Mosher J C, Lewis P S, Leahy R M
TRW Systems Engineering & Development Division, One Space Park, Redondo Beach, CA 90278.
IEEE Trans Biomed Eng. 1992 Jun;39(6):541-57. doi: 10.1109/10.141192.
An array of biomagnetometers may be used to measure the spatio-temporal neuromagnetic field or magnetoencephalogram (MEG) produced by neural activity in the brain. A popular model for the neural activity produced in response to a given sensory stimulus is a set of current dipoles, where each dipole represents the primary current associated with the combined activation of a large number of neurons located in a small volume of the brain. An important problem in the interpretation of MEG data from evoked response experiments is the localization of these neural current dipoles. We present here a linear algebraic framework for three common spatio-temporal dipole models: i) unconstrained dipoles, ii) dipoles with a fixed location, and iii) dipoles with a fixed orientation and location. In all cases, we assume that the location, orientation, and magnitude of the dipoles are unknown. With a common model, we show how the parameter estimation problem may be decomposed into the estimation of the time invariant parameters using nonlinear least-squares minimization, followed by linear estimation of the associated time varying parameters. A subspace formulation is presented and used to derive a suboptimal least-squares subspace scanning method. The resulting algorithm is a special case of the well-known MUltiple SIgnal Classification (MUSIC) method, in which the solution (multiple dipole locations) is found by scanning potential locations using a simple one dipole model. Principal components analysis (PCA) dipole fitting has also been used to individually fit single dipoles in a multiple dipole problem. Analysis is presented here to show why PCA dipole fitting will fail in general, whereas the subspace method presented here will generally succeed. Numerically efficient means of calculating the cost functions are presented, and problems of model order selection and missing moments are discussed. Results from a simulation and a somatosensory experiment are presented.
可以使用一系列生物磁力计来测量大脑中神经活动产生的时空神经磁场或脑磁图（MEG）。针对给定感觉刺激产生的神经活动，一种常用模型是一组电流偶极子，其中每个偶极子代表与位于大脑小体积区域内大量神经元的联合激活相关的初级电流。在解释诱发反应实验的MEG数据时，一个重要问题是这些神经电流偶极子的定位。我们在此提出一个线性代数框架，用于三种常见的时空偶极子模型：i）无约束偶极子，ii）位置固定的偶极子，以及iii）方向和位置固定的偶极子。在所有情况下，我们假设偶极子的位置、方向和大小是未知的。通过一个通用模型，我们展示了如何将参数估计问题分解为使用非线性最小二乘法最小化来估计时不变参数，随后对相关时变参数进行线性估计。提出了一种子空间公式，并用于推导一种次优最小二乘子空间扫描方法。所得算法是著名的多重信号分类（MUSIC）方法的一个特例，其中通过使用简单的单偶极子模型扫描潜在位置来找到解（多个偶极子位置）。主成分分析（PCA）偶极子拟合也已用于在多偶极子问题中单独拟合单个偶极子。这里给出的分析表明了为什么PCA偶极子拟合通常会失败，而这里提出的子空间方法通常会成功。给出了计算代价函数的数值有效方法，并讨论了模型阶数选择和缺失矩的问题。还给出了模拟和体感实验的结果。
