Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem
Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem
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球形多壳脑磁图问题的矢量值样条法
DOI：
10.1088/1361-6420/ac62f5
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发表时间：
2022
期刊：
影响因子：
2.1
通讯作者：
V. Michel
中科院分区：
文献类型：
--
作者：
S. Leweke;O. Hauk;V. Michel
人脑活动基于电化学过程，只能进行侵入性测量。因此，在医学和研究中可以无创地测量磁通密度 (MEG) 或电位差 (EEG) 等量。尽管大脑活动的可视化是认知神经科学的主要研究工具之一，但根据测量结果重建神经元电流是一个严重不适定的问题。在这里，我们使用人体头部的各向同性多壳模型和电磁过程的准静态方法，推导出一种基于再现核希尔伯特空间的新颖的矢量值样条方法，以便根据测量结果重建电流。所提出的方法遵循以前样条方法的路径，并提供经典的最小范数属性。此外，它还最小化了处理反问题不稳定性的（无限维）Tikhonov-Philips 泛函。该优化问题简化为求解有限维线性方程组，并且由于其构造而不会丢失信息。它产生了独特的解决方案，该解决方案考虑到只有神经元电流的谐波和螺线管分量影响测量。此外，我们证明了收敛结果：随着测量次数的增加，通过新方法实现的解收敛到数据生成器。矢量样条应用于三个综合测试用例的反演，可以很好地处理不规则分布的数据情况。结合五种参数选择方法，显示了具有和不具有附加高斯白噪声的综合测试用例的数值结果。就归一化均方根误差而言，新颖的矢量样条结果优于以前基于标量样条的方法。最后，演示了视觉刺激任务期间获取的真实数据的结果。它们可以快速计算并且相对于生理预期是合理的。
Human brain activity is based on electrochemical processes, which can only be measured invasively. Thus, quantities such as magnetic flux density (MEG) or electric potential differences (EEG) are measured non-invasively in medicine and research. The reconstruction of the neuronal current from the measurements is a severely ill-posed problem though the visualization of the cerebral activity is one of the main research tools in cognitive neuroscience. Here, using an isotropic multiple-shell model for the human head and a quasi-static approach for the electro-magnetic processes, we derive a novel vector-valued spline method based on reproducing kernel Hilbert spaces in order to reconstruct the current from the measurements. The presented method follows the path of former spline approaches and provides classical minimum norm properties. Besides, it minimizes the (infinite-dimensional) Tikhonov–Philips functional which handles the instability of the inverse problem. This optimization problem reduces to solving a finite-dimensional system of linear equations without loss of information, due to its construction. It results in a unique solution which takes into account that only the harmonic and solenoidal component of the neuronal current affects the measurements. Furthermore, we prove a convergence result: the solution achieved by the novel method converges to the generator of the data as the number of measurements increases. The vector splines are applied to the inversion of three synthetic test cases, where the irregularly distributed data situation could be handled very well. Combined with five parameter choice methods, numerical results are shown for synthetic test cases with and without additional Gaussian white noise. Former approaches based on scalar splines are outperformed by the novel vector splines results with respect to the normalized root mean square error. Finally, results for real data acquired during a visual stimulation task are demonstrated. They can be computed quickly and are reasonable with respect to physiological expectations.
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影响因子：
1.1
作者：
V. Michel;S. Orzlowski
通讯作者：
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DOI：
--
发表时间：
2008
期刊：
影响因子：
--
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DOI：
--
发表时间：
2010
期刊：
影响因子：
--
作者：
P. Berkel;V. Michel
通讯作者：
V. Michel
影响因子：
5.7
作者：
Vorwerk, Johannes;Cho, Jae-Hyun;Wolters, Carsten H.
通讯作者：
Wolters, Carsten H.
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DOI：
10.3389/fams.2017.00010
发表时间：
2016
期刊：
Frontiers Appl. Math. Stat.
影响因子：
--
作者：
M. Gutting;Bianca Kretz;V. Michel;R. Telschow
通讯作者：
R. Telschow