Networks: On the relation of bi- and multivariate measures.

A reliable inference of networks from observations of the nodes' dynamics is a major challenge in physics. Interdependence measures such as a the correlation coefficient or more advanced methods based on, e.g., analytic phases of signals are employed. For several of these interdependence measures, multivariate counterparts exist that promise to enable distinguishing direct and indirect connections. Here, we demonstrate analytically how bivariate measures relate to the respective multivariate ones; this knowledge will in turn be used to demonstrate the implications of thresholded bivariate measures for network inference. Particularly, we show, that random networks are falsely identified as small-world networks if observations thereof are treated by bivariate methods. We will employ the correlation coefficient as an example for such an interdependence measure. The results can be readily transferred to all interdependence measures partializing for information of thirds in their multivariate counterparts.

Assessing the strength of directed influences among neural signals: an approach to noisy data.

BACKGROUND: Measurements in the neurosciences are afflicted with observational noise. Granger-causality inference typically does not take this effect into account. We demonstrate that this leads to false positives conclusions and spurious causalities. NEW METHOD: State space modelling provides a convenient framework to obtain reliable estimates for Granger-causality. Despite its previous application in several studies, the analytical derivation of the statistics for parameter estimation in the state space model was missing. This prevented a rigorous evaluation of the results. RESULTS: In this manuscript we derive the statistics for parameter estimation in the state space model. We demonstrate in an extensive simulation study that our novel approach outperforms standard approaches and avoids false positive conclusions about Granger-causality. COMPARISON WITH EXISTING METHODS: In comparison with the naive application of Granger-causality inference, we demonstrate the superiority of our novel approach. The wide-spread applicability of our procedure provides a statistical framework for future studies. The application to mice electroencephalogram data demonstrates the immediate applicability of our approach. CONCLUSIONS: The analytical derivation of the statistics presented in this manuscript enables a rigorous evaluation of the results of Granger causal network inference. It is noteworthy that the statistics can be readily applied to various measures for Granger causality and other approaches that are based on vector autoregressive models.

In vitro study to simulate the intracardiac magnetohydrodynamic effect.

PURPOSE: Blood flow causes induced voltages via the magnetohydrodynamic (MHD) effect distorting electrograms (EGMs) made during magnetic resonance imaging. To investigate the MHD effect in this context MHD voltages occurring inside the human heart were simulated in an in vitro model system inside a 1.5 T MR system. METHODS: The model was developed to produce MHD signals similar to those produced by intracardiac flow and to acquire them using standard clinical equipment. Additionally, a new approach to estimate MHD distortions on intracardiac electrograms is proposed based on the analytical calculation of the MHD signal from MR phase contrast data. RESULTS: The recorded MHD signals were similar in magnitude to intracardiac signals that would be measured by an electrogram of the left ventricle. The dependency of MHD signals on magnetic field strength and electrode separation was well reflected by an analytical model. MHD signals reconstructed from MR flow data were in excellent agreement with the MHD signal measured by clinical equipment. CONCLUSION: The in vitro model allows investigation of MHD effects on intracardiac electrograms. A phase contrast MR scan was successfully applied to characterize and estimate the MHD distortion on intracardiac signals allowing correction of these effects.

Statistical evaluation of forecasts.

Reliable forecasts of extreme but rare events, such as earthquakes, financial crashes, and epileptic seizures, would render interventions and precautions possible. Therefore, forecasting methods have been developed which intend to raise an alarm if an extreme event is about to occur. In order to statistically validate the performance of a prediction system, it must be compared to the performance of a random predictor, which raises alarms independent of the events. Such a random predictor can be obtained by bootstrapping or analytically. We propose an analytic statistical framework which, in contrast to conventional methods, allows for validating independently the sensitivity and specificity of a forecasting method. Moreover, our method accounts for the periods during which an event has to remain absent or occur after a respective forecast.

Optimized spectral estimation for nonlinear synchronizing systems.

In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.

Detection of preclinical neural dysfunction from functional connectivity graphs derived from task fMRI. An example from degeneration.

The early, preferably pre-clinical, identification of neurodegenerative diseases is important as treatment will be most successful before substantial neuronal loss. Here, we reasoned that functional brain changes as measured using functional magnetic resonance imaging (fMRI) will precede neurodegeneration. Three independent cohorts of patients with the genetic mutation leading to Huntington's Disease (HD) but without any clinical symptoms and matched controls performed three different fMRI tasks: Sequential finger tapping engaged the motor system, which is primarily affected by HD, whereas a working-memory task and a task aiming to induce irritation represented the range of low- and high-level cognitive functions also affected by HD. Each diagnostic group of every cohort included 11-16 subjects. After segmentation into 76 cortical and 14 subcortical regions, we extracted functional connectivity patterns through pairwise correlation between the signals in the regions. The resulting coefficients were directly embedded as input to a pattern classifier aiming to separate controls from gene mutation carriers. Alternatively, graph-theory measures such as degree and clustering coefficient were used as features for the discrimination. Classification accuracy never outperformed the accuracy of a grouping based on parameter estimates from a general-linear model approach or a grouping based on features extracted from anatomical images as reported in a previous analysis. Despite good within-subject stability between two runs of the same task, a high between-subject variability led to chance-level accuracy. These results indicate that standard graph-metrics are insufficient to detect subtle disease related changes when within-group variability is high. Developing methods that reduce variability related to noise should be the focus of future studies.

Block-bootstrapping for noisy data.

BACKGROUND: Statistical inference of signals is key to understand fundamental processes in the neurosciences. It is essential to distinguish true from random effects. To this end, statistical concepts of confidence intervals, significance levels and hypothesis tests are employed. Bootstrap-based approaches complement the analytical approaches, replacing the latter whenever these are not possible. NEW METHOD: Block-bootstrap was introduced as an adaption of the ordinary bootstrap for serially correlated data. For block-bootstrap, the signals are cut into independent blocks, yielding independent samples. The key parameter for block-bootstrapping is the block length. In the presence of noise, naïve approaches to block-bootstrapping fail. Here, we present an approach based on block-bootstrapping which can cope even with high noise levels. This method naturally leads to an algorithm of block-bootstrapping that is immediately applicable to observed signals. RESULTS: While naïve block-bootstrapping easily results in a misestimation of the block length, and therefore in an over-estimation of the confidence bounds by 50%, our new approach provides an optimal determination of these, still keeping the coverage correct. COMPARISON WITH EXISTING METHODS: In several applications bootstrapping replaces analytical statistics. Block-bootstrapping is applied to serially correlated signals. Noise, ubiquitous in the neurosciences, is typically neglected. Our new approach not only explicitly includes the presence of (observational) noise in the statistics but also outperforms conventional methods and reduces the number of false-positive conclusions. CONCLUSIONS: The presence of noise has impacts on statistical inference. Our ready-to-apply method enables a rigorous statistical assessment based on block-bootstrapping for noisy serially correlated data.

The stomatogastric nervous system as a model for studying sensorimotor interactions in real-time closed-loop conditions.

The perception of proprioceptive signals that report the internal state of the body is one of the essential tasks of the nervous system and helps to continuously adapt body movements to changing circumstances. Despite the impact of proprioceptive feedback on motor activity it has rarely been studied in conditions in which motor output and sensory activity interact as they do in behaving animals, i.e., in closed-loop conditions. The interaction of motor and sensory activities, however, can create emergent properties that may govern the functional characteristics of the system. We here demonstrate a method to use a well-characterized model system for central pattern generation, the stomatogastric nervous system, for studying these properties in vitro. We created a real-time computer model of a single-cell muscle tendon organ in the gastric mill of the crab foregut that uses intracellular current injections to control the activity of the biological proprioceptor. The resulting motor output of a gastric mill motor neuron is then recorded intracellularly and fed into a simple muscle model consisting of a series of low-pass filters. The muscle output is used to activate a one-dimensional Hodgkin-Huxley type model of the muscle tendon organ in real-time, allowing closed-loop conditions. Model properties were either hand tuned to achieve the best match with data from semi-intact muscle preparations, or an exhaustive search was performed to determine the best set of parameters. We report the real-time capabilities of our models, its performance and its interaction with the biological motor system.

Network modulation during complex syntactic processing.

Complex sentence processing is supported by a left-lateralized neural network including inferior frontal cortex and posterior superior temporal cortex. This study investigates the pattern of connectivity and information flow within this network. We used fMRI BOLD data derived from 12 healthy participants reported in an earlier study (Thompson, C. K., Den Ouden, D. B., Bonakdarpour, B., Garibaldi, K., & Parrish, T. B. (2010b). Neural plasticity and treatment-induced recovery of sentence processing in agrammatism. Neuropsychologia, 48(11), 3211-3227) to identify activation peaks associated with object-cleft over syntactically less complex subject-cleft processing. Directed Partial Correlation Analysis was conducted on time series extracted from participant-specific activation peaks and showed evidence of functional connectivity between four regions, linearly between premotor cortex, inferior frontal gyrus, posterior superior temporal sulcus and anterior middle temporal gyrus. This pattern served as the basis for Dynamic Causal Modeling of networks with a driving input to posterior superior temporal cortex, which likely supports thematic role assignment, and networks with a driving input to inferior frontal cortex, a core region associated with syntactic computation. The optimal model was determined through both frequentist and Bayesian Model Selection and turned out to reflect a network with a primary drive from inferior frontal cortex and modulation of the connection between inferior frontal cortex and posterior superior temporal cortex by complex sentence processing. The winning model also showed a substantive role for a feedback mechanism from posterior superior temporal cortex back to inferior frontal cortex. We suggest that complex syntactic processing is driven by word-order analysis, supported by inferior frontal cortex, in an interactive relation with posterior superior temporal cortex, which supports verb argument structure processing.

Combining functional and anatomical connectivity reveals brain networks for auditory language comprehension.

Cognitive functions are organized in distributed, overlapping, and interacting brain networks. Investigation of those large-scale brain networks is a major task in neuroimaging research. Here, we introduce a novel combination of functional and anatomical connectivity to study the network topology subserving a cognitive function of interest. (i) In a given network, direct interactions between network nodes are identified by analyzing functional MRI time series with the multivariate method of directed partial correlation (dPC). This method provides important improvements over shortcomings that are typical for ordinary (partial) correlation techniques. (ii) For directly interacting pairs of nodes, a region-to-region probabilistic fiber tracking on diffusion tensor imaging data is performed to identify the most probable anatomical white matter fiber tracts mediating the functional interactions. This combined approach is applied to the language domain to investigate the network topology of two levels of auditory comprehension: lower-level speech perception (i.e., phonological processing) and higher-level speech recognition (i.e., semantic processing). For both processing levels, dPC analyses revealed the functional network topology and identified central network nodes by the number of direct interactions with other nodes. Tractography showed that these interactions are mediated by distinct ventral (via the extreme capsule) and dorsal (via the arcuate/superior longitudinal fascicle fiber system) long- and short-distance association tracts as well as commissural fibers. Our findings demonstrate how both processing routines are segregated in the brain on a large-scale network level. Combining dPC with probabilistic tractography is a promising approach to unveil how cognitive functions emerge through interaction of functionally interacting and anatomically interconnected brain regions.

Motor pattern selection by combinatorial code of interneuronal pathways.

We use a modeling approach to examine ideas derived from physiological network analyses, pertaining to the switch of a motor control network between two opposite control modes. We studied the femur-tibia joint control system of the insect leg, and its switch between resistance reflex in posture control and "active reaction" in walking, both elicited by the same sensory input. The femur-tibia network was modeled by fitting the responses of model neurons to those obtained in animals. The strengths of 16 interneuronal pathways that integrate sensory input were then assigned three different values and varied independently, generating a database of more than 43 million network variants. We demonstrate that the same neural network can produce the two different behaviors, depending on the combinatorial code of interneuronal pathways. That is, a switch between behaviors, such as standing to walking, can be brought about by altering the strengths of selected sensory integration pathways.

The insecticide pymetrozine selectively affects chordotonal mechanoreceptors.

Pymetrozine is a neuroactive insecticide but its site of action in the nervous system is unknown. Based on previous studies of symptoms in the locust, the feedback loop controlling the femur-tibia joint of the middle leg was chosen to examine possible targets of the insecticide. The femoral chordotonal organ, which monitors joint position and movement, turned out to be the primary site of pymetrozine action, while interneurons, motoneurons and central motor control circuitry in general did not noticeably respond to the insecticide. The chordotonal organs associated with the wing hinge stretch receptor and the tegula were influenced by pymetrozine in the same way as the femoral chordotonal organ, indicating that the insecticide affects chordotonal sensillae in general. Pymetrozine at concentrations down to 10(-8) mol l(-1) resulted in the loss of stimulus-related responses and either elicited (temporary) tonic discharges or eliminated spike activity altogether. Remarkably, pymetrozine affected the chordotonal organs in an all-or-none fashion, in agreement with previous independent studies. Other examined sense organs did not respond to pymetrozine, namely campaniform sensillae on the tibia and the subcosta vein, hair sensillae of the tegula (type I sensillae), and the wing hinge stretch receptor (type II sensillae).