Roberto C. Sotero

Studying the human brain anatomical network via diffusion-weighted MRI and Graph Theory.

Our goal is to study the human brain anatomical network. For this, the anatomical connection probabilities (ACP) between 90 cortical and subcortical brain gray matter areas are estimated from diffusion-weighted Magnetic Resonance Imaging (DW-MRI) techniques. The ACP between any two areas gives the probability that those areas are connected at least by a single nervous fiber. Then, the brain is modeled as a non-directed weighted graph with continuous arc weights given by the ACP matrix. Based on this approach, complex networks properties such as small-world attributes, efficiency, degree distribution, vulnerability, betweenness centrality and motifs composition are studied. The analysis was carried out for 20 right-handed healthy subjects (mean age: 31.10, S.D.: 7.43). According to the results, all networks have small-world and broad-scale characteristics. Additionally, human brain anatomical networks present bigger local efficiency and smaller global efficiency than the corresponding random networks. In a vulnerability and betweenness centrality analysis, the most indispensable and critical anatomical areas were identified: putamens, precuneus, insulas, superior parietals and superior frontals. Interestingly, some areas have a negative vulnerability (e.g. superior temporal poles, pallidums, supramarginals and hechls), which suggest that even at the cost of losing in global anatomical efficiency, these structures were maintained through the evolutionary processes due to their important functions. Finally, symmetrical characteristic building blocks (motifs) of size 3 and 4 were calculated, obtaining that motifs of size 4 are the expanded version of motif of size 3. These results are in agreement with previous anatomical studies in the cat and macaque cerebral cortex.

Model driven EEG/fMRI fusion of brain oscillations

This article reviews progress and challenges in model driven EEG/fMRI fusion with a focus on brain oscillations. Fusion is the combination of both imaging modalities based on a cascade of forward models from ensemble of post‐synaptic potentials (ePSP) to net primary current densities (nPCD) to EEG; and from ePSP to vasomotor feed forward signal (VFFSS) to BOLD. In absence of a model, data driven fusion creates maps of correlations between EEG and BOLD or between estimates of nPCD and VFFS. A consistent finding has been that of positive correlations between EEG alpha power and BOLD in both frontal cortices and thalamus and of negative ones for the occipital region. For model driven fusion we formulate a neural mass EEG/fMRI model coupled to a metabolic hemodynamic model. For exploratory simulations we show that the Local Linearization (LL) method for integrating stochastic differential equations is appropriate for highly nonlinear dynamics. It has been successfully applied to small and medium sized networks, reproducing the described EEG/BOLD correlations. A new LL‐algebraic method allows simulations with hundreds of thousands of neural populations, with connectivities and conduction delays estimated from diffusion weighted MRI. For parameter and state estimation, Kalman filtering combined with the LL method estimates the innovations or prediction errors. From these the likelihood of models given data are obtained. The LL‐innovation estimation method has been already applied to small and medium scale models. With improved Bayesian computations the practical estimation of very large scale EEG/fMRI models shall soon be possible. Hum Brain Mapp, 2009.

Realistically Coupled Neural Mass Models Can Generate EEG Rhythms

We study the generation of EEG rhythms by means of realistically coupled neural mass models. Previous neural mass models were used to model cortical voxels and the thalamus. Interactions between voxels of the same and other cortical areas and with the thalamus were taken into account. Voxels within the same cortical area were coupled (short-range connections) with both excitatory and inhibitory connections, while coupling between areas (long-range connections) was considered to be excitatory only. Short-range connection strengths were modeled by using a connectivity function depending on the distance between voxels. Coupling strength parameters between areas were defined from empirical anatomical data employing the information obtained from probabilistic paths, which were tracked by water diffusion imaging techniques and used to quantify white matter tracts in the brain. Each cortical voxel was then described by a set of 16 random differential equations, while the thalamus was described by a set of 12 random differential equations. Thus, for analyzing the neuronal dynamics emerging from the interaction of several areas, a large system of differential equations needs to be solved. The sparseness of the estimated anatomical connectivity matrix reduces the number of connection parameters substantially, making the solution of this system faster. Simulations of human brain rhythms were carried out in order to test the model. Physiologically plausible results were obtained based on this anatomically constrained neural mass model.

Biophysical model for integrating neuronal activity, EEG, fMRI and metabolism

Our goal is to model the coupling between neuronal activity, cerebral metabolic rates of glucose and oxygen consumption, cerebral blood flow (CBF), electroencephalography (EEG) and blood oxygenation level-dependent (BOLD) responses. In order to accomplish this, two previous models are coupled: a metabolic/hemodynamic model (MHM) for a voxel, linking BOLD signals and neuronal activity, and a neural mass model describing the neuronal dynamics within a voxel and its interactions with voxels of the same area (short-range interactions) and other areas (long-range interactions). For coupling both models, we take as the input to the BOLD model, the number of active synapses within the voxel, that is, the average number of synapses that will receive an action potential within the time unit. This is obtained by considering the action potentials transmitted between neuronal populations within the voxel, as well as those arriving from other voxels. Simulations are carried out for testing the integrated model. Results show that realistic evoked potentials (EP) at electrodes on the scalp surface and the corresponding BOLD signals for each voxel are produced by the model. In another simulation, the alpha rhythm was reproduced and reasonable similarities with experimental data were obtained when calculating correlations between BOLD signals and the alpha power curve. The origin of negative BOLD responses and the characteristics of EEG, PET and BOLD signals in Alzheimers disease were also studied.

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 Alzheimers 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 brains 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 Alzheimers 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.

Identification and comparison of stochastic metabolic/hemodynamic models (sMHM) for the generation of the BOLD signal.

This paper extends a previously formulated deterministic metabolic/hemodynamic model for the generation of blood oxygenated level dependent (BOLD) responses to include both physiological and observation stochastic components (sMHM). This adds a degree of flexibility when fitting the model to actual data by accounting for un-modelled activity. We then show how the innovation method can be used to estimate unobserved metabolic/hemodynamic as well as vascular variables of the sMHM, from simulated and actual BOLD data. The proposed estimation method allowed for doing model comparison by calculating the model’s AIC and BIC. This methodology was then used to select between different neurovascular coupling assumptions underlying sMHM. The proposed framework was first validated on simulations and then applied to BOLD data from a motor task experiment. The models under comparison in the analysis of the actual data considered that vascular response was coupled to: (I) inhibition, (II) excitation, (III) both excitation and inhibition. Data was best described by model II, although model III was also supported.

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

ABSTRACT 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‐&bgr; (A&bgr;) 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 A&bgr;) 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 A&bgr; 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. Graphical abstract Symbol Symbol. No Caption available. HighlightsA multifactorial causal model (MCM) of brain (dis)organization and therapeutic intervention is proposed.Prediction of complex multifactorial alterations in Alzheimer’s disease, using six different neuroimaging modalities and the MCM.Identification of potential triggering pathological events and associated “epicenter” brain regions.Identification and characterization of direct multifactorial interactions, vulnerability, and influence level of each biological factor.Identification of optimum therapeutic strategies to stop/reverse disease.

Dynamical mean field model of a neural-glial mass

Our goal is to model the behavior of an ensemble of interacting neurons and astrocytes (the neural-glial mass). For this, a model describing N tripartite synapses is proposed. Each tripartite synapse consists of presynaptic and postsynaptic nerve terminals, as well as the synaptically associated astrocytic microdomain, and is described by a system of 13 stochastic differential equations. Then, by applying the dynamical mean field approximation (DMA) (Hasegawa, 2003a, 2003b) the system of 13N equations is reduced to 13(13 2) 195 deterministic differential equations for the means and the second-order moments of local and global variables. Simulations are carried out for studying the response of the neural-glial mass to external inputs applied to either the presynaptic terminals or the astrocytes. Three cases were considered: the astrocytes influence only the presynaptic terminal, only the postsynaptic terminal, or both the presynaptic and postsynaptic terminals. As a result, a wide range of responses varying from singles spikes to train of spikes was evoked on presynaptic and postsynaptic terminals. The experimentally observed phenomenon of spontaneous activity in astrocytes was replicated on the neural-glial mass. The model predicts that astrocytes can have a strong and activity-dependent influence on synaptic transmission. Finally, simulations show that the dynamics of astrocytes influences the synchronization ratio between neurons, predicting a peak in the synchronization for specific values of the astrocytes parameters.

ANATOMICALLY-CONSTRAINED EFFECTIVE CONNECTIVITY AMONG LAYERS IN A CORTICAL COLUMN MODELED AND ESTIMATED FROM LOCAL FIELD POTENTIALS

We propose a neural mass model for anatomically-constrained effective connectivity among neuronal populations residing in four layers (L2/3, L4, L5 and L6) within a cortical column. Eight neuronal populations in a given column--an excitatory population and an inhibitory population per layer--are assumed to be coupled via effective connections of unknown strengths that need to be estimated. The effective connections are constrained to anatomical connections that have been shown to exist in previous anatomical studies. The neural input to a cortical column is directed into the two populations in L4. The anatomically-constrained effective connectivity is captured by a system of 16 stochastic differential equations. Solving these equations yields the average postsynaptic potentials and transmembrane currents generated in each population. The current source density (CSD) responses in each layer, which serve as the model observations, are equated in the model to the sum of all currents generated within that layer. The model is implemented in a continuous-discrete state-space framework, and the innovation method is used for estimating the model parameters from CSD data. To this end, local field potential (LFP) responses to forepaw stimulation were recorded in rat area S1 using multi-channel linear probes. LFPs were converted to CSD signals, which were averaged within each layer, yielding one CSD response per layer. To estimate the effective strengths of connections between all cortical layers, the model was fitted to these CSD signals. The results show that the pattern of effective interactions is strongly influenced by the pattern of strengths of the anatomical connections; however, these two patterns are not identical. The estimated anatomically-constrained effective connectivity matrix and the anatomical connectivity matrix shared five of their six strongest connections, although rankings according to connection strength differed. The strongest effective connections were from excitatory neurons in layer 4 to excitatory neurons in layer 2/3. Our study shows the feasibility of estimating anatomically-constrained effective connectivity within a cortical column, and indicates that there is a strong influence of anatomical connectivity on effective connectivity between cortical layers.

Random fields—Union intersection tests for detecting functional connectivity in EEG/MEG imaging

Electrophysiological (EEG/MEG) imaging challenges statistics by providing two views of the same underlying spatio‐temporal brain activity: a topographic view (EEG/MEG) and tomographic view (EEG/MEG source reconstructions). It is a common practice that statistical parametric mapping (SPM) for these two situations is developed separately. In particular, assessing statistical significance of functional connectivity is a major challenge in these types of studies. This work introduces statistical tests for assessing simultaneously the significance of spatio‐temporal correlation structure between ERP/ERF components as well as that of their generating sources. We introduce a greatest root statistic as the multivariate test statistic for detecting functional connectivity between two sets of EEG/MEG measurements at a given time instant. We use some new results in random field theory to solve the multiple comparisons problem resulting from the correlated test statistics at each time instant. In general, our approach using the union‐intersection (UI) principle provides a framework for hypothesis testing about any linear combination of sensor data, which allows the analysis of the correlation structure of both topographic and tomographic views. The performance of the proposed method is illustrated with real ERP data obtained from a face recognition experiment. Hum Brain Mapp 2009.