Kevin M. Aquino

Bistability and Non-Gaussian Fluctuations in Spontaneous Cortical Activity

The brain is widely assumed to be a paradigmatic example of a complex, self-organizing system. As such, it should exhibit the classic hallmarks of nonlinearity, multistability, and “nondiffusivity” (large coherent fluctuations). Surprisingly, at least at the very large scale of neocortical dynamics, there is little empirical evidence to support this, and hence most computational and methodological frameworks for healthy brain activity have proceeded very reasonably from a purely linear and diffusive perspective. By studying the temporal fluctuations of power in human resting-state electroencephalograms, we show that, although these simple properties may hold true at some temporal scales, there is strong evidence for bistability and nondiffusivity in key brain rhythms. Bistability is manifest as nonclassic bursting between high- and low-amplitude modes in the alpha rhythm. Nondiffusivity is expressed through the irregular appearance of high amplitude “extremal” events in beta rhythm power fluctuations. The statistical robustness of these observations was confirmed through comparison with Gaussian-rendered phase-randomized surrogate data. Although there is a good conceptual framework for understanding bistability in cortical dynamics, the implications of the extremal events challenge existing frameworks for understanding large-scale brain systems.

Hemodynamic traveling waves in human visual cortex.

Functional MRI (fMRI) experiments rely on precise characterization of the blood oxygen level dependent (BOLD) signal. As the spatial resolution of fMRI reaches the sub-millimeter range, the need for quantitative modelling of spatiotemporal properties of this hemodynamic signal has become pressing. Here, we find that a detailed physiologically-based model of spatiotemporal BOLD responses predicts traveling waves with velocities and spatial ranges in empirically observable ranges. Two measurable parameters, related to physiology, characterize these waves: wave velocity and damping rate. To test these predictions, high-resolution fMRI data are acquired from subjects viewing discrete visual stimuli. Predictions and experiment show strong agreement, in particular confirming BOLD waves propagating for at least 5–10 mm across the cortical surface at speeds of 2–12 mm s-1. These observations enable fundamentally new approaches to fMRI analysis, crucial for fMRI data acquired at high spatial resolution.

Spatiotemporal hemodynamic response functions derived from physiology

Probing neural activity with functional magnetic resonance imaging (fMRI) relies upon understanding the hemodynamic response to changes in neural activity. Although existing studies have extensively characterized the temporal hemodynamic response, less is understood about the spatial and spatiotemporal hemodynamic responses. This study systematically characterizes the spatiotemporal response by deriving the hemodynamic response due to a short localized neural drive, i.e., the spatiotemporal hemodynamic response function (stHRF) from a physiological model of hemodynamics based on a poroelastic model of cortical tissue. In this study, the models boundary conditions are clarified and a resulting nonlinear hemodynamic wave equation is derived. From this wave equation, damped linear hemodynamic waves are predicted from the stHRF. The main features of these waves depend on two physiological parameters: wave propagation speed, which depends on mean cortical stiffness, and damping which depends on effective viscosity. Some of these predictions were applied and validated in a companion study (Aquino et al., 2012). The advantages of having such a theory for the stHRF include improving the interpretation of spatiotemporal dynamics in fMRI data; improving estimates of neural activity with fMRI spatiotemporal deconvolution; and enabling wave interactions between hemodynamic waves to be predicted and exploited to improve the signal to noise ratio of fMRI.

The spatiotemporal hemodynamic response function for depth-dependent functional imaging of human cortex.

The gray matter of human cortex is characterized by depth-dependent differences in neuronal activity and connections (Shipp, 2007) as well as in the associated vasculature (Duvernoy et al., 1981). The resolution limit of functional magnetic resonance imaging (fMRI) measurements is now below a millimeter, promising the non-invasive measurement of these properties in awake and behaving humans (Muckli et al., 2015; Olman et al., 2012; Ress et al., 2007). To advance this endeavor, we present a detailed spatiotemporal hemodynamic response function (HRF) reconstructed through the use of high-resolution, submillimeter fMRI. We decomposed the HRF into directions tangential and perpendicular to the cortical surface and found that key spatial properties of the HRF change significantly with depth from the cortical surface. Notably, we found that the spatial spread of the HRF increases linearly from 4.8mm at the gray/white matter boundary to 6.6mm near the cortical surface. Using a hemodynamic model, we posit that this effect can be explained by the depth profile of the cortical vasculature, and as such, must be taken into account to properly estimate the underlying neuronal responses at different cortical depths.

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

ABSTRACT The effects of astrocytic dynamics on the blood oxygen‐level dependent (BOLD) response are modeled. The dynamics are represented via an astrocytic response function that approximates the effects of astrocytic activity, including delay between neural activity and hemodynamic response. The astrocytic response function is incorporated into a spatiotemporal hemodynamic model to predict the BOLD response measured using functional magnetic resonance imaging (fMRI). Adding astrocytic dynamics is shown to significantly improve the ability of the model to robustly reproduce the spatiotemporal properties of the experimental data such as characteristic frequency and time‐to‐peak. Moreover, the results are consistent across different astrocytic response functions, thus a simple impulsive form suffices to model the effective time delay of astrocytic responses. Finally, the results yield improved estimates of previously reported hemodynamic parameters, such as natural frequency and decay rate of the flow signal, which are consistent with experimentally verified physiological limits. The techniques developed in this study will contribute to improved analysis of BOLD‐fMRI data. HIGHLIGHTSAstrocytic dynamics are incorporated into a spatiotemporal hemodynamic model.The effects approximate time delay between neural activity and hemodynamic response.Adding astrocytic dynamics improves prediction and interpretation of fMRI data.Better estimates of previously reported hemodynamic parameters are obtained.Results can improve future data analyses and spatiotemporal fMRI deconvolution.

Inference of direct and multistep effective connectivities from functional connectivity of the brain and of relationships to cortical geometry

BACKGROUND The problem of inferring effective brain connectivity from functional connectivity is under active investigation, and connectivity via multistep paths is poorly understood. NEW METHOD A method is presented to calculate the direct effective connection matrix (deCM), which embodies direct connection strengths between brain regions, from functional CMs (fCMs) by minimizing the difference between an experimental fCM and one calculated via neural field theory from an ansatz deCM based on an experimental anatomical CM. RESULTS The best match between fCMs occurs close to a critical point, consistent with independent published stability estimates. Residual mismatch between fCMs is identified to be largely due to interhemispheric connections that are poorly estimated in an initial ansatz deCM due to experimental limitations; improved ansatzes substantially reduce the mismatch and enable interhemispheric connections to be estimated. Various levels of significant multistep connections are then imaged via the neural field theory (NFT) result that these correspond to powers of the deCM; these are shown to be predictable from geometric distances between regions. COMPARISON WITH EXISTING METHODS This method gives insight into direct and multistep effective connectivity from fCMs and relating to physiology and brain geometry. This contrasts with other methods, which progressively adjust connections without an overarching physiologically based framework to deal with multistep or poorly estimated connections. CONCLUSIONS deCMs can be usefully estimated using this method and the results enable multistep connections to be investigated systematically.

Shock-like haemodynamic responses induced in the primary visual cortex by moving visual stimuli

It is shown that recently discovered haemodynamic waves can form shock-like fronts when driven by stimuli that excite the cortex in a patch that moves faster than the haemodynamic wave velocity. If stimuli are chosen in order to induce shock-like behaviour, the resulting blood oxygen level-dependent (BOLD) response is enhanced, thereby improving the signal to noise ratio of measurements made with functional magnetic resonance imaging. A spatio-temporal haemodynamic model is extended to calculate the BOLD response and determine the main properties of waves induced by moving stimuli. From this, the optimal conditions for stimulating shock-like responses are determined, and ways of inducing these responses in experiments are demonstrated in a pilot study.

Biophysically based method to deconvolve spatiotemporal neurovascular signals from fMRI data

BACKGROUND Functional magnetic resonance imaging (fMRI) is commonly used to infer hemodynamic changes in the brain after increased neural activity, measuring the blood oxygen level-dependent (BOLD) signal. An important challenge in the analyses of fMRI data is to develop methods that can accurately deconvolve the BOLD signal to extract the driving neural activity and the underlying cerebrovascular effects. NEW METHOD A biophysically based method is developed, which combines an extensively verified physiological hemodynamic model with a Wiener filter, to deconvolve the BOLD signal. RESULTS The method is able to simultaneously obtain spatiotemporal images of underlying neurovascular signals, including neural activity, cerebral blood flow, cerebral blood volume, and deoxygenated hemoglobin concentration. The method is tested on simulated data and applied to various experimental data to demonstrate its stability, accuracy, and utility. COMPARISON WITH EXISTING METHODS The resulting profiles of the deconvolved signals are consistent with measurements reported in the literature, obtained via multiple neuroimaging modalities. CONCLUSIONS The method provides new testable predictions of the spatiotemporal relations of the deconvolved signals for future studies. This demonstrates the ability of the method to quantify and analyze the neurovascular mechanisms that underlie fMRI, thereby expanding its potential uses.

Towards a complete forward prediction from visual stimulus to BOLD.

Functional magnetic resonance imaging (fMRI) has become a standard tool in vision science, and some properties of visual cortex are fairly well understood and modelled, such as retinotopic organisation, contrast response functions and the spatiotemporal Hemodynamic Response Function (stHRF). Here we combine these individual models into a new framework, integrating existing models. The key components are (i) retinal processing; (ii) accurate retino cortical projection (Schira et al 2010); (iii) neural responses; and a (iv) spatiotemporal hemodynamic modeling (Aquino et al. 2012 PLoS CB), combined to a modular toolbox. We argue that the result is greater than the sum of its parts, allowing the complete simulation of fMRI experiments, from visual input (video) to BOLD responses in space and time on an average cortical surface (FS_average) within a few minutes. This supports a number of novel applications. Firstly, exploring interactions between the models and generating exact predictions for a more realistic testing of each of the integrated models. Secondly, a more precise planning of fMRI experiments by generating concrete hypothesis in the space that is actually measured, such as estimating the effect of spatial and temporal interactions between multiple stimulus components. Thirdly, it provides a novel teaching tool, with approximately 5-10 minutes from stimulus video to simulated BOLD responses on a normal desktop computer. Meeting abstract presented at VSS 2015.