... at the nerve ends is considered as a particular case of the cable equation with oblique linear boundary conditions. A variational approach is taken to derive a weak solution of the problem. This extends classical results and removes a major obstacle of nonorthogonal boundary conditions in standard analysis...

... of synaptic “weight” during long-term potentiation (see Chap. 13). Actin filaments Boutons Calmodulin Diffusion Electrotonic length Glomerulus Information processing Input delay Linear cable equation Mitochondria Dendritic spines, sometimes also called dendritic thorns, are tiny...

...This chapter, which addresses the partial differential equations (PDEs) with the example of finding the speed and profile of a propagating impulse for a Hodgkin-Huxley-like cable equation, highlights a few properties of differential equations and concepts for understanding them. It mentions...

... that is determined by the stimulation device and the geometric and electric parameters of the head. The imposed electric field drives an electric current through the brain tissue, which macroscopically behaves as a volume conductor. The electric field polarizes neuronal membranes as described by the cable equation...

... need to understand the behavior of these extended systems having a cablelike structure. The basic equation governing the dynamics of the membrane potential in thin and elongated neuronal processes, such as axons or dendrites, is the cable equation. It originated in the middle of the last century...

... lipid bilayer lipids membrane potential prototypes action potential McCulloch Warren Pitts Walter voltage gradient capacitors capacity central processing unit CPU electrical capacity time constant transistors cable equation as analogy for cell membrane Kelvin Lord Thompson William Lord...

...0 12 11 1998 The previous chapter dealt with the solution of the cable equation in response to current pulses and steps within a single unbranched cable. However, real nerve cells possess highly branched and extended dendritic trees with quite distinct morphologies. Figure 3.1 illustrates...

... and back into a postsynaptic electrical signal. Amino acids Bicuculline Cable equation Dendritic spines Ephaptic transmission Firing rate Glial cells Hebbian learning Input conductance How information circulates in the brain was the subject of a heated debate lasting a decade or more among...

... of, and the strength of the interaction depends on the relative spatial positioning, as we will see now. That this can be put to good use by the nervous system is shown by the following experimental observation and simple model. Absolute synaptic suppression Cable equation Dendritic spikes Excitation Glutamate...

... variable neuronal firing really is. Absolute refractory period Brownian motion Cable equation Deterministic chaos Fano factor Gain normalization Interspike intervals (ISIs) Leak resistance Mean rate code Point processes The majority of experiments in neurophysiology are based upon spike...