Kai Görgen

On the interpretation of weight vectors of linear models in multivariate neuroimaging.

The increase in spatiotemporal resolution of neuroimaging devices is accompanied by a trend towards more powerful multivariate analysis methods. Often it is desired to interpret the outcome of these methods with respect to the cognitive processes under study. Here we discuss which methods allow for such interpretations, and provide guidelines for choosing an appropriate analysis for a given experimental goal: For a surgeon who needs to decide where to remove brain tissue it is most important to determine the origin of cognitive functions and associated neural processes. In contrast, when communicating with paralyzed or comatose patients via brain-computer interfaces, it is most important to accurately extract the neural processes specific to a certain mental state. These equally important but complementary objectives require different analysis methods. Determining the origin of neural processes in time or space from the parameters of a data-driven model requires what we call a forward model of the data; such a model explains how the measured data was generated from the neural sources. Examples are general linear models (GLMs). Methods for the extraction of neural information from data can be considered as backward models, as they attempt to reverse the data generating process. Examples are multivariate classifiers. Here we demonstrate that the parameters of forward models are neurophysiologically interpretable in the sense that significant nonzero weights are only observed at channels the activity of which is related to the brain process under study. In contrast, the interpretation of backward model parameters can lead to wrong conclusions regarding the spatial or temporal origin of the neural signals of interest, since significant nonzero weights may also be observed at channels the activity of which is statistically independent of the brain process under study. As a remedy for the linear case, we propose a procedure for transforming backward models into forward models. This procedure enables the neurophysiological interpretation of the parameters of linear backward models. We hope that this work raises awareness for an often encountered problem and provides a theoretical basis for conducting better interpretable multivariate neuroimaging analyses.

The Decoding Toolbox (TDT): a versatile software package for multivariate analyses of functional imaging data

The multivariate analysis of brain signals has recently sparked a great amount of interest, yet accessible and versatile tools to carry out decoding analyses are scarce. Here we introduce The Decoding Toolbox (TDT) which represents a user-friendly, powerful and flexible package for multivariate analysis of functional brain imaging data. TDT is written in Matlab and equipped with an interface to the widely used brain data analysis package SPM. The toolbox allows running fast whole-brain analyses, region-of-interest analyses and searchlight analyses, using machine learning classifiers, pattern correlation analysis, or representational similarity analysis. It offers automatic creation and visualization of diverse cross-validation schemes, feature scaling, nested parameter selection, a variety of feature selection methods, multiclass capabilities, and pattern reconstruction from classifier weights. While basic users can implement a generic analysis in one line of code, advanced users can extend the toolbox to their needs or exploit the structure to combine it with external high-performance classification toolboxes. The toolbox comes with an example data set which can be used to try out the various analysis methods. Taken together, TDT offers a promising option for researchers who want to employ multivariate analyses of brain activity patterns.

Compositionality of Rule Representations in Human Prefrontal Cortex

Rules are widely used in everyday life to organize actions and thoughts in accordance with our internal goals. At the simplest level, single rules can be used to link individual sensory stimuli to their appropriate responses. However, most tasks are more complex and require the concurrent application of multiple rules. Experiments on humans and monkeys have shown the involvement of a frontoparietal network in rule representation. Yet, a fundamental issue still needs to be clarified: Is the neural representation of multiple rules compositional, that is, built on the neural representation of their simple constituent rules? Subjects were asked to remember and apply either simple or compound rules. Multivariate decoding analyses were applied to functional magnetic resonance imaging data. Both ventrolateral frontal and lateral parietal cortex were involved in compound representation. Most importantly, we were able to decode the compound rules by training classifiers only on the simple rules they were composed of. This shows that the code used to store rule information in prefrontal cortex is compositional. Compositional coding in rule representation suggests that it might be possible to decode other complex action plans by learning the neural patterns of the known composing elements.

The point of no return in vetoing self-initiated movements

Significance Many studies have shown that movements are preceded by early brain signals. There has been a debate as to whether subjects can still cancel a movement after onset of these early signals. We tested whether subjects can win a “duel” against a brain–computer interface designed to predict their movements in real time from observations of their EEG activity. Our findings suggest that subjects can exert a “veto” even after onset of this preparatory process. However, the veto has to occur before a point of no return is reached after which participants cannot avoid moving. In humans, spontaneous movements are often preceded by early brain signals. One such signal is the readiness potential (RP) that gradually arises within the last second preceding a movement. An important question is whether people are able to cancel movements after the elicitation of such RPs, and if so until which point in time. Here, subjects played a game where they tried to press a button to earn points in a challenge with a brain–computer interface (BCI) that had been trained to detect their RPs in real time and to emit stop signals. Our data suggest that subjects can still veto a movement even after the onset of the RP. Cancellation of movements was possible if stop signals occurred earlier than 200 ms before movement onset, thus constituting a point of no return.

Distributed representations of rule identity and rule order in human frontal cortex and striatum

Humans are able to flexibly devise and implement rules to reach their desired goals. For simple situations, we can use single rules, such as “if traffic light is green then cross the street.” In most cases, however, more complex rule sets are required, involving the integration of multiple layers of control. Although it has been shown that prefrontal cortex is important for rule representation, it has remained unclear how the brain encodes more complex rule sets. Here, we investigate how the brain represents the order in which different parts of a rule set are evaluated. Participants had to follow compound rule sets that involved the concurrent application of two single rules in a specific order, where one of the rules always had to be evaluated first. The rules and their assigned order were independently manipulated. By applying multivariate decoding to fMRI data, we found that the identity of the current rule was encoded in a frontostriatal network involving right ventrolateral prefrontal cortex, right superior frontal gyrus, and dorsal striatum. In contrast, rule order could be decoded in the dorsal striatum and in the right premotor cortex. The nonhomogeneous distribution of information across brain areas was confirmed by follow-up analyses focused on relevant regions of interest. We argue that the brain encodes complex rule sets by “decomposing” them in their constituent features, which are represented in different brain areas, according to the aspect of information to be maintained.

Parameter interpretation, regularization and source localization in multivariate linear models

Neuroimaging data are frequently analyzed with multivariate methods. Models expressing the data as a function of underlying factors related to the brain processes under study (signals) are called forward models, while models reversing this functional relationship are called backward models. Weigth vectors of backward models (called extraction filters) indicate the measurement channels informative with respect to isolating the signals. However, being a function of both signal and noise, significant weights may be observed at channels containing pure noise, while a proportion of signal-related channels may be given zero or insignificant weight. In contrast, forward model parameters (activation patterns) may exhibit significant weights only at signal-related channels, and are therefore interpretable with respect to the origin of the brain processes under study. It is sometimes incorrectly assumed that regularization (e.g., sparsification) of backward models makes extraction filters interpretable in the same sense. However, by transforming filters into patterns of corresponding forward models, as outlined here for the linear case, this can be indeed achieved. While these considerations hold for all types of data, the distinction between filters and patterns is particularly crucial for EEG and MEG data: only activation patterns can be localized to brain anatomy using customary inverse methods. We illustrate our theoretical results using a real EEG data example.

FMRI decoding of intentions: Compositionality, hierarchy and prospective memory

In recent years multivariate decoding has allowed to test where and how mental representations can be decoded from neuroimaging signals, which sheds light on how these representations are encoded in the brain. In one line of experiments, we investigated how intentions are encoded in fMRI signals, thus revealing information in medial and lateral prefrontal regions. These informative neural representations were even present prior to the persons awareness of their chosen intention. In comparison, for cued intentions we found information predominantly in lateral, but not medial prefrontal cortex. Intention coding in prefrontal cortex followed a compositional code and could also be observed across extended delays during which participants were busy performing other tasks. Taken together, our results suggest a systematic, compositional and hierarchical code in prefrontal cortex which intentions are encoded across delays while the mind is busy working on other tasks.