Dynamic directed interictal connectivity in left and right temporal lobe epilepsy.

OBJECTIVE There is increasing evidence that epileptic activity involves widespread brain networks rather than single sources and that these networks contribute to interictal brain dysfunction. We investigated the fast-varying behavior of epileptic networks during interictal spikes in right and left temporal lobe epilepsy (RTLE and LTLE) at a whole-brain scale using directed connectivity. METHODS In 16 patients, 8 with LTLE and 8 with RTLE, we estimated the electrical source activity in 82 cortical regions of interest (ROIs) using high-density electroencephalography (EEG), individual head models, and a distributed linear inverse solution. A multivariate, time-varying, and frequency-resolved Granger-causal modeling (weighted Partial Directed Coherence) was applied to the source signal of all ROIs. A nonparametric statistical test assessed differences between spike and baseline epochs. Connectivity results between RTLE and LTLE were compared between RTLE and LTLE and with neuropsychological impairments. RESULTS Ipsilateral anterior temporal structures were identified as key drivers for both groups, concordant with the epileptogenic zone estimated invasively. We observed an increase in outflow from the key driver already before the spike. There were also important temporal and extratemporal ipsilateral drivers in both conditions, and contralateral only in RTLE. A different network pattern between LTLE and RTLE was found: in RTLE there was a much more prominent ipsilateral to contralateral pattern than in LTLE. Half of the RTLE patients but none of the LTLE patients had neuropsychological deficits consistent with contralateral temporal lobe dysfunction, suggesting a relationship between connectivity changes and cognitive deficits. SIGNIFICANCE The different patterns of time-varying connectivity in LTLE and RTLE suggest that they are not symmetrical entities, in line with our neuropsychological results. The highest outflow region was concordant with invasive validation of the epileptogenic zone. This enhanced characterization of dynamic connectivity patterns could better explain cognitive deficits and help the management of epilepsy surgery candidates.

Altered directed functional connectivity in temporal lobe epilepsy in the absence of interictal spikes: A high density EEG study.

OBJECTIVE In patients with epilepsy, seizure relapse and behavioral impairments can be observed despite the absence of interictal epileptiform discharges (IEDs). Therefore, the characterization of pathologic networks when IEDs are not present could have an important clinical value. Using Granger-causal modeling, we investigated whether directed functional connectivity was altered in electroencephalography (EEG) epochs free of IED in left and right temporal lobe epilepsy (LTLE and RTLE) compared to healthy controls. METHODS Twenty LTLE, 20 RTLE, and 20 healthy controls underwent a resting-state high-density EEG recording. Source activity was obtained for 82 regions of interest (ROIs) using an individual head model and a distributed linear inverse solution. Granger-causal modeling was applied to the source signals of all ROIs. The directed functional connectivity results were compared between groups and correlated with clinical parameters (duration of the disease, age of onset, age, and learning and mood impairments). RESULTS We found that: (1) patients had significantly reduced connectivity from regions concordant with the default-mode network; (2) there was a different network pattern in patients versus controls: the strongest connections arose from the ipsilateral hippocampus in patients and from the posterior cingulate cortex in controls; (3) longer disease duration was associated with lower driving from contralateral and ipsilateral mediolimbic regions in RTLE; (4) aging was associated with a lower driving from regions in or close to the piriform cortex only in patients; and (5) outflow from the anterior cingulate cortex was lower in patients with learning deficits or depression compared to patients without impairments and to controls. SIGNIFICANCE Resting-state network reorganization in the absence of IEDs strengthens the view of chronic and progressive network changes in TLE. These resting-state connectivity alterations could constitute an important biomarker of TLE, and hold promise for using EEG recordings without IEDs for diagnosis or prognosis of this disorder.

Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root is either the central vertex or, in the more challenging problem, a pendant vertex of the star graph. At all other pendant vertices Dirichlet conditions are imposed; at the central vertex, at which a mass may be placed, continuity and Kirchhoff conditions are assumed. We derive conditions on two sets of real numbers to be the spectra of the above Dirichlet and Neumann problems. Our solution for the inverse problems is constructive: we establish algorithms to recover the mass distribution on the star graph (i.e. the point masses and lengths of subintervals between them) from these two spectra and from the lengths of the separate strings. If the root is a pendant vertex, the two spectra uniquely determine the parameters on the main string (i.e. the string incident to the root) if the length of the main string is known. The mass distribution on the other edges need not be unique; the reason for this is the non-uniqueness caused by the non-strict interlacing of the given data in the case when the root is the central vertex. Finally, we relate of our results to tree-patterned matrix inverse problems.