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H C Tuckwell

Publications and source records attributed to H C Tuckwell.

14 recordsLinked to original sources
PubMed1979

The response of a spatially distributed neuron to white noise current injection.

The depolarization of passive nerve cylinder or dendritic tree in the equivalent cylinder representation is assumed to satisfy the cable equation. We consider in detail the effects of white noise current injection at a given location for the case of sealed end boundary conditions and for an initial resting state. The depolarization at a point is a Gaussian random process but is not Markovian. Expression (infinite series) are obtained for the expectation, variance, spatial and temporal covariances of the depolarization. We examine the steady state expectation and variance and investigate how these are approached in time over the whole neuronal surface. We consider the relative contributions of various terms in the series for the expectation and variance of the depolarization at x = 0 (soma, trigger zone, recording electrode) for various positions of the input process. It is found that different numbers of terms must be taken to obtain a reasonable approximation depending on whether the stimulus is at proximal, central or distal parts of the dendritic tree. We consider briefly the interspike time problem and see in an approximate way how spatial effects are important in determining the mean time between impulses.

Action Potentials↗
PubMed1978

A mathematical model for spreading cortical depression.

A mathematical model is derived from physiological considerations for slow potential waves (called spreading depression) in cortical neuronal structures. The variables taken into account are the intra- and extracellular concentrations of Na+, Cl-, K+, and Ca++, together with excitatory and inhibitor transmitter substances. The general model includes conductance changes for these various ions, which may occur at nonsynaptic and synaptic membrane together with active transport mechanisms (pumps). A detailed consideration of only the conductance changes due to transmitter release leads to a system of nonlinear diffusion equations coupled with a system or ordinary differential equations. We obtain numerical solutions of a set of simplified model equations involving only K+ and Ca++ concentrations. The solutions agree qualitatively with experimentally obtained time-courses of these two ionic concentrations during spreading depression. The numerical solutions exhibit the observed phenomena of solitary waves and annihilation of colliding waves.

Cortical Spreading Depression↗