The Reconstruction Of Multiple Current Dipoles With MEG Data

Magnetoencephalography (MEG) is a method for determining brain activities by measuring the corresponding magnetic field non-invasively outside a human head. Since the neuromagnetic field is very weak (50-500 fT), it is usually measured by superconducting quantum interference devices (SQUIDs). The time resolution of MEG is better than 1 ms and the spatial discrimination is about 2—4 mm for sources in the cerebral cortex. MEG has become a promising technique for brain functional imaging/study and diagnosis of brain diseases.Mainly two kinds of source models are used in MEG research: multi-dipole model and current-distribution model. In this dissertation, I focus my research to the former one.This thesis is organized as follows.The first chapter gives an overview on the current status of MEG research. The neural basis, the forward and inverse problems of MEG are introduced in detail in the next three chapters. The numerical methods used in this thesis such as the boundary element method (BEM), the genetic algorithm, the Marquardt method are also introduced.In chapter 5, a method to calculate the MEG lead field based on the reciprocity theorem is introduced. Compared with the standard BEM, the reciprocal formulation yields a faster computation speed and requires less computer memory. In addition, for dipoles close to the brain's surface, this formulation can obtain a higher numerical accuracy without a local refinement of the mesh. Using interpolation method based on the "lead field mesh" in theprecalculation, we can speed the solver of the forward problem 104 times than the standard BEM.In chapter 6, a fast algorithm for localising multiple current dipoles in a human brain is presented. A genetic algorithm is used first for a rough estimate_of the dipole locations. To speed up the global optimisation algorithm, an analytical solution for a spherical head model is used. This rough estimate is then used as the input value of a gradient-based algorithm which will search for the final dipole positions. In this algorithm, a boundary element solution for a realistic brain-shaped head model is used. Numerical simulation indicates that the present algorithm converges about four times faster than an algorithm using a brain-shaped head model in all the steps. Further simulation tests show that the combined optimization method with the combined brain model can work well when the total number of dipole sources is small, however, it is not suitable when there are many dipoles (more than five dipoles). The combined optimization method with a realistic brain-shape model works well for all situations of dipole sources. Furthermore, a new iterative approach for determining the local optimal dipole (which could be used in the optimization method to reduce the total number of unknown parameters) is proposed. The reconstruction results using the proposed approach are compared with those of the standard "singular value decomposition method" in terms of the stability to noise in the input data. It is found that the new approach is considerably more stable to noise (compared with the standard one), especially when thenoise level is high.In chapter 7, a combined model for MEG is introduced to localize a current dipole inside a human brain. A geometrical description of the difference between the sphere model and the brain-shape model is presented, and used to divide the brain into "large difference areas (LDAs)" and "small difference areas (SDAs)". The current dipole is localized with an optimization method, in which the sphere and brain-shape models are used when the trial dipole is located inside an SDA and an LDA, respectively. When the trial dipole is located inside an LDA, the boundary element method (BEM) is accelerated by utilizing the potential of a dipole at the centre of the LDA in an iterative algorithm. The present method is fast while keeping a reasonably good accuracy.In chapter 8, the MEG-MUSIC algorithm is used to solve the MEG inverse problem with the realistic brain-shape model.In chapter 9, a summary of this thesis and some...