Effect of Coupling on the Epidemic Threshold in Interconnected Complex Networks: A Spectral Analysis

In epidemic modeling, the term infection strength indicates the ratio of infection rate and cure rate. If the infection strength is higher than a certain threshold -- which we define as the epidemic threshold - then the epidemic spreads through the population and persists in the long run. For a single generic graph representing the contact network of the population under consideration, the epidemic threshold turns out to be equal to the inverse of the spectral radius of the contact graph. However, in a real world scenario it is not possible to isolate a population completely: there is always some interconnection with another network, which partially overlaps with the contact network. Results for epidemic threshold in interconnected networks are limited to homogeneous mixing populations and degree distribution arguments. In this paper, we adopt a spectral approach. We show how the epidemic threshold in a given network changes as a result of being coupled with another network with fixed infection strength. In our model, the contact network and the interconnections are generic. Using bifurcation theory and algebraic graph theory, we rigorously derive the epidemic threshold in interconnected networks. These results have implications for the broad field of epidemic modeling and control. Our analytical results are supported by numerical simulations.Comment: 7 page

Multiple mechanisms shape the relationship between pathway and duration of focal seizures

A seizure’s electrographic dynamics are characterized by its spatiotemporal evolution, also termed dynamical ‘pathway’, and the time it takes to complete that pathway, which results in the seizure’s duration. Both seizure pathways and durations have been shown to vary within the same patient. However, it is unclear whether seizures following the same pathway will have the same duration or if these features can vary independently. We compared within-subject variability in these seizure features using (i) epilepsy monitoring unit intracranial EEG (iEEG) recordings of 31 patients (mean: 6.7 days, 16.5 seizures/subject), (ii) NeuroVista chronic iEEG recordings of 10 patients (mean: 521.2 days, 252.6 seizures/subject) and (iii) chronic iEEG recordings of three dogs with focal-onset seizures (mean: 324.4 days, 62.3 seizures/subject). While the strength of the relationship between seizure pathways and durations was highly subject-specific, in most subjects, changes in seizure pathways were only weakly to moderately associated with differences in seizure durations. The relationship between seizure pathways and durations was strengthened by seizures that were ‘truncated’ versions, both in pathway and duration, of other seizures. However, the relationship was weakened by seizures that had a common pathway, but different durations (‘elasticity’), or had similar durations, but followed different pathways (‘semblance’). Even in subjects with distinct populations of short and long seizures, seizure durations were not a reliable indicator of different seizure pathways. These findings suggest that seizure pathways and durations are modulated by multiple different mechanisms. Uncovering such mechanisms may reveal novel therapeutic targets for reducing seizure duration and severity

Supplementation of Fish-oil and Soy-oil During Pregnancy and Psychomotor Development of Infants

Supplementation of docosahexaenoic acid (DHA) in infancy improves neuro-developmental outcomes, but there is limited information about the impact of supplementing pregnant mothers with DHA on the development of their infants. In a follow-up of a randomized, double-blind controlled trial with 400 pregnant mothers, the effects of supplementation of fish-oil or soy-oil (4 g/day) during the last trimester of pregnancy on psychomotor development and behaviour of infants at 10 months of age (n=249) were assessed. The quality of psychosocial stimulation at home (HOME) and nutritional status of the subjects were also measured. There were no significant differences in the fish-oil group and soy-oil group in any of the developmental (mean\ub1SD mental development index: 102.5\ub18.0 vs 101.5\ub17.8, psychomotor development index: 101.7\ub110.0 vs 100.5\ub110.1) or behavioural outcomes. It may, therefore, be concluded that supplementation of fish-oil during the last trimester of pregnancy does not have any added benefit over supplementation of soy-oil on the development or behaviour of infants in this population

Diminished circadian and ultradian rhythms in pathological brain tissue in human in vivo

Chronobiological rhythms, such as the circadian rhythm, have long been linked to neurological disorders, but it is currently unknown how pathological processes affect the expression of biological rhythms in the brain. Here, we use the unique opportunity of long-term, continuous intracranially recorded EEG from 38 patients (totalling 6338 hours) to delineate circadian and ultradian rhythms in different brain regions. We show that functional circadian and ultradian rhythms are diminished in pathological tissue, independent of regional variations. We further demonstrate that these diminished rhythms are persistent in time, regardless of load or occurrence of pathological events. These findings provide the first evidence that brain pathology is functionally associated with persistently diminished chronobiological rhythms in vivo in humans, independent of regional variations or pathological events. Future work interacting with, and restoring, these modulatory chronobiological rhythms may allow for novel therapies

Interictal MEG abnormalities to guide intracranial electrode implantation and predict surgical outcome

Intracranial EEG (iEEG) is the gold standard technique for epileptogenic zone (EZ) localisation, but requires a hypothesis of which tissue is epileptogenic, guided by qualitative analysis of seizure semiology and other imaging modalities such as magnetoencephalography (MEG). We hypothesised that if quantifiable MEG band power abnormalities were sampled by iEEG, then patients' post-resection seizure outcome were better. Thirty-two individuals with neocortical epilepsy underwent MEG and iEEG recordings as part of pre-surgical evaluation. Interictal MEG band power abnormalities were derived using 70 healthy controls as a normative baseline. MEG abnormality maps were compared to electrode implantation, with the spatial overlap of iEEG electrodes and MEG abnormalities recorded. Finally, we assessed if the implantation of electrodes in abnormal tissue, and resection of the strongest abnormalities determined by MEG and iEEG explained surgical outcome. Intracranial electrodes were implanted in brain tissue with the most abnormal MEG findings in individuals that were seizure-free post-resection (T=3.9, p=0.003). The overlap between MEG abnormalities and iEEG electrodes distinguished outcome groups moderately well (AUC=0.68). In isolation, the resection of the strongest MEG and iEEG abnormalities separated surgical outcome groups well (AUC=0.71, AUC=0.74 respectively). A model incorporating all three features separated outcome groups best (AUC=0.80). Intracranial EEG is a key tool to delineate the EZ and help render patients seizure-free after resection. We showed that data-driven abnormalities derived from interictal MEG recordings have clinical value and may help guide electrode placement in individuals with neocortical epilepsy. Finally, our predictive model of post-operative seizure-freedom, which leverages both MEG and iEEG recordings, may aid patient counselling of expected outcome.Comment: 22 pages, 6 figure

Interictal magnetoencephalography abnormalities to guide intracranial electrode implantation and predict surgical outcome

Intracranial EEG is the gold standard technique for epileptogenic zone localization but requires a preconceived hypothesis of the location of the epileptogenic tissue. This placement is guided by qualitative interpretations of seizure semiology, MRI, EEG and other imaging modalities, such as magnetoencephalography. Quantitative abnormality mapping using magnetoencephalography has recently been shown to have potential clinical value. We hypothesized that if quantifiable magnetoencephalography abnormalities were sampled by intracranial EEG, then patients’ post-resection seizure outcome may be better. Thirty-two individuals with refractory neocortical epilepsy underwent magnetoencephalography and subsequent intracranial EEG recordings as part of presurgical evaluation. Eyes-closed resting-state interictal magnetoencephalography band power abnormality maps were derived from 70 healthy controls as a normative baseline. Magnetoencephalography abnormality maps were compared to intracranial EEG electrode implantation, with the spatial overlap of intracranial EEG electrode placement and cerebral magnetoencephalography abnormalities recorded. Finally, we assessed if the implantation of electrodes in abnormal tissue and subsequent resection of the strongest abnormalities determined by magnetoencephalography and intracranial EEG corresponded to surgical success. We used the area under the receiver operating characteristic curve as a measure of effect size. Intracranial electrodes were implanted in brain tissue with the most abnormal magnetoencephalography findings—in individuals that were seizure-free postoperatively (T = 3.9, P = 0.001) but not in those who did not become seizure-free. The overlap between magnetoencephalography abnormalities and electrode placement distinguished surgical outcome groups moderately well (area under the receiver operating characteristic curve = 0.68). In isolation, the resection of the strongest abnormalities as defined by magnetoencephalography and intracranial EEG separated surgical outcome groups well, area under the receiver operating characteristic curve = 0.71 and area under the receiver operating characteristic curve = 0.74, respectively. A model incorporating all three features separated surgical outcome groups best (area under the receiver operating characteristic curve = 0.80). Intracranial EEG is a key tool to delineate the epileptogenic zone and help render individuals seizure-free postoperatively. We showed that data-driven abnormality maps derived from resting-state magnetoencephalography recordings demonstrate clinical value and may help guide electrode placement in individuals with neocortical epilepsy. Additionally, our predictive model of postoperative seizure freedom, which leverages both magnetoencephalography and intracranial EEG recordings, could aid patient counselling of expected outcome

Intracranial EEG structure-function coupling predicts surgical outcomes in focal epilepsy

Alterations to structural and functional brain networks have been reported across many neurological conditions. However, the relationship between structure and function -- their coupling -- is relatively unexplored, particularly in the context of an intervention. Epilepsy surgery alters the brain structure and networks to control the functional abnormality of seizures. Given that surgery is a structural modification aiming to alter the function, we hypothesized that stronger structure-function coupling preoperatively is associated with a greater chance of post-operative seizure control. We constructed structural and functional brain networks in 39 subjects with medication-resistant focal epilepsy using data from intracranial EEG (pre-surgery), structural MRI (pre-and post-surgery), and diffusion MRI (pre-surgery). We investigated pre-operative structure-function coupling at two spatial scales a) at the global iEEG network level and b) at the resolution of individual iEEG electrode contacts using virtual surgeries. At global network level, seizure-free individuals had stronger structure-function coupling pre-operatively than those that were not seizure-free regardless of the choice of interictal segment or frequency band. At the resolution of individual iEEG contacts, the virtual surgery approach provided complementary information to localize epileptogenic tissues. In predicting seizure outcomes, structure-function coupling measures were more important than clinical attributes, and together they predicted seizure outcomes with an accuracy of 85% and sensitivity of 87%. The underlying assumption that the structural changes induced by surgery translate to the functional level to control seizures is valid when the structure-functional coupling is strong. Mapping the regions that contribute to structure-functional coupling using virtual surgeries may help aid surgical planning

Complementary structural and functional abnormalities to localise epileptogenic tissue

BACKGROUND: When investigating suitability for epilepsy surgery, people with drug-refractory focal epilepsy may have intracranial EEG (iEEG) electrodes implanted to localise seizure onset. Diffusion-weighted magnetic resonance imaging (dMRI) may be acquired to identify key white matter tracts for surgical avoidance. Here, we investigate whether structural connectivity abnormalities, inferred from dMRI, may be used in conjunction with functional iEEG abnormalities to aid localisation of the epileptogenic zone (EZ), improving surgical outcomes in epilepsy. METHODS: We retrospectively investigated data from 43 patients (42% female) with epilepsy who had surgery following iEEG. Twenty-five patients (58%) were free from disabling seizures (ILAE 1 or 2) at one year. Interictal iEEG functional, and dMRI structural connectivity abnormalities were quantified by comparison to a normative map and healthy controls. We explored whether the resection of maximal abnormalities related to improved surgical outcomes, in both modalities individually and concurrently. Additionally, we suggest how connectivity abnormalities may inform the placement of iEEG electrodes pre-surgically using a patient case study. FINDINGS: Seizure freedom was 15 times more likely in patients with resection of maximal connectivity and iEEG abnormalities (p = 0.008). Both modalities separately distinguished patient surgical outcome groups and when used simultaneously, a decision tree correctly separated 36 of 43 (84%) patients. INTERPRETATION: Our results suggest that both connectivity and iEEG abnormalities may localise epileptogenic tissue, and that these two modalities may provide complementary information in pre-surgical evaluations. FUNDING: This research was funded by UKRI, CDT in Cloud Computing for Big Data, NIH, MRC, Wellcome Trust and Epilepsy Research UK

Complementary structural and functional abnormalities to localise epileptogenic tissue

When investigating suitability for surgery, people with drug-refractory focal epilepsy may have intracranial EEG (iEEG) electrodes implanted to localise seizure onset. Diffusion-weighted magnetic resonance imaging (dMRI) may be acquired to identify key white matter tracts for surgical avoidance. Here, we investigate whether structural connectivity abnormalities, inferred from dMRI, may be used in conjunction with functional iEEG abnormalities to aid localisation and resection of the epileptogenic zone (EZ), and improve surgical outcomes in epilepsy. We retrospectively investigated data from 43 patients with epilepsy who had surgery following iEEG. Twenty five patients (58%) were free from disabling seizures (ILAE 1 or 2) at one year. For all patients, T1-weighted and diffusion-weighted MRIs were acquired prior to iEEG implantation. Interictal iEEG functional, and dMRI structural connectivity abnormalities were quantified by comparison to a normative map and healthy controls respectively. First, we explored whether the resection of maximal (dMRI and iEEG) abnormalities related to improved surgical outcomes. Second, we investigated whether the modalities provided complementary information for improved prediction of surgical outcome. Third, we suggest how dMRI abnormalities may be useful to inform the placement of iEEG electrodes as part of the pre-surgical evaluation using a patient case study. Seizure freedom was 15 times more likely in those patients with resection of maximal dMRI and iEEG abnormalities (p=0.008). Both modalities were separately able to distinguish patient outcome groups and when combined, a decision tree correctly separated 36 out of 43 (84%) patients based on surgical outcome. Structural dMRI could be used in pre-surgical evaluations, particularly when localisation of the EZ is uncertain, to inform personalised iEEG implantation and resection.Comment: 5 figure