The PLI performed at least as well as the PC in detecting true changes in synchronization in model and real data but, at the same token and like-wise the IC, it was much less affected by the influence of common sources and active reference electrodes.

Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others.

In this study we examined changes in the large-scale structure of resting-state brain networks in patients with Alzheimer's disease compared with non-demented controls, using concepts from graph theory. Magneto-encephalograms (MEG) were recorded in 18 Alzheimer's disease patients and 18 non-demented control subjects in a no-task, eyes-closed condition. For the main frequency bands, synchronization between all pairs of MEG channels was assessed using a phase lag index (PLI, a synchronization measure insensitive to volume conduction). PLI-weighted connectivity networks were calculated, and characterized by a mean clustering coefficient and path length. Alzheimer's disease patients showed a decrease of mean PLI in the lower alpha and beta band. In the lower alpha band, the clustering coefficient and path length were both decreased in Alzheimer's disease patients. Network changes in the lower alpha band were better explained by a 'Targeted Attack' model than by a 'Random Failure' model. Thus, Alzheimer's disease patients display a loss of resting-state functional connectivity in lower alpha and beta bands even when a measure insensitive to volume conduction effects is used. Moreover, the large-scale structure of lower alpha band functional networks in Alzheimer's disease is more random. The modelling results suggest that highly connected neural network 'hubs' may be especially at risk in Alzheimer's disease.

No abstract

Understanding the fundamental mechanisms governing fluctuating oscillations in large-scale cortical circuits is a crucial prelude to a proper knowledge of their role in both adaptive and pathological cortical processes. Neuroscience research in this area has much to gain from understanding the Kuramoto model, a mathematical model that speaks to the very nature of coupled oscillating processes, and which has elucidated the core mechanisms of a range of biological and physical phenomena. In this paper, we provide a brief introduction to the Kuramoto model in its original, rather abstract, form and then focus on modifications that increase its neurobiological plausibility by incorporating topological properties of local cortical connectivity. The extended model elicits elaborate spatial patterns of synchronous oscillations that exhibit persistent dynamical instabilities reminiscent of cortical activity. We review how the Kuramoto model may be recast from an ordinary differential equation to a population level description using the nonlinear Fokker–Planck equation. We argue that such formulations are able to provide a mechanistic and unifying explanation of oscillatory phenomena in the human cortex, such as fluctuating beta oscillations, and their relationship to basic computational processes including multistability, criticality, and information capacity.

Low back pain (LBP) is often accompanied by changes in gait, such as a decreased (preferred) walking velocity. Previous studies have shown that LBP diminishes the normal velocity-induced transverse counter-rotation between thorax and pelvis, and that it globally affects mean erector spinae (ES) activity. The exact nature and causation of these effects, however, are not well understood. The aim of the present study was to examine in detail the effect of walking velocity on global trunk coordination and ES activity as well as their variability to gain further insights into the effects of non-specific LBP on gait. The study included 19 individuals with non-specific LBP and 14 healthy controls. Gait kinematics and ES activity were recorded during treadmill walking at (1) a self-selected (comfortable) velocity, and (2) sequentially increased velocities from 1.4 up to maximally 7.0 km/h. Pain intensity, fear of movement and disability were measured before the experiment. The angular movements of thorax, lumbar and pelvis were recorded in three dimensions. ES activity was recorded with pairs of surface electrodes. Trunk-pelvis coordination and mean amplitude of ES activity were analyzed. In addition, invariant and variant properties of trunk kinematics and ES activity were studied using principal component analysis (PCA). Comfortable walking velocity was significantly lower in the LBP participants. In the transverse plane, the normal velocity-induced change in pelvis-thorax coordination from more in-phase to more antiphase was diminished in the LBP participants, while lumbar and pelvis rotations were more in-phase compared to the control group. In the frontal plane, intersegmental timing was more variable in the LBP than in the control participants, with additional irregular movements of the thorax. Rotational amplitudes were not significantly different between the LBP and control participants. In the LBP participants, the pattern of ES activity was affected in terms of increased (residual) variability, timing deficits, amplitude modifications and frequency changes. The gait of the LBP participants was characterized by a more rigid and less variable kinematic coordination in the transverse plane, and a less tight and more variable coordination in the frontal plane, accompanied by poorly coordinated activity of the lumbar ES. Pain intensity, fear of movement and disability were all unrelated to the observed changes in coordination, suggesting that the observed changes in trunk coordination and ES activ- Eur Spine J (2006) 15: 23-40

These results confirm in an independent sample that stroke patients with mild to moderate initial impairments show an almost fixed proportional upper extremity motor recovery. Patients who will most likely not achieve the predicted amount of recovery were identified using clinical determinants measured within 72 hours poststroke.

In a recent study, De Haart et al. (Arch Phys Med Rehabil 85:886-895, 2004) investigated the recovery of balance in stroke patients using traditional analyses of center-of-pressure (COP) trajectories to assess the effects of health status, rehabilitation, and task conditions like standing with eyes open or closed and standing while performing a cognitive dual task. To unravel the underlying control processes, we reanalyzed these data in terms of stochastic dynamics using more advanced analyses. Dimensionality, local stability, regularity, and scaling behavior of COP trajectories were determined and compared with shuffled and phase-randomized surrogate data. The presence of long-range correlations discarded the possibility that the COP trajectories were purely random. Compared to the healthy controls, the COP trajectories of the stroke patients were characterized by increased dimensionality and instability, but greater regularity in the frontal plane. These findings were taken to imply that the stroke patients actively (i.e., cognitively) coped with the stroke-induced impairment of posture, as reflected in the increased regularity and decreased local stability, by recruiting additional control processes (i.e., more degrees of freedom) and/or by tightening the present control structure while releasing non-essential degrees of freedom from postural control. In the course of rehabilitation, dimensionality stayed fairly constant, whereas local stability increased and regularity decreased. The progressively less regular COP trajectories were interpreted to indicate a reduction of cognitive involvement in postural control as recovery from stroke progressed. Consistent with this interpretation, the dual task condition resulted in less regular COP trajectories of greater dimensionality, reflecting a task-related decrease of active, cognitive contributions to postural control. In comparison with conventional posturography, our results show a clear surplus value of dynamical measures in studying postural control.