边界元法求解脑电正问题初探-电子科技大学.pptVIP

边界元法求解脑电正问题初探--A Modifield Boundary Element Methed for the Estimation of Potential Fields on the Scalp 赵旭 电子科技大学生命科学与技术学院 内容提要 1·课题及边界元法简介 2·Modifield BEM 简介 3·Modifield BEM 的实现 4·初步总结以及展望 1·课题及边界元法简介 电流偶极子源的假设 脑电正问题（Forward Problem) 脑电逆问题 (Inverse Problem) 1·课题及边界元法简介 边界元法的一般原理 许多物理问题可通过不同的途径归结为不同的 数学模型（大多数没有解析解）： a· 偏微分方程的边值问题－－有限差分法 b· 区域上的变分问题－－有限元法 C· 边界上的积分问题－－边界元法 1·课题及边界元法简介 边界元法是将区域内微分方程 通过积分定理变为边界上的积分方程 再将积分方程在边界上离散为代数方程。 2·Modifield BEM 简介 Let us start by formulating the BEM equations as Where Vi and gi are vectors of potentials on the Ith surface,and Bij is a matrix. 2·Modifield BEM 简介 2·Modifield BEM 简介 Consider the expression for the potentials on the inner surface S3 of a three-surface head model For V1 and V2 are much more smaller than V3,we can ignore V1 and V2 entirely and still achieve a good estimate of V3 . 2·Modifield BEM 简介 By Green’s theorem we can get : Pxy a matrix with coefficients equal to ?pi times the solid angle subtended by an element of unit area on surface y at a point on surface x; Gxy a matrix with coefficients equal to ds an areal element of surface y, r the distance between a point on surface x and element ds; the normal component of the gradient of V3 2·Modifield BEM 简介 First,since the surfaces are relatively smooth ,the ‘self’ matrices,P11,P33,and G33 are strongly diagonal.Also ,as already noted,we do not have to maintain the accuracy of the magnitude of the scalp field,so we can take the self matrices as identity matrity matrices.Thus 2·Modifield BEM 简介 We can get: Premultiply by G13 to give However ,all the terms of the matrix product G13P13 are much smaller than one and 2·Modifield BEM 简介 (I-G13P31) is dominated by the identity matrix,so 3·Modifield BEM 的实现 采用三层球模型并归一化半径为一。 每层都离散成642个点，1280个三角形。 第一层为头皮层，二层为颅骨层，三层为大脑组织层。 三层的电导率分别取为：1；1/80；1 3·Modifield BEM 的实