in native fMRI space. 

7.1.3. Functional connectivity

For each of the 194 regions, alongside the 24 parameter motion model time courses, partial correlations were calculated between all couples of time courses (i,j), non-neural time courses (CSF, white matter and motion) were discarded from the resulting functional connectivity matrices, resulting in a 169 region cortical/subcortical functional connectivity corrected for motion and additional non-neural signals (white matter/CSF). 

7.2. Persistent homology computation

For each subject in the two groups, we have a set of persistence diagrams relative to the persistent homology groups H_n. In this paper, we use the H₁ persistence diagrams of each group to construct the corresponding persistence probability densities for H₁ cycles. 

Filtrations were obtained from the raw partial-correlation matrices through the Python package Holes and fed to javaplex [46] via a Jython subroutine in order to extract the persistence intervals and the representative cycles. The details of the implementation can be found in reference [30], and the software is available at Holes [59].

Funding statement

G.P. and F.V. are supported by the TOPDRIM project supported by the Future and Emerging Technologies programme of the European Commission under Contract IST-318121. I.D. P.E. and F.T. are supported by a PET methodology programme grant from the Medical Research Council UK (ref no. G1100809/1). The authors acknowledge support of Amanda Feilding and the Beckley Foundation and the anonymous referees for their critical and constructive contribution to this paper.

© 2014 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

References at the Journal of the Royal Society Interface site

This is an old article (from 2011), but it offers an excellent overview of the progress that has been made in applying dynamic systems theory to cognitive development. The following is from a book chapter on Dynamic Systems Theories by Esther Thelen and Linda B. Smith:

Dynamic systems is a recent theoretical approach to the study of development. In its contemporary formulation, the theory grows directly from advances in understanding complex and nonlinear systems in physics and mathematics, but it also follows a long and rich tradition of systems thinking in biology and psychology. The term dynamic systems, in its most generic form, means systems of elements that change over time.

The authors then offer two themes that recur frequently in the history of developmental theory and in dynamic systems theory:

1. Development can only be understood as the multiple, mutual, and continuous interaction of all the levels of the developing system, from the molecular to the cultural.

2. Development can only be understood as nested processes that unfold over many timescales from milliseconds to years.

Thelen, E. & Smith, L.B. (2006). Dynamic Systems Theories. In Handbook of Child Psychology, Volume 1, Theoretical Models of Human Development, 6th Edition, William Damon (Editor), Richard M. Lerner (Volume editor), pp 258-312. 

For more general background, see the following articles:

• Complex Dynamical Systems Theory, by Professor Alicia Juarrero, author of Dynamics in action: Intentional behavior as a complex system. www.cognitive-edge.com
• Cognition as a dynamic system: Principles from embodiment, by Linda B. Smith; Developmental Review 25 (2005) 278–298.
• Development as a dynamic system, by Linda B. Smith and Esther Thelen; Trends in Cognitive Sciences, Vol.7 No.8, August 2003.

With that background, then, here is the feature article:

Full Citation:
Spencer, JP, Perone, S, and Buss, AT. (2011, Dec). Twenty years and going strong: A dynamic systems revolution in motor and cognitive development. Child Dev Perspect. 5(4): 260–266. doi:  10.1111/j.1750-8606.2011.00194.x

Twenty years and going strong: A dynamic systems revolution in motor and cognitive development

John P. Spencer, Sammy Perone, and Aaron T. Buss

Abstract

This article reviews the major contributions of dynamic systems theory in advancing thinking about development, the empirical insights the theory has generated, and the key challenges for the theory on the horizon. The first section discusses the emergence of dynamic systems theory in developmental science, the core concepts of the theory, and the resonance it has with other approaches that adopt a systems metatheory. The second section reviews the work of Esther Thelen and colleagues, who revolutionized how researchers think about the field of motor development. It also reviews recent extensions of this work to the domain of cognitive development. Here, the focus is on dynamic field theory, a formal, neurally grounded approach that has yielded novel insights into the embodied nature of cognition. The final section proposes that the key challenge on the horizon is to formally specify how interactions among multiple levels of analysis interact across multiple time scales to create developmental change.

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Twenty years is a long time for an individual scientist, but a relatively brief period for a scientific theory. This tension of time scales underlies our evaluation of dynamic systems theory (DST) and development below. In particular, we take the long view in our evaluation—to evaluate a new theoretical perspective in its infancy. From this vantage point, the differential success of individual variants of DST is normal; most critical is the evaluation en masse. In our view, DST has been extremely successful on the whole—in some cases, “revolutionary.” In the sections that follow, we explain our optimism, grounding our evaluation both in past accomplishments and in future prospects. Time will tell whether the word “revolution” reflects more than just our optimism.

What are the greatest contributions of the DST approach to development over the past 20 years?

Recent decades have seen a shift in thinking about development. Instead of characterizing what changes over development, there is a new emphasis on the how of developmental change (see Elman et al., 1997; Plumert & Spencer, 2007; Thelen & Smith, 1994). These explorations have revealed that simple notions of cause and effect are inadequate to explain development. Rather, change occurs within complex systems with many components that interact over multiple time scales, from the second-to-second unfolding of behavior to the longer time scales of learning, development, and evolution (see Christiansen & Kirby, 2003).

The introduction of DST into psychology has spurred this new way of thinking about change. Critically, DST did not emerge in isolation. Rather, it is one contributor to a broad shift in developmental science toward a systems metatheory (see Lerner, 2006) that encompasses a wide range of work from developmental systems theory (e.g., Gottlieb, 1991; Kuo, 1921; Lehrman, 1950), sociocultural and situated approaches (e.g., Baltes, 1987; Bronfrenbrenner & Ceci, 1994; Elder, 1998), ecological psychology (e.g., Adolph, 1997; Gibson & Pick, 2000; Turvey, 1990), and connectionism (e.g., Bates & Elman, 1993; Elman, 1990; Rumelhart & McClelland, 1986).

Within this family of work, confusion can arise in the distinction between two DSTs: dynamic systems theory and developmental systems theory (see Fox-Keller, 2005). These perspectives share many core principles; we can distinguish them by their histories and foci. Developmental systems theory was based on early work at the intersection of behavioral development, biology, and evolution by pioneers such as Lehrman and Kuo (see Ford & Lerner, 1992; Gottlieb, 1991; Griffiths & Gray, 1994; Kuo, 1921). This approach has focused on how development unfolds through an epigenetic process with cascading interactions across multiple levels of causation, from genes to environments (Johnston & Edwards, 2002). Dynamic systems theory, by contrast, developed from the mathematical analysis of complex physical systems (Gleick, 1998; Smith & Thelen, 2003). Consequently, this approach provides a way of mathematically specifying the concepts of systems metatheory while supporting the abstraction of these concepts into more cognitive domains (see, Spencer & Schöner, 2003). Thus, the aim of many dynamic systems approaches is to formally implement developmental processes to shed light on how behavior changes over time (Spencer et al., 2009; van Geert, 1991, 1998; van der Maas & Molenaar, 1992; van der Maas & Dolan, 2006; Warren, 2006). In this sense, dynamic systems theory and developmental systems theory share an emphasis on the step-by-step processes and multilevel interactions that shape development.

A key characteristic of systems metatheory that both approaches share is the rejection of classical dichotomies that have pervaded psychology for centuries: nature versus nurture, stability versus change, and so on (for discussion, see Spencer et al., 2009). In their place, systems metatheory takes the “organism in context” as its central unit of study, an inseparable unit in which it is impossible to isolate the behavioral and developmental state of the organism from external influences. Furthermore, behavior and development are emergent properties of system-wide interactions that can create something new from the many interacting components in the system (see Munakata & McClelland, 2003; Spencer & Perone, 2008; Thelen, 1992).

It is often helpful to consider historical change through the lens of contrast. According to Lerner (2006), systems metatheory has supplanted other influential metatheories, but which ones? To answer this, we conducted a survey of the fourth through sixth editions of the Handbook of Child Psychology: Theoretical Models of Human Development. These editions span more than 20 years in developmental psychology (from 1983 to 2006). Although this book is just one indication of how the field is changing, our survey revealed that four theoretical viewpoints have disappeared from the Handbook over time: nativism, cognitive and information processing, symbolic approaches, and Piaget’s theory. Of course, scholars still actively pursue all of these perspectives. It is notable, however, that they have something in common—an attempt to carve up behavior and development into parts (broad parts like nature versus nurture; specific parts like cognitive modules; or temporal partitions such as stages of processing or stages of development). Systems metatheory rejects this inherent partitioning.

Within the broad class of theories that make up systems metatheory, a central challenge is to examine what each perspective contributes. DST has had a particularly strong influence, bringing several critical concepts into mainstream developmental science. The first concept is that systems are self-organizing. Complex physical systems (such as the human child) comprise many interacting elements that span multiple levels from the molecular (for example, genes) to the neural to the behavioral to the social. Within the DS perspective, organization and structure come “for free” from the nonlinear and time-dependent interactions that emerge from this multilevel and high-dimensional mix (e.g., Prigogine & Nicolis, 1971). Thus, there is no need to build pattern into the system ahead of time because the system has an intrinsic tendency to create pattern. This gives physical systems a creative spark that we contend is central to the very notion of development—development is fundamentally about the emergence of something qualitatively new that was not there before.

Of course, the notion of qualitative change over development is not unique to DST (see, e.g., Gottlieb, 1991; Munakata & McClelland, 2003; Piaget, 1954; von Bertalannfy, 1950). But we contend that DST clarifies the distinction between quantitative and qualitative change (see Spencer & Perone, 2008; van Geert, 1998). According to DST, qualitative change occurs when there is a change in the layout of attractors, or special “habitual” states around which behavior coheres: when a new attractor appears, there is a qualitative change in the system. Although qualitative change can be special—it can reflect the emergence of something new that was not there before—it is not in opposition to quantitative change. Rather, quantitative changes in one aspect of the system can give rise to qualitatively new behaviors. This is one example where a classic dichotomy withers away in the face of a formal, systems viewpoint.

One of the historical challenges in defining qualitative and quantitative change is that changes occur over multiple time scales. For instance, a skilled infant can go from a crawling posture to a walking posture within a matter of seconds, but how is this “on-the-fly” transition related to the more gradual shift in the likelihood of crawling versus walking that unfolds across months in development (see Adolph, 1997)? In particular, it can be difficult to specify when the infant “has” walking, why walking comes and goes in different situations, and what drives this change over time. Again, DST has a unique perspective on these challenges. There is no competence/performance distinction in DST (see Thelen & Smith, 1994); rather, the emphasis is on how people assemble behavior in the moment in context. But because DST integrates processes over multiple time scales, it can explain why behavioral attractors—which form in real time—can emerge and become more likely over the longer times of learning and development (for discussion, see Spencer & Perone, 2008).

Another issue that researchers have directly examined using DST is the concept of “soft assembly.” According to this concept, behavior is always assembled from multiple interacting components that can be freely combined from moment to moment on the basis of the context, task, and developmental history of the organism. Esther Thelen talked about this as a form of improvisation in which components freely interact and assemble themselves in new, inventive ways (like musicians playing jazz). This gives behavior an intrinsic sense of exploration and flexibility, issues that Goldfield and colleagues (Goldfield, Kay, & Warren, 1993) have examined formally.

This characterization of behavior and development has led to an additional insight about the embodied nature of cognition. In particular, if behavior is softly assembled from many components in the moment, then the brain is not the “controller” of behavior. Rather, it is necessary to understand how the brain capitalizes on the dynamics of the body and how the body informs the brain in the construction of behavior. This has led to an emphasis on embodied cognitive dynamics (see Schöner, 2009; Spencer, Perone, & Johnson, 2009), that is, to a view of cognition in which brain and body are in continual dialogue from second to second.

A final strength of the DS approach is that it has generated a host of productive tools, including rich empirical programs (Samuelson & Horst, 2008; Smith, Thelen, Titzer, & McLin, 1999; Thelen & Ulrich, 1991; van der Maas & Dolan, 2006), formal modeling tools that can capture and quantify the emergence and construction of behavior over development (such as growth models, oscillator models, dynamic neural field models), and statistical tools that can describe the patterns of behavior observed over development (Lewis, Lamey, & Douglas, 1999; Molenaar, Boomsma, & Dolan, 1993; van der Maas & Dolan, 2006). These tools have enabled researchers to move beyond the characterization of what changes over development toward a deeper understanding of how these changes occur.

What is your critical evaluation of the progress of DS-inspired empirical research?

DST has led to a revolutionary change in how people think about motor development, and this type of revolutionary thinking is starting to take hold in cognitive development as well. We review the basis for this optimistic assessment below. Note that we focus on motor and cognitive development because these are our “home” domains. We will leave it to the other authors in this issue to evaluate other fields.

The dominant view of motor development for much of the 20th century was that the development of action occurred in a series of relatively fixed motor milestones. The emphasis was on normative development, the concept of motor programs that controlled action, and a sequence of milestones that was largely under genetic or biological control (for review, see Adolph & Berger, 2006). The landscape has shifted dramatically in the last 20 years, thanks in large part to the work of Esther Thelen (as well as other systems thinkers, most notably, Gibson, 1988; see Adolph & Berger, 2006). Today the field views motor development as emergent and exploratory with a new emphasis on individual development in context. Although this revolution in thinking was spurred by dynamic systems concepts, it was also driven forward by a wealth of empirical research.

For instance, Esther Thelen conducted a now-classic set of studies investigating the early disappearance of the stepping reflex. Thelen’s early work on stepping revealed that the coordination patterns that underlie stepping and kicking were strikingly similar. The puzzle was that newborn stepping disappeared within the first three months, whereas kicking continued and increased in frequency. To explain the disappearance of stepping, several researchers had proposed that maturing cortical centers inhibit the primitive stepping reflex or that stepping was phylogenetically programmed to disappear (e.g., Andre-Thomas & Autgaerden, 1966).

To probe the mystery of the disappearing steps, Thelen conducted a longitudinal study that focused on the detailed development of individual infants. Thelen, Fisher, and Ridley-Johnson (1984) found a clue in the fact that chubby babies and those who gained weight fastest were the first to stop stepping. This led to the hypothesis that it requires more strength for young infants to lift their legs when upright (in a stepping position) than when lying down (in a kicking position). To test this idea, Thelen and colleagues conducted two ingenious studies. In one, they placed small leg weights on two-month-old babies, similar in amount to the weight they would gain in the ensuing month. This significantly reduced stepping. In the other, they submerged older infants whose stepping had begun to wane in water up to chest levels. Robust stepping now reappeared. These data demonstrated that traditional explanations of neural maturation and innate capacities were insufficient to explain the emergence of new patterns and the flexibility of motor behavior.

Since this seminal work, Thelen and her colleagues have intensively examined the development of alternating leg movements (Thelen & Ulrich, 1991), the emergence of crawling (Adolph, Vereijken, & Denny, 1988), the emergence of walking (e.g., Adolph, 1997; Thelen & Ulrich, 1991), and the development of reaching (Corbetta, Thelen, & Johnson, 2000; Thelen, Corbetta & Spencer, 1996; Thelen et al., 1993). In all cases, these researchers have shown that new action patterns emerge in the moment from the self-organization of multiple components. The stepping studies elegantly illustrated this, showing how multiple factors cohere in a moment in time to create or hinder leg movements. And, further, these studies illustrate how changes in the components of the motor system over the longer time scale of development interact with real-time behavior.

In summary, DS concepts have led to a radical change in the conceptualization of motor development. But what about cognition? There have been a variety of DS approaches to cognitive development. For instance, researchers have used the concepts of DST to study early word learning (e.g., Samuelson, Schutte & Horst, 2008), language development (e.g., van Geert, 1991), the development of intelligence (e.g., Fischer & Bidell, 1998), and conceptual development and conservation behavior (e.g., van der Maas & Molenaar, 1992). A survey of these different approaches is beyond the scope of this article (see Spencer, Thomas & McClelland, 2009). We focus, instead, on one particular flavor of cognitive dynamics—dynamic field theory (DFT)—that emerged out of the motor approach that Thelen and colleagues pioneered (for discussion, see Spencer & Schöner, 2003).

The starting point for the DF approach was to consider several facts about neural systems. Neural systems are noisy, densely interconnected, and time-dependent; they pass continuous, graded, and metric information to one another; and they are continuously coupled via both short-range and long-range connections (Braitenberg & Schüz, 1991; Constantinidis & Steinmetz, 1996; Edelman, 1987; Rao, Rainer, & Miller, 1997). These neural facts raise deep theoretical challenges. How can a collection of neurons “represent” information amidst near-constant bombardment by other neural signals (Skarda & Freeman, 1987), and how do neurons, in concert with the body, generate stable, reliable behavior? To address these challenges, the DF framework emphasizes stable patterns of neural interaction at the level of population dynamics (see also Spivey, 2007). That is, rather than building networks that start from a set of spiking neurons, we have chosen to focus on the emergent product of the dynamics at the neural level—attractors at the level of the neural population.

The first steps toward a neurally grounded theory of cognitive development came from Thelen and Smith’s studies of the Piagetian A-not-B error (see Smith et al., 1999; Thelen, Schöner, Scheier, & Smith, 2001). This early work formalized a DFT of infant perseverative reaching, arguably the most comprehensive theory of infants’ performance in the Piagetian A-not-B task (Clearfield, Dineva, Smith, Diedrich, & Thelen, 2009; Smith et al., 1999; Spencer, Dineva, & Smith, 2009; Thelen et al., 2001). DFT has generated a host of novel behavioral predictions, and it explains how perseverative reaching arises as a function of (1) the infants’ history of prior reaches to A (Smith et al., 1999), (2) a bodily feel and visual perspective of reaching to A (Smith et al., 1999), (3) the distinctiveness of the targets and perceptual cues in the task space (Clearfield et al, 2009), (4) the delay between the cueing and reaching events (Diamond, 1985), (5) the number of targets in the task space, (6) the characteristics of the hidden object (and whether there is any hidden object whatsoever; see Smith et al., 1999), and (7) changes in infants’ reaching skill and working memory abilities over development (Clearfield, Diedrich, Smith, & Thelen, 2006; for related studies with older children, see Schutte, Spencer, & Schöner, 2003; Spencer, Smith, & Thelen, 2001).

More recently, we have extended the DF approach to a host of other topics in cognitive development. These topics include the processes that underlie habituation in infancy (Perone & Spencer, 2009; Schöner & Thelen, 2006), the control of autonomous robots and the development of exploratory motor behavior (Dineva, Faubel, Sandamirskaya, Spencer, & Schöner, 2008; Steinhage & Schöner, 1998), the development of visuospatial cognition (Simmering, Spencer, & Schutte, 2008), the processes that underlie visual working memory and the development of change detection abilities (Simmering, 2008), the processes that underlie early word learning behaviors (Samuelson et al., 2008), and the development of executive function (Buss & Spencer, 2008). This broad coverage of multiple aspects of development with the same theoretical framework underlies our optimism that the concepts of DST can have a revolutionary impact on cognitive development just as they had in motor development. Time will tell.

What are the challenges and necessary directions for the next 20 years?

A major accomplishment of DS approaches has been to move beyond the conceptual level to establish a tight link between formal theory and empirical research, leading to a greater understanding of the processes that underlie developmental change. Although there have been many successful applications of DS concepts, significant challenges remain. For instance, soft assembly makes it difficult to define the components of the “system” or subsystem under study. Similarly, the multiply determined nature of dynamic systems makes it difficult to identify “cause” because different factors can lead to different outcomes depending on the context and history of the individual.

In addition to these conceptual challenges, researchers in the next 20 years will have to build theories that formally connect processes across multiple levels of analysis. Figure 1 shows the nested, interacting systems that contribute to the organization of behavioral development from genetic to social levels. Each of these levels and the interactions among them are highly complex; thus, understanding how development happens as these levels interact over time will require formal theories that specify the nature of those interactions (for related ideas, see Gottlieb, 1991; Johnston & Edwards, 2002; Johnston & Lickliter, 2009). To date, multiple approaches have attempted to understand behavioral development at the different levels shown in Figure 1, but these efforts have not been tightly integrated across levels.

Figure 1
A central challenge on the horizon for dynamic systems theory is to formally integrate across reciprocally interacting levels from genetic to social and to integrate these levels across multiple time scales from in-the-moment interactions to learning ...

In addition to the challenge of formally connecting processes at multiple levels, it will be important to tackle a second challenge: integrating time scales. Within DST, nested, interacting systems come together to create developmental change as those systems interact through time. In particular, the multiple systems in Figure 1 produce a coherent behavioral system in the moment, and those in-the-moment behaviors have consequences that carry forward across the longer time scales of learning and development (see Smith & Thelen, 2003 for a discussion). Our research using DFT has effectively integrated real-time behavior with changes over learning (see, e.g., Lipinski, Spencer, & Samuelson, 2010; Schöner & Thelen, 2006; Thelen et al., 2001). Other approaches have examined these time scales as well (e.g., French, Mareschal, Mermillod, & Quinn, 2004; McMurray, Horst, Toscano, & Samuelson, 2009), but the longer time scales of development have been more elusive (but see Simmering et al., 2008; Schutte et al., 2003; Schutte & Spencer, 2009, for efforts in this direction).

One difficulty in this regard is that it is often hard to get a clear sense of developmental change empirically. Adolph, Robinson, Young, and Gill-Alvarez (2008), for example, showed how different views of developmental change are created simply by sampling rate of change. But developmental scientists face theoretical challenges in terms of integrating behavior over very long time scales. Spencer and Perone (2008) have taken one step toward addressing this issue by probing change in neural dynamics over relatively long time scales. In particular, they showed that the gradual accumulation of neural excitation in a simple, dynamic neural system created qualitative changes in the state in which the system operated. That is, as the system gradually accumulated a history, the system was biased to settle into new neural attractor states. We believe that it is possible to generalize from these concepts, and we are currently working to scale this demonstration up guided by a rich, longitudinal empirical data set (see Perone & Spencer, 2009).

Integrating dynamics across multiple systems and time scales is a daunting task. Even more challenging is to achieve this integration at the level of the individual child in context. But this is a critically important goal because it opens the door for examining atypical development. If we understand the complex dynamics through which systems interact over time at the level of individual children, we will be well positioned to create individual interventions that help steer the child toward positive developmental outcomes. That would indeed be revolutionary. Perhaps in the next 20 years we will realize this vision.

Acknowledgments

Preparation of this manuscript was supported by NIH RO1MH62480 awarded to John P. Spencer.

References available at the NHI/NCBI site.