Convergence of formula for forward problem in brain physics

In brain physics, the forward problem is the process of predicting scalp potentials distribution from known brain electric source. The convergence of a forward problem algorithm was analyzed and proved through mathematical method for the first time. This formula calculated the scalp potentials distribution of the three layers concentric sphere head model caused by single dipole located at any point within the model. The convergence was further confirmed by numerical simulation. Thus the finite progression could be used to calculate the scalp potentials distribution instead of the infinitive progression in a certain error range. A study on the convergence speed was conducted too. The result gives a theoretical guarantee for the finite approximation of the formula that is an infinite series. The approximation provides a useful tool for the backward problem, which is the process of predicting brain electric source from known scalp potentials.