Progress on the strong Eshelby's conjecture and extremal structures for the elastic moment tensor
Progress on the strong Eshelby's conjecture and extremal structures for the elastic moment tensor
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DOI：
10.1016/j.matpur.2010.01.003
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
H. Ammari;Yves Capdeboscq;Hyeonbae Kang;Hyundae Lee;G. Milton;Habib Zribi
中科院分区：
文献类型：
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作者：
H. Ammari;Yves Capdeboscq;Hyeonbae Kang;Hyundae Lee;G. Milton;Habib Zribi
在休息时的BOLD fMRI信号中观察到的时空组织低频波动（< 0.1 Hz）表明存在潜在的网络动力学，这些网络动力学是从内在的大脑过程中自发出现的。此外，不同的解剖区域或功能连接（FC）之间的显着相关性，导致了几个广泛分布的静息态网络（RSN）的识别。这种缓慢的动力学似乎是高度结构化的解剖连接，但其背后的机制及其与神经活动的关系，特别是在伽马频率范围内，仍然在很大程度上是未知的。事实上，神经元活动的直接测量已经揭示了类似的大规模相关性，特别是在局部场电位伽马频率范围振荡的缓慢功率波动中。为了解决这些问题，我们研究了人类大脑神经活动的大规模模型中的神经动力学。该模型的一个关键组成部分是一个结构性大脑网络，该网络由经验推导的长距离大脑连接以及相应的传导延迟定义。假设在伽马频率范围内自发振荡的神经种群被放置在每个网络节点处。当这些振荡单元集成在网络中时，它们表现为弱耦合振荡器。节点之间的时滞相互作用由相振荡器的仓本模型描述，相振荡器是一种基于生物学的耦合振荡系统模型。对于一个现实的设置轴突传导速度，我们表明，时间延迟的网络相互作用导致出现缓慢的神经活动波动，其模式与经验测量的FC显着相关。的模拟FC与经验测量的FC的最佳协议被发现的一组参数，其中节点的子集往往同步，但网络不是全局同步。在这样的集群内，节点之间的模拟BOLD信号被发现是相关的，实例化经验观察到的RSN。如实验研究所述，在集群之间，观察到正相关和负相关的模式。这些结果被认为是强大的生物合理的模型参数范围。总之，我们的模型表明，休息状态的神经活动可以从局部神经动力学和大脑的大规模结构之间的相互作用起源。
Spatio-temporally organized low-frequency fluctuations (< 0.1 Hz), observed in BOLD fMRI signal during rest, suggest the existence of underlying network dynamics that emerge spontaneously from intrinsic brain processes. Furthermore, significant correlations between distinct anatomical regions—or functional connectivity (FC)—have led to the identification of several widely distributed resting-state networks (RSNs). This slow dynamics seems to be highly structured by anatomical connectivity but the mechanism behind it and its relationship with neural activity, particularly in the gamma frequency range, remains largely unknown. Indeed, direct measurements of neuronal activity have revealed similar large-scale correlations, particularly in slow power fluctuations of local field potential gamma frequency range oscillations. To address these questions, we investigated neural dynamics in a large-scale model of the human brain's neural activity. A key ingredient of the model was a structural brain network defined by empirically derived long-range brain connectivity together with the corresponding conduction delays. A neural population, assumed to spontaneously oscillate in the gamma frequency range, was placed at each network node. When these oscillatory units are integrated in the network, they behave as weakly coupled oscillators. The time-delayed interaction between nodes is described by the Kuramoto model of phase oscillators, a biologically-based model of coupled oscillatory systems. For a realistic setting of axonal conduction speed, we show that time-delayed network interaction leads to the emergence of slow neural activity fluctuations, whose patterns correlate significantly with the empirically measured FC. The best agreement of the simulated FC with the empirically measured FC is found for a set of parameters where subsets of nodes tend to synchronize although the network is not globally synchronized. Inside such clusters, the simulated BOLD signal between nodes is found to be correlated, instantiating the empirically observed RSNs. Between clusters, patterns of positive and negative correlations are observed, as described in experimental studies. These results are found to be robust with respect to a biologically plausible range of model parameters. In conclusion, our model suggests how resting-state neural activity can originate from the interplay between the local neural dynamics and the large-scale structure of the brain.