Deep EEG source localization via EMD-based fMRI high spatial frequency.

Brain imaging with a high-spatiotemporal resolution is crucial for accurate brain-function mapping. Electroencephalography (EEG) and functional Magnetic Resonance Imaging (fMRI) are two popular neuroimaging modalities with complementary features that record brain function with high temporal and spatial resolution, respectively. One popular non-invasive way to obtain data with both high spatial and temporal resolutions is to combine the fMRI activation map and EEG data to improve the spatial resolution of the EEG source localization. However, using the whole fMRI map may cause spurious results for the EEG source localization, especially for deep brain regions. Considering the head's conductivity, deep regions' sources with low activity are unlikely to be detected by the EEG electrodes at the scalp. In this study, we use fMRI's high spatial-frequency component to identify the local high-intensity activations that are most likely to be captured by the EEG. The 3D Empirical Mode Decomposition (3D-EMD), a data-driven method, is used to decompose the fMRI map into its spatial-frequency components. Different validation measurements for EEG source localization show improved performance for the EEG inverse-modeling informed by the fMRI's high-frequency spatial component compared to the fMRI-informed EEG source-localization methods. The level of improvement varies depending on the voxels' intensity and their distribution. Our experimental results also support this conclusion.

Solving large-scale MEG/EEG source localisation and functional connectivity problems simultaneously using state-space models.

State-space models are widely employed across various research disciplines to study unobserved dynamics. Conventional estimation techniques, such as Kalman filtering and expectation maximisation, offer valuable insights but incur high computational costs in large-scale analyses. Sparse inverse covariance estimators can mitigate these costs, but at the expense of a trade-off between enforced sparsity and increased estimation bias, necessitating careful assessment in low signal-to-noise ratio (SNR) situations. To address these challenges, we propose a three-fold solution: (1) Introducing multiple penalised state-space (MPSS) models that leverage data-driven regularisation; (2) Developing novel algorithms derived from backpropagation, gradient descent, and alternating least squares to solve MPSS models; (3) Presenting a K-fold cross-validation extension for evaluating regularisation parameters. We validate this MPSS regularisation framework through lower and more complex simulations under varying SNR conditions, including a large-scale synthetic magneto- and electro-encephalography (MEG/EEG) data analysis. In addition, we apply MPSS models to concurrently solve brain source localisation and functional connectivity problems for real event-related MEG/EEG data, encompassing thousands of sources on the cortical surface. The proposed methodology overcomes the limitations of existing approaches, such as constraints to small-scale and region-of-interest analyses. Thus, it may enable a more accurate and detailed exploration of cognitive brain functions.

Holo-Hilbert spectral-based noise removal method for EEG high-frequency bands.

Simultaneous EEG-fMRI is a growing and promising field, as it has great potential to further our understanding of the spatiotemporal dynamics of brain function in health and disease. In particular, there is much interest in understanding the fMRI correlates of brain activity in the gamma band (> 30 Hz), as these frequencies are thought to be associated with cognitive processes involving perception, attention, and memory, as well as with disorders such as schizophrenia and autism. However, progress in this area has been limited due to issues such as MR-induced artifacts in EEG recordings, which seem to be more problematic for gamma frequencies. This paper presents a noise removal method for the gamma band of EEG that is based on the Holo-Hilbert spectral analysis (HHSA), but with a new implementation strategy. HHSA uses a nested empirical mode decomposition (EMD) to identify amplitude and frequency modulations (AM and FM, respectively) by averaging over frequencies with high and significant powers. Our method examines gamma band by applying two layers of EMD to the FM and AM components, removing components with very low power based on the power-instantaneous frequency spectrum, and subsequently reconstructs the denoised gamma-band signal from the remaining components. Simulations demonstrate that our proposed method efficiently reduces artifacts while preserving the original gamma signal which is especially critical for simultaneous EEG/fMRI studies.

Detecting brain network communities: Considering the role of information flow and its different temporal scales.

The identification of community structure in graphs continues to attract great interest in several fields. Network neuroscience is particularly concerned with this problem considering the key roles communities play in brain processes and functionality. Most methods used for community detection in brain graphs are based on the maximization of a parameter-dependent modularity function that often obscures the physical meaning and hierarchical organization of the partitions of network nodes. In this work, we present a new method able to detect communities at different scales in a natural, unrestricted way. First, to obtain an estimation of the information flow in the network we release random walkers to freely move over it. The activity of the walkers is separated into oscillatory modes by using empirical mode decomposition. After grouping nodes by their co-occurrence at each time scale, k-modes clustering returns the desired partitions. Our algorithm was first tested on benchmark graphs with favorable performance. Next, it was applied to real and simulated anatomical and/or functional connectomes in the macaque and human brains. We found a clear hierarchical repertoire of community structures in both the anatomical and the functional networks. The observed partitions range from the evident division in two hemispheres -in which all processes are managed globally- to specialized communities seemingly shaped by physical proximity and shared function. Additionally, the spatial scales of a network's community structure (characterized by a measure we term within-communities path length) appear inversely proportional to the oscillatory modes' average frequencies. The proportionality constant may constitute a network-specific propagation velocity for the information flow. Our results stimulate the research of hierarchical community organization in terms of temporal scales of information flow in the brain network.

What Can Local Transfer Entropy Tell Us about Phase-Amplitude Coupling in Electrophysiological Signals?

Modulation of the amplitude of high-frequency cortical field activity locked to changes in the phase of a slower brain rhythm is known as phase-amplitude coupling (PAC). The study of this phenomenon has been gaining traction in neuroscience because of several reports on its appearance in normal and pathological brain processes in humans as well as across different mammalian species. This has led to the suggestion that PAC may be an intrinsic brain process that facilitates brain inter-area communication across different spatiotemporal scales. Several methods have been proposed to measure the PAC process, but few of these enable detailed study of its time course. It appears that no studies have reported details of PAC dynamics including its possible directional delay characteristic. Here, we study and characterize the use of a novel information theoretic measure that may address this limitation: local transfer entropy. We use both simulated and actual intracranial electroencephalographic data. In both cases, we observe initial indications that local transfer entropy can be used to detect the onset and offset of modulation process periods revealed by mutual information estimated phase-amplitude coupling (MIPAC). We review our results in the context of current theories about PAC in brain electrical activity, and discuss technical issues that must be addressed to see local transfer entropy more widely applied to PAC analysis. The current work sets the foundations for further use of local transfer entropy for estimating PAC process dynamics, and extends and complements our previous work on using local mutual information to compute PAC (MIPAC).

Estimation of global and local complexities of brain networks: A random walks approach.

The complexity of brain activity has been observed at many spatial scales and has been proposed to differentiate between mental states and disorders. Here we introduced a new measure of (global) network complexity, constructed as the sum of the complexities of its nodes (i.e., local complexity). The complexity of each node is obtained by comparing the sample entropy of the time series generated by the movement of a random walker on the network resulting from removing the node and its connections, with the sample entropy of the time series obtained from a regular lattice (ordered state) and a random network (disordered state). We studied the complexity of fMRI-based resting-state networks. We found that positively correlated (pos) networks comprising only the positive functional connections have higher complexity than anticorrelation (neg) networks (comprising the negative connections) and the network consisting of the absolute value of all connections (abs). We also observed a significant correlation between complexity and the strength of functional connectivity in the pos network. Our results suggest that the pos network is related to the information processing in the brain and that functional connectivity studies should analyze pos and neg networks separately instead of the abs network, as is commonly done.

The Importance of Anti-correlations in Graph Theory Based Classification of Autism Spectrum Disorder.

With the release of the multi-site Autism Brain Imaging Data Exchange, many researchers have applied machine learning methods to distinguish between healthy subjects and autistic individuals by using features extracted from resting state functional MRI data. An important part of applying machine learning to this problem is extracting these features. Specifically, whether to include negative correlations between brain region activities as relevant features and how best to define these features. For the second question, the graph theoretical properties of the brain network may provide a reasonable answer. In this study, we investigated the first issue by comparing three different approaches. These included using the positive correlation matrix (comprising only the positive values of the original correlation matrix), the absolute value of the correlation matrix, or the anticorrelation matrix (comprising only the negative correlation values) as the starting point for extracting relevant features using graph theory. We then trained a multi-layer perceptron in a leave-one-site out manner in which the data from a single site was left out as testing data and the model was trained on the data from the other sites. Our results show that on average, using graph features extracted from the anti-correlation matrix led to the highest accuracy and AUC scores. This suggests that anti-correlations should not simply be discarded as they may include useful information that would aid the classification task. We also show that adding the PCA transformation of the original correlation matrix to the feature space leads to an increase in accuracy.

Spatiotemporal Empirical Mode Decomposition of Resting-State fMRI Signals: Application to Global Signal Regression.

Resting-state functional connectivity MRI (rs-fcMRI) is a common method for mapping functional brain networks. However, estimation of these networks is affected by the presence of a common global systemic noise, or global signal (GS). Previous studies have shown that the common preprocessing steps of removing the GS may create spurious correlations between brain regions. In this paper, we decompose fMRI signals into 5 spatial and 3 temporal intrinsic mode functions (SIMF and TIMF, respectively) by means of the empirical mode decomposition (EMD), which is an adaptive data-driven method widely used to analyze non-linear and non-stationary phenomena. For each SIMF, functional connectivity matrices were computed by means of Pearson correlation between TIMFs of different brain areas. Thus, instead of a single connectivity matrix, we obtained 5 × 3 = 15 functional connectivity matrices. Given the high correlation and global efficiency values of the connectivity matrices related to the low spatial maps (SIMF3, SIMF4, and SIMF5), our results suggest that these maps can be considered as spatial global signal masks. Thus, by summing up the first two SIMFs extracted from the fMRI signals, we have automatically excluded the GS which is now voxel-specific. We compared the performance of our method with the conventional GS regression and to the results when the GS was not removed. While the correlation pattern identified by the other methods suffers from a low level of precision in identifying the correct brain network connectivity, our approach demonstrated expected connectivity patterns for the default mode network and task-positive network.

Measuring transient phase-amplitude coupling using local mutual information.

Here we demonstrate the suitability of a local mutual information measure for estimating the temporal dynamics of cross-frequency coupling (CFC) in brain electrophysiological signals. In CFC, concurrent activity streams in different frequency ranges interact and transiently couple. A particular form of CFC, phase-amplitude coupling (PAC), has raised interest given the growing amount of evidence of its possible role in healthy and pathological brain information processing. Although several methods have been proposed for PAC estimation, only a few have addressed the estimation of the temporal evolution of PAC, and these typically require a large number of experimental trials to return a reliable estimate. Here we explore the use of mutual information to estimate a PAC measure (MIPAC) in both continuous and event-related multi-trial data. To validate these two applications of the proposed method, we first apply it to a set of simulated phase-amplitude modulated signals and show that MIPAC can successfully recover the temporal dynamics of the simulated coupling in either continuous or multi-trial data. Finally, to explore the use of MIPAC to analyze data from human event-related paradigms, we apply it to an actual event-related human electrocorticographic (ECoG) data set that exhibits strong PAC, demonstrating that the MIPAC estimator can be used to successfully characterize amplitude-modulation dynamics in electrophysiological data.

Design of optimal nonlinear network controllers for Alzheimer's disease.

Brain stimulation can modulate the activity of neural circuits impaired by Alzheimer's disease (AD), having promising clinical benefit. However, all individuals with the same condition currently receive identical brain stimulation, with limited theoretical basis for this generic approach. In this study, we introduce a control theory framework for obtaining exogenous signals that revert pathological electroencephalographic activity in AD at a minimal energetic cost, while reflecting patients' biological variability. We used anatomical networks obtained from diffusion magnetic resonance images acquired by the Alzheimer's Disease Neuroimaging Initiative (ADNI) as mediators for the interaction between Duffing oscillators. The nonlinear nature of the brain dynamics is preserved, given that we extend the so-called state-dependent Riccati equation control to reflect the stimulation objective in the high-dimensional neural system. By considering nonlinearities in our model, we identified regions for which control inputs fail to correct abnormal activity. There are changes to the way stimulated regions are ranked in terms of the energetic cost of controlling the entire network, from a linear to a nonlinear approach. We also found that limbic system and basal ganglia structures constitute the top target locations for stimulation in AD. Patients with highly integrated anatomical networks-namely, networks having low average shortest path length, high global efficiency-are the most suitable candidates for the propagation of stimuli and consequent success on the control task. Other diseases associated with alterations in brain dynamics and the self-control mechanisms of the brain can be addressed through our framework.

Topological Properties of Resting-State fMRI Functional Networks Improve Machine Learning-Based Autism Classification.

Automatic algorithms for disease diagnosis are being thoroughly researched for use in clinical settings. They usually rely on pre-identified biomarkers to highlight the existence of certain problems. However, finding such biomarkers for neurodevelopmental disorders such as Autism Spectrum Disorder (ASD) has challenged researchers for many years. With enough data and computational power, machine learning (ML) algorithms can be used to interpret the data and extract the best biomarkers from thousands of candidates. In this study, we used the fMRI data of 816 individuals enrolled in the Autism Brain Imaging Data Exchange (ABIDE) to introduce a new biomarker extraction pipeline for ASD that relies on the use of graph theoretical metrics of fMRI-based functional connectivity to inform a support vector machine (SVM). Furthermore, we split the dataset into 5 age groups to account for the effect of aging on functional connectivity. Our methodology achieved better results than most state-of-the-art investigations on this dataset with the best model for the >30 years age group achieving an accuracy, sensitivity, and specificity of 95, 97, and 95%, respectively. Our results suggest that measures of centrality provide the highest contribution to the classification power of the models.

White Matter Structural Connectivity Is Not Correlated to Cortical Resting-State Functional Connectivity over the Healthy Adult Lifespan.

Structural connectivity (SC) of white matter (WM) and functional connectivity (FC) of cortical regions undergo changes in normal aging. As WM tracts form the underlying anatomical architecture that connects regions within resting state networks (RSNs), it is intuitive to expect that SC and FC changes with age are correlated. Studies that investigated the relationship between SC and FC in normal aging are rare, and have mainly compared between groups of elderly and younger subjects. The objectives of this work were to investigate linear SC and FC changes across the healthy adult lifespan, and to define relationships between SC and FC measures within seven whole-brain large scale RSNs. Diffusion tensor imaging (DTI) and resting-state functional MRI (rs-fMRI) data were acquired from 177 healthy participants (male/female = 69/108; aged 18-87 years). Forty cortical regions across both hemispheres belonging to seven template-defined RSNs were considered. Mean diffusivity (MD), fractional anisotropy (FA), mean tract length, and number of streamlines derived from DTI data were used as SC measures, delineated using deterministic tractography, within each RSN. Pearson correlation coefficients of rs-fMRI-obtained BOLD signal time courses between cortical regions were used as FC measure. SC demonstrated significant age-related changes in all RSNs (decreased FA, mean tract length, number of streamlines; and increased MD), and significant FC decrease was observed in five out of seven networks. Among the networks that showed both significant age related changes in SC and FC, however, SC was not in general significantly correlated with FC, whether controlling for age or not. The lack of observed relationship between SC and FC suggests that measures derived from DTI data that are commonly used to infer the integrity of WM microstructure are not related to the corresponding changes in FC within RSNs. The possible temporal lag between SC and FC will need to be addressed in future longitudinal studies to better elucidate the links between SC and FC changes in normal aging.

Multifactorial causal model of brain (dis)organization and therapeutic intervention: Application to Alzheimer's disease.

Generative models focused on multifactorial causal mechanisms in brain disorders are scarce and generally based on limited data. Despite the biological importance of the multiple interacting processes, their effects remain poorly characterized from an integrative analytic perspective. Here, we propose a spatiotemporal multifactorial causal model (MCM) of brain (dis)organization and therapeutic intervention that accounts for local causal interactions, effects propagation via physical brain networks, cognitive alterations, and identification of optimum therapeutic interventions. In this article, we focus on describing the model and applying it at the population-based level for studying late onset Alzheimer's disease (LOAD). By interrelating six different neuroimaging modalities and cognitive measurements, this model accurately predicts spatiotemporal alterations in brain amyloid-ß (Aß) burden, glucose metabolism, vascular flow, resting state functional activity, structural properties, and cognitive integrity. The results suggest that a vascular dysregulation may be the most-likely initial pathologic event leading to LOAD. Nevertheless, they also suggest that LOAD it is not caused by a unique dominant biological factor (e.g. vascular or Aß) but by the complex interplay among multiple relevant direct interactions. Furthermore, using theoretical control analysis of the identified population-based multifactorial causal network, we show the crucial advantage of using combinatorial over single-target treatments, explain why one-target Aß based therapies might fail to improve clinical outcomes, and propose an efficiency ranking of possible LOAD interventions. Although still requiring further validation at the individual level, this work presents the first analytic framework for dynamic multifactorial brain (dis)organization that may explain both the pathologic evolution of progressive neurological disorders and operationalize the influence of multiple interventional strategies.

Topology, Cross-Frequency, and Same-Frequency Band Interactions Shape the Generation of Phase-Amplitude Coupling in a Neural Mass Model of a Cortical Column.

Phase-amplitude coupling (PAC), a type of cross-frequency coupling (CFC) where the phase of a low-frequency rhythm modulates the amplitude of a higher frequency, is becoming an important indicator of information transmission in the brain. However, the neurobiological mechanisms underlying its generation remain undetermined. A realistic, yet tractable computational model of the phenomenon is thus needed. Here we analyze a neural mass model of a cortical column, comprising fourteen neuronal populations distributed across four layers (L2/3, L4, L5 and L6). A control analysis showed that the conditional transfer entropy (cTE) measure is able to correctly estimate the flow of information between neuronal populations. Then, we computed cTE from the phases to the amplitudes of the oscillations generated in the cortical column. This approach provides information regarding directionality by distinguishing PAC from APC (amplitude-phase coupling), i.e. the information transfer from amplitudes to phases, and can be used to estimate other types of CFC such as amplitude-amplitude coupling (AAC) and phase-phase coupling (PPC). While experiments often only focus on one or two PAC combinations (e.g., theta-gamma or alpha-gamma), we found that a cortical column can simultaneously generate almost all possible PAC combinations, depending on connectivity parameters, time constants, and external inputs. PAC interactions with and without an anatomical equivalent (direct and indirect interactions, respectively) were analyzed. We found that the strength of PAC between two populations was strongly correlated with the strength of the effective connections between the populations and, on average, did not depend on whether the PAC connection was direct or indirect. When considering a cortical column circuit as a complex network, we found that neuronal populations making indirect PAC connections had, on average, higher local clustering coefficient, efficiency, and betweenness centrality than populations making direct connections and populations not involved in PAC connections. This suggests that their interactions were more effective when transmitting information. Since approximately 60% of the obtained interactions represented indirect connections, our results highlight the importance of the topology of cortical circuits for the generation of the PAC phenomenon. Finally, our results demonstrated that indirect PAC interactions can be explained by a cascade of direct CFC and same-frequency band interactions, suggesting that PAC analysis of experimental data should be accompanied by the estimation of other types of frequency interactions for an integrative understanding of the phenomenon.

Modeling the Generation of Phase-Amplitude Coupling in Cortical Circuits: From Detailed Networks to Neural Mass Models.

Phase-amplitude coupling (PAC), the phenomenon where the amplitude of a high frequency oscillation is modulated by the phase of a lower frequency oscillation, is attracting an increasing interest in the neuroscience community due to its potential relevance for understanding healthy and pathological information processing in the brain. PAC is a diverse phenomenon, having been experimentally detected in at least ten combinations of rhythms: delta-theta, delta-alpha, delta-beta, delta-gamma, theta-alpha, theta-beta, theta-gamma, alpha-beta, alpha-gamma, and beta-gamma. However, a complete understanding of the biophysical mechanisms generating this diversity is lacking. Here we review computational models of PAC generation that range from detailed models of neuronal networks, where each cell is described by Hodgkin-Huxley-type equations, to neural mass models (NMMs) where only the average activities of neuronal populations are considered. We argue that NMMs are an appropriate mathematical framework (due to the small number of parameters and variables involved and the richness of the dynamics they can generate) to study the PAC phenomenon.

Laminar Distribution of Phase-Amplitude Coupling of Spontaneous Current Sources and Sinks.

Although resting-state functional connectivity is a commonly used neuroimaging paradigm, the underlying mechanisms remain unknown. Thalamo-cortical and cortico-cortical circuits generate oscillations at different frequencies during spontaneous activity. However, it remains unclear how the various rhythms interact and whether their interactions are lamina-specific. Here we investigated intra- and inter-laminar spontaneous phase-amplitude coupling (PAC). We recorded local-field potentials using laminar probes inserted in the forelimb representation of rat area S1. We then computed time-series of frequency-band- and lamina-specific current source density (CSD), and PACs of CSD for all possible pairs of the classical frequency bands in the range of 1-150 Hz. We observed both intra- and inter-laminar spontaneous PAC. Of 18 possible combinations, 12 showed PAC, with the highest measures of interaction obtained for the pairs of the theta/gamma and delta/gamma bands. Intra- and inter-laminar PACs involving layers 2/3-5a were higher than those involving layer 6. Current sinks (sources) in the delta band were associated with increased (decreased) amplitudes of high-frequency signals in the beta to fast gamma bands throughout layers 2/3-6. Spontaneous sinks (sources) of the theta and alpha bands in layers 2/3-4 were on average linked to dipoles completed by sources (sinks) in layer 6, associated with high (low) amplitudes of the beta to fast-gamma bands in the entire cortical column. Our findings show that during spontaneous activity, delta, theta, and alpha oscillations are associated with periodic excitability, which for the theta and alpha bands is lamina-dependent. They further emphasize the differences between the function of layer 6 and that of the superficial layers, and the role of layer 6 in controlling activity in those layers. Our study links theories on the involvement of PAC in resting-state functional connectivity with previous work that revealed lamina-specific anatomical thalamo-cortico-cortical connections.

Epidemic spreading model to characterize misfolded proteins propagation in aging and associated neurodegenerative disorders.

Misfolded proteins (MP) are a key component in aging and associated neurodegenerative disorders. For example, misfolded Amyloid-ß (Aß) and tau proteins are two neuropathogenic hallmarks of Alzheimer's disease. Mechanisms underlying intra-brain MP propagation/deposition remain essentially uncharacterized. Here, is introduced an epidemic spreading model (ESM) for MP dynamics that considers propagation-like interactions between MP agents and the brain's clearance response across the structural connectome. The ESM reproduces advanced Aß deposition patterns in the human brain (explaining 46∼56% of the variance in regional Aß loads, in 733 subjects from the ADNI database). Furthermore, this model strongly supports a) the leading role of Aß clearance deficiency and early Aß onset age during Alzheimer's disease progression, b) that effective anatomical distance from Aß outbreak region explains regional Aß arrival time and Aß deposition likelihood, c) the multi-factorial impact of APOE e4 genotype, gender and educational level on lifetime intra-brain Aß propagation, and d) the modulatory impact of Aß propagation history on tau proteins concentrations, supporting the hypothesis of an interrelated pathway between Aß pathophysiology and tauopathy. To our knowledge, the ESM is the first computational model highlighting the direct link between structural brain networks, production/clearance of pathogenic proteins and associated intercellular transfer mechanisms, individual genetic/demographic properties and clinical states in health and disease. In sum, the proposed ESM constitutes a promising framework to clarify intra-brain region to region transference mechanisms associated with aging and neurodegenerative disorders.

Energy-based stochastic control of neural mass models suggests time-varying effective connectivity in the resting state.

Several studies posit energy as a constraint on the coding and processing of information in the brain due to the high cost of resting and evoked cortical activity. This suggestion has been addressed theoretically with models of a single neuron and two coupled neurons. Neural mass models (NMMs) address mean-field based modeling of the activity and interactions between populations of neurons rather than a few neurons. NMMs have been widely employed for studying the generation of EEG rhythms, and more recently as frameworks for integrated models of neurophysiology and functional MRI (fMRI) responses. To date, the consequences of energy constraints on the activity and interactions of ensembles of neurons have not been addressed. Here we aim to study the impact of constraining energy consumption during the resting-state on NMM parameters. To this end, we first linearized the model, then used stochastic control theory by introducing a quadratic cost function, which transforms the NMM into a stochastic linear quadratic regulator (LQR). Solving the LQR problem introduces a regime in which the NMM parameters, specifically the effective connectivities between neuronal populations, must vary with time. This is in contrast to current NMMs, which assume a constant parameter set for a given condition or task. We further simulated energy-constrained stochastic control of a specific NMM, the Wilson and Cowan model of two coupled neuronal populations, one of which is excitatory and the other inhibitory. These simulations demonstrate that with varying weights of the energy-cost function, the NMM parameters show different time-varying behavior. We conclude that constraining NMMs according to energy consumption may create more realistic models. We further propose to employ linear NMMs with time-varying parameters as an alternative to traditional nonlinear NMMs with constant parameters.

From blood oxygenation level dependent (BOLD) signals to brain temperature maps.

A theoretical framework is presented for converting Blood Oxygenation Level Dependent (BOLD) images to brain temperature maps, based on the idea that disproportional local changes in cerebral blood flow (CBF) as compared with cerebral metabolic rate of oxygen consumption (CMRO2) during functional brain activity, lead to both brain temperature changes and the BOLD effect. Using an oxygen limitation model and a BOLD signal model, we obtain a transcendental equation relating CBF and CMRO2 changes with the corresponding BOLD signal, which is solved in terms of the Lambert W function. Inserting this result in the dynamic bioheat equation describing the rate of temperature changes in the brain, we obtain a nonautonomous ordinary differential equation that depends on the BOLD response, which is solved numerically for each brain voxel. Temperature maps obtained from a real BOLD dataset registered in an attention to visual motion experiment were calculated, obtaining temperature variations in the range: (-0.15, 0.1) which is consistent with experimental results. The statistical analysis revealed that significant temperature activations have a similar distribution pattern than BOLD activations. An interesting difference was the activation of the precuneus in temperature maps, a region involved in visuospatial processing, an effect that was not observed on BOLD maps. Furthermore, temperature maps were more localized to gray matter regions than the original BOLD maps, showing less activated voxels in white matter and cerebrospinal fluid.