On the importance of modeling fMRI transients when estimating effective connectivity: A dynamic causal modeling study using ASL data

Evaluating Models of the Ageing BOLD Response

Neural activity cannot be directly observed using fMRI; rather it must be inferred from the hemodynamic responses that neural activity causes. Solving this inverse problem is made possible through the use of forward models, which generate predicted hemodynamic responses given hypothesised underlying neural activity. Commonly-used hemodynamic models were developed to explain data from healthy young participants; however, studies of ageing and dementia are increasingly shifting the focus toward elderly populations. We evaluated the validity of a range of hemodynamic models across the healthy adult lifespan: from basis sets for the linear convolution models commonly used to analyse fMRI studies, to more advanced models including nonlinear fitting of a parameterised hemodynamic response function (HRF) and nonlinear fitting of a biophysical generative model (hemodynamic modelling, HDM). Using an exceptionally large sample of participants, and a sensorimotor task optimized for detecting the shape of the BOLD response to brief stimulation, we first characterised the effects of age on descriptive features of the response (e.g., peak amplitude and latency). We then compared these to features from more complex nonlinear models, fit to four regions of interest engaged by the task, namely left auditory cortex, bilateral visual cortex, left (contralateral) motor cortex and right (ipsilateral) motor cortex. Finally, we validated the extent to which parameter estimates from these models have predictive validity, in terms of how well they predict age in cross-validated multiple regression. We conclude that age-related differences in the BOLD response can be captured effectively by models with three free parameters. Furthermore, we show that biophysical models like the HDM have predictive validity comparable to more common models, while additionally providing insights into underlying mechanisms, which go beyond descriptive features like peak amplitude or latency, and include estimation of nonlinear effects. Here, the HDM revealed that most of the effects of age on the BOLD response could be explained by an increased rate of vasoactive signal decay and decreased transit rate of blood, rather than changes in neural activity per se. However, in the absence of other types of neural/hemodynamic data, unique interpretation of HDM parameters is difficult from fMRI data alone, and some brain regions in some tasks (e.g., ipsilateral motor cortex) can show responses that are more difficult to capture using current models.

Physiological modeling of the BOLD signal and implications for effective connectivity: A primer

In this primer, I provide an overview of the physiological processes that contribute to the observed BOLD signal (i.e., the generative biophysical model), including their time course properties within the framework of the physiologically-informed dynamic causal modeling (P-DCM). The BOLD signal is primarily determined by the change in paramagnetic deoxygenated hemoglobin, which results from combination of changes in oxygen metabolism, and cerebral blood flow and volume. Specifically, the physiological origin of the so-called BOLD signal "transients" will be discussed, including the initial overshoot, steady-state activation and the post-stimulus undershoot. I argue that incorrect physiological assumptions in the generative model of the BOLD signal can lead to incorrect inferences pertaining to both local neuronal activity and effective connectivity between brain regions. In addition, I introduce the recent laminar BOLD signal model, which extends P-DCM to cortical depths-resolved BOLD signals, allowing for laminar neuronal activity to be determined using high-resolution fMRI data.

A Survey on Brain Effective Connectivity Network Learning

Human brain effective connectivity characterizes the causal effects of neural activities among different brain regions. Studies of brain effective connectivity networks (ECNs) for different populations contribute significantly to the understanding of the pathological mechanism associated with neuropsychiatric diseases and facilitate finding new brain network imaging markers for the early diagnosis and evaluation for the treatment of cerebral diseases. A deeper understanding of brain ECNs also greatly promotes brain-inspired artificial intelligence (AI) research in the context of brain-like neural networks and machine learning. Thus, how to picture and grasp deeper features of brain ECNs from functional magnetic resonance imaging (fMRI) data is currently an important and active research area of the human brain connectome. In this survey, we first show some typical applications and analyze existing challenging problems in learning brain ECNs from fMRI data. Second, we give a taxonomy of ECN learning methods from the perspective of computational science and describe some representative methods in each category. Third, we summarize commonly used evaluation metrics and conduct a performance comparison of several typical algorithms both on simulated and real datasets. Finally, we present the prospects and references for researchers engaged in learning ECNs.

Toward an integrative neurovascular framework for studying brain networks

Brain functional connectivity based on the measure of blood oxygen level-dependent (BOLD) functional magnetic resonance imaging (fMRI) signals has become one of the most widely used measurements in human neuroimaging. However, the nature of the functional networks revealed by BOLD fMRI can be ambiguous, as highlighted by a recent series of experiments that have suggested that typical resting-state networks can be replicated from purely vascular or physiologically driven BOLD signals. After going through a brief review of the key concepts of brain network analysis, we explore how the vascular and neuronal systems interact to give rise to the brain functional networks measured with BOLD fMRI. This leads us to emphasize a view of the vascular network not only as a confounding element in fMRI but also as a functionally relevant system that is entangled with the neuronal network. To study the vascular and neuronal underpinnings of BOLD functional connectivity, we consider a combination of methodological avenues based on multiscale and multimodal optical imaging in mice, used in combination with computational models that allow the integration of vascular information to explain functional connectivity.

Predicting neuronal response properties from hemodynamic responses in the auditory cortex

Recent functional MRI (fMRI) studies have highlighted differences in responses to natural sounds along the rostral-caudal axis of the human superior temporal gyrus. However, due to the indirect nature of the fMRI signal, it has been challenging to relate these fMRI observations to actual neuronal response properties. To bridge this gap, we present a forward model of the fMRI responses to natural sounds combining a neuronal model of the auditory cortex with physiological modeling of the hemodynamic BOLD response. Neuronal responses are modeled with a dynamic recurrent firing rate model, reflecting the tonotopic, hierarchical processing in the auditory cortex along with the spectro-temporal tradeoff in the rostral-caudal axis of its belt areas. To link modeled neuronal response properties with human fMRI data in the auditory belt regions, we generated a space of neuronal models, which differed parametrically in spectral and temporal specificity of neuronal responses. Then, we obtained predictions of fMRI responses through a biophysical model of the hemodynamic BOLD response (P-DCM). Using Bayesian model comparison, our results showed that the hemodynamic BOLD responses of the caudal belt regions in the human auditory cortex were best explained by modeling faster temporal dynamics and broader spectral tuning of neuronal populations, while rostral belt regions were best explained through fine spectral tuning combined with slower temporal dynamics. These results support the hypotheses of complementary neural information processing along the rostral-caudal axis of the human superior temporal gyrus.

Determining laminar neuronal activity from BOLD fMRI using a generative model

Laminar fMRI using the BOLD contrast enables the non-invasive investigation of mesoscopic functional circuits in the human brain. However, the laminar neuronal activity is spatiotemporally biased in the observed cortical depth profiles of the BOLD signal. In this study, we propose a generative fMRI signal model, comprehensively covering the relationship between cortical depth-dependent changes in excitatory and inhibitory neuronal activity with the sampling of the BOLD signal with finite voxels. The generative model allowed us to investigate pertinent questions regarding the accuracy of the laminar BOLD signal relative to the neuronal activity, and we found that: a) condition differences in laminar BOLD signals may be more reflective of neuronal activity than single condition BOLD signal depth profiles; b) angular dependence of the BOLD signal induces significant signal variability, which can mask underlying activity profiles; c) even if only three neuronal depths are of interest, more BOLD signal depths should be considered in the analysis. In addition, we recommend that the laminar BOLD data should be displayed using the centroid method to appreciate its spatial distribution in the original resolution. Finally, we showed that Bayesian model inversion of the generative model can improve sensitivity and specificity of assessing depth-dependent neuronal changes both for steady-state and dynamically.

Sub-millimetre resolution laminar fMRI using Arterial Spin Labelling in humans at 7 T

Laminar fMRI at ultra-high magnetic field strength is typically carried out using the Blood Oxygenation Level-Dependent (BOLD) contrast. Despite its unrivalled sensitivity to detecting activation, the BOLD contrast is limited in its spatial specificity due to signals stemming from intra-cortical ascending and pial veins. Alternatively, regional changes in perfusion (i.e., cerebral blood flow through tissue) are colocalised to neuronal activation, which can be non-invasively measured using Arterial Spin Labelling (ASL) MRI. In addition, ASL provides a quantitative marker of neuronal activation in terms of perfusion signal, which is simultaneously acquired along with the BOLD signal. However, ASL for laminar imaging is challenging due to the lower SNR of the perfusion signal and higher RF power deposition i.e., specific absorption rate (SAR) of ASL sequences. In the present study, we present for the first time in humans, isotropic sub-millimetre spatial resolution functional perfusion images using Flow-sensitive Alternating Inversion Recovery (FAIR) ASL with a 3D-EPI readout at 7 T. We show that robust statistical activation maps can be obtained with perfusion-weighting in a single session. We observed the characteristic BOLD amplitude increase towards the superficial laminae, and, in apparent discrepancy, the relative perfusion profile shows a decrease of the amplitude and the absolute perfusion profile a much smaller increase towards the cortical surface. Considering the draining vein effect on the BOLD signal using model-based spatial “convolution”, we show that the empirically measured perfusion and BOLD profiles are, in fact, consistent with each other. This study demonstrates that laminar perfusion fMRI in humans is feasible at 7 T and that caution must be exercised when interpreting BOLD signal laminar profiles as direct representation of the cortical distribution of neuronal activity.

ACOEC-FD: Ant Colony Optimization for Learning Brain Effective Connectivity Networks From Functional MRI and Diffusion Tensor Imaging

Identifying brain effective connectivity (EC) networks from neuroimaging data has become an effective tool that can evaluate normal brain functions and the injuries associated with neurodegenerative diseases. So far, there are many methods used to identify EC networks. However, most of the research currently focus on learning EC networks from single modal imaging data such as functional magnetic resonance imaging (fMRI) data. This paper proposes a new method, called ACOEC-FD, to learn EC networks from fMRI and diffusion tensor imaging (DTI) using ant colony optimization (ACO). First, ACOEC-FD uses DTI data to acquire some positively correlated relations among regions of interest (ROI), and takes them as anatomical constraint information to effectively restrict the search space of candidate arcs in an EC network. ACOEC-FD then achieves multi-modal imaging data integration by incorporating anatomical constraint information into the heuristic function of probabilistic transition rules to effectively encourage ants more likely to search for connections between structurally connected regions. Through simulation studies on generated datasets and real fMRI-DTI datasets, we demonstrate that the proposed approach results in improved inference results on EC compared to some methods that only used fMRI data.

Quantitative relations between transient BOLD responses, cortical energetics, and impulse firing in different cortical regions

The blood oxygen level-dependent (BOLD) functional magnetic resonance imaging signal arises as a consequence of changes in blood flow (cerebral blood flow) and oxygen usage (cerebral metabolic rate of oxygen) that in turn are modulated by changes in neuronal activity. Much attention has been given to both theoretical and experimental aspects of the energetics but not to the neuronal activity. Here we use our previous theory relating the steady-state BOLD signal to neuronal activity and amalgamate it with the standard dynamic causal model (DCM, Friston) theory to produce a quantitative model relating the time-dependent BOLD signal to the underlying neuronal activity. Unlike existing treatments, this new theory incorporates a nonzero baseline activity in a completely consistent way and is thus able to account for both positive and negative BOLD signals. It can reproduce a wide variety of experimental BOLD signals reported in the literature solely by adjusting the neuronal input activity. In this way it provides support for the claim that the main features of the signals, including poststimulus undershoot and overshoot, are principally a result of changes in neuronal activity.NEW & NOTEWORTHY A previous model relating the steady-state blood oxygen level-dependent (BOLD) signal to neuronal activity, both above and below baseline, is extended to account for transient BOLD signals. This allows for a detailed investigation of the role neuronal activity can play in such signals and also encompasses poststimulus undershoot and overshoot. A wide variety of experimental BOLD signals are reproduced solely by adjusting the neuronal input activity, including recent results regarding the BOLD signal in patients with schizophrenia.

Applications of dynamic functional connectivity to pain and its modulation

Since early work attempting to characterize the brain's role in pain, it has been clear that pain is not generated by a specific brain region, but rather by coordinated activity across a network of brain regions, the "neuromatrix." The advent of noninvasive whole-brain neuroimaging, including functional magnetic resonance imaging, has provided insight on coordinated activity in the pain neuromatrix and how correlations in activity between regions, referred to as "functional connectivity," contribute to pain and its modulation. Initial functional connectivity investigations assumed interregion connectivity remained stable over time, and measured variability across individuals. However, new dynamic functional connectivity (dFC) methods allow researchers to measure how connectivity changes over time within individuals, permitting insights on the dynamic reorganization of the pain neuromatrix in humans. We review how dFC methods have been applied to pain, and insights afforded on how brain connectivity varies across time, either spontaneously or as a function of psychological states, cognitive demands, or the external environment. Specifically, we review psychophysiological interaction, dynamic causal modeling, state-based dynamic community structure, and sliding-window analyses and their use in human functional neuroimaging of acute pain, chronic pain, and pain modulation. We also discuss promising uses of dFC analyses for the investigation of chronic pain conditions and predicting pain treatment efficacy and the relationship between state- and trait-based pain measures. Throughout this review, we provide information regarding the advantages and shortcomings of each approach, and highlight potential future applications of these methodologies for better understanding the brain processes associated with pain.

Scale-invariant rearrangement of resting state networks in the human brain under sustained stimulation

Brain activity at rest is characterized by widely distributed and spatially specific patterns of synchronized low-frequency blood-oxygenation level-dependent (BOLD) fluctuations, which correspond to physiologically relevant brain networks. This network behaviour is known to persist also during task execution, yet the details underlying task-associated modulations of within- and between-network connectivity are largely unknown. In this study we exploited a multi-parametric and multi-scale approach to investigate how low-frequency fluctuations adapt to a sustained n-back working memory task. We found that the transition from the resting state to the task state involves a behaviourally relevant and scale-invariant modulation of synchronization patterns within both task-positive and default mode networks. Specifically, decreases of connectivity within networks are accompanied by increases of connectivity between networks. In spite of large and widespread changes of connectivity strength, the overall topology of brain networks is remarkably preserved. We show that these findings are strongly influenced by connectivity at rest, suggesting that the absolute change of connectivity (i.e., disregarding the baseline) may not be the most suitable metric to study dynamic modulations of functional connectivity. Our results indicate that a task can evoke scale-invariant, distributed changes of BOLD fluctuations, further confirming that low frequency BOLD oscillations show a specialized response and are tightly bound to task-evoked activation.

Variational Bayesian inversion for hierarchical unsupervised generative embedding (HUGE)

A recently introduced hierarchical generative model unified the inference of effective connectivity in individual subjects and the unsupervised identification of subgroups defined by connectivity patterns. This hierarchical unsupervised generative embedding (HUGE) approach combined a hierarchical formulation of dynamic causal modelling (DCM) for fMRI with Gaussian mixture models and relied on Markov chain Monte Carlo (MCMC) sampling for inference. While well suited for the inversion of complex hierarchical models, MCMC-based sampling suffers from a computational burden that is prohibitive for many applications. To address this problem, this paper derives an efficient variational Bayesian (VB) inversion scheme for HUGE that simultaneously provides approximations to the posterior distribution over model parameters and to the log model evidence. The face validity of the VB scheme was tested using two synthetic fMRI datasets with known ground truth. Additionally, an empirical fMRI dataset of stroke patients and healthy controls was used to evaluate the practical utility of the method in application to real-world problems. Our analyses demonstrate good performance of our VB scheme, with a marked speed-up of model inversion by two orders of magnitude compared to MCMC, while maintaining a similar level of accuracy. Notably, additional acceleration would be possible if parallel computing techniques were applied. Generally, our VB implementation of HUGE is fast enough to support multi-start procedures for whole-group analyses, a useful strategy to ameliorate problems with local extrema. HUGE thus represents a potentially useful practical solution for an important problem in clinical neuromodeling and computational psychiatry, i.e., the unsupervised detection of subgroups in heterogeneous populations that are defined by effective connectivity.

From correlation to causation: Estimating effective connectivity from zero-lag covariances of brain signals

Knowing brain connectivity is of great importance both in basic research and for clinical applications. We are proposing a method to infer directed connectivity from zero-lag covariances of neuronal activity recorded at multiple sites. This allows us to identify causal relations that are reflected in neuronal population activity. To derive our strategy, we assume a generic linear model of interacting continuous variables, the components of which represent the activity of local neuronal populations. The suggested method for inferring connectivity from recorded signals exploits the fact that the covariance matrix derived from the observed activity contains information about the existence, the direction and the sign of connections. Assuming a sparsely coupled network, we disambiguate the underlying causal structure via L¹-minimization, which is known to prefer sparse solutions. In general, this method is suited to infer effective connectivity from resting state data of various types. We show that our method is applicable over a broad range of structural parameters regarding network size and connection probability of the network. We also explored parameters affecting its activity dynamics, like the eigenvalue spectrum. Also, based on the simulation of suitable Ornstein-Uhlenbeck processes to model BOLD dynamics, we show that with our method it is possible to estimate directed connectivity from zero-lag covariances derived from such signals. In this study, we consider measurement noise and unobserved nodes as additional confounding factors. Furthermore, we investigate the amount of data required for a reliable estimate. Additionally, we apply the proposed method on full-brain resting-state fast fMRI datasets. The resulting network exhibits a tendency for close-by areas being connected as well as inter-hemispheric connections between corresponding areas. In addition, we found that a surprisingly large fraction of more than one third of all identified connections were of inhibitory nature.

Changes in brain connectivity are considered an important biomarker for certain brain diseases. This directly raises the question of accessibility of connectivity from measured brain signals. Here we show how directed effective connectivity can be inferred from continuous brain signals, like fMRI. The main idea is to extract the connectivity from the inverse zero-lag covariance matrix of the measured signals. This is done using L¹-minimization via gradient descent algorithm on the manifold of unitary matrices. This ensures that the resulting network always fits the same covariance structure as the measured data, assuming a canonical linear model. Applying the estimation method on noise-free covariance matrices shows that the method works nicely on sparsely coupled networks with more than 40 nodes, provided network interaction is strong enough. Applying the estimation on simulated Ornstein-Uhlenbeck processes supposed to model BOLD signals demonstrates robustness against observation noise and unobserved nodes. In general, the proposed method can be applied to time-resolved covariance matrices in the frequency domain (cross-spectral densities), leading to frequency-resolved networks. We are able to demonstrate that our method leads to reliable results, if the sampled signals are long enough.

Determining Excitatory and Inhibitory Neuronal Activity from Multimodal fMRI Data Using a Generative Hemodynamic Model

Hemodynamic responses, in general, and the blood oxygenation level-dependent (BOLD) fMRI signal, in particular, provide an indirect measure of neuronal activity. There is strong evidence that the BOLD response correlates well with post-synaptic changes, induced by changes in the excitatory and inhibitory (E-I) balance between active neuronal populations. Typical BOLD responses exhibit transients, such as the early-overshoot and post-stimulus undershoot, that can be linked to transients in neuronal activity, but they can also result from vascular uncoupling between cerebral blood flow (CBF) and venous cerebral blood volume (venous CBV). Recently, we have proposed a novel generative hemodynamic model of the BOLD signal within the dynamic causal modeling framework, inspired by physiological observations, called P-DCM (Havlicek et al., 2015). We demonstrated the generative model's ability to more accurately model commonly observed neuronal and vascular transients in single regions but also effective connectivity between multiple brain areas (Havlicek et al., 2017b). In this paper, we additionally demonstrate the versatility of the generative model to jointly explain dynamic relationships between neuronal and hemodynamic physiological variables underlying the BOLD signal using multi-modal data. For this purpose, we utilized three distinct data-sets of experimentally induced responses in the primary visual areas measured in human, cat, and monkey brain, respectively: (1) CBF and BOLD responses; (2) CBF, total CBV, and BOLD responses (Jin and Kim, 2008); and (3) positive and negative neuronal and BOLD responses (Shmuel et al., 2006). By fitting the generative model to the three multi-modal experimental data-sets, we showed that the presence or absence of dynamic features in the BOLD signal is not an unambiguous indication of presence or absence of those features on the neuronal level. Nevertheless, the generative model that takes into account the dynamics of the physiological mechanisms underlying the BOLD response allowed dissociating neuronal from vascular transients and deducing excitatory and inhibitory neuronal activity time-courses from BOLD data alone and from multi-modal data.

Post-stimulus fMRI and EEG responses: Evidence for a neuronal origin hypothesised to be inhibitory

Post-stimulus undershoots, negative responses following cessation of stimulation, are widely observed in functional magnetic resonance (fMRI) blood oxygenation level dependent (BOLD) data. However, the debate surrounding whether the origin of this response phase is neuronal or vascular, and whether it provides functionally relevant information, that is additional to what is contained in the primary response, means that undershoots are widely overlooked. We simultaneously recorded electroencephalography (EEG), BOLD and cerebral blood-flow (CBF) [obtained from arterial spin labelled (ASL) fMRI] fMRI responses to hemifield checkerboard stimulation to test the potential neural origin of the fMRI post-stimulus undershoot. The post-stimulus BOLD and CBF signal amplitudes in both contralateral and ipsilateral visual cortex depended on the post-stimulus power of the occipital 8-13Hz (alpha) EEG neuronal activity, such that trials with highest EEG power showed largest fMRI undershoots in contralateral visual cortex. This correlation in post-stimulus EEG-fMRI responses was not predicted by the primary response amplitude. In the contralateral visual cortex we observed a decrease in both cerebral rate of oxygen metabolism (CMRO₂) and CBF during the post-stimulus phase. In addition, the coupling ratio (n) between CMRO₂ and CBF was significantly lower during the positive contralateral primary response phase compared with the post-stimulus phase and we propose that this reflects an altered balance of excitatory and inhibitory neuronal activity. Together our data provide strong evidence that the post-stimulus phase of the BOLD response has a neural origin which reflects, at least partially, an uncoupling of the neuronal responses driving the primary and post-stimulus responses, explaining the uncoupling of the signals measured in the two response phases. We suggest our results are consistent with inhibitory processes driving the post-stimulus EEG and fMRI responses. We therefore propose that new methods are required to model the post-stimulus and primary responses independently, enabling separate investigation of response phases in cognitive function and neurological disease.