This textbook, available in two volumes, has been developed from a course taught at Harvard over the last decade. The course covers principally the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The authors adopt the ''spiral method'' of teaching, covering the same topic several times at increasing levels of sophistication and range of application. Thus the reader develops a deep, intuitive understanding of the subject as a whole, and an appreciation of the natural progression of ideas. Topics covered include many items previously dealt with at a much more advanced level, such as algebraic topology (introduced via the analysis of electrical networks), exterior calculus, Lie derivatives, and star operators (which are applied to Maxwell''s equations and optics). This then is a text which breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Any student, interpreted in the widest sense, with an interest in physics and mathematics, will gain from its study. New imaging sensors, molecular probes, and neuromarkers for faster temporal resolution, smaller spatial resolution, and higher anatomic accuracy have made brain neuroimaging highly valuable in studying neuropathologies. Provocative insights into how the human brain actually works in real time and in vivo are now possible. In Bioimaging in Neurodegeneration, prominent physicians, researchers, and inventors of cutting-edge technologies review the new imaging tools available for diagnosing, treating, and discovering the underlying causes of Parkinson's and Alzheimer's disease, epilepsy, and leukodystrophy. The new technologies demonstrated include novel sequences for magnetic resonance imaging (MRI), such as magnetization-prepared rapid acquisition gradient echo (MPRAGE); proton magnetic resonance spectroscopy (1H MRS); new tracers for positron emission tomography (PET) and single-photon emission tomography (SPECT), such as tropane analogs and altropane; neuromolecular imaging (NMI) of neurotransmitters directly in brain synapses of epilepsy patients with unique carbon-based electrochemical sensors; and intrinsic optical signal imaging (IOS), useful in diagnosing "spreading epileptiform depression." NMI and IOS also promise applications in intraoperative guided neurosurgery. Pediatric mitochondrial cytopathies are discussed, as well as nanotechnology, microtechnology, nanoimaging, and microimaging are presented. Devices for diagnosing tumors are also described. To enhance understanding of the potential of these developing technologies, a companion compact disk contains color versions of selected black-and-white illustrations used in the book.
Authoritative and state-of-the art, Bioimaging in Neurodegeneration offers both the physician and researcher a critical survey of the best new technologies for studying neurodegeneration, as well as describing their optimal use in the diagnosis and treatment of specific neurodegenerative diseases.