Effects of astrocytic dynamics on spatiotemporal hemodynamics: Modeling and enhanced data analysis

Computational modeling of neuron-glia signaling interactions to unravel cellular and neural circuit functioning

Glial cells have been shown to be vital for various brain functions, including homeostasis, information processing, and cognition. Over the past 30 years, various signaling interactions between neuronal and glial cells have been shown to underlie these functions. This review summarizes the interactions, particularly between neurons and astrocytes, which are types of glial cells. Some of the interactions remain controversial in part due to the nature of experimental methods and preparations used. Based on the accumulated data, computational models of the neuron-astrocyte interactions have been developed to explain the complex functions of astrocytes in neural circuits and to test conflicting hypotheses. This review presents the most significant recent models, modeling methods and simulation tools for neuron-astrocyte interactions. In the future, we will especially need more experimental research on awake animals in vivo and new computational models of neuron-glia interactions to advance our understanding of cellular dynamics and the functioning of neural circuits in different brain regions.

Geometric constraints on human brain function

The anatomy of the brain necessarily constrains its function, but precisely how remains unclear. The classical and dominant paradigm in neuroscience is that neuronal dynamics are driven by interactions between discrete, functionally specialized cell populations connected by a complex array of axonal fibres1-3. However, predictions from neural field theory, an established mathematical framework for modelling large-scale brain activity4-6, suggest that the geometry of the brain may represent a more fundamental constraint on dynamics than complex interregional connectivity7,8. Here, we confirm these theoretical predictions by analysing human magnetic resonance imaging data acquired under spontaneous and diverse task-evoked conditions. Specifically, we show that cortical and subcortical activity can be parsimoniously understood as resulting from excitations of fundamental, resonant modes of the brain's geometry (that is, its shape) rather than from modes of complex interregional connectivity, as classically assumed. We then use these geometric modes to show that task-evoked activations across over 10,000 brain maps are not confined to focal areas, as widely believed, but instead excite brain-wide modes with wavelengths spanning over 60 mm. Finally, we confirm predictions that the close link between geometry and function is explained by a dominant role for wave-like activity, showing that wave dynamics can reproduce numerous canonical spatiotemporal properties of spontaneous and evoked recordings. Our findings challenge prevailing views and identify a previously underappreciated role of geometry in shaping function, as predicted by a unifying and physically principled model of brain-wide dynamics.

Modeling the relationship between neuronal activity and the BOLD signal: contributions from astrocyte calcium dynamics

Functional magnetic resonance imaging relies on the coupling between neuronal and vascular activity, but the mechanisms behind this coupling are still under discussion. Recent experimental evidence suggests that calcium signaling may play a significant role in neurovascular coupling. However, it is still controversial where this calcium signal is located (in neurons or elsewhere), how it operates and how relevant is its role. In this paper we introduce a biologically plausible model of the neurovascular coupling and we show that calcium signaling in astrocytes can explain main aspects of the dynamics of the coupling. We find that calcium signaling can explain so-far unrelated features such as the linear and non-linear regimes, the negative vascular response (undershoot) and the emergence of a (calcium-driven) Hemodynamic Response Function. These features are reproduced here for the first time by a single model of the detailed neuronal-astrocyte-vascular pathway. Furthermore, we analyze how information is coded and transmitted from the neuronal to the vascular system and we predict that frequency modulation of astrocytic calcium dynamics plays a key role in this process. Finally, our work provides a framework to link neuronal activity to the BOLD signal, and vice-versa, where neuronal activity can be inferred from the BOLD signal. This opens new ways to link known alterations of astrocytic calcium signaling in neurodegenerative diseases (e.g. Alzheimer's and Parkinson's diseases) with detectable changes in the neurovascular coupling.

External drivers of BOLD signal's non-stationarity

A fundamental challenge in neuroscience is to uncover the principles governing how the brain interacts with the external environment. However, assumptions about external stimuli fundamentally constrain current computational models. We show in silico that unknown external stimulation can produce error in the estimated linear time-invariant dynamical system. To address these limitations, we propose an approach to retrieve the external (unknown) input parameters and demonstrate that the estimated system parameters during external input quiescence uncover spatiotemporal profiles of external inputs over external stimulation periods more accurately. Finally, we unveil the expected (and unexpected) sensory and task-related extra-cortical input profiles using functional magnetic resonance imaging data acquired from 96 subjects (Human Connectome Project) during the resting-state and task scans. This dynamical systems model of the brain offers information on the structure and dimensionality of the BOLD signal's external drivers and shines a light on the likely external sources contributing to the BOLD signal's non-stationarity. Our findings show the role of exogenous inputs in the BOLD dynamics and highlight the importance of accounting for external inputs to unravel the brain's time-varying functional dynamics.

On the intersection between data quality and dynamical modelling of large-scale fMRI signals

Large-scale dynamics of the brain are routinely modelled using systems of nonlinear dynamical equations that describe the evolution of population-level activity, with distinct neural populations often coupled according to an empirically measured structural connectivity matrix. This modelling approach has been used to generate insights into the neural underpinnings of spontaneous brain dynamics, as recorded with techniques such as resting state functional MRI (fMRI). In fMRI, researchers have many degrees of freedom in the way that they can process the data and recent evidence indicates that the choice of pre-processing steps can have a major effect on empirical estimates of functional connectivity. However, the potential influence of such variations on modelling results are seldom considered. Here we show, using three popular whole-brain dynamical models, that different choices during fMRI preprocessing can dramatically affect model fits and interpretations of findings. Critically, we show that the ability of these models to accurately capture patterns in fMRI dynamics is mostly driven by the degree to which they fit global signals rather than interesting sources of coordinated neural dynamics. We show that widespread deflections can arise from simple global synchronisation. We introduce a simple two-parameter model that captures these fluctuations and performs just as well as more complex, multi-parameter biophysical models. From our combined analyses of data and simulations, we describe benchmarks to evaluate model fit and validity. Although most models are not resilient to denoising, we show that relaxing the approximation of homogeneous neural populations by more explicitly modelling inter-regional effective connectivity can improve model accuracy at the expense of increased model complexity. Our results suggest that many complex biophysical models may be fitting relatively trivial properties of the data, and underscore a need for tighter integration between data quality assurance and model development.

Cortical depth-dependent modeling of visual hemodynamic responses

A physiologically based three-dimensional (3D) hemodynamic model is developed to predict the experimentally observed blood oxygen level dependent (BOLD) responses versus the cortical depth induced by visual stimuli. Prior 2D approximations are relaxed in order to analyze 3D blood flow dynamics as a function of cortical depth. Comparison of the predictions with experimental data for evoked stimuli demonstrates that the full 3D model performs at least as well as previous approaches while remaining parsimonious. In particular, the 3D model requires significantly fewer assumptions and model parameters than previous models such that there is no longer need to define depth-specific parameter values for spatial spreading, peak amplitude, and hemodynamic velocity.

Exploring the relation between BOLD fMRI and cognitive performance using a computer-based quantitative systems pharmacology model: Applications to the COMTVAL158MET genotype and ketamine

BOLD fMRI is increasingly used mostly in an observational way to probe the effect of genotypes or therapeutic intervention in normal and diseased subjects. We use a mechanism-based quantitative systems pharmacology computer model of a human cortical microcircuit, previously calibrated for the 2-back working memory paradigm, adding established biophysical principles, of glucose metabolism, oxygen consumption, neurovascular effects and the paramagnetic impact on blood oxygen levels to calculate a readout for the voxel-based BOLD fMRI signal. The objective was to study the effect of the Catechol-O-methyl Transferase Val158Met (COMT) genotype on performance and BOLD fMRI. While the simulation suggests that on average virtual COMTVV genotype subjects perform worse, subjects with lower GABA, lower 5-HT₃ and higher 5-HT_1A activation can improve cognitive performance to the level of COMTMM subjects but at the expense of higher BOLD fMRI signal. In a schizophrenia condition, increased NMDA, GABA tone and noise levels, and lower D₁R activity can improve cognitive outcome with greater BOLD fMRI signal in COMT Val-carriers. We further generate hypotheses about why ketamine in healthy controls increases the BOLD fMRI signal but reduces cognitive performance. These simulations suggest a strong non-linear relationship between BOLD fMRI signal and cognitive performance. When validated, this mechanistic approach can be useful for moving beyond the descriptive nature of BOLD fMRI imaging and supporting the proper interpretation of imaging biomarkers in CNS disorders.

Assessing Uncertainty and Reliability of Connective Field Estimations From Resting State fMRI Activity at 3T

Connective Field (CF) modeling estimates the local spatial integration between signals in distinct cortical visual field areas. As we have shown previously using 7T data, CF can reveal the visuotopic organization of visual cortical areas even when applied to BOLD activity recorded in the absence of external stimulation. This indicates that CF modeling can be used to evaluate cortical processing in participants in which the visual input may be compromised. Furthermore, by using Bayesian CF modeling it is possible to estimate the co-variability of the parameter estimates and therefore, apply CF modeling to single cases. However, no previous studies evaluated the (Bayesian) CF model using 3T resting-state fMRI data. This is important since 3T scanners are much more abundant and more often used in clinical research compared to 7T scanners. Therefore in this study, we investigate whether it is possible to obtain meaningful CF estimates from 3T resting state (RS) fMRI data. To do so, we applied the standard and Bayesian CF modeling approaches on two RS scans, which were separated by the acquisition of visual field mapping data in 12 healthy participants. Our results show good agreement between RS- and visual field (VF)- based maps using either the standard or Bayesian CF approach. In addition to quantify the uncertainty associated with each estimate in both RS and VF data, we applied our Bayesian CF framework to provide the underlying marginal distribution of the CF parameters. Finally, we show how an additional CF parameter, beta, can be used as a data-driven threshold on the RS data to further improve CF estimates. We conclude that Bayesian CF modeling can characterize local functional connectivity between visual cortical areas from RS data at 3T. Moreover, observations obtained using 3T scanners were qualitatively similar to those reported for 7T. In particular, we expect the ability to assess parameter uncertainty in individual participants will be important for future clinical studies.

Propagation of BOLD Activity Reveals Task-dependent Directed Interactions Across Human Visual Cortex

It has recently been shown that large-scale propagation of blood-oxygen-level-dependent (BOLD) activity is constrained by anatomical connections and reflects transitions between behavioral states. It remains to be seen, however, if the propagation of BOLD activity can also relate to the brain's anatomical structure at a more local scale. Here, we hypothesized that BOLD propagation reflects structured neuronal activity across early visual field maps. To explore this hypothesis, we characterize the propagation of BOLD activity across V1, V2, and V3 using a modeling approach that aims to disentangle the contributions of local activity and directed interactions in shaping BOLD propagation. It does so by estimating the effective connectivity (EC) and the excitability of a noise-diffusion network to reproduce the spatiotemporal covariance structure of the data. We apply our approach to 7T fMRI recordings acquired during resting state (RS) and visual field mapping (VFM). Our results reveal different EC interactions and changes in cortical excitability in RS and VFM, and point to a reconfiguration of feedforward and feedback interactions across the visual system. We conclude that the propagation of BOLD activity has functional relevance, as it reveals directed interactions and changes in cortical excitability in a task-dependent manner.

Comparing dynamic causal models of neurovascular coupling with fMRI and EEG/MEG

This technical note presents a dynamic causal modelling (DCM) procedure for evaluating different models of neurovascular coupling in the human brain - using combined electromagnetic (M/EEG) and functional magnetic resonance imaging (fMRI) data. This procedure compares the evidence for biologically informed models of neurovascular coupling using Bayesian model comparison. First, fMRI data are used to localise regionally specific neuronal responses. The coordinates of these responses are then used as the location priors in a DCM of electrophysiological responses elicited by the same paradigm. The ensuing estimates of model parameters are then used to generate neuronal drive functions, which model pre- or post-synaptic activity for each experimental condition. These functions form the input to a model of neurovascular coupling, whose parameters are estimated from the fMRI data. Crucially, this enables one to evaluate different models of neurovascular coupling, using Bayesian model comparison - asking, for example, whether instantaneous or delayed, pre- or post-synaptic signals mediate haemodynamic responses. We provide an illustrative application of the procedure using a single-subject auditory fMRI and MEG dataset. The code and exemplar data accompanying this technical note are available through the statistical parametric mapping (SPM) software.

Power spectrum of resting-state blood-oxygen-level-dependent signal

Hemodynamic modeling is used to explore the origin, predict, and analyze the power spectrum of the resting-state blood-oxygen-level-dependent (BOLD) signal measured by functional magnetic resonance imaging (fMRI), which has been reported to have a power-law form, i.e., P(f)∝f^{-s}, where P(f) is the power, f is the frequency, and s>0 is the power-law exponent. However, current fMRI experimental paradigms have limited acquisition durations, affecting the spectral resolution of fMRI data at the low-frequency regime. Here, the claimed power-law spectrum is investigated by using a recent hemodynamic model to analytically derive the BOLD power spectrum, with parameters that are related to neurophysiology. The theoretical results show that, for all realistic parameter combinations, the BOLD power spectrum is flat at f≲0.01Hz, has a weak resonance originating from intrinsic oscillations of vasodilatory response, and becomes a power law for high frequencies, all of which is in agreement with an empirical data set that describes the spectrum of one subject and brain region. However, the results are contrary to studies reporting a pure power-law spectrum at f≲0.2Hz. The discrepancy is attributed largely to data averaging employed by current approaches that averages together important properties of the BOLD power spectrum, such as its resonance, that biases the spectrum to only show a power law. Data averaging also reduces the high-frequency power-law exponent relative to individual cases. Overall, this work demonstrates how the model can reproduce BOLD dynamics and further analyze its low-frequency behavior. Moreover, it also uses the model to explain the impact of procedures, such as data averaging, on the reported features of the BOLD power spectrum.

Feasibility of functional magnetic resonance imaging of ocular dominance and orientation preference in primary visual cortex

A recent hemodynamic model is extended and applied to simulate and explore the feasibility of detecting ocular dominance (OD) and orientation preference (OP) columns in primary visual cortex by means of functional magnetic resonance imaging (fMRI). The stimulation entails a short oriented bar stimulus being presented to one eye and mapped to cortical neurons with corresponding OD and OP selectivity. Activated neurons project via patchy connectivity to excite other neurons with similar OP in nearby visual fields located preferentially along the direction of stimulus orientation. The resulting blood oxygen level dependent (BOLD) response is estimated numerically via the model's spatiotemporal hemodynamic response function. The results are then used to explore the feasibility of detecting spatial OD-OP modulation, either directly measuring BOLD or by using Wiener deconvolution to filter the image and estimate the underlying neural activity. The effect of noise is also considered and it is estimated that direct detection can be robust for fMRI resolution of around 0.5 mm, whereas detection with Wiener deconvolution is possible at a broader range from 0.125 mm to 1 mm resolution. The detection of OD-OP features is strongly dependent on hemodynamic parameters, such as low velocity and high damping reduce response spreads and result in less blurring. The short-bar stimulus that gives the most detectable response is found to occur when neural projections are at 45 relative to the edge of local OD boundaries, which provides a constraint on the OD-OP architecture even when it is not fully resolved.

Cognitive neuroscience using wearable magnetometer arrays: Non-invasive assessment of language function

Recent work has demonstrated that Optically Pumped Magnetometers (OPMs) can be utilised to create a wearable Magnetoencephalography (MEG) system that is motion robust. In this study, we use this system to map eloquent cortex using a clinically validated language lateralisation paradigm (covert verb generation: 120 trials, ∼10 min total duration) in healthy adults (n = 3). We show that it is possible to lateralise and localise language function on a case by case basis using this system. Specifically, we show that at a sensor and source level we can reliably detect a lateralising beta band (15-30 Hz) desynchronization in all subjects. This is the first study of human cognition using OPMs and not only highlights this technology's utility as tool for (developmental) cognitive neuroscience but also its potential to contribute to surgical planning via mapping of eloquent cortex, especially in young children.

Phase-synchronization-based parcellation of resting state fMRI signals reveals topographically organized clusters in early visual cortex

Resting-state fMRI is widely used to study brain function and connectivity. However, interpreting patterns of resting state (RS) fMRI activity remains challenging as they may arise from different neuronal mechanisms than those triggered by exogenous events. Currently, this limits the use of RS-fMRI for understanding cortical function in health and disease. Here, we examine the phase synchronization (PS) properties of blood-oxygen level dependent (BOLD) signals obtained during visual field mapping (VFM) and RS with 7T fMRI. This data-driven approach exploits spatiotemporal covariations in the phase of BOLD recordings to establish the presence of clusters of synchronized activity. We find that, in both VFM and RS data, selecting the most synchronized neighboring recording sites identifies spatially localized PS clusters that follow the topographic organization of the visual cortex. However, in activity obtained during VFM, PS is spatially more extensive than in RS activity, likely reflecting stimulus-driven interactions between local responses. Nevertheless, the similarity of the PS clusters obtained for RS and stimulus-driven fMRI suggest that they share a common neuroanatomical origin. Our finding justifies and facilitates direct comparison of RS and stimulus-evoked activity.