Heller L
Theoretical Division, Los Alamos National Laboratory, New Mexico 87545.
Biophys J. 1990 Mar;57(3):601-6. doi: 10.1016/S0006-3495(90)82575-3.
The encephalographic problem of finding the electric potential V and the return current associated with any assumed primary current, Jp, is put in the form of a variational principle. With Jp and the conductivity specified, the correct V is one which makes an integral quantity P[V] a maximum. The terms in P[V] are related to the rates at which work is done by the electric field on the primary and return currents. It is shown that there is a unique solution for the electric field, and it satisfies the conservation of energy; this condition can serve as a check on any numerical solution. With the conductivity a different constant in different regions, the variational principle is recast in terms of the charge density on the surfaces of discontinuity. An iteration-variation method for finding the solution is outlined, and possible computational advantages over other approaches are discussed.
寻找与任何假定的初级电流Jp相关的电势V和返回电流的脑电图问题，被表述为一个变分原理的形式。在给定Jp和电导率的情况下，正确的V是使积分量P[V]达到最大值的那个值。P[V]中的各项与电场对初级电流和返回电流所做的功的速率有关。结果表明，电场存在唯一解，并且它满足能量守恒；这个条件可用于检验任何数值解。当电导率在不同区域为不同常数时，变分原理根据不连续面处的电荷密度重新表述。概述了一种用于求解的迭代-变分方法，并讨论了相对于其他方法可能具有的计算优势。
