SUMMARYA novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented. The spatial domain is partitioned into a set of totally disconnected subdomains, each assigned to an individual processor. Lagrange multipliers are introduced to enforce compatibility at the interface nodes. In the static case, each floating subdomain induces a local singularity that is resolved in two phases. First, the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution. Next, the contributions of these modes are related to the Lagrange multipliers through an orthogonality condition. A parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and Lagrange multipliers, which completes the solution of the problem. When implemented on local memory multiprocessors, this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory. Moreover, unlike parallel direct solvers, it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations.

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Interictal hypometabolism is commonly found in mesio-temporal lobe epilepsy (MTLE), but its pathophysiology remains incompletely understood. We hypothesized that metabolic changes reflect the preferential networks involved by ictal discharges. We analysed the topography of interictal hypometabolism according to electro-clinical patterns in 50 patients with unilateral hippocampal sclerosis (HS) and consistent features of MTLE. Based on electro-clinical correlations, we identified four groups: (i) mesial group (13 cases) characterized by mesial seizure onset without evidence of early spread beyond the temporal lobe; (ii) anterior mesio-lateral group (AML; 18 cases) with early anterior spread involving the anterior lateral temporal cortex and insulo-fronto-opercular areas; (iii) widespread mesio-lateral group (WML; 15 cases) with wide spread (involving both anterior and posterior lateral temporal and perisylvian areas); and (iv) bitemporal (BT) group (four cases) with early contralateral temporal spread. Results of [18F]fluorodeoxyglucose-PET imaging in each group were compared with those of 10 control subjects using statistical parametric mapping software (SPM99). MRI data and surgical outcome in each group were compared with metabolic findings. Hypometabolism was limited to hippocampal gyrus, temporal pole and insula in the mesial group. Gradual involvement of lateral temporal cortex, insula and perisylvian areas was observed in the AML and WML groups. The BT group differed from the others with mild bitemporal involvement, bilateral insular hypometabolism and longer epilepsy duration. MRI structural abnormalities outside of the mesial formations were detected in 65% of the cases. Neither the severity of HS nor temporal atrophy appeared related to the topography of hypometabolism. However, temporal hypometabolism was more extended when temporo-polar signal changes were detected. Among operated patients (n = 43), seizure-free outcome was obtained in 82%. Surgical outcome appeared more favourable in the mesial group. However, the difference between the four groups was not significant. Our results suggest that hypometabolism in MTLE may be related to ictal discharge generation and spread pathways, even if structural changes and epilepsy duration may also play a role.

This study demonstrates, using a multiscale correlative approach, that conventional MRI underestimates the actual spatial extent of diffuse low-grade gliomas (DLGGs), even when they are well delineated. These results suggest that an extended resection of a margin beyond MRI-defined abnormalities, whenever feasible in noneloquent brain areas, might improve the outcome of DLGGs.