The spatio-temporal mapping of epileptic networks: Combination of EEG–fMRI and EEG source imaging

Simultaneous EEG–fMRI acquisitions in patients with epilepsy often reveal distributed patterns of Blood Oxygen Level Dependant (BOLD) change correlated with epileptiform discharges. We investigated if electrical source imaging (ESI) performed on the interictal epileptiform discharges (IED) acquired during fMRI acquisition could be used to study the dynamics of the networks identified by the BOLD effect, thereby avoiding the limitations of combining results from separate recordings. Nine selected patients (13 IED types identified) with focal epilepsy underwent EEG–fMRI. Statistical analysis was performed using SPM5 to create BOLD maps. ESI was performed on the IED recorded during fMRI acquisition using a realistic head model (SMAC) and a distributed linear inverse solution (LAURA). ESI could not be performed in one case. In 10/12 remaining studies, ESI at IED onset (ESIo) was anatomically close to one BOLD cluster. Interestingly, ESIo was closest to the positive BOLD cluster with maximal statistical significance in only 4/12 cases and closest to negative BOLD responses in 4/12 cases. Very small BOLD clusters could also have clinical relevance in some cases. ESI at later time frame (ESIp) showed propagation to remote sources co-localised with other BOLD clusters in half of cases. In concordant cases, the distance between maxima of ESI and the closest EEG–fMRI cluster was less than 33 mm, in agreement with previous studies. We conclude that simultaneous ESI and EEG–fMRI analysis may be able to distinguish areas of BOLD response related to initiation of IED from propagation areas. This combination provides new opportunities for investigating epileptic networks

Bright squeezed vacuum in a nonlinear interferometer: frequency/temporal Schmidt-mode description

Control over the spectral properties of the bright squeezed vacuum (BSV), a highly multimode non-classical macroscopic state of light that can be generated through high-gain parametric down conversion, is crucial for many applications. In particular, in several recent experiments BSV is generated in a strongly pumped SU(1,1) interferometer to achieve phase supersensitivity, perform broadband homodyne detection, or tailor the frequency spectrum of squeezed light. In this work, we present an analytical approach to the theoretical description of BSV in the frequency domain based on the Bloch-Messiah reduction and the Schmidt-mode formalism. As a special case we consider a strongly pumped SU(1,1) interferometer. We show that different moments of the radiation at its output depend on the phase, dispersion and the parametric gain in a nontrivial way, thereby providing additional insights on the capabilities of nonlinear interferometers. In particular, a dramatic change in the spectrum occurs as the parametric gain increases

Nonlinear interferometer for tailoring the frequency spectrum of bright squeezed vacuum

We propose a method for tailoring the frequency spectrum of bright squeezed vacuum by generating it in a nonlinear interferometer, consisting of two down-converting nonlinear crystals separated by a dispersive medium. Due to a faster dispersive spreading of higher-order Schmidt modes, the spectral width of the radiation at the output is reduced as the length of the dispersive medium is increased. Preliminary results show 30\% spectral narrowing.Comment: 9 pages, 6 figure

EEG–fMRI mapping of asymmetrical delta activity in a patient with refractory epilepsy is concordant with the epileptogenic region determined by intracranial EEG

We studied a patient with refractory focal epilepsy using continuous EEG-correlated fMRI. Seizures were characterized by head turning to the left and clonic jerking of the left arm, suggesting a right frontal epileptogenic region. Interictal EEG showed occasional runs of independent nonlateralized slow activity in the delta band with right frontocentral dominance and had no lateralizing value. Ictal scalp EEG had no lateralizing value. Ictal scalp EEG suggested right-sided central slow activity preceding some seizures. Structural 3-T MRI showed no abnormality. There was no clear epileptiform abnormality during simultaneous EEG–fMRI. We therefore modeled asymmetrical EEG delta activity at 1–3 Hz near frontocentral electrode positions. Significant blood oxygen level-dependent (BOLD) signal changes in the right superior frontal gyrus correlated with right frontal oscillations at 1–3 Hz but not at 4–7 Hz and with neither of the two frequency bands when derived from contralateral or posterior electrode positions, which served as controls. Motor fMRI activations with a finger-tapping paradigm were asymmetrical: they were more anterior for the left hand compared with the right and were near the aforementioned EEG-correlated signal changes. A right frontocentral perirolandic seizure onset was identified with a subdural grid recording, and electric stimulation of the adjacent contact produced motor responses in the left arm and after discharges. The fMRI localization of the left hand motor and the detected BOLD activation associated with modeled slow activity suggest a role for localization of the epileptogenic region with EEG–fMRI even in the absence of clear interictal discharges

Functional MRI with active, fully implanted, deep brain stimulation systems: Safety and experimental confounds

We investigated safety issues and potential experimental confounds when performing functional magnetic resonance imaging (fMRI) investigations in human subjects with fully implanted, active, deep brain stimulation (DBS) systems. Measurements of temperature and induced voltage were performed in an in vitro arrangement simulating bilateral DBS during magnetic resonance imaging (MRI) using head transmit coils in both 1.5 and 3.0 T MRI systems. For MRI sequences typical of an fMRI study with coil-averaged specific absorption rates (SARs) less than 0.4 W/kg, no MRI-induced temperature change greater than the measurement sensitivity (0.1 °C) was detected at 1.5 T, and at 3 T temperature elevations were less than 0.5 °C, i.e. within safe limits. For the purposes of demonstration, MRI pulse sequences with SARs of 1.45 W/kg and 2.34 W/kg (at 1.5 T and 3 T, respectively) were prescribed and elicited temperature increases (> 1 °C) greater than those considered safe for human subjects. Temperature increases were independent of the presence or absence of active stimulator pulsing. At both field strengths during echo planar MRI, the perturbations of DBS equipment performance were sufficiently slight, and temperature increases sufficiently low to suggest that thermal or electromagnetically mediated experimental confounds to fMRI with DBS are unlikely. We conclude that fMRI studies performed in subjects with subcutaneously implanted DBS units can be both safe and free from DBS-specific experimental confounds. Furthermore, fMRI in subjects with fully implanted rather than externalised DBS stimulator units may offer a significant safety advantage. Further studies are required to determine the safety of MRI with DBS for other MRI systems, transmit coil configurations and DBS arrangements

Properties of bright squeezed vacuum at increasing brightness

A bright squeezed vacuum (BSV) is a nonclassical macroscopic state of light, which is generated through high-gain parametric down-conversion or four-wave mixing. Although the BSV is an important tool in quantum optics and has a lot of applications, its theoretical description is still not complete. In particular, the existing description in terms of Schmidt modes with gain-independent shapes fails to explain the spectral broadening observed in the experiment as the mean number of photons increases. Meanwhile, the semiclassical description accounting for the broadening does not allow us to decouple the intermodal photon-number correlations. In this work, we present a new generalized theoretical approach to describe the spatial properties of a multimode BSV. In the multimode case, one has to take into account the complicated interplay between all involved modes: each plane-wave mode interacts with all other modes, which complicates the problem significantly. The developed approach is based on exchanging the (k, t ) and (ω, z) representations and solving a system of integrodifferential equations. Our approach predicts correctly the dynamics of the Schmidt modes and the broadening of the angular distribution with the increase in the BSV mean photon number due to a stronger pumping. Moreover, the model correctly describes various properties of a widely used experimental configuration with two crystals and an air gap between them, namely, an SU(1,1) interferometer. In particular, it predicts the narrowing of the intensity distribution, the reduction and shift of the side lobes, and the decline in the interference visibility as the mean photon number increases due to stronger pumping. The presented experimental results confirm the validity of the new approach. The model can be easily extended to the case of the frequency spectrum, frequency Schmidt modes, and other experimental configurations

Multimodal imaging of human brain activity: rational, biophysical aspects and modes of integration

Until relatively recently the vast majority of imaging and electrophysiological studies of human brain activity have relied on single-modality measurements usually correlated with readily observable or experimentally modified behavioural or brain state patterns. Multi-modal imaging is the concept of bringing together observations or measurements from different instruments. We discuss the aims of multi-modal imaging and the ways in which it can be accomplished using representative applications. Given the importance of haemodynamic and electrophysiological signals in current multi-modal imaging applications, we also review some of the basic physiology relevant to understanding their relationship

Diffusion at constant speed in a model phase space

We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the equations for the probability density function using the ``formulae of differentiation'' of Shapiro and Loginov. The model is an advancement over similiar models of photon migration in multiply scattering media in that it results in a true diffusion at constant speed in the limit of large dimensions.Comment: Final corrected version RevTeX, 6 pages, 1 figur

Simultaneous intracranial EEG and fMRI of interictal epileptic discharges in humans

Simultaneous scalp EEG–fMRI measurements allow the study of epileptic networks and more generally, of the coupling between neuronal activity and haemodynamic changes in the brain. Intracranial EEG (icEEG) has greater sensitivity and spatial specificity than scalp EEG but limited spatial sampling. We performed simultaneous icEEG and functional MRI recordings in epileptic patients to study the haemodynamic correlates of intracranial interictal epileptic discharges (IED). Two patients undergoing icEEG with subdural and depth electrodes as part of the presurgical assessment of their pharmaco-resistant epilepsy participated in the study. They were scanned on a 1.5 T MR scanner following a strict safety protocol. Simultaneous recordings of fMRI and icEEG were obtained at rest. IED were subsequently visually identified on icEEG and their fMRI correlates were mapped using a general linear model (GLM). On scalp EEG–fMRI recordings performed prior to the implantation, no IED were detected. icEEG–fMRI was well tolerated and no adverse health effect was observed. intra-MR icEEG was comparable to that obtained outside the scanner. In both cases, significant haemodynamic changes were revealed in relation to IED, both close to the most active electrode contacts and at distant sites. In one case, results showed an epileptic network including regions that could not be sampled by icEEG, in agreement with findings from magneto-encephalography, offering some explanation for the persistence of seizures after surgery. Hence, icEEG–fMRI allows the study of whole-brain human epileptic networks with unprecedented sensitivity and specificity. This could help improve our understanding of epileptic networks with possible implications for epilepsy surgery