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

Evaluation of atlas-based segmentation of hippocampi in healthy humans

Introduction and aim: Region of interest (ROI)-based functional magnetic resonance imaging (fMRI) data analysis relies on extracting signals from a specific area which is presumed to be involved in the brain activity being studied. The hippocampus is of interest in many functional connectivity studies for example in epilepsy as it plays an important role in epileptogenesis. In this context, ROI may be defined using different techniques. Our study aims at evaluating the spatial correspondence of hippocampal ROIs obtained using three brain atlases with hippocampal ROI obtained using an automatic segmentation algorithm dedicated to the hippocampus. Material and methods: High-resolution volumetric T1-weighted MR images of 18 healthy volunteers (five females) were acquired on a 3T scanner. Individual ROIs for both hippocampi of each subject were segmented from the MR images using an automatic hippocampus and amygdala segmentation software called SACHA providing the gold standard ROI for comparison with the atlas-derived results. For each subject, hippocampal ROIs were also obtained using three brain atlases: PickAtlas available as a commonly used software toolbox; automated anatomical labeling (AAL) atlas included as a subset of ROI into PickAtlas toolbox and a frequency-based brain atlas by Hammers et al. The levels of agreement between the SACHA results and those obtained using the atlases were assessed based on quantitative indices measuring volume differences and spatial overlap. The comparison was performed in standard Montreal Neurological Institute space, the registration being obtained with SPM5 (http://www.fil.ion.ucl.ac.uk/spm/). Results: The mean volumetric error across all subjects was 73% for hippocampal ROIs derived from AAL atlas; 20% in case of ROIs derived from the Hammers atlas and 107% for ROIs derived from PickAtlas. The mean false-positive and false-negative classification rates were 60% and 10% respectively for the AAL atlas; 16% and 32% for the Hammers atlas and 6% and 72% for the PickAtlas. Conclusion: Though atlas-based ROI definition may be convenient, the resulting ROIs may be poor representations of the hippocampus in some studies critical to under- or oversampling. Performance of the AAL atlas was inferior to that of the Hammers atlas. Hippocampal ROIs derived from PickAtlas are highly significantly smaller, and this results in the worst performance out of three atlases. It is advisable that the defined ROIs should be verified with knowledge of neuroanatomy before using it for further data analysis

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

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

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

Independent component analysis of interictal fMRI in focal epilepsy: comparison with general linear model-based EEG-correlated fMRI

The general linear model (GLM) has been used to analyze simultaneous EEG–fMRI to reveal BOLD changes linked to interictal epileptic discharges (IED) identified on scalp EEG. This approach is ineffective when IED are not evident in the EEG. Data-driven fMRI analysis techniques that do not require an EEG derived model may offer a solution in these circumstances. We compared the findings of independent components analysis (ICA) and EEG-based GLM analyses of fMRI data from eight patients with focal epilepsy. Spatial ICA was used to extract independent components (IC) which were automatically classified as either BOLD-related, motion artefacts, EPI-susceptibility artefacts, large blood vessels, noise at high spatial or temporal frequency. The classifier reduced the number of candidate IC by 78%, with an average of 16 BOLD-related IC. Concordance between the ICA and GLM-derived results was assessed based on spatio-temporal criteria. In each patient, one of the IC satisfied the criteria to correspond to IED-based GLM result. The remaining IC were consistent with BOLD patterns of spontaneous brain activity and may include epileptic activity that was not evident on the scalp EEG. In conclusion, ICA of fMRI is capable of revealing areas of epileptic activity in patients with focal epilepsy and may be useful for the analysis of EEG–fMRI data in which abnormalities are not apparent on scalp EEG

Altered brain connectivity in sudden unexpected death in epilepsy (SUDEP) revealed using resting-state fMRI.

The circumstances surrounding SUDEP suggest autonomic or respiratory collapse, implying central failure of regulation or recovery. Characterisation of the communication among brain areas mediating such processes may shed light on mechanisms and noninvasively indicate risk. We used rs-fMRI to examine network properties among brain structures in people with epilepsy who suffered SUDEP (n = 8) over an 8-year follow-up period, compared with matched high- and low-risk subjects (n = 16/group) who did not suffer SUDEP during that period, and a group of healthy controls (n = 16). Network analysis was employed to explore connectivity within a 'regulatory-subnetwork' of brain regions involved in autonomic and respiratory regulation, and over the whole-brain. Modularity, the extent of network organization into separate modules, was significantly reduced in the regulatory-subnetwork, and the whole-brain, in SUDEP and high-risk. Increased participation, a local measure of inter-modular belonging, was evident in SUDEP and high-risk groups, particularly among thalamic structures. The medial prefrontal thalamus was increased in SUDEP compared with all other control groups, including high-risk. Patterns of hub topology were similar in SUDEP and high-risk, but were more extensive in low-risk patients, who displayed greater hub prevalence and a radical reorganization of hubs in the subnetwork. SUDEP is associated with reduced functional organization among cortical and sub-cortical brain regions mediating autonomic and respiratory regulation. Living high-risk subjects demonstrated similar patterns, suggesting such network measures may provide prospective risk-indicating value, though a crucial difference between SUDEP and high-risk was altered connectivity of the medial thalamus in SUDEP, which was also elevated compared with all sub-groups. Disturbed thalamic connectivity may reflect a potential non-invasive marker of elevated SUDEP risk

EEG correlated functional MRI and postoperative outcome in focal epilepsy

Background: The main challenge in assessing patients with epilepsy for resective surgery is localising seizure onset. Frequently, identification of the irritative and seizure onset zones requires invasive EEG. EEG correlated functional MRI (EEG-fMRI) is a novel imaging technique which may provide localising information with regard to these regions. In patients with focal epilepsy, interictal epileptiform discharge (IED) correlated blood oxygen dependent level (BOLD) signal changes were observed in approximately 50% of patients in whom IEDs are recorded. In 70%, these are concordant with expected seizure onset defined by non-invasive electroclinical information. Assessment of clinical validity requires post-surgical outcome studies which have, to date, been limited to case reports of correlation with intracranial EEG. The value of EEG-fMRI was assessed in patients with focal epilepsy who subsequently underwent epilepsy surgery, and IED correlated fMRI signal changes were related to the resection area and clinical outcome. Methods: Simultaneous EEG-fMRI was recorded in 76 patients undergoing presurgical evaluation and the locations of IED correlated preoperative BOLD signal change were compared with the resected area and postoperative outcome. Results: 21 patients had activations with epileptic activity on EEG-fMRI and 10 underwent surgical resection. Seven of 10 patients were seizure free following surgery and the area of maximal BOLD signal change was concordant with resection in six of seven patients. In the remaining three patients, with reduced seizure frequency post-surgically, areas of significant IED correlated BOLD signal change lay outside the resection. 42 of 55 patients who had no IED related activation underwent resection. Conclusion: These results show the potential value of EEG-fMRI in presurgical evaluation