By Henry C. Tuckwell
ISBN-10: 0521350964
ISBN-13: 9780521350969
The human mind includes billions of nerve cells whose job performs a serious position within the approach we behave, think, understand, and imagine. This two-volume set explains the elemental houses of a neuron--an electrically lively nerve cell--and develops mathematical theories for how neurons reply to some of the stimuli they obtain. quantity 1 includes descriptions and analyses of the primary mathematical versions which were built for neurons some time past thirty years. It presents a quick evaluate of the elemental neuroanatomical and neurophysiological proof that may shape the point of interest of the mathematical remedy. Tuckwell discusses the mathematical theories, starting with the speculation of membrane potentials. He then is going directly to deal with the Lapicque version, linear cable idea, and time-dependent recommendations of the cable equations. He concludes with an outline of Rall's version nerve telephone. as the point of arithmetic raises progressively upward from bankruptcy a few familiarity with differential equations and linear algebra is fascinating.
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Additional info for Introduction to Theoretical Neurobiology: Volume 1, Linear Cable Theory and Dendritic Structure
Example text
9, is impaling the motoneuron with an electrode and passing current into the cell. This is the current-injection method. Third, an electric shock can be delivered to the ventral root and an action potential, if elicited, will now travel "backward" into the initial segment and into the cell body. The normal manner in which an action potential propagates in a spinal motoneuron is away from the cell body and such an action potential (as in the first two methods of elicitation) is said to propagate orthodromically, or in the orthodromic direction.
In addition, motoneurons recurrently excite themselves via this pathway. 19. PLITEAL NERVE. 50 40 30 20 10 FEMORAL NERVE 40 30 20 10 o 20 10 08TURAT0R LATERAL POPLITEAL NERVE NERVE. 4. 22. Graphs of motoneurons in some of the lumbar (L) and sacral (S) regions of the cat spinal cord. Distance down the cord (in millimeters) goes from left to right. [From Romanes (1951). Reproduced with the permission of Alan R. 23. How some of the la fibers cross over in the spinal cord to innervate motoneurons on the contralateral side.
Usually we speak of a refractory period after an action-potential that divides into two parts. An absolute refractory period occurs when a stimulus is incapable of eliciting another action potential, followed by a relative refractory period when a spike may be initiated but with a different threshold. The absolute refractory period is usually only on the order of 1 ms in duration. During the delayed depolarization a spike may be easier to elicit and this is sometimes called a supernormal period.
Introduction to Theoretical Neurobiology: Volume 1, Linear Cable Theory and Dendritic Structure by Henry C. Tuckwell
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