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Nonlinear Oscillations of Hamiltonian PDEs

Massimiliano Berti

Resumen/Descripción – provisto por la editorial

No disponible.

Palabras clave – provistas por la editorial

Partial Differential Equations; Dynamical Systems and Ergodic Theory; Approximations and Expansions; Number Theory; Applications of Mathematics; Mathematical Methods in Physics

Disponibilidad
Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2007 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-8176-4680-6

ISBN electrónico

978-0-8176-4681-3

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Birkhäuser Boston 2007

Tabla de contenidos

Finite Dimension

Massimiliano Berti

Brain stimulation has been receiving increasing attention as an alternative therapy for epilepsy that cannot be treated by either antiepileptic medication or surgical resection of the epileptogenic focus. The stimulation methods include transcranial magnetic stimulation (TMS) or electrical stimulation by implanted devices of the vagus nerve (VNS), deep brain structures (DBS) (thalamic or hippocampal), cerebellar or cortical areas. TMS is the simplest and least invasive approach. However, the most common epileptogenic areas (mesial temporal structures) probably lie too deep beneath the surface of the skull for effective TMS. The efficacy of VNS in reducing the frequency or severity of seizures is quite variable and depends on many factors which are currently investigated. VNS is well-tolerated and approved in many countries. DBS is much more invasive than either TMS or VNS. Currently, a number of targets for DBS are investigated including caudate, centromedian or anterior thalamic nuclei, and subthalamic nucleus. Direct stimulation of the epileptic cortical focus is another approach to the neuromodulation in epilepsy. Finally, another line of research investigates the usefulness of implantable seizure detection devices. The current chapter presents the most important evidence on the above methods. Furthermore, other important issues are reviewed such as the selection criteria of patients for brain stimulation and the potential role of brain stimulation in the treatment of depression in epileptic patients.

Pp. 1-27

Infinite Dimension

Massimiliano Berti

Brain stimulation has been receiving increasing attention as an alternative therapy for epilepsy that cannot be treated by either antiepileptic medication or surgical resection of the epileptogenic focus. The stimulation methods include transcranial magnetic stimulation (TMS) or electrical stimulation by implanted devices of the vagus nerve (VNS), deep brain structures (DBS) (thalamic or hippocampal), cerebellar or cortical areas. TMS is the simplest and least invasive approach. However, the most common epileptogenic areas (mesial temporal structures) probably lie too deep beneath the surface of the skull for effective TMS. The efficacy of VNS in reducing the frequency or severity of seizures is quite variable and depends on many factors which are currently investigated. VNS is well-tolerated and approved in many countries. DBS is much more invasive than either TMS or VNS. Currently, a number of targets for DBS are investigated including caudate, centromedian or anterior thalamic nuclei, and subthalamic nucleus. Direct stimulation of the epileptic cortical focus is another approach to the neuromodulation in epilepsy. Finally, another line of research investigates the usefulness of implantable seizure detection devices. The current chapter presents the most important evidence on the above methods. Furthermore, other important issues are reviewed such as the selection criteria of patients for brain stimulation and the potential role of brain stimulation in the treatment of depression in epileptic patients.

Pp. 29-57

A Tutorial in Nash–Moser Theory

Massimiliano Berti

Brain stimulation has been receiving increasing attention as an alternative therapy for epilepsy that cannot be treated by either antiepileptic medication or surgical resection of the epileptogenic focus. The stimulation methods include transcranial magnetic stimulation (TMS) or electrical stimulation by implanted devices of the vagus nerve (VNS), deep brain structures (DBS) (thalamic or hippocampal), cerebellar or cortical areas. TMS is the simplest and least invasive approach. However, the most common epileptogenic areas (mesial temporal structures) probably lie too deep beneath the surface of the skull for effective TMS. The efficacy of VNS in reducing the frequency or severity of seizures is quite variable and depends on many factors which are currently investigated. VNS is well-tolerated and approved in many countries. DBS is much more invasive than either TMS or VNS. Currently, a number of targets for DBS are investigated including caudate, centromedian or anterior thalamic nuclei, and subthalamic nucleus. Direct stimulation of the epileptic cortical focus is another approach to the neuromodulation in epilepsy. Finally, another line of research investigates the usefulness of implantable seizure detection devices. The current chapter presents the most important evidence on the above methods. Furthermore, other important issues are reviewed such as the selection criteria of patients for brain stimulation and the potential role of brain stimulation in the treatment of depression in epileptic patients.

Pp. 59-71

Application to the Nonlinear Wave Equation

Massimiliano Berti

Brain stimulation has been receiving increasing attention as an alternative therapy for epilepsy that cannot be treated by either antiepileptic medication or surgical resection of the epileptogenic focus. The stimulation methods include transcranial magnetic stimulation (TMS) or electrical stimulation by implanted devices of the vagus nerve (VNS), deep brain structures (DBS) (thalamic or hippocampal), cerebellar or cortical areas. TMS is the simplest and least invasive approach. However, the most common epileptogenic areas (mesial temporal structures) probably lie too deep beneath the surface of the skull for effective TMS. The efficacy of VNS in reducing the frequency or severity of seizures is quite variable and depends on many factors which are currently investigated. VNS is well-tolerated and approved in many countries. DBS is much more invasive than either TMS or VNS. Currently, a number of targets for DBS are investigated including caudate, centromedian or anterior thalamic nuclei, and subthalamic nucleus. Direct stimulation of the epileptic cortical focus is another approach to the neuromodulation in epilepsy. Finally, another line of research investigates the usefulness of implantable seizure detection devices. The current chapter presents the most important evidence on the above methods. Furthermore, other important issues are reviewed such as the selection criteria of patients for brain stimulation and the potential role of brain stimulation in the treatment of depression in epileptic patients.

Pp. 73-109

Forced Vibrations

Massimiliano Berti

Brain stimulation has been receiving increasing attention as an alternative therapy for epilepsy that cannot be treated by either antiepileptic medication or surgical resection of the epileptogenic focus. The stimulation methods include transcranial magnetic stimulation (TMS) or electrical stimulation by implanted devices of the vagus nerve (VNS), deep brain structures (DBS) (thalamic or hippocampal), cerebellar or cortical areas. TMS is the simplest and least invasive approach. However, the most common epileptogenic areas (mesial temporal structures) probably lie too deep beneath the surface of the skull for effective TMS. The efficacy of VNS in reducing the frequency or severity of seizures is quite variable and depends on many factors which are currently investigated. VNS is well-tolerated and approved in many countries. DBS is much more invasive than either TMS or VNS. Currently, a number of targets for DBS are investigated including caudate, centromedian or anterior thalamic nuclei, and subthalamic nucleus. Direct stimulation of the epileptic cortical focus is another approach to the neuromodulation in epilepsy. Finally, another line of research investigates the usefulness of implantable seizure detection devices. The current chapter presents the most important evidence on the above methods. Furthermore, other important issues are reviewed such as the selection criteria of patients for brain stimulation and the potential role of brain stimulation in the treatment of depression in epileptic patients.

Pp. 111-137