Differential diagnoses between vegetative and minimally conscious states (VS and MCS, respectively) are frequently incorrect. Hence, further research is necessary to improve the diagnostic accuracy at the bedside. The main neuropathological feature of VS is the diffuse damage of cortical and subcortical connections. Starting with this premise, we used electroencephalography (EEG) recordings to evaluate the cortical reactivity and effective connectivity during transcranial magnetic stimulation (TMS) in chronic VS or MCS patients. Moreover, the TMS-EEG data were compared with the results from standard somatosensory-evoked potentials (SEPs) and event-related potentials (ERPs). Thirteen patients with chronic consciousness disorders were examined at their bedsides. A group of healthy volunteers served as the control group. The amplitudes (reactivity) and scalp distributions (connectivity) of the cortical potentials evoked by TMS (TEPs) of the primary motor cortex were measured. Short-latency median nerve SEPs and auditory ERPs were also recorded. Reproducible TEPs were present in all control subjects in both the ipsilateral and the contralateral hemispheres relative to the site of the TMS. The amplitudes of the ipsilateral and contralateral TEPs were reduced in four of the five MCS patients, and the TEPs were bilaterally absent in one MCS patient. Among the VS patients, five did not manifest ipsilateral or contralateral TEPs, and three of the patients exhibited only ipsilateral TEPs with reduced amplitudes. The SEPs were altered in five VS and two MCS patients but did not correlate with the clinical diagnosis. The ERPs were impaired in all patients and did not correlate with the clinical diagnosis. These TEP results suggest that cortical reactivity and connectivity are severely impaired in all VS patients, whereas in most MCS patients, the TEPs are preserved but with abnormal features. Therefore, TEPs may add valuable information to the current clinical and neurophysiological assessment of chronic consciousness disorders.
The simulation of fluid dynamics, typically by numerically solving partial differential equations, is an essential tool in many areas of science and engineering. However, the high computational cost can limit application in practice and may prohibit exploring large parameter spaces. Recent deep-learning approaches have demonstrated the potential to yield surrogate models for the simulation of fluid dynamics. While such models exhibit lower accuracy in comparison, their low runtime makes them appealing for design-space exploration. We introduce two novel graph neural network (GNN) models, multi-scale GNN (MuS-GNN) and rotation-equivariant multi-scale GNN (REMuS-GNN), for extrapolating the time evolution of fluid flow. In both models, previous states are processed through multiple coarsenings of the graph, which enables faster information propagation through the network and improves the capture and forecast of the system state, particularly in problems encompassing phenomena spanning a range of length scales. Additionally, REMuS-GNN is architecturally equivariant to rotations, which allows the network to learn the underlying physics more efficiently, leading to improved accuracy and generalisation. We analyse these models using two canonical fluid models: advection and incompressible fluid dynamics. Our results show that the proposed GNN models can generalise from uniform advection fields to high-gradient fields on complex domains. The multi-scale graph architecture allows for inference of incompressible Navier-Stokes solutions, within a range of Reynolds numbers and design parameters, more effectively than a baseline single-scale GNN. Simulations obtained with MuS-GNN and REMuS-GNN are between two and four orders of magnitude faster than the numerical solutions on which they were trained.
Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine learning approaches have demonstrated their ability to accelerate spatio-temporal predictions, although, with only moderate accuracy in comparison. Here we introduce MultiScaleGNN, a novel multi-scale graph neural network model for learning to infer unsteady continuum mechanics. MultiScaleGNN represents the physical domain as an unstructured set of nodes, and it constructs one or more graphs, each of them encoding different scales of spatial resolution. Successive learnt message passing between these graphs improves the ability of GNNs to capture and forecast the system state in problems encompassing a range of length scales. Using graph representations, MultiScaleGNN can impose periodic boundary conditions as an inductive bias on the edges in the graphs, and achieve independence to the nodes' positions. We demonstrate this method on advection problems and incompressible fluid dynamics. Our results show that the proposed model can generalise from uniform advection fields to high-gradient fields on complex domains at test time and infer long-term Navier-Stokes solutions within a range of Reynolds numbers. Simulations obtained with MultiScaleGNN are between two and four orders of magnitude faster than the ones on which it was trained.Preprint. Under review.
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