Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809

PET and SPECT Imaging in Hyperkinetic Movement Disorders

Movement disorders can be classified in hypokinetic (e.g., Parkinson's disease, PD) and hyperkinetic disorders (e.g., dystonia, chorea, tremor, tics, myoclonus, and restless legs syndrome). In this chapter, we will discuss results from positron emission tomography (PET) and single photon emission computed tomography (SPECT) imaging studies in patients with tremor, tics, myoclonus, and restless legs syndrome. Most studies in patients with tremor included patients with essential tremor (ET): a bilateral, largely symmetric, postural or kinetic tremor mainly involving the upper limbs and sometimes the head. Other studies evaluated patients with orthostatic tremor (OT): an unusually high frequent tremor in the legs that mainly occurs when patients are standing still. Increased regional cerebral blood flow (rCBF) and increased glucose metabolism have been found in the cerebellum, sensorimotor cortex, and thalamus in both patients with ET and OT compared to controls. Both PET and SPECT studies have evaluated the dopamine system in patients with ET and OT. Most imaging studies in patients with ET showed no, or only subtle loss of striatal tracer binding to the dopamine transporter indicating that ET is not characterized by nigrostriatal cell loss. The serotonin and/or gamma-aminobutyric acid (GABA) systems may play a role in the pathophysiology of ET. PET and SPECT imaging of the dopamine and serotonin system in patients with OT showed no abnormalities. Tics, the clinical hallmark of Gilles de la Tourette syndrome (TS), are relatively brief and intermittent involuntary movements (motor tic) and sounds (phonic tic). The essential features of tics are that (1) they can be temporarily suppressed; after suppression a rebound usually occurs with a flurry of tics; (2) the patient experiences an urge to tic, and (3) the tic is followed by a short moment of relief. Using 18F-FDG PET, it was shown that TS is a network disorder where multiple brain areas are active or inactive at the same time. The exact composition of this network is yet to be determined. Using rCBF PET and SPECT many brain regions were found to be abnormal, however, tics mostly correlated with hypoperfusion of the caudate nucleus and cingulate cortex. Both dopamine and serotonin are likely to play a role in the pathophysiology of TS. It is hypothesized that TS is characterized by low serotonin levels that modulate increased phasic dopamine release. Myoclonus is defined as a brief muscle jerk and occurs in many neurologic and non-neurologic disorders. Imaging with PET and SPECT in patients with myoclonus mainly showed abnormalities consistent with the underlying disorder. We described PET and SPECT imaging results in patients in which myoclonus was a prominent symptom. Hypoperfusion and/or hypometabolism of the frontoparietal cortex was found in patients with negative epileptic myoclonus, Alzheimer's disease, corticobasal degeneration, Creutzfeldt-Jakob disease, fatal familiar insomnia, and posthypoxic myoclonus. Other findings that were frequently reported were decreased rCBF and/or glucose metabolism in the cerebellum and thalamus and abnormalities in the dopamine system. Restless legs syndrome (RLS) is defined as an urge to move the legs accompanied with an unpleasant sensation in the legs or in another body part that is especially present during the evening and night and that can be accompanied by periodic limb movements in sleep (PLMS). Imaging studies in these patients have mainly focused on the dopamine system. Most PET studies found decreased tracer binding to the dopamine transporter, although this was not found in SPECT studies. Both PET and SPECT studies showed conflicting results regarding dopamine D2/3 receptor binding: both increased and decreased tracer binding was reported. Furthermore, it is likely that the serotonin and opioid systems also play a role in the pathophysiology of RLS.</p

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black spacetime. A prime application of characteristic evolution is to compute waveforms via Cauchy-characteristic matching, which is also reviewed.Comment: Published version http://www.livingreviews.org/lrr-2005-1