Wolfgang Mader

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.

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.

On the Detection of Direct Directed Information Flow in fMRI

To infer interactions from functional magnetic resonance imaging (fMRI) data, structural equation modeling (SEM) as well as dynamic causal modeling (DCM) has been suggested. Directed partial correlation (dPC) is a measure which detects Granger causality in multivariate systems. To demonstrate the strengths as well as the limitations of directed partial correlation we first applied it to simulated data tailored to the problem at hand. Second, after dPC has proven to be useful for fMRI data analysis, we applied it to actual fMRI data.

Overarching framework for data-based modelling

One of the main modelling paradigms for complex physical systems are networks. When estimating the network structure from measured signals, typically several assumptions such as stationarity are made in the estimation process. Violating these assumptions renders standard analysis techniques fruitless. We here propose a framework to estimate the network structure from measurements of arbitrary non-linear, non-stationary, stochastic processes. To this end, we propose a rigorous mathematical theory that underlies this framework. Based on this theory, we present a highly efficient algorithm and the corresponding statistics that are immediately sensibly applicable to measured signals. We demonstrate its performance in a simulation study. In experiments of transitions between vigilance stages in rodents, we infer small network structures with complex, time-dependent interactions; this suggests biomarkers for such transitions, the key to understand and diagnose numerous diseases such as dementia. We argue that the suggested framework combines features that other approaches followed so far lack.

A numerically efficient implementation of the expectation maximization algorithm for state space models

Empirical time series are subject to observational noise. Naive approaches that estimate parameters in stochastic models for such time series are likely to fail due to the error-in-variables challenge. State space models (SSM) explicitly include observational noise. Applying the expectation maximization (EM) algorithm together with the Kalman filter constitute a robust iterative procedure to estimate model parameters in the SSM as well as an approach to denoise the signal. The EM algorithm provides maximum likelihood parameter estimates at convergence. The drawback of this approach is its high computational demand. Here, we present an optimized implementation and demonstrate its superior performance to naive algorithms or implementations.

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.

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.

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 Huntingtons 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.

In vitro study to simulate the intracardiac magnetohydrodynamic effect.

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.