Scholz B, Schwierz G
Medical Engineering Group, Siemens AG, Erlangen, Germany.
IEEE Trans Biomed Eng. 1994 Aug;41(8):735-42. doi: 10.1109/10.310089.
Focal biomagnetic sources are described as pointlike current dipoles. The dipole parameters, position, and moment coordinates are commonly determined from biomagnetic data using iterative nonlinear optimization algorithms such as the Levenberg-Marquardt algorithm. However, even for single-dipole sources, mislocalizations can occur due to side minima of the cost function or due to a wrong choice of the start vector. This can be shown by introducing a cost function where the independent variables are only the position coordinates instead of position and moment coordinates. This dimensional reduction--which is also possible for multiple dipole sources--is achieved by calculating the cost function at each position with the position and data-dependent, optimum dipole moments. We call these dipoles with--in a least squares sense--optimum moments, locally optimal dipoles. The visualization of such a single-dipole cost function and of the iteration steps of the Levenberg-Marquardt algorithm show why mislocalizations cannot be avoided. Therefore, we propose an alternative noniterative localization algorithm for single-dipole sources without this drawback. It uses localization probabilities calculated by means of the locally optimal dipoles. Besides the determination of the dipole parameters, the proposed algorithm furnishes a reliable error for each localization. Its effectiveness is shown with simulated and real patient data.
局灶性生物磁源被描述为点状电流偶极子。偶极子参数、位置和矩坐标通常使用诸如Levenberg-Marquardt算法等迭代非线性优化算法从生物磁数据中确定。然而，即使对于单偶极子源，由于代价函数的旁极小值或起始向量选择错误，也可能发生定位错误。通过引入一个代价函数可以证明这一点，其中自变量仅为位置坐标而非位置和矩坐标。这种降维——对于多个偶极子源也是可能的——是通过用与位置和数据相关的最优偶极矩在每个位置计算代价函数来实现的。我们将这些在最小二乘意义上具有最优矩的偶极子称为局部最优偶极子。这种单偶极子代价函数以及Levenberg-Marquardt算法迭代步骤的可视化展示了为什么无法避免定位错误。因此，我们提出了一种针对单偶极子源的替代非迭代定位算法，该算法没有这个缺点。它使用通过局部最优偶极子计算的定位概率。除了确定偶极子参数外，所提出的算法还为每次定位提供可靠的误差。其有效性通过模拟和真实患者数据得以证明。
