The port-Hamiltonian formulation is a powerful method for modeling and interconnecting systems of different natures. In this paper, the port-Hamiltonian formulation in tensorial form of a thick plate described by the Mindlin-Reissner model is presented. Boundary control and observation are taken into account. Thanks to tensorial calculus, it can be seen that the Mindlin plate model mimics the interconnection structure of its one-dimensional counterpart, i.e. the Timoshenko beam. The Partitioned Finite Element Method (PFEM 1 ) is then extended to both the vectorial and tensorial formulations in order to obtain a suitable, i.e. structure-preserving, finite-dimensional port-Hamiltonian system (PHs 2 ), which preserves the structure and properties of the original distributed parameter system. Mixed boundary conditions are finally handled by introducing some algebraic constraints. Numerical examples are finally presented to validate this approach. * andrea.brugnoli@isae.fr † daniel.alazard@isae.fr ‡ valerie.budinger@isae.fr § denis.matignon@isae.fr 1 PFEM stands for partitioned finite element method. 2 PHs stands for port-Hamiltonian systems.
The mechanical model of a thin plate with boundary control and observation is presented as a port-Hamiltonian system (PHs 1 ), both in vectorial and tensorial forms: the Kirchhoff-Love model of a plate is described by using a Stokes-Dirac structure and this represents a novelty with respect to the existing literature. This formulation is carried out both in vectorial and tensorial forms. Thanks to tensorial calculus, this model is found to mimic the interconnection structure of its one-dimensional counterpart, i.e. the Euler-Bernoulli beam. The Partitioned Finite Element Method (PFEM 2 ) is then extended to obtain a suitable, i.e. structure-preserving, weak form. The discretization procedure, performed on the vectorial formulation, leads to a finite-dimensional port-Hamiltonian system. This part II of the companion paper extends part I, dedicated to the Mindlin model for thick plates. The thin plate model comes along with additional difficulties, because of the higher order of the differential operator under consideration. * andrea.brugnoli@isae.fr † daniel.alazard@isae.fr ‡ valerie.budinger@isae.fr § denis.matignon@isae.fr 1 PHs stands for port-Hamiltonian systems. 2 PFEM stands for partitioned finite element method.
Safinamide (Xadago) is a novel dual-mechanism drug that has been approved in the European Union and United States as add-on treatment to levodopa in Parkinson's disease therapy. In addition to its selective and reversible monoamine oxidase B inhibition, safinamide through use-dependent sodium channel blockade reduces overactive glutamatergic transmission in basal ganglia, which is believed to contribute to motor symptoms and complications including levodopa-induced dyskinesia (LID). The present study investigated the effects of safinamide on the development of LID in 6-hydroxydopamine (6-OHDA)-lesioned rats, evaluating behavioral, molecular, and neurochemical parameters associated with LID appearance. 6-OHDA-lesioned rats were treated with saline, levodopa (6 mg/kg), or levodopa plus safinamide (15 mg/kg) for 21 days. Abnormal involuntary movements, motor performance, molecular composition of the striatal glutamatergic synapse, glutamate, and GABA release were analyzed. In the striatum, safinamide prevented the rearrangement of the subunit composition of N-methyl-Daspartate receptors and the levodopa-induced increase of glutamate release associated with dyskinesia without affecting the levodopa-stimulated motor performance and dyskinesia. Overall, these findings suggest that the striatal glutamate-modulating component of safinamide's activity may contribute to its clinical effects, where its long-term use as levodopa add-on therapy significantly improves motor function and "on" time without troublesome dyskinesia.This work was supported by Zambon S.P.A. F.G. and M.M. contributed equally to this work.
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