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CHAPTER 7

Magnetic stimulation and therapy

7.1 Introduction
From the arborizations of cerebellar Purkinje dendritic cells to motor neurons that transmit
the control signals from the central nervous system to the distal muscles, the complexity
and spatial extent of neurons vary significantly (Niebur, 2008). Arborescent networks
allow neurons to accept and transmit a vast number of synaptic inputs that may interact in
complex ways to enable dendritic computations.
The difficulties encountered in measuring the distal parts of the cell limit the
knowledge of the integration of the neurons’ distal synaptic input. The nervous fiber
has a complex structure (Villegas and Villegas, 1965; Cole, 1968; Plonsey and Barr,
1988). During the biological evolution, its structure, size, and shape morphed into an
optimal construct that is consistently described through the cable theory (Plonsey and
Barr, 1988; Malmivuo and Plonsey, 1995; Morega, 1999; Timotin, 2004). The cable
theory presents how electrical signals from different synapses merge and circulate
through the system of branches that forms the dendritic tree of a cell. In this approach,
the electrical signal (voltage) varies mainly along the axis of the neural process than
orthogonal to it, and neurites (also called “neural processes”) are used to model this
part of a dendrite or axon—these limitations are the consequence of reducing the
morphological complexity of a neuron by neglecting the small radial variations and
only considering the variation along its axis. This assumption, which is based on scale
analysis has important consequences: it reduces the model from three dimensions to
just one, paving the path to an equivalent electric circuit and the pending cable model.
The first section in this chapter is devoted to the cable theory and model as needed for
stimulation analysis and analytic solutions are proposed to this end.
Magnetic stimulation (MS) represents, in fact, the activation of excitable tissues
(nerve, muscle, or sensitive cells), which is produced noninvasively by applying an
electric stimulus near the cell membrane, by electromagnetic induction. Electric cur-
rent impulses are released through a stimulation applicator (coil), which is placed at
the surface of the skin; the variable magnetic field induces eddy current impulses inside
the body. MS began to be scientifically studied and tested for clinical use by a group
of researchers from the University of Sheffield, UK, in the early 1980s. From the stim-
ulation of peripheral nerves [peripheral magnetic stimulation (PMS)], the procedure
has evolved to apply to the central nervous system through transcranial magnetic stim-
ulation (TMS). It is more and more used in neurology, both for therapeutic purposes

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