{"title":"Semi-analytic three-shell forward calculation for magnetoencephalography","authors":"","doi":"10.1016/j.neuroimage.2024.120836","DOIUrl":null,"url":null,"abstract":"<div><p>In previous studies, the magnetic lead field theorem in the quasi-static approximation was derived and used for the development of a method for the forward problem of MEG. It was applied and tested on a single-shell model of the human head and the question whether one shell is adequate enough for the calculation of the magnetic field is the main reason for this study. This forward method is based on the fundamental concept that one can calculate the lead field for MEG by decomposing it into two parts: the lead field of an arbitrary volume conductor that is already known and the gradient of basis functions that have to be harmonic, here derived from spherical harmonics. The problem then is reduced to evaluating the coefficients found in the basis functions. In this research we aim to improve the accuracy of the forward model, hence improving the localization accuracy in inverse methods by introducing a more detailed realistic head model. We here generalize the algorithm developed for a single-shell volume conductor to a three-shell volume conductor representing the brain, the skull and the skin with homogenous and isotropic conductivities in realistic ratios. The expansion to three shells could be tested as the three-shell algorithm is approaching the single-shell with high accuracy in special cases where three-shell solutions can also be calculated using a single-shell solution, especially for higher levels of expansion. The deviation in the calculation of the lead field is also evaluated when using three shells with realistic conductivities. The magnetic field turned out to differ to an important measurable extend in particular for deeper sources, making the three-shell algorithm substantially more accurate for these dipole locations.</p></div>","PeriodicalId":19299,"journal":{"name":"NeuroImage","volume":null,"pages":null},"PeriodicalIF":4.7000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1053811924003331/pdfft?md5=0a9251a7ae10c3d26551cba22d884b35&pid=1-s2.0-S1053811924003331-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"NeuroImage","FirstCategoryId":"3","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1053811924003331","RegionNum":2,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"NEUROIMAGING","Score":null,"Total":0}
引用次数: 0
Abstract
In previous studies, the magnetic lead field theorem in the quasi-static approximation was derived and used for the development of a method for the forward problem of MEG. It was applied and tested on a single-shell model of the human head and the question whether one shell is adequate enough for the calculation of the magnetic field is the main reason for this study. This forward method is based on the fundamental concept that one can calculate the lead field for MEG by decomposing it into two parts: the lead field of an arbitrary volume conductor that is already known and the gradient of basis functions that have to be harmonic, here derived from spherical harmonics. The problem then is reduced to evaluating the coefficients found in the basis functions. In this research we aim to improve the accuracy of the forward model, hence improving the localization accuracy in inverse methods by introducing a more detailed realistic head model. We here generalize the algorithm developed for a single-shell volume conductor to a three-shell volume conductor representing the brain, the skull and the skin with homogenous and isotropic conductivities in realistic ratios. The expansion to three shells could be tested as the three-shell algorithm is approaching the single-shell with high accuracy in special cases where three-shell solutions can also be calculated using a single-shell solution, especially for higher levels of expansion. The deviation in the calculation of the lead field is also evaluated when using three shells with realistic conductivities. The magnetic field turned out to differ to an important measurable extend in particular for deeper sources, making the three-shell algorithm substantially more accurate for these dipole locations.
在以前的研究中,推导出准静态近似的磁导场定理,并将其用于 MEG 正向问题方法的开发。该方法在单壳人体头部模型上进行了应用和测试,而单壳是否足以计算磁场是本研究的主要原因。这种前瞻性方法基于一个基本概念,即可以通过将 MEG 的导磁场分解为两部分来计算:已知的任意体积导体的导磁场和必须是谐波的基函数梯度,这里的基函数是由球面谐波导出的。然后,问题就简化为评估基函数中的系数。在这项研究中,我们的目标是提高前向模型的精度,从而通过引入更详细的现实头部模型,提高逆向方法的定位精度。在此,我们将针对单壳体积导体开发的算法推广到代表大脑、头骨和皮肤的三壳体积导体,三壳体积导体具有同质和各向同性的传导率,且比例逼真。由于三壳算法在特殊情况下接近单壳算法时具有很高的精确度,因此可以对扩展到三壳进行测试,三壳解法也可以使用单壳解法进行计算,特别是对于较高的扩展水平。在使用具有实际电导率的三壳时,还对铅场计算的偏差进行了评估。结果表明,磁场的偏差达到了可测量的重要程度,特别是对于较深的磁源,使得三壳算法对于这些偶极位置的计算精度大大提高。
期刊介绍:
NeuroImage, a Journal of Brain Function provides a vehicle for communicating important advances in acquiring, analyzing, and modelling neuroimaging data and in applying these techniques to the study of structure-function and brain-behavior relationships. Though the emphasis is on the macroscopic level of human brain organization, meso-and microscopic neuroimaging across all species will be considered if informative for understanding the aforementioned relationships.