Agranular frontal cortical microcircuit underlying cognitive control in macaques

The error-related negativity and an N2-component recorded over medial frontal cortex index core functions of cognitive control. While they are known to originate from agranular frontal areas, the underlying microcircuit mechanisms remain elusive. Most insights about microcircuit function have been derived from variations of the so-called canonical microcircuit model. These microcircuit architectures are based extensively on studies from granular sensory cortical areas in monkeys, cats, and rodents. However, evidence has shown striking cytoarchitectonic differences across species and differences in the functional relationships across cortical layers in agranular compared to granular sensory areas. In this minireview, we outline a tentative microcircuit model underlying cognitive control in the agranular frontal cortex of primates. The model incorporates the main GABAergic interneuron subclasses with specific laminar arrangements and target regions on pyramidal cells. We emphasize the role of layer 5 pyramidal cells in error and conflict detection. We offer several specific questions necessary for creating a specific intrinsic microcircuit model of the agranular frontal cortex.

Cortical origin of theta error signals

A multi-scale approach elucidated the origin of the error-related-negativity (ERN), with its associated theta-rhythm, and the post-error-positivity (Pe) in macaque supplementary eye field (SEF). Using biophysical modeling, synaptic inputs to a subpopulation of layer-3 (L3) and layer-5 (L5) pyramidal cells (PCs) were optimized to reproduce error-related spiking modulation and inter-spike intervals. The intrinsic dynamics of dendrites in L5 but not L3 error PCs generate theta rhythmicity with random phases. Saccades synchronized the phases of the theta-rhythm, which was magnified on errors. Contributions from error PCs to the laminar current source density (CSD) observed in SEF were negligible and could not explain the observed association between error-related spiking modulation in L3 PCs and scalp-EEG. CSD from recorded laminar field potentials in SEF was comprised of multipolar components, with monopoles indicating strong electro-diffusion, dendritic/axonal electrotonic current leakage outside SEF, or violations of the model assumptions. Our results also demonstrate the involvement of secondary cortical regions, in addition to SEF, particularly for the later Pe component. The dipolar component from the observed CSD paralleled the ERN dynamics, while the quadrupolar component paralleled the Pe. These results provide the most advanced explanation to date of the cellular mechanisms generating the ERN.

Resolving the mesoscopic missing link: Biophysical modeling of EEG from cortical columns in primates

Event-related potentials (ERP) are among the most widely measured indices for studying human cognition. While their timing and magnitude provide valuable insights, their usefulness is limited by our understanding of their neural generators at the circuit level. Inverse source localization offers insights into such generators, but their solutions are not unique. To address this problem, scientists have assumed the source space generating such signals comprises a set of discrete equivalent current dipoles, representing the activity of small cortical regions. Based on this notion, theoretical studies have employed forward modeling of scalp potentials to understand how changes in circuit-level dynamics translate into macroscopic ERPs. However, experimental validation is lacking because it requires in vivo measurements of intracranial brain sources. Laminar local field potentials (LFP) offer a mechanism for estimating intracranial current sources. Yet, a theoretical link between LFPs and intracranial brain sources is missing. Here, we present a forward modeling approach for estimating mesoscopic intracranial brain sources from LFPs and predict their contribution to macroscopic ERPs. We evaluate the accuracy of this LFP-based representation of brain sources utilizing synthetic laminar neurophysiological measurements and then demonstrate the power of the approach in vivo to clarify the source of a representative cognitive ERP component. To that end, LFP was measured across the cortical layers of visual area V4 in macaque monkeys performing an attention demanding task. We show that area V4 generates dipoles through layer-specific transsynaptic currents that biophysically recapitulate the ERP component through the detailed forward modeling. The constraints imposed on EEG production by this method also revealed an important dissociation between computational and biophysical contributors. As such, this approach represents an important bridge between laminar microcircuitry, through the mesoscopic activity of cortical columns to the patterns of EEG we measure at the scalp.

Identification of Negative BOLD Responses in Epilepsy Using Windkessel Models

Alongside positive blood oxygenation level–dependent (BOLD) responses associated with interictal epileptic discharges, a variety of negative BOLD responses (NBRs) are typically found in epileptic patients. Previous studies suggest that, in general, up to four mechanisms might underlie the genesis of NBRs in the brain: (i) neuronal disruption of network activity, (ii) altered balance of neurometabolic/vascular couplings, (iii) arterial blood stealing, and (iv) enhanced cortical inhibition. Detecting and classifying these mechanisms from BOLD signals are pivotal for the improvement of the specificity of the electroencephalography–functional magnetic resonance imaging (EEG-fMRI) image modality to identify the seizure-onset zones in refractory local epilepsy. This requires models with physiological interpretation that furnish the understanding of how these mechanisms are fingerprinted by their BOLD responses. Here, we used a Windkessel model with viscoelastic compliance/inductance in combination with dynamic models of both neuronal population activity and tissue/blood O₂ to classify the hemodynamic response functions (HRFs) linked to the above mechanisms in the irritative zones of epileptic patients. First, we evaluated the most relevant imprints on the BOLD response caused by variations of key model parameters. Second, we demonstrated that a general linear model is enough to accurately represent the four different types of NBRs. Third, we tested the ability of a machine learning classifier, built from a simulated ensemble of HRFs, to predict the mechanism underlying the BOLD signal from irritative zones. Cross-validation indicates that these four mechanisms can be classified from realistic fMRI BOLD signals. To demonstrate proof of concept, we applied our methodology to EEG-fMRI data from five epileptic patients undergoing neurosurgery, suggesting the presence of some of these mechanisms. We concluded that a proper identification and interpretation of NBR mechanisms in epilepsy can be performed by combining general linear models and biophysically inspired models.

Fully Passive Flexible Wireless Neural Recorder for the Acquisition of Neuropotentials from a Rat Model

Wireless implantable neural interfaces can record high-resolution neuropotentials without constraining patient movement. Existing wireless systems often require intracranial wires to connect implanted electrodes to an external head stage or/and deploy an application-specific integrated circuit (ASIC), which is battery-powered or externally power-transferred, raising safety concerns such as infection, electronics failure, or heat-induced tissue damage. This work presents a biocompatible, flexible, implantable neural recorder capable of wireless acquisition of neuropotentials without wires, batteries, energy harvesting units, or active electronics. The recorder, fabricated on a thin polyimide substrate, features a small footprint of 9 mm × 8 mm × 0.3 mm and is composed of passive electronic components. The absence of active electronics on the device leads to near zero power consumption, inherently avoiding the catastrophic failure of active electronics. We performed both in vitro validation in a tissue-simulating phantom and in vivo validation in an epileptic rat. The fully passive wireless recorder was implanted under rat scalp to measure neuropotentials from its contact electrodes. The implanted wireless recorder demonstrated its capability to capture low voltage neuropotentials, including somatosensory evoked potentials (SSEPs), and interictal epileptiform discharges (IEDs). Wirelessly recorded SSEP and IED signals were directly compared to those from wired electrodes to demonstrate the efficacy of the wireless data. In addition, a convoluted neural network-based machine learning algorithm successfully achieved IED signal recognition accuracy as high as 100 and 91% in wired and wireless IED data, respectively. These results strongly support the fully passive wireless neural recorder's capability to measure neuropotentials as low as tens of microvolts. With further improvement, the recorder system presented in this work may find wide applications in future brain machine interface systems.

Validating Non-invasive EEG Source Imaging Using Optimal Electrode Configurations on a Representative Rat Head Model

The curtain of technical limitations impeding rat multichannel non-invasive electroencephalography (EEG) has risen. Given the importance of this preclinical model, development and validation of EEG source imaging (ESI) is essential. We investigate the validity of well-known human ESI methodologies in rats which individual tissue geometries have been approximated by those extracted from an MRI template, leading also to imprecision in electrode localizations. With the half and fifth sensitivity volumes we determine both the theoretical minimum electrode separation for non-redundant scalp EEG measurements and the electrode sensitivity resolution, which vary over the scalp because of the head geometry. According to our results, electrodes should be at least ~3 to 3.5 mm apart for an optimal configuration. The sensitivity resolution is generally worse for electrodes at the boundaries of the scalp measured region, though, by analogy with human montages, concentrates the sensitivity enough to localize sources. Cramér-Rao lower bounds of source localization errors indicate it is theoretically possible to achieve ESI accuracy at the level of anatomical structures, such as the stimulus-specific somatosensory areas, using the template. More validation for this approximation is provided through the comparison between the template and the individual lead field matrices, for several rats. Finally, using well-accepted inverse methods, we demonstrate that somatosensory ESI is not only expected but also allows exploring unknown phenomena related to global sensory integration. Inheriting the advantages and pitfalls of human ESI, rat ESI will boost the understanding of brain pathophysiological mechanisms and the evaluation of ESI methodologies, new pharmacological treatments and ESI-based biomarkers.

Histological Characterization of the Irritative Zones in Focal Cortical Dysplasia Using a Preclinical Rat Model

Current clinical practice in focal epilepsy involves brain source imaging (BSI) to localize brain areas where from interictal epileptiform discharges (IEDs) emerge. These areas, named irritative zones, have been useful to define candidate seizures-onset zones during pre-surgical workup. Since human histological data are mostly available from final resected zones, systematic studies characterizing pathophysiological mechanisms and abnormal molecular/cellular substrates in irritative zones—independent of them being epileptogenic—are challenging. Combining BSI and histological analysis from all types of irritative zones is only possible through the use of preclinical animal models. Here, we recorded 32-channel spontaneous electroencephalographic data from rats that have focal cortical dysplasia (FCD) and chronic seizures. BSI for different IED subtypes was performed using the methodology presented in Bae et al. (2015). Post-mortem brain sections containing irritative zones were stained to quantify anatomical, functional, and inflammatory biomarkers specific for epileptogenesis, and the results were compared with those obtained using the contralateral healthy brain tissue. We found abnormal anatomical structures in all irritative zones (i.e., larger neuronal processes, glioreactivity, and vascular cuffing) and larger expressions for neurotransmission (i.e., NR2B) and inflammation (i.e., ILβ1, TNFα and HMGB1). We conclude that irritative zones in this rat preclinical model of FCD comprise abnormal tissues disregarding whether they are actually involved in icto-genesis or not. We hypothesize that seizure perpetuation happens gradually; hence, our results could support the use of IED-based BSI for the early diagnosis and preventive treatment of potential epileptic foci. Further verifications in humans are yet needed.

Quantitative assessment of hemodynamic and structural characteristics of in vivo brain tissue using total diffuse reflectance spectrum measured in a non-contact fashion

Here we present a new methodology that investigates the intrinsic structural and hemodynamic characteristics of in vivo brain tissue, in a non-contact fashion, and can be easily incorporated in an intra-operative environment. Within this methodology, relative total diffuse reflectance spectra (R_TD(λ)) were acquired from targets using a hybrid spectroscopy imaging system. A spectral interpretation algorithm was subsequently applied to R_TD(λ) to retrieve optical properties related to the compositional and structural characteristics of each target. Estimation errors of the proposed methodology were computationally evaluated using a Monte Carlo simulation model for photon migration under various conditions. It was discovered that this new methodology could handle moderate noise and achieve very high accuracy, but only if the refractive index of the target is known. The accuracy of the technique was also validated using a series of tissue phantom studies, and consistent and accurate estimates of μ_s'(λ)/μ_a(λ) were obtained from all the phantoms tested. Finally, a small-scale animal study was conducted to demonstrate the clinical utility of the reported method, wherein a forepaw stimulation model was utilized to induce transient hemodynamic responses in somatosensory cortices. With this approach, significant stimulation-related changes (p < 0.001) in cortical hemodynamic and structural characteristics were successfully measured.

Noninvasive targeting delivery and in vivo magnetic resonance tracking method for live apoptotic cells in cerebral ischemia with functional Fe2O3 magnetic nanoparticles

Background

Apoptotic neuronal death is known as programmed cell death. Inhibition of this progression might contribute to a new treatment strategy. However, methods for in vivo detection of live apoptotic cells are in need to be developed and established.

Context and purpose

The purpose of this study is to develop a new method for in vivo brain imaging for live apoptotic lesions using magnetic resonance imaging (MRI). We focused on the specific accumulation of our recently developed functional magnetic nanoparticles (FMNPs) into apoptotic cells using a rat cerebral ischemia model. Sulphorhodamine B, fluorescent dye was linked to valylalanylaspartic acid fluoromethyl ketone as a pan-caspase inhibitor to form SR-FLIVO. SR-FLIVO was bound with FMNPs to develop SR-FLIVO-FMNP probe. Ischemic rat brains were scanned by 7T MRI before and after intravenous injection of SR-FLIVO-FMNP and the distribution was evaluated by subtraction images of T2* colored mapping. SR-FLIVO, intracellular FMNPs, and T2* reduction area were histologically analyzed. The distribution of SR-FLIVO-FMNP was evaluated by subtracting the T2* signal images and was significantly correlated with the histological findings by TUNEL staining.

Results

Our experimental results revealed several findings where our newly developed probe SR-FLIVO-FMNP was intravenously administered into ischemic rats and FLIVO expression was tracked and found in apoptotic cells in rat brains after cerebral ischemia. A remarkable T2* reduction within the ischemic lesion was recorded using MRI based SR-FLIVO-FMNP probe as a contrasting agent due to the specific probe accumulation in apoptotic cells whereas, no observation of T2* reduction within the non-ischemic lesion due to no probe accumulation in non-apoptotic cells. Histological analysis based on the correlation between FLIVO and TUNEL staining showed that almost all FLIVO-positive cells were positive for TUNEL staining. These findings suggest the possibility for establishment of in vivo targeting delivery methods to live apoptotic cells based on conjugation of magnetic and fluorescent dual functional probes.

Conclusion

A newly developed probe SR-FLIVO-FMNP might be considered as a useful probe for in vivo apoptotic detection, and FMNPs might be a strong platform for noninvasive imaging and targeting delivery.

Electronic supplementary material

The online version of this article (doi:10.1186/s12951-016-0173-1) contains supplementary material, which is available to authorized users.

Intraoperative optical mapping of epileptogenic cortices during non-ictal periods in pediatric patients

Complete removal of epileptogenic cortex while preserving eloquent areas is crucial in patients undergoing epilepsy surgery. In this manuscript, the feasibility was explored of developing a new methodology based on dynamic intrinsic optical signal imaging (DIOSI) to intraoperatively detect and differentiate epileptogenic from eloquent cortices in pediatric patients with focal epilepsy. From 11 pediatric patients undergoing epilepsy surgery, negatively-correlated hemodynamic low-frequency oscillations (LFOs, ~ 0.02-0.1 Hz) were observed from the exposed epileptogenic and eloquent cortical areas, as defined by electrocorticography (ECoG), using a DIOSI system. These LFOs were classified into multiple groups in accordance with their unique temporal profiles. Causal relationships within these groups were investigated using the Granger causality method, and 83% of the ECoG-defined epileptogenic cortical areas were found to have a directed influence on one or more cortical areas showing LFOs within the field of view of the imaging system. To understand the physiological origins of LFOs, blood vessel density was compared between epileptogenic and normal cortical areas and a statistically-significant difference (p < 0.05) was detected. The differences in blood-volume and blood-oxygenation dynamics between eloquent and epileptogenic cortices were also uncovered using a stochastic modeling approach. This, in turn, yielded a means by which to separate epileptogenic from eloquent cortex using hemodynamic LFOs. The proposed methodology detects epileptogenic cortices by exploiting the effective connectivity that exists within cortical regions displaying LFOs and the biophysical features contributed by the altered vessel networks within the epileptogenic cortex. It could be used in conjunction with existing technologies for epileptogenic/eloquent cortex localization and thereby facilitate clinical decision-making.

A methodology for fast assessments to the electrical activity of barrel fields in vivo: from population inputs to single unit outputs

Here we propose a methodology to analyze volumetric electrical activity of neuronal masses in the somatosensory barrel field of Wistar rats. The key elements of the proposed methodology are a three-dimensional microelectrode array, which was customized by our group to observe extracellular recordings from an extended area of the barrel field, and a novel method for the current source density analysis. By means of this methodology, we were able to localize single barrels from their event-related responses to single whisker deflection. It was also possible to assess the spatiotemporal dynamics of neuronal aggregates in several barrels at the same time with the resolution of single neurons. We used simulations to study the robustness of our methodology to unavoidable physiological noise and electrode configuration. We compared the accuracy to reconstruct neocortical current sources with that obtained with a previous method. This constitutes a type of electrophysiological microscopy with high spatial and temporal resolution, which could change the way we analyze the activity of cortical neurons in the future.

Transplantation of bone marrow stromal cell-derived neural precursor cells ameliorates deficits in a rat model of complete spinal cord transection

After severe spinal cord injury, spontaneous functional recovery is limited. Numerous studies have demonstrated cell transplantation as a reliable therapeutic approach. However, it remains unknown whether grafted neuronal cells could replace lost neurons and reconstruct neuronal networks in the injured spinal cord. To address this issue, we transplanted bone marrow stromal cell-derived neural progenitor cells (BM-NPCs) in a rat model of complete spinal cord transection 9 days after the injury. BM-NPCs were induced from bone marrow stromal cells (BMSCs) by gene transfer of the Notch-1 intracellular domain followed by culturing in the neurosphere method. As reported previously, BM-NPCs differentiated into neuronal cells in a highly selective manner in vitro. We assessed hind limb movements of the animals weekly for 7 weeks to monitor functional recovery after local injection of BM-NPCs to the transected site. To test the sensory recovery, we performed functional magnetic resonance imaging (fMRI) using electrical stimulation of the hind limbs. In the injured spinal cord, transplanted BM-NPCs were confirmed to express neuronal markers 7 weeks following the transplantation. Grafted cells successfully extended neurites beyond the transected portion of the spinal cord. Adjacent localization of synaptophysin and PSD-95 in the transplanted cells suggested synaptic formations. These results indicated survival and successful differentiation of BM-NPCs in the severely injured spinal cord. Importantly, rats that received BM-NPCs demonstrated significant motor recovery when compared to the vehicle injection group. Volumes of the fMRI signals in somatosensory cortex were larger in the BM-NPC-grafted animals. However, neuronal activity was diverse and not confined to the original hind limb territory in the somatosensory cortex. Therefore, reconstruction of neuronal networks was not clearly confirmed. Our results indicated BM-NPCs as an effective method to deliver neuronal lineage cells in a severely injured spinal cord. However, reestablishment of neuronal networks in completed transected spinal cord was still a challenging task.

Pitfalls in the dipolar model for the neocortical EEG sources

For about six decades, primary current sources of the electroencephalogram (EEG) have been assumed dipolar in nature. In this study, we used electrophysiological recordings from anesthetized Wistar rats undergoing repeated whisker deflections to revise the biophysical foundations of the EEG dipolar model. In a first experiment, we performed three-dimensional recordings of extracellular potentials from a large portion of the barrel field to estimate intracortical multipolar moments generated either by single spiking neurons (i.e., pyramidal cells, PC; spiny stellate cells, SS) or by populations of them while experiencing synchronized postsynaptic potentials. As expected, backpropagating spikes along PC dendrites caused dipolar field components larger in the direction perpendicular to the cortical surface (49.7 ± 22.0 nA·mm). In agreement with the fact that SS cells have “close-field” configurations, their dipolar moment at any direction was negligible. Surprisingly, monopolar field components were detectable both at the level of single units (i.e., −11.7 ± 3.4 nA for PC) and at the mesoscopic level of mixed neuronal populations receiving extended synaptic inputs within either a cortical column (−0.44 ± 0.20 μA) or a 2.5-m3-voxel volume (−3.32 ± 1.20 μA). To evaluate the relationship between the macroscopically defined EEG equivalent dipole and the mesoscopic intracortical multipolar moments, we performed concurrent recordings of high-resolution skull EEG and laminar local field potentials. From this second experiment, we estimated the time-varying EEG equivalent dipole for the entire barrel field using either a multiple dipole fitting or a distributed type of EEG inverse solution. We demonstrated that mesoscopic multipolar components are altogether absorbed by any equivalent dipole in both types of inverse solutions. We conclude that the primary current sources of the EEG in the neocortex of rodents are not precisely represented by a single equivalent dipole and that the existence of monopolar components must be also considered at the mesoscopic level.

Coupling between gamma oscillation and fMRI signal in the rat somatosensory cortex: its dependence on systemic physiological parameters

The simultaneous recordings of neuronal and hemodynamic signals have revealed a significant involvement of high frequency bands (e.g., gamma range, 25-70 Hz) in neurovascular coupling. However, the dependence on a physiological parameter is unknown. In this study, we performed simultaneous electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) recordings in 12 Wistar rats using a conventional forepaw stimulation paradigm and concurrently monitored the systemic physiological parameters of the partial pressure of arterial oxygen, partial pressure of arterial carbon dioxide, pH, mean arterial blood pressure, and heart rate through the rat femoral artery. The high frequency bands in the artifact-free EEG signals, especially those in the gamma range, demonstrated a maximum correlation with fMRI signals in the rat somatosensory cortex. A multiple linear regression analysis demonstrated that the correlation coefficient between the gamma power and fMRI signal depended on the actual values of the physiological parameters (R(2)=0.20, p<0.05), whereas the gamma power and fMRI signal by itself were independent. Among the parameters, the heart rate had a statistically significant slope (95% CI: 0.00027-0.0016, p<0.01) in a multiple linear regression model. These results indicate that neurovascular coupling is mainly driven by gamma oscillations, as expected, but coupling or potential decoupling is strongly influenced by systemic physiological parameters, which dynamically reflect the baseline vital status of the subject.

An in vivo MRI Template Set for Morphometry, Tissue Segmentation, and fMRI Localization in Rats

Over the last decade, several papers have focused on the construction of highly detailed mouse high field magnetic resonance image (MRI) templates via non-linear registration to unbiased reference spaces, allowing for a variety of neuroimaging applications such as robust morphometric analyses. However, work in rats has only provided medium field MRI averages based on linear registration to biased spaces with the sole purpose of approximate functional MRI (fMRI) localization. This precludes any morphometric analysis in spite of the need of exploring in detail the neuroanatomical substrates of diseases in a recent advent of rat models. In this paper we present a new in vivo rat T2 MRI template set, comprising average images of both intensity and shape, obtained via non-linear registration. Also, unlike previous rat template sets, we include white and gray matter probabilistic segmentations, expanding its use to those applications demanding prior-based tissue segmentation, e.g., statistical parametric mapping (SPM) voxel-based morphometry. We also provide a preliminary digitalization of latest Paxinos and Watson atlas for anatomical and functional interpretations within the cerebral cortex. We confirmed that, like with previous templates, forepaw and hindpaw fMRI activations can be correctly localized in the expected atlas structure. To exemplify the use of our new MRI template set, were reported the volumes of brain tissues and cortical structures and probed their relationships with ontogenetic development. Other in vivo applications in the near future can be tensor-, deformation-, or voxel-based morphometry, morphological connectivity, and diffusion tensor-based anatomical connectivity. Our template set, freely available through the SPM extension website, could be an important tool for future longitudinal and/or functional extensive preclinical studies.

The Brain Connectivity Workshops: moving the frontiers of computational systems neuroscience

Understanding the link between neurobiology and cognition requires that neuroscience moves beyond mere structure-function correlations. An explicit systems perspective is needed in which putative mechanisms of how brain function is constrained by brain structure are mathematically formalized and made accessible for experimental investigation. Such a systems approach critically rests on a better understanding of brain connectivity in its various forms. Since 2002, frontier topics of connectivity and neural system analysis have been discussed in a multidisciplinary annual meeting, the Brain Connectivity Workshop (BCW), bringing together experimentalists and theorists from various fields. This article summarizes some of the main discussions at the two most recent workshops, 2006 at Sendai, Japan, and 2007 at Barcelona, Spain: (i) investigation of cortical micro- and macrocircuits, (ii) models of neural dynamics at multiple scales, (iii) analysis of "resting state" networks, and (iv) linking anatomical to functional connectivity. Finally, we outline some central challenges and research trajectories in computational systems neuroscience for the next years.

The micro-architecture of the cerebral cortex: functional neuroimaging models and metabolism

In order to interpret/integrate data obtained with different functional neuroimaging modalities (e.g. fMRI, EEG/MEG, PET/SPECT, fNIRS), forward-generative models of a diversity of brain mechanisms at the mesoscopic level are considered necessary. For the cerebral cortex, the brain structure with possibly the most relevance for functional neuroimaging, a variety of such biophysical models has been proposed over the last decade. The development of technological tools to investigate in vitro the physiological, anatomical and biochemical principles at the microscopic scale in comparative studies formed the basis for such theoretical progresses. However, with the most recent introduction of systems to record electrical (e.g. miniaturized probes chronically/acutely implantable in the brain), optical (e.g. two-photon laser scanning microscopy) and atomic nuclear spectral (e.g. nuclear magnetic resonance spectroscopy) signals using living laboratory animals, the field is receiving even greater attention. Major advances have been achieved by combining such sophisticated recording systems with new experimental strategies (e.g. transgenic/knock-out animals, high resolution stereotaxic manipulation systems for probe-guidance and cellular-scale chemical-delivery). Theoreticians may now be encouraged to re-consider previously formulated mesoscopic level models in order to incorporate important findings recently made at the microscopic scale. In this series of reviews, we summarize the background at the microscopic scale, which we suggest will constitute the foundations for upcoming representations at the mesoscopic level. In this first part, we focus our attention on the nerve ending particles in order to summarize basic principles and mechanisms underlying cellular metabolism in the cerebral cortex. It will be followed by two parts highlighting major features in its organization/working-principles to regulate both cerebral blood circulation and neuronal activity, respectively. Contemporary theoretical models for functional neuroimaging will be revised in the fourth part, with particular emphasis in their applications, advantages/limitations and future prospects.

Nonlinear local electrovascular coupling. II: From data to neuronal masses

In the companion article a local electrovascular coupling (LEVC) model was proposed to explain the continuous dynamics of electrical and vascular states within a cortical unit. These states produce certain mesoscopic reflections whose discrete time series can be reconstructed from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). In this article we develop a recursive optimization algorithm based on the local linearization (LL) filter and an innovation method to make statistical inferences about the LEVC model from both EEG and fMRI data, i.e., to estimate the unobserved states and the unknown parameters of the model. For a better understanding, the LL filter is described from a Bayesian point of view, providing the particulars for the case of hybrid data (e.g., EEG and fMRI), which could be sampled at different rates. The dynamics of the exogenous synaptic inputs going into the cortical unit are also estimated by introducing a set of Gaussian radial basis functions. In order to study the dynamics of the electrical and vascular states in the striate cortex of humans as well as their local interrelationships, we applied this algorithm to EEG and fMRI recordings obtained concurrently from two subjects while passively observing a radial checkerboard with a white/black pattern reversal. The EEG and fMRI data from the first subject was used to estimate the electrical/vascular states and parameters of the LEVC model in V1 for a 4.0 Hz reversion frequency. We used the EEG data from the second subject to investigate the changes in the dynamics of the electrical states when the frequency of reversion is varied from 0.5-4.0 Hz. Then we made use of the estimated electrical states to predict the effects on the vasculature that such variations produce.

Nonlinear local electrovascular coupling. I: A theoretical model

Here we present a detailed biophysical model of how brain electrical and vascular dynamics are generated within a basic cortical unit. The model was obtained from coupling a canonical neuronal mass and an expandable vasculature. In this proposal, we address several aspects related to electroencephalographic and functional magnetic resonance imaging data fusion: (1) the impact of the cerebral architecture (at different physical levels) on the observations; (2) the physiology involved in electrovascular coupling; and (3) energetic considerations to gain a better understanding of how the glucose budget is used during neuronal activity. The model has three components. The first is the canonical neural mass model of three subpopulations of neurons that respond to incoming excitatory synaptic inputs. The generation of the membrane potentials in the somas of these neurons and the electric currents flowing in the neuropil are modeled by this component. The second and third components model the electrovascular coupling and the dynamics of vascular states in an extended balloon approach, respectively. In the first part we describe, in some detail, the biophysical model and establish its face validity using simulations of visually evoked responses under different flickering frequencies and luminous contrasts. In a second part, a recursive optimization algorithm is developed and used to make statistical inferences about this forward/generative model from actual data.

fMRI MODELS OF DENDRITIC AND ASTROCYTIC NETWORKS

In order to elucidate the relationships between hierarchical structures within the neocortical neuropil and the information carried by an ensemble of neurons encompassing a single voxel, it is essential to predict through volume conductor modeling LFPs representing average extracellular potentials, which are expressed in terms of interstitial potentials of individual cells in networks of gap-junctionally connected astrocytes and synaptically connected neurons. These relationships have been provided and can then be used to investigate how the underlying neuronal population activity can be inferred from the measurement of the BOLD signal through electrovascular coupling mechanisms across the blood-brain barrier. The importance of both synaptic and extrasynaptic transmission as the basis of electrophysiological indices triggering vascular responses between dendritic and astrocytic networks, and sequential configurations of firing patterns in composite neural networks is emphasized. The purpose of this review is to show how fMRI data may be used to draw conclusions about the information transmitted by individual neurons in populations generating the BOLD signal.

A theoretical formulation of the electrophysiological inverse problem on the sphere

The construction of three-dimensional images of the primary current density (PCD) produced by neuronal activity is a problem of great current interest in the neuroimaging community, though being initially formulated in the 1970s. There exist even now enthusiastic debates about the authenticity of most of the inverse solutions proposed in the literature, in which low resolution electrical tomography (LORETA) is a focus of attention. However, in our opinion, the capabilities and limitations of the electro and magneto encephalographic techniques to determine PCD configurations have not been extensively explored from a theoretical framework, even for simple volume conductor models of the head. In this paper, the electrophysiological inverse problem for the spherical head model is cast in terms of reproducing kernel Hilbert spaces (RKHS) formalism, which allows us to identify the null spaces of the implicated linear integral operators and also to define their representers. The PCD are described in terms of a continuous basis for the RKHS, which explicitly separates the harmonic and non-harmonic components. The RKHS concept permits us to bring LORETA into the scope of the general smoothing splines theory. A particular way of calculating the general smoothing splines is illustrated, avoiding a brute force discretization prematurely. The Bayes information criterion is used to handle dissimilarities in the signal/noise ratios and physical dimensions of the measurement modalities, which could affect the estimation of the amount of smoothness required for that class of inverse solution to be well specified. In order to validate the proposed method, we have estimated the 3D spherical smoothing splines from two data sets: electric potentials obtained from a skull phantom and magnetic fields recorded from subjects performing an experiment of human faces recognition.

A state-space model of the hemodynamic approach: nonlinear filtering of BOLD signals

In this paper, a new procedure is presented which allows the estimation of the states and parameters of the hemodynamic approach from blood oxygenation level dependent (BOLD) responses. The proposed method constitutes an alternative to the recently proposed Friston [Neuroimage 16 (2002) 513] method and has some advantages over it. The procedure is based on recent groundbreaking time series analysis techniques that have been, in this case, adopted to characterize hemodynamic responses in functional magnetic resonance imaging (fMRI). This work represents a fundamental improvement over existing approaches to system identification using nonlinear hemodynamic models and is important for three reasons. First, our model includes physiological noise. Previous models have been based upon ordinary differential equations that only allow for noise or error to enter at the level of observation. Secondly, by using the innovation method and the local linearization filter, not only the parameters, but also the underlying states of the system generating responses can be estimated. These states can include things like a flow-inducing signal triggered by neuronal activation, de-oxyhemoglobine, cerebral blood flow and volume. Finally, radial basis functions have been introduced as a parametric model to represent arbitrary temporal input sequences in the hemodynamic approach, which could be essential to understanding those brain areas indirectly related to the stimulus. Hence, thirdly, by inferring about the radial basis parameters, we are able to perform a blind deconvolution, which permits both the reconstruction of the dynamics of the most likely hemodynamic states and also, to implicitly reconstruct the underlying synaptic dynamics, induced experimentally, which caused these states variations. From this study, we conclude that in spite of the utility of the standard discrete convolution approach used in statistical parametric maps (SPM), nonlinear BOLD phenomena and unspecific input temporal sequences must be included in the fMRI analysis.

Evaluation of inverse methods and head models for EEG source localization using a human skull phantom

We used a real-skull phantom head to investigate the performances of representative methods for EEG source localization when considering various head models. We describe several experiments using a montage with current sources located at multiple positions and orientations inside a human skull filled with a conductive medium. The robustness of selected methods based on distributed source models is evaluated as various solutions to the forward problem (from the sphere to the finite element method) are considered. Experimental results indicate that inverse methods using appropriate cortex-based source models are almost always able to locate the active source with excellent precision, with little or no spurious activity in close or distant regions, even when two sources are simultaneously active. Superior regularization schemes for solving the inverse problem can dramatically help the estimation of sparse and focal active zones, despite significant approximation of the head geometry and the conductivity properties of the head tissues. Realistic head models are necessary, though, to fit the data with a reasonable level of residual variance.

Electric lead field for a piecewise homogeneous volume conductor model of the head

A new method is presented for computing the electric lead field of a realistic head shape model which has piecewise homogeneous conductivity. The basic formulae are derived using the well-known reciprocity theorem. Previously described methods are also based upon this theorem, but these first calculate the electric potential inside the head by a scalar boundary element method (BEM), and then approximate the ohmic current density by some sort of gradient. In contrast, this paper proposes the direct evaluation of the ohmic current density by discretizing the vector Green's second identity which leads to a vector version of BEM. This approach also allows the derivation of the same equations for the three concentric spheres model as obtained by Rush and Driscoll [8]. The results of simulations on a spherical head model indicate that the use of a vector BEM leads to an improvement of accuracy in the computation of the ohmic current density with respect to those reported previously, in term of different measures of error.