Model assessment and model building in fMRI

Brain signals of a Surprise-Actor-Critic model: Evidence for multiple learning modules in human decision making

Learning how to reach a reward over long series of actions is a remarkable capability of humans, and potentially guided by multiple parallel learning modules. Current brain imaging of learning modules is limited by (i) simple experimental paradigms, (ii) entanglement of brain signals of different learning modules, and (iii) a limited number of computational models considered as candidates for explaining behavior. Here, we address these three limitations and (i) introduce a complex sequential decision making task with surprising events that allows us to (ii) dissociate correlates of reward prediction errors from those of surprise in functional magnetic resonance imaging (fMRI); and (iii) we test behavior against a large repertoire of model-free, model-based, and hybrid reinforcement learning algorithms, including a novel surprise-modulated actor-critic algorithm. Surprise, derived from an approximate Bayesian approach for learning the world-model, is extracted in our algorithm from a state prediction error. Surprise is then used to modulate the learning rate of a model-free actor, which itself learns via the reward prediction error from model-free value estimation by the critic. We find that action choices are well explained by pure model-free policy gradient, but reaction times and neural data are not. We identify signatures of both model-free and surprise-based learning signals in blood oxygen level dependent (BOLD) responses, supporting the existence of multiple parallel learning modules in the brain. Our results extend previous fMRI findings to a multi-step setting and emphasize the role of policy gradient and surprise signalling in human learning.

An empirical investigation of the benefit of increasing the temporal resolution of task-evoked fMRI data with multi-band imaging

Objective

There is a tendency for reducing TR in MRI experiments with multi-band imaging. We empirically investigate its benefit for the group-level statistical outcome in task-evoked fMRI.

Methods

Three visual fMRI data sets were collected from 17 healthy adult participants. Multi-band acquisition helped vary the TR (2000/1000/410 ms, respectively). Because these data sets capture different temporal aspects of the haemodynamic response (HRF), we tested several HRF models. We computed a composite descriptive statistic, H, from β’s of each first-level model fit and carried it to the group-level analysis. The number of activated voxels and the t value of the group-level analysis as well as a goodness-of-fit measure were used as surrogate markers of data quality for comparison.

Results

Increasing the temporal sampling rate did not provide a universal improvement in the group-level statistical outcome. Rather, both the voxel-wise and ROI-averaged group-level results varied widely with anatomical location, choice of HRF and the setting of the TR. Correspondingly, the goodness-of-fit of HRFs became worse with increasing the sampling frequency.

Conclusion

Rather than universally increasing the temporal sampling rate in cognitive fMRI experiments, these results advocate the performance of a pilot study for the specific ROIs of interest to identify the appropriate temporal sampling rate for the acquisition and the correspondingly suitable HRF for the analysis of the data.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10334-021-00918-z.

MACS - a new SPM toolbox for model assessment, comparison and selection

BACKGROUND

In cognitive neuroscience, functional magnetic resonance imaging (fMRI) data are widely analyzed using general linear models (GLMs). However, model quality of GLMs for fMRI is rarely assessed, in part due to the lack of formal measures for statistical model inference.

NEW METHOD

We introduce a new SPM toolbox for model assessment, comparison and selection (MACS) of GLMs applied to fMRI data. MACS includes classical, information-theoretic and Bayesian methods of model assessment previously applied to GLMs for fMRI as well as recent methodological developments of model selection and model averaging in fMRI data analysis.

RESULTS

The toolbox - which is freely available from GitHub - directly builds on the Statistical Parametric Mapping (SPM) software package and is easy-to-use, general-purpose, modular, readable and extendable. We validate the toolbox by reproducing model selection and model averaging results from earlier publications.

COMPARISON WITH EXISTING METHODS

A previous toolbox for model diagnosis in fMRI has been discontinued and other approaches to model comparison between GLMs have not been translated into reusable computational resources in the past.

CONCLUSIONS

Increased attention on model quality will lead to lower false-positive rates in cognitive neuroscience and increased application of the MACS toolbox will increase the reproducibility of GLM analyses and is likely to increase the replicability of fMRI studies.

How to improve parameter estimates in GLM-based fMRI data analysis: cross-validated Bayesian model averaging

In functional magnetic resonance imaging (fMRI), model quality of general linear models (GLMs) for first-level analysis is rarely assessed. In recent work (Soch et al., 2016: "How to avoid mismodelling in GLM-based fMRI data analysis: cross-validated Bayesian model selection", NeuroImage, vol. 141, pp. 469-489; http://dx.doi.org/10.1016/j.neuroimage.2016.07.047), we have introduced cross-validated Bayesian model selection (cvBMS) to infer the best model for a group of subjects and use it to guide second-level analysis. While this is the optimal approach given that the same GLM has to be used for all subjects, there is a much more efficient procedure when model selection only addresses nuisance variables and regressors of interest are included in all candidate models. In this work, we propose cross-validated Bayesian model averaging (cvBMA) to improve parameter estimates for these regressors of interest by combining information from all models using their posterior probabilities. This is particularly useful as different models can lead to different conclusions regarding experimental effects and the most complex model is not necessarily the best choice. We find that cvBMS can prevent not detecting established effects and that cvBMA can be more sensitive to experimental effects than just using even the best model in each subject or the model which is best in a group of subjects.

Bootstrapping fMRI Data: Dealing with Misspecification

The validity of inference based on the General Linear Model (GLM) for the analysis of functional magnetic resonance imaging (fMRI) time series has recently been questioned. Bootstrap procedures that partially avoid modeling assumptions may offer a welcome solution. We empirically compare two voxelwise GLM-based bootstrap approaches: a semi-parametric approach, relying solely on a model for the expected signal; and a fully parametric bootstrap approach, requiring an additional parameterization of the temporal structure. While the fully parametric approach assumes independent whitened residuals, the semi-parametric approach relies on independent blocks of residuals. The evaluation is based on inferential properties and the potential to reproduce important data characteristics. Different noise structures and data-generating mechanisms for the signal are simulated. When the model for the noise and expected signal is correct, we find that the fully parametric approach works well, with respect to both inference and reproduction of data characteristics. However, in the presence of misspecification, the fully parametric approach can be improved with additional blocking. The semi-parametric approach performs worse than the (fully) parametric approach with respect to inference but achieves comparable results as the parametric approach with additional blocking with respect to image reproducibility. We demonstrate that when the expected signal is incorrect GLM-based bootstrapping can overcome the poor performance of classical (non-bootstrap) parametric inference. We illustrate both approaches on a study exploring the neural representation of object representation in the visual pathway.

Paradigm free mapping with sparse regression automatically detects single-trial functional magnetic resonance imaging blood oxygenation level dependent responses

The ability to detect single trial responses in functional magnetic resonance imaging (fMRI) studies is essential, particularly if investigating learning or adaptation processes or unpredictable events. We recently introduced paradigm free mapping (PFM), an analysis method that detects single trial blood oxygenation level dependent (BOLD) responses without specifying prior information on the timing of the events. PFM is based on the deconvolution of the fMRI signal using a linear hemodynamic convolution model. Our previous PFM method (Caballero-Gaudes et al., 2011: Hum Brain Mapp) used the ridge regression estimator for signal deconvolution and required a baseline signal period for statistical inference. In this work, we investigate the application of sparse regression techniques in PFM. In particular, a novel PFM approach is developed using the Dantzig selector estimator, solved via an efficient homotopy procedure, along with statistical model selection criteria. Simulation results demonstrated that, using the Bayesian information criterion to select the regularization parameter, this method obtains high detection rates of the BOLD responses, comparable with a model-based analysis, but requiring no information on the timing of the events and being robust against hemodynamic response function variability. The practical operation of this sparse PFM method was assessed with single-trial fMRI data acquired at 7T, where it automatically detected all task-related events, and was an improvement on our previous PFM method, as it does not require the definition of a baseline state and amplitude thresholding and does not compromise on specificity and sensitivity.

Development of the Complex General Linear Model in the Fourier Domain: Application to fMRI Multiple Input-Output Evoked Responses for Single Subjects

A linear time-invariant model based on statistical time series analysis in the Fourier domain for single subjects is further developed and applied to functional MRI (fMRI) blood-oxygen level-dependent (BOLD) multivariate data. This methodology was originally developed to analyze multiple stimulus input evoked response BOLD data. However, to analyze clinical data generated using a repeated measures experimental design, the model has been extended to handle multivariate time series data and demonstrated on control and alcoholic subjects taken from data previously analyzed in the temporal domain. Analysis of BOLD data is typically carried out in the time domain where the data has a high temporal correlation. These analyses generally employ parametric models of the hemodynamic response function (HRF) where prewhitening of the data is attempted using autoregressive (AR) models for the noise. However, this data can be analyzed in the Fourier domain. Here, assumptions made on the noise structure are less restrictive, and hypothesis tests can be constructed based on voxel-specific nonparametric estimates of the hemodynamic transfer function (HRF in the Fourier domain). This is especially important for experimental designs involving multiple states (either stimulus or drug induced) that may alter the form of the response function.

Identifying FMRI model violations with Lagrange multiplier tests

The standard modeling framework in functional magnetic resonance imaging (fMRI) is predicated on assumptions of linearity, time invariance and stationarity. These assumptions are rarely checked because doing so requires specialized software, although failure to do so can lead to bias and mistaken inference. Identifying model violations is an essential but largely neglected step in standard fMRI data analysis. Using Lagrange multiplier testing methods we have developed simple and efficient procedures for detecting model violations such as nonlinearity, nonstationarity and validity of the common double gamma specification for hemodynamic response. These procedures are computationally cheap and can easily be added to a conventional analysis. The test statistic is calculated at each voxel and displayed as a spatial anomaly map which shows regions where a model is violated. The methodology is illustrated with a large number of real data examples.

The impact of physiologic noise correction applied to functional MRI of pain at 1.5 and 3.0 T

This study quantified the impact of the well-known physiologic noise correction algorithm RETROICOR applied to a pain functional magnetic resonance imaging (FMRI) experiment at two field strengths: 1.5 and 3.0 T. In the 1.5-T acquisition, there was an 8.2% decrease in time course variance (σ) and a 227% improvement in average model fit (increase in mean R(2)(a)). In the 3.0-T acquisition, significantly greater improvements were seen: a 10.4% decrease in σ and a 240% increase in mean R(2)(a). End-tidal carbon dioxide data were also collected during scanning and used to account for low-frequency changes in cerebral blood flow; however, the impact of this correction was trivial compared to applying RETROICOR. Comparison between two implementations of RETROICOR demonstrated that oversampled physiologic data can be applied by either downsampling or modification of the timing in the RETROICOR algorithm, with equivalent results. Furthermore, there was no significant effect from manually aligning the physiologic data with corresponding image slices from an interleaved acquisition, indicating that RETROICOR accounts for timing differences between physiologic changes and MR signal changes. These findings suggest that RETROICOR correction, as it is commonly implemented, should be included as part of the data analysis for pain FMRI studies performed at 1.5 and 3.0 T.

Statistical Analysis of fMRI Time-Series: A Critical Review of the GLM Approach

Functional magnetic resonance imaging (fMRI) is one of the most widely used tools to study the neural underpinnings of human cognition. Standard analysis of fMRI data relies on a general linear model (GLM) approach to separate stimulus induced signals from noise. Crucially, this approach relies on a number of assumptions about the data which, for inferences to be valid, must be met. The current paper reviews the GLM approach to analysis of fMRI time-series, focusing in particular on the degree to which such data abides by the assumptions of the GLM framework, and on the methods that have been developed to correct for any violation of those assumptions. Rather than biasing estimates of effect size, the major consequence of non-conformity to the assumptions is to introduce bias into estimates of the variance, thus affecting test statistics, power, and false positive rates. Furthermore, this bias can have pervasive effects on both individual subject and group-level statistics, potentially yielding qualitatively different results across replications, especially after the thresholding procedures commonly used for inference-making.

Analysis of fMRI data using improved self-organizing mapping and spatio-temporal metric hierarchical clustering

The self-organizing mapping (SOM) and hierarchical clustering (HC) methods are integrated to detect brain functional activation; functional magnetic resonance imaging (fMRI) data are first processed by SOM to obtain a primary merged neural nodes image, and then by HC to obtain further brain activation patterns. The conventional Euclidean distance metric was replaced by the correlation distance metric in SOM to improve clustering and merging of neural nodes. To improve the use of spatial and temporal information in fMRI data, a new spatial distance (node coordinates in the 2-D lattice) and temporal correlation (correlation degree of each time course in the exemplar matrix) are introduced in HC to merge the primary SOM results. Two simulation studies and two in vivo fMRI data that both contained block-design and event-related experiments revealed that brain functional activation can be effectively detected and that different response patterns can be distinguished using these methods. Our results demonstrate that the improved SOM and HC methods are clearly superior to the statistical parametric mapping (SPM), independent component analysis (ICA), and conventional SOM methods in the block-design, especially in the event-related experiment, as revealed by their performance measured by receiver operating characteristic (ROC) analysis. Our results also suggest that the proposed new integrated approach could be useful in detecting block-design and event-related fMRI data.

Source of low-frequency fluctuations in functional MRI signal

PURPOSE

To investigate the source of native low-frequency fluctuations (LFF) in functional MRI (fMRI) signal.

MATERIALS AND METHODS

Phase analysis was performed on tissue-segmented fMRI data acquired at systematically varying sampling rates.

RESULTS

LFF in fMRI signal were both native and aliased in origin. Scanner instability did not contribute to native or aliased LFF. Aliased LFF arose from cardiorespiratory processes and head motion. Native LFF did not arise from cardiorespiratory processes, but did so, at least in part, from head motion. Motion correction reduced native LFF, but did not eliminate them. The residual native LFF in motion-corrected fMRI data showed a systematic phase difference among different tissue structures. The native LFF in fMRI signals of cerebral blood vessels and CSF were synchronous, and preceded those of gray and white matter, indicating that the vascular fluctuations lead the metabolic fluctuations.

CONCLUSION

The primary physiologic source of native LFF in fMRI signal is vasomotion.

The power of spectral density analysis for mapping endogenous BOLD signal fluctuations

FMRI has revealed the presence of correlated low-frequency cerebro-vascular oscillations within functional brain systems, which are thought to reflect an intrinsic feature of large-scale neural activity. The spatial correlations shown by these fluctuations has been their identifying feature, distinguishing them from fluctuations associated with other processes. Major analysis methods characterize these correlations, identifying networks and their interactions with various factors. However, other analysis approaches are required to fully characterize the regional signal dynamics contributing to these correlations between regions. In this study we show that analysis of the power spectral density (PSD) of regional signals can identify changes in oscillatory dynamics across conditions, and is able to characterize the nature and spatial extent of signal changes underlying changes in measures of connectivity. We analyzed spectral density changes in sessions consisting of both resting-state scans and scans recording 2 min blocks of continuous unilateral finger tapping and rest. We assessed the relationship of PSD and connectivity measures by additionally tracking correlations between selected motor regions. Spectral density gradually increased in gray and white matter during the experiment. Finger tapping produced widespread decreases in low-frequency spectral density. This change was symmetric across the cortex, and extended beyond both the lateralized task-related signal increases, and the established "resting-state" motor network. Correlations between motor regions also reduced with task performance. In conclusion, analysis of PSD is a sensitive method for detecting and characterizing BOLD signal oscillations that can enhance the analysis of network connectivity.

Modeling low-frequency fluctuation and hemodynamic response timecourse in event-related fMRI

Functional magnetic resonance imaging (fMRI) suffers from many problems that make signal estimation difficult. These include variation in the hemodynamic response across voxels and low signal-to-noise ratio (SNR). We evaluate several analysis techniques that address these problems for event-related fMRI. (1) Many fMRI analyses assume a canonical hemodynamic response function, but this assumption may lead to inaccurate data models. By adopting the finite impulse response model, we show that voxel-specific hemodynamic response functions can be estimated directly from the data. (2) There is a large amount of low-frequency noise fluctuation (LFF) in blood oxygenation level dependent (BOLD) time-series data. To compensate for this problem, we use polynomials as regressors for LFF. We show that this technique substantially improves SNR and is more accurate than high-pass filtering of the data. (3) Model overfitting is a problem for the finite impulse response model because of the low SNR of the BOLD response. To reduce overfitting, we estimate a hemodynamic response timecourse for each voxel and incorporate the constraint of time-event separability, the constraint that hemodynamic responses across event types are identical up to a scale factor. We show that this technique substantially improves the accuracy of hemodynamic response estimates and can be computed efficiently. For the analysis techniques we present, we evaluate improvement in modeling accuracy via 10-fold cross-validation.

The role of imaging in United States courtrooms

The rapid evolution of brain imaging techniques has increasingly offered more detailed diagnostic and prognostic information about neurologic and psychiatric disorders and the structural and functional brain changes that may influence behavior. Coupled with these developments is the increasing use of neuroimages in courtrooms, where they are used as evidence in criminal cases to challenge a defendant's competency or culpability and in civil cases to establish physical injury or toxic exposure. Several controversies exist, including the admissibility of neuroimages in legal proceedings, the reliability of expert testimony, and the appropriateness of drawing conclusions in individual cases based on the findings of research uses of imaging technology. This article reviews and discusses the current state of these issues.

Flexible statistical modelling detects clinical functional magnetic resonance imaging activation in partially compliant subjects

Clinical functional magnetic resonance imaging (fMRI) occasionally fails to detect significant activation, often due to variability in task performance. The present study seeks to test whether a more flexible statistical analysis can better detect activation, by accounting for variance associated with variable compliance to the task over time. Experimental results and simulated data both confirm that even at 80% compliance to the task, such a flexible model outperforms standard statistical analysis when assessed using the extent of activation (experimental data), goodness of fit (experimental data), and area under the operator characteristic curve (simulated data). Furthermore, retrospective examination of 14 clinical fMRI examinations reveals that in patients where the standard statistical approach yields activation, there is a measurable gain in model performance in adopting the flexible statistical model, with little or no penalty in lost sensitivity. This indicates that a flexible model should be considered, particularly for clinical patients who may have difficulty complying fully with the study task.

Using voxel-specific hemodynamic response function in EEG-fMRI data analysis: An estimation and detection model

Research groups who study epileptic spikes with simultaneous EEG-fMRI have used mostly the general linear model (GLM). A shortcoming of the GLM is that the specification of a simple hemodynamic response function (HRF) may lead to biased results. Other methods, which predict the hemodynamic response from the measured data, have been termed "recognition models". The merit of recognition models lies in the power of estimating the region-specific or voxel-specific HRF. We propose an approach that merges these two models in a general framework: estimate the HRF on the training data sets, and applying the estimated HRF on the other part of the data sets. The merit of this framework is that it can utilize the advantages of both models. A comparison of performance is made between the GLM with three fixed HRFs and the new model with voxel-specific HRFs. The main results are as follows: (1) in 18 of the 21 patients, the new model has a higher adjusted coefficient of multiple determination than the GLM with fixed HRF; (2) in some subjects, with the new model, we found areas of activation that had not been detected with the three fixed HRFs at our threshold of significance. The results suggest that the new model can do better than the fixed HRF GLM for the analysis of epileptic activity with EEG-fMRI.

Using voxel-specific hemodynamic response function in EEG-fMRI data analysis

Most existing analytical techniques for EEG-fMRI data need specific assumptions about the hemodynamic response function (HRF). These assumptions may not be appropriate when the HRF varies from subject to subject or from region to region. In this article, we introduce a deconvolution method for EEG-fMRI activation detection, which can be implemented with voxel-specific HRFs. A comparison of performance is made between three fixed HRFs and the deconvolution method under the framework of the general linear model. The main results are as follows: (1) the volume of detected regions from the deconvolved HRFs is larger. (2) In some subjects, the deconvolution technique can find areas of activation that have not been detected with the three fixed HRFs at our threshold of significance. (3) Deconvolution obtained higher adjusted coefficients of multiple determination compared to those obtained with the three fixed HRFs. The results suggest that the fixed HRF methods may not be the most appropriate for the analysis of epileptic activity with EEG-fMRI, and the deconvolution method may be a better choice.

Analysis of speech-related variance in rapid event-related fMRI using a time-aware acquisition system

Speech production introduces signal changes in fMRI data that can mimic or mask the task-induced BOLD response. Rapid event-related designs with variable ISIs address these concerns by minimizing the correlation of task and speech-related signal changes without sacrificing efficiency; however, the increase in residual variance due to speech still decreases statistical power and must be explicitly addressed primarily through post-processing techniques. We investigated the timing, magnitude, and location of speech-related variance in an overt picture naming fMRI study with a rapid event-related design, using a data acquisition system that time-stamped image acquisitions, speech, and a pneumatic belt signal on the same clock. Using a spectral subtraction algorithm to remove scanner gradient noise from recorded speech, we related the timing of speech, stimulus presentation, chest wall movement, and image acquisition. We explored the relationship of an extended speech event time course and respiration on signal variance by performing a series of voxelwise regression analyses. Our results demonstrate that these effects are spatially heterogeneous, but their anatomic locations converge across subjects. Affected locations included basal areas (orbitofrontal, mesial temporal, brainstem), areas adjacent to CSF spaces, and lateral frontal areas. If left unmodeled, speech-related variance can result in regional detection bias that affects some areas critically implicated in language function. The results establish the feasibility of detecting and mitigating speech-related variance in rapid event-related fMRI experiments with single word utterances. They further demonstrate the utility of precise timing information about speech and respiration for this purpose.