Excitation propagation

In the last section we briefly discussed the mechanisms of the generation and propagation of the excitation impulse in the two physicochemical models of the nerve fiber. In a more general case one faces the problem of impulse propagation in a certain excitable biological medium, be it a nerve fiber, an electrically excitable syncytium, a neuron network, or some other object. As a rule, such a system may be characterized by the dynamic distribution of electric potential described by an equation of the type of Eq. (9)  

The other aspect consists in determining the properties and molecular nature of the objects responsible for the specific features of the functions C, R, and i. Within the framework of the theory of excitable media one may ignore the molecular mechanisms of activity and introduce some phenomenological description of the local properties of the medium. 

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The use of the surface ultrasonic waves seems to be convenient for these purposes. However, this method has not found wide practical application. Peculiarities of excitation, propagation and registration of surface waves created before these time great difficulties for their application in automatic systems of duality testing. It is connected with the fact that the surface waves are weakened by soil on the surface itself In addition, the methods of testing by the surface waves do not yield to automation due to the difficulties of creation of the acoustic contact. In particular, a flow of contact liquid out of the zone of an acoustic line, presence of immersion liquid, availability of chink interval leads to the adsorption and reflection of waves on tlie front meniscus of a contact layer. The liquid for the acoustic contact must be located only in the places of contact, otherwise the influence on the amplitude will be uncontrolled. This phenomenon distorts the results of testing procedure. 

Cardiac muscle contraction is an electrical event initiated at the sinoatrial node. Each cardiac muscle cell fires an action potential as a result of excitation propagated from the sinoatrial node, which produces muscle cell contraction. A wave of action potentials spreads across the organ to produce coordinated contraction of the heart and efficient ejection of blood to the body. Excitation and the subsequent return of a cardiac muscle cell to rest (repolarization) during the action potential is dictated by the flow of ions across the cell membrane. Membrane repolarization is produced by the flow of potassium ions through various types of potassium channels. 

In the case of excitation propagation, the potential is described by Eq. (9) in which C stands for the double layer capacitance per unit wire length, R for the resistance per unit length of solution, i for the current through unit surface length equal to lirrio (r is wire radius, / o is current density). As noted above. 

Figure 9 is a diagram of the local currents flowing along the nerve fiber during passage of an excitation impulse. To review the excitation propagation mechanism described in Section 1 it is convenient to consider Figure 9. The downstream-oriented axial current inside the fiber crosses the membrane as capacitive current, i.e., charges the membrane. When a certain threshold is exceeded, an inward ionic current appears apart from capacitive current. Further on, the outward current begins to dominate and returns the potential...

Figure 12. The hysteresis of excitation propagation along a nerve fiber whose outlines are shown beneath the figure. The impulse direction is marked with arrows beside the corresponding curves.

The energy representations in Eq. (4.13) or Eq. (4.17) show that the appropriate energy differences corresponding to excitations of the A -electron system are obtained from the excitation propagator, ie., the one with the field operator basis... 

For real orbitals and geminal coefficients gi, the excitation propagator P E) is written in the geometric approximations as before, but now with the augmented set of field operators. Considering the block... 

The excitation propagator (particle-hole propagator) at the RPA level of approximation can be expressed as... 

From the equation of motion of a (excitation) propagator A B))e, it follows that... 

The T amplitudes contain infinite order contributions to each excitation level from the HF state. Thus, replacing the RSPT K amplitudes with the CC T amplitudes may be considered a renormalization procedure since certain classes of perturbation terms or diagrams are summed to infinite order. This idea was employed in work on both the electron propagator and the excitation propagator... 

The excitation propagator is of importance for the understanding of electronic excitation spectra, polarizabilities, indirect nuclear spin-spin coupling tensors, and many other quantities. It has been treated in higher order approximations and is capable of yielding predictive results. An approach analogous to the one followed for the electron propagator is quite feasible. 

An explicit treatment of the excitation propagator through second order in electron interaction is presented in the following. First the projection manifold is limited to f = (q ql qq), and the superoperator... 

Through second order, the excitation propagator can then be expressed as P- E) = ) (12-16)... 

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