Fast construction of voxel-level functional connectivity graphs.

BACKGROUND: Graph-based analysis of fMRI data has recently emerged as a promising approach to study brain networks. Based on the assessment of synchronous fMRI activity at separate brain sites, functional connectivity graphs are constructed and analyzed using graph-theoretical concepts. Most previous studies investigated region-level graphs, which are computationally inexpensive, but bring along the problem of choosing sensible regions and involve blurring of more detailed information. In contrast, voxel-level graphs provide the finest granularity attainable from the data, enabling analyses at superior spatial resolution. They are, however, associated with considerable computational demands, which can render high-resolution analyses infeasible. In response, many existing studies investigating functional connectivity at the voxel-level reduced the computational burden by sacrificing spatial resolution. METHODS: Here, a novel, time-efficient method for graph construction is presented that retains the original spatial resolution. Performance gains are instead achieved through data reduction in the temporal domain based on dichotomization of voxel time series combined with tetrachoric correlation estimation and efficient implementation. RESULTS: By comparison with graph construction based on Pearson's r, the technique used by the majority of previous studies, we find that the novel approach produces highly similar results an order of magnitude faster. CONCLUSIONS: Its demonstrated performance makes the proposed approach a sensible and efficient alternative to customary practice. An open source software package containing the created programs is freely available for download.

Widespread temporo-occipital lobe dysfunction in amyotrophic lateral sclerosis.

Recent studies suggest that amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD) lie on a single clinical continuum. However, previous neuroimaging studies have found only limited involvement of temporal lobe regions in ALS. To better delineate possible temporal lobe involvement in ALS, the present study aimed to examine changes in functional connectivity across the whole brain, particularly with regard to extra-motor regions, in a group of 64 non-demented ALS patients and 38 healthy controls. To assess between-group differences in connectivity, we computed edge-level statistics across subject-specific graphs derived from resting-state functional MRI data. In addition to expected ALS-related decreases in functional connectivity in motor-related areas, we observed extensive changes in connectivity across the temporo-occipital cortex. Although ALS patients with comorbid FTD were deliberately excluded from this study, the pattern of connectivity alterations closely resembles patterns of cerebral degeneration typically seen in FTD. This evidence for subclinical temporal dysfunction supports the idea of a common pathology in ALS and FTD.

Memory-Efficient Analysis of Dense Functional Connectomes.

The functioning of the human brain relies on the interplay and integration of numerous individual units within a complex network. To identify network configurations characteristic of specific cognitive tasks or mental illnesses, functional connectomes can be constructed based on the assessment of synchronous fMRI activity at separate brain sites, and then analyzed using graph-theoretical concepts. In most previous studies, relatively coarse parcellations of the brain were used to define regions as graphical nodes. Such parcellated connectomes are highly dependent on parcellation quality because regional and functional boundaries need to be relatively consistent for the results to be interpretable. In contrast, dense connectomes are not subject to this limitation, since the parcellation inherent to the data is used to define graphical nodes, also allowing for a more detailed spatial mapping of connectivity patterns. However, dense connectomes are associated with considerable computational demands in terms of both time and memory requirements. The memory required to explicitly store dense connectomes in main memory can render their analysis infeasible, especially when considering high-resolution data or analyses across multiple subjects or conditions. Here, we present an object-based matrix representation that achieves a very low memory footprint by computing matrix elements on demand instead of explicitly storing them. In doing so, memory required for a dense connectome is reduced to the amount needed to store the underlying time series data. Based on theoretical considerations and benchmarks, different matrix object implementations and additional programs (based on available Matlab functions and Matlab-based third-party software) are compared with regard to their computational efficiency. The matrix implementation based on on-demand computations has very low memory requirements, thus enabling analyses that would be otherwise infeasible to conduct due to insufficient memory. An open source software package containing the created programs is available for download.

Test statistics for the identification of assembly neurons in parallel spike trains.

In recent years numerous improvements have been made in multiple-electrode recordings (i.e., parallel spike-train recordings) and spike sorting to the extent that nowadays it is possible to monitor the activity of up to hundreds of neurons simultaneously. Due to these improvements it is now potentially possible to identify assembly activity (roughly understood as significant synchronous spiking of a group of neurons) from these recordings, which-if it can be demonstrated reliably-would significantly improve our understanding of neural activity and neural coding. However, several methodological problems remain when trying to do so and, among them, a principal one is the combinatorial explosion that one faces when considering all potential neuronal assemblies, since in principle every subset of the recorded neurons constitutes a candidate set for an assembly. We present several statistical tests to identify assembly neurons (i.e., neurons that participate in a neuronal assembly) from parallel spike trains with the aim of reducing the set of neurons to a relevant subset of them and this way ease the task of identifying neuronal assemblies in further analyses. These tests are an improvement of those introduced in the work by Berger et al. (2010) based on additional features like spike weight or pairwise overlap and on alternative ways to identify spike coincidences (e.g., by avoiding time binning, which tends to lose information).

Statistical evaluation of synchronous spike patterns extracted by frequent item set mining.

We recently proposed frequent itemset mining (FIM) as a method to perform an optimized search for patterns of synchronous spikes (item sets) in massively parallel spike trains. This search outputs the occurrence count (support) of individual patterns that are not trivially explained by the counts of any superset (closed frequent item sets). The number of patterns found by FIM makes direct statistical tests infeasible due to severe multiple testing. To overcome this issue, we proposed to test the significance not of individual patterns, but instead of their signatures, defined as the pairs of pattern size z and support c. Here, we derive in detail a statistical test for the significance of the signatures under the null hypothesis of full independence (pattern spectrum filtering, PSF) by means of surrogate data. As a result, injected spike patterns that mimic assembly activity are well detected, yielding a low false negative rate. However, this approach is prone to additionally classify patterns resulting from chance overlap of real assembly activity and background spiking as significant. These patterns represent false positives with respect to the null hypothesis of having one assembly of given signature embedded in otherwise independent spiking activity. We propose the additional method of pattern set reduction (PSR) to remove these false positives by conditional filtering. By employing stochastic simulations of parallel spike trains with correlated activity in form of injected spike synchrony in subsets of the neurons, we demonstrate for a range of parameter settings that the analysis scheme composed of FIM, PSF and PSR allows to reliably detect active assemblies in massively parallel spike trains.

Finding neural assemblies with frequent item set mining.

Cell assemblies, defined as groups of neurons exhibiting precise spike coordination, were proposed as a model of network processing in the cortex. Fortunately, in recent years considerable progress has been made in multi-electrode recordings, which enable recording massively parallel spike trains of hundred(s) of neurons simultaneously. However, due to the challenges inherent in multivariate approaches, most studies in favor of cortical cell assemblies still resorted to analyzing pairwise interactions. However, to recover the underlying correlation structures, higher-order correlations need to be identified directly. Inspired by the Accretion method proposed by Gerstein et al. (1978) we propose a new assembly detection method based on frequent item set mining (FIM). In contrast to Accretion, FIM searches effectively and without redundancy for individual spike patterns that exceed a given support threshold. We study different search methods, with which the space of potential cell assemblies may be explored, as well as different test statistics and subset conditions with which candidate assemblies may be assessed and filtered. It turns out that a core challenge of cell assembly detection is the problem of multiple testing, which causes a large number of false discoveries. Unfortunately, criteria that address individual candidate assemblies and try to assess them with statistical tests and/or subset conditions do not help much to tackle this problem. The core idea of our new method is that in order to cope with the multiple testing problem one has to shift the focus of statistical testing from specific assemblies (consisting of a specific set of neurons) to spike patterns of a certain size (i.e., with a certain number of neurons). This significantly reduces the number of necessary tests, thus alleviating the multiple testing problem. We demonstrate that our method is able to reliably suppress false discoveries, while it is still very sensitive in discovering synchronous activity. Since we exploit high-speed computational techniques from FIM for the tests, our method is also computationally efficient.

Complexity distribution as a measure for assembly size and temporal precision.

The efficient detection of higher-order synchronization in massively parallel data is of great importance in understanding computational processes in the cortex and represents a significant statistical challenge. To overcome the combinatorial explosion of different spike patterns taking place as the number of neurons increases, a method based on population measures would prove very useful. Following previous work in this direction, we examine the distribution of spike counts across neurons per time bin ('complexity distribution') and devise a method to reliably extract the size and temporal precision of synchronous groups of neurons, even in the presence of strong rate covariations.

Efficient identification of assembly neurons within massively parallel spike trains.

The chance of detecting assembly activity is expected to increase if the spiking activities of large numbers of neurons are recorded simultaneously. Although such massively parallel recordings are now becoming available, methods able to analyze such data for spike correlation are still rare, as a combinatorial explosion often makes it infeasible to extend methods developed for smaller data sets. By evaluating pattern complexity distributions the existence of correlated groups can be detected, but their member neurons cannot be identified. In this contribution, we present approaches to actually identify the individual neurons involved in assemblies. Our results may complement other methods and also provide a way to reduce data sets to the "relevant" neurons, thus allowing us to carry out a refined analysis of the detailed correlation structure due to reduced computation time.