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.

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.

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

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.

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.

Response-mode decomposition of spatio-temporal haemodynamics.

The blood oxygen-level dependent (BOLD) response to a neural stimulus is analysed using the transfer function derived from a physiologically based poroelastic model of cortical tissue. The transfer function is decomposed into components that correspond to distinct poles, each related to a response mode with a natural frequency and dispersion relation; together these yield the total BOLD response. The properties of the decomposed components provide a deeper understanding of the nature of the BOLD response, via the components' frequency dependences, spatial and temporal power spectra, and resonances. The transfer function components are then used to separate the BOLD response to a localized impulse stimulus, termed the Green function or spatio-temporal haemodynamic response function, into component responses that are explicitly related to underlying physiological quantities. The analytical results also provide a quantitative tool to calculate the linear BOLD response to an arbitrary neural drive, which is faster to implement than direct Fourier transform methods. The results of this study can be used to interpret functional magnetic resonance imaging data in new ways based on physiology, to enhance deconvolution methods and to design experimental protocols that can selectively enhance or suppress particular responses, to probe specific physiological phenomena.

Eigenmodes of brain activity: Neural field theory predictions and comparison with experiment.

Neural field theory of the corticothalamic system is applied to predict and analyze the activity eigenmodes of the bihemispheric brain, focusing particularly on their spatial structure. The eigenmodes of a single brain hemisphere are found to be close analogs of spherical harmonics, which are the natural modes of the sphere. Instead of multiple eigenvalues being equal, as in the spherical case, cortical folding splits them to have distinct values. Inclusion of interhemispheric connections between homologous regions via the corpus callosum leads to further splitting that depends on symmetry or antisymmetry of activity between brain hemispheres, and the strength and sign of the interhemispheric connections. Symmetry properties of the lowest observed eigenmodes strongly constrain the interhemispheric connectivity strengths and unihemispheric mode spectra, and it is predicted that most spontaneous brain activity will be symmetric between hemispheres, consistent with observations. Comparison with the eigenmodes of an experimental anatomical connectivity matrix confirms these results, permits the relative strengths of intrahemispheric and interhemispheric connectivities to be approximately inferred from their eigenvalues, and lays the foundation for further experimental tests. The results are consistent with brain activity being in corticothalamic eigenmodes, rather than discrete "networks" and open the way to new approaches to brain analysis.

Deconvolution of neural dynamics from fMRI data using a spatiotemporal hemodynamic response function.

Functional magnetic resonance imaging (fMRI) is a powerful and broadly used means of non-invasively mapping human brain activity. However fMRI is an indirect measure that rests upon a mapping from neuronal activity to the blood oxygen level dependent (BOLD) signal via hemodynamic effects. The quality of estimated neuronal activity hinges on the validity of the hemodynamic model employed. Recent work has demonstrated that the hemodynamic response has non-separable spatiotemporal dynamics, a key property that is not implemented in existing fMRI analysis frameworks. Here both simulated and empirical data are used to demonstrate that using a physiologically based model of the spatiotemporal hemodynamic response function (stHRF) results in a quantitative improvement of the estimated neuronal response relative to unphysical space-time separable forms. To achieve this, an integrated spatial and temporal deconvolution is established using a recently developed stHRF. Simulated data allows the variation of key parameters such as noise and the spatial complexity of the neuronal drive, while knowing the neuronal input. The results demonstrate that the use of a spatiotemporally integrated HRF can avoid "ghost" neuronal responses that can otherwise be falsely inferred. Applying the spatiotemporal deconvolution to high resolution fMRI data allows the recovery of neuronal responses that are consistent with independent electrophysiological measures.

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 model's 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.

Spatiotemporal BOLD dynamics from a poroelastic hemodynamic model.

A quantitative theory is developed for the relationship between stimulus and the resulting blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal, including both spatial and temporal dynamics for the first time. The brain tissue is modeled as a porous elastic medium, whose interconnected pores represent the vasculature. The model explicitly incorporates conservation of blood mass, interconversion of oxygenated and deoxygenated hemoglobin, force balance within the blood and of blood pressure with vessel walls, and blood flow modulation due to neuronal activity. In appropriate limits it is shown to reproduce prior Balloon models of hemodynamic response, which do not include spatial variations. The regime of validity of such models is thereby clarified by elucidating their assumptions, and when these break down, for example when voxel sizes become small.