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Tổng số tiền điện hiện nay đang được tiêm vào các đoạn cáp của con số 6,6 sau đó, tức là 2πa x. Bởi vì hiện tại điện cực thường theo quy định của Tức là, không phải bởi một đơn vị diện tích hiện nay cho mỗi, tất cả các kết quả chúng ta có được cuối cùng sẽ được tái hiện trong các điều khoản của Ie | 12 Model Neurons II Conductances and Morphology define ie to be the total electrode current flowing into a given region of the neuronal cable divided by the surface area of that region. The total amount of electrode current being injected into the cable segment of figure 6.6 is then ie2naAx. Because the electrode current is normally specified by Ie not by a current per unit area all the results we obtain will ultimately be re-expressed in terms of Ie. Following the standard convention membrane and synaptic currents are defined as positive when they are outward and electrode currents are defined as positive when they are inward. The cable equation is derived by setting the sum of all the currents shown in figure 6.6 equal to the current needed to charge the membrane. The total longitudinal current entering the cylinder is the difference between the current flowing in on the left and that flowing out on the right. Thus dV n dV na2 dV 2naAxCm - I - -X- . - 2naAx im - ie dt rL dx J left rL dx J right 6.9 Dividing both sides of this equation by 2naAx we note that the right side involves the term 1 2arLAx y dx J right 2 y dx J left d fna2 8V 9x y rL dx 6.10 boundary conditions on the cable equation The arrow refers to the limit Ax 0 which we now take. We have moved rL outside the derivative in this equation under the assumption that it is not a function of position. However the factor of a2 must remain inside the integral unless it is independent of x. Substituting the result 6.10 into 6.9 we obtain the cable equation CmV d a2 dVi - im ie 6.11 at 2arL dx y dx f To determine the membrane potential equation 6.11 must be augmented by appropriate boundary conditions. The boundary conditions specify what happens to the membrane potential when the neuronal cable branches or terminates. The point at which a cable branches or equivalently where multiple cable segments join is called a node. At such a branching node the potential must be continuous that is the functions V x t .
