Multiscale communication in cortical-cortical networks

Signals in the brain networks in more than one topology scale an.Area can exchange information through the local circuit,Including direct neighbors and has similar function area,Or through a global circuit exchange information,Including far neighbor with different functions.在这里,We looked at the cortex-How the cortical network through parametric adjustment signal transmission to the range of adjustment in the white matter connecting local and global communication.我们发现,Brain regions on preferred communication scale is different.By studying the area of the brain in multiple scales tend to communicate with neighbors,We naturally reveals the diversity of their functions,：Single-mode state area showed a preference for local communication,The multimodal area showed a preference for global communication.我们表明,These preferences for specific area and scale structure-功能耦合.即,Single-mode state the function of the regional connection in small scale circuits of single synaptic communication,And across the mode of connection in the large scale circuit of synaptic communication more.总之,目前的研究结果表明,Communication preferences between the cerebral cortex is highly heterogeneous,structure is formed-Regional differences in functional coupling.

1.简介
The brain is a network of anatomical connections of neurons.This complex to connect to the Internet as a communication network,Promote signals between brain regions.Groups of neurons with similar functions of interconnected trend,Creates a nested hierarchy,Made up of more and more multifunctional circuits,across multiple topological scales.

The research of network communication will usually signal event concept into a global process,To avoid the possibility of communication occurs in multiple topology scales.也就是说,Areas may include direct neighbors and the small compact area with similar functions to exchange information on the road,Or in include neighbors far more widely with different functions to exchange information on the road.An intuitive example is the world's air transport network.Allow the in transit between domestic regions or the purpose of domestic flights and allow the international airport transit between the different aims of international flights.The importance of the airport in the network will in turn depends on the type of flight.例如,Denver and Philadelphia airport flights to the United States is very important,而纽约、Los Angeles or Chicago airport for international flights is very important.换句话说,A node in the network topology effect depends on the scale it is evaluated.

出于同样的原因,A single brain regions may be in multiple topological dimension characteristic of the interaction and communication mode.The modular structure of the brain,Connected to the high degree of the core region of echo,Created the information can be isolated to the height of the local cluster related areas of the brain,or conditions of global integration.例如,A region may promote and adjacent area information integration,But the lack of radio signals to the whole world in the whole brain ability.换句话说,An area to communication or interaction with functional diversity should depend on the scale.

Recently in the connection body structure and function are the prominent found on the coupling is region specific,The sensory cortex is highly related to structural and functional connectivity,Cross-modal cortical correlations were weak.A prominent assumption is that,Across the model area connection less predictable,Because these areas have a large number of parallel and reentrant path,Characteristics of microstructure and macrostructure connection cannot be directly capture.We are here to directly test another hypothesis is that,Multi-scale communication structure connection support.因此,Cross modal cortex itself does not exist-功能解耦.相反,结构-Functional coupling exists in all areas,But in different areas in a specific scale way.

在这里,We study how the communication between brain regions in multiple scales.for a given area,We systematically defines the increasing size of the local neighborhood.然后,How we track a single brain region of centricity as detection area increases with the size of the change.我们发现,Centricity in different scales are different,These changes are formed by functional diversity.We proved unimodal-Cross modal function gradient naturally emerged from the individual preferences of the scale of the region,For example, the single mode state area in the center of the local is,The cross modal area in the centre of global.最后,We prove the structure-Functional coupling is scale-specific,这样,Single-mode state the function of the regional connection profile can be achieved by small scale structure in the area of communication to better capture the,And across the functional connectivity in model area can be through the communication of large structure in the community to better capture.

2.结果
The results are organized as follows.We through parametric adjustment range of signal transmission in the white matter connecting to describe multi-scale neighborhood.随后,We use regional tightness centricity weighted method of measurement,In multiple scales the tendency of the research area of the brain communicate with adjacent area.最后,We consider the similarity of two area embedded how to forecast their functional connectivity.An overview of the different measurements is shown in FigS1.

数据源包括(See Materials and methods for specific steps):Structural connectivity.67The structure of the healthy participants connect body is generated(来源:Lausanne University Hospital).Compose a using diffusion and deterministic flow weighted network wiring harness imaging reconstruction of individual.

Functional connectivity.Use the resting state functional magnetic resonance imaging (fmri)(rs-fMRI)to the same individualN = 67functional connectivity assessment.

通过1000A layer node network partition analysis.Then use a coarser resolution(114、219和448个节点)and independently collected datasets(HCP;N = 327)Repeat these data.(有关Validation数据集的更多信息,See Materials and methods).

2.1 Multiscale regional centrality

We first describe the structure of each local neighborhood within the body,Use an unbiased random walk.具体来说,We use the transition probability of the random walk in a single brain region planting,to delineate its local neighborhood(See Methods for more details).The transition probability is in 100个时间尺度t上测量.图1aBuckle straps at the rear are shown (红色)、Upper parietal lobe (蓝色)、transverse temporal(绿色)和岛叶(紫色)Cortex of the node of the effect of the change of the scale of the random walk.随着时间的增加,The random walk takes longer,The size of the probe neighbor becomes larger,This makes we can consider in the wider part of the network communication.

图1 Multiscale regional centrality
for each time scale,We calculated the adjacent of each area of the brain in mindCmulti.图1b显示了随着t增长的Cmulti区域值,The mean of each subject.In order to facilitate the comparison between the scale,CmultiScore relative to the distribution of the scores of each scale standardization.Four samples of the center of the brain regions trajectory was highlighted,Other areas are shown in grey.A single brain region relative centrality changes with the increase of the scale is quite large,例如,according to the size of the surrounding area,Some areas are closer to the center,And some areas are not so close to the center.图1cShows in four different topology scales,The mean of each area of the brain centricity.在局部,We observed the distribution in the whole brain the height of the central area of the brain cluster;These clusters gradually evolved into a larger global scale system.

2.2 Multiscale functional diversity

In the topological characteristics of homogeneous network nodes with similar,Node local centricity expectations with its global centricity similar.然而,在异构网络中,Local properties do not necessarily reflect global properties.例如,A node with a small amount of node has strong connectivity,And the other a node with a large number of nodes with medium but different connectivity.The former is more important in a local sense,While the latter is more important in the global sense.Because the two nodes each functional diversity,They're different contribution to the global communications,This is reflected in their different close to track.

We use an artificial network with the predefined modular architecture to illustrate this concept.n=2000Nodes in the network, there are two same size of the community,Each community is further divided into two sub(The method of the parameter refer to build network).使用ForceAtlas2Two-dimensional embedding algorithm to generate network as shown in figure2a所示.Highlighted fromi)到iv)的四个节点.In order to understand their contribution to the global communication,Not only to measure the strength of their interactions with direct neighbor(即度),And to quantify their relations of diversity.in a modular network,Node connection diversity can use participation coefficients to represent.节点(ii)、节点(iv)participation coefficient is high,The priority node is connected with outside their own communities,而节点(i)、节点(iii)participation coefficient is small(图2b),The priority connection to a node within their own communities.由于节点(i)Priority connection to a node form within their own communities,Its global centricity is less than the local centricity,但由于节点(iv)Priority and outside their community nodes to form connections,Its global centricity is greater than the local centricity.The same reasoning applies to nodes(ii)和(iii).These changes caused by the diversity of the node connection centricity can use them closely track the slope to quantitative.In a predefined community modular network,In the slope of node participation coefficient is larger,With negative slope coefficient of node in smaller(图2d).有趣的是,The slope can be measured to any value,The diversity of highlight on the scale of the selected node connection.The slope is associated with local diversity measure,如聚类系数(负相关),When the calculated value is small,The slope is associated with a growing number of global diversity measure(图2e).

图2 Approach trajectories in a random block model

在大脑中,A versatile area is a beneficial to communicate across different functional modules of topology position.因此,Different areas have better support global integration properties.In order to recognition of different brain regions in different scales,We calculated the local slope near the center of a single node.图3aShown at the rear buckle、Upper parietal lobe、Transverse temporal cortex and island four nodes track(来自图1a、b),Color according to its slope.Highly diversified areas of the brain has a positive slope(红色),With low diversity in areas of the brain has a negative slope(蓝色).图3bShows how the slope of the terrain distribution in the brain change in different scales.重要的是,The slope considering the relationship between the nodes in the neighborhoods of any size of diversity,Not like participation coefficient measurement,The latter only measure the diversity of its direct connection.

图3 Multiscale functional diversity

In order to show the changes of local proxemics how to highlight the area of the brain functional diversity in multiple scales,我们计算了7个度量,Capture a node connection diversity in different topologies scales.These metrics are node strength,Clustering coefficient and the participation coefficients of modularization is divided into16,12,9,6和4community network.图3cShows the measurement and evaluation of across the time scale of local gradient correlation between.According to their associated with close to slope largest scale,Measurements are sorted from top to bottom.local measure,such as strength and clustering coefficient,Tend to be in the lower scale biggest related.在较大的t值时,Diversity index in a given area between modules connected tend to close degree coefficient of the participation of the local changes related to.As the block resolution gradually decreases,从16groups reduced to4个群落,当t的值较大时,The best correlation.总之,这些结果表明,Node centricity change is mediated by its functional diversity.有趣的是,The current method in the absence of predefined division highlights the function diversity,Make it a more traditional diversity statistics(such as participation factor)supplementary measure,Without the need for a clearly defined or assume that hard division.

2.3 optimal communication scale

Communication between each area of the brain how much is the best measure of?图4aShows the structure connecting the individual brain areas in central peak(t opti)的尺度(t).这些t optiValues ​​are the mean of each subject.The color of the cooler said the priority for local communication area,And the color of the warmer said the priority for global communication area.一般来说,We observed in the primary sensory area(Peripheral calcaroid cortex、颞横回、中央后回)and in the marginal cortex,Local communication is preferred;相反,We observed associative cortex(Including the dorsolateral prefrontal cortex and parietal lobe cortex)Preference for global communication.图4b给出了7The optimum distribution of the eigen function network.图4cIn the same way is shown byvon EconomoAtlas of seven kinds of cellular structure of the definition of classt opti值分布.我们发现,on a local scale,With single-mode sensory and motor function and integration of related terms and central value distribution of correlation peak,And terms associated with higher-order cognitive function in the correlation peak on a global scale(图4d).

图4 optimal communication scale

2.4 Multiscale structure-function coupling

接下来,We will study the multi-scale connection mode how to affect the structure-功能耦合.The function of the connection between a pair of brain regions usually through their respectivefMRI BOLDTime series signal measured in terms of the correlation between.Neural activity of coherent wave is considered to be caused by the interaction of potential connection body structure.People put forward various pairs of measurement,From the structure of the connection between brain regions to predict function connection,Including structural connection strength、路径长度、搜索信息、Path transitivity and communicability.

在这里,We assessed across multiple dimensions of structure-功能耦合.Different by measurementtValue defined by the similarity between the two brain regions adjacent area,We asked around them on the dynamic process of how similar.We assume that have overlapping neighborhood node(i.e. larger neighborhood similarity)Will belong to different neighborhood node shows a more functional coupling.因此,对于每一个t值(图5a),We by calculating their transition probability vector to quantify each pair of cosine similarity between structure connecting the brain area neighborhood similarity.

图5 多尺度结构-功能耦合

重要的是,The current framework does not assume the structure of the whole brain-The functional relationship is unified,相反,It opens up a possibility,Function of the interaction in different areas of the brain in different size.为了研究这种可能性,We calculated the similarity profile and individual brain regions nearby the spearman correlation between positive function connection profile.On average we each value in a single connection body correlation,And make sure each brain region of maximum correlation(ρmax)(图5b).我们发现,Regional correlation of the best scale biggest significant differences between different brain regions(图5c).

as discussed in the previous section,The best communication measure of brain regions along the single-mode condition-Multimodal axis changes.因此,我们假设,Best to capture a single zone structure-Scale of functional coupling,The neighborhood similarity and functional connectivity of the correlation between the biggest scale,Likewise along a single modality-Multimodal axis changes.图5dBounded domain correlation similarity and functional connectivity's biggesttTopographic distribution of values.我们看到,The model is outlined assumes that the single mode of state-Multimodal Hierarchy,这样,Single-mode state functional connectivity distribution more easily captured by a smaller adjacent area,And the function of the multimodal region connectivity distribution more easily captured by a wider range of adjacent area.The optimal value of functional connectivity with the first(主要)Significant correlation between gradient highlights this with single-mode state-Relationships across modal hierarchies(图5e, f).

2.5 Sensitivity and repeatability

We ended up asking,Whether these results are sensitive to different treatment choice,Whether they can use different partitions copy,And whether or not they can be obtained in a separate data set copy.在本报告中,We use unbiased random walk describes a local topological neighborhood.In order to ensure that the observed result does not depend on us for that particular dynamic process of selection,We use personalizationPageRank向量(i.e. a restarted random walk)and the normalized Laplacian matrix(the diffusion process)重复分析.These optional also allows the dynamic process of multi-scale study,Parameters can be tuned,to limit its length(See Methods for more details).We also repeated use of the key network analysis,以确保logConvert simplified density unbiased results,We copy all experiment with simplified density ratio value in0和1之间的权重(而不是他们的log-transform)结构连接.In order to ensure that the result is not dependent on the zoning resolution,We use the same data set to copy all the experiment,But split the dataset into 114、219或448cerebral cortex area.最后,In order to ensure that the results in the independent access to the data set can be copied,We are validating the dataset(HCP, N=201)Our analysis was repeated in ,This dataset is based on800Division of the functional partition of nodes is.我们得到了相似的结果,All sensitivity and replication experiments.

3.讨论

在本报告中,We studied how the communication between the area between the area of the brain in multiple topology scales happened.By tracking an area within the extended neighborhood tightness trajectory,We identified from a more localized communication transition to a more global topological properties of.我们发现,Diversity of smaller single-mode state region showed a preference for local communication,And multimodal diversity larger area showed a preference for global communication.These preferences of small-scale circuits single-mode state of the local communication occurring in the area of functional connectivity and large-scale multiple synaptic circuits of the global communication occurring in the specificity of the scale of the modal function of regional connectivity structure-功能关系.

总之,目前的研究结果表明,Only consider the global level of communication may be the function of the fuzzy brain network related characteristics.Through the study of regional scale across multiple topology embedded,We reveal a forming structure-Scope of function relationship of continuous communication preferences.通过这样做,We will in the long existing in neuroscience concept,such as integration and isolation、Functional hierarchy and connectivity diversity,Conceptually linked to a step.

参考文献：Multiscale communication in cortico-cortical networks