Research On Forward And Inverse Problems In Brain Electromagnetic Tomography

As a non-invasive brain imaging technique,brain electromagnetic tomography(BEMT)can be used to quantitatively map the electromagnetic properties of the complex human brain(including permittivity,conductivity and permeability)by using electromagnetic field and inversion methods.BEMT has merits like strong penetrability,high contrast and ease of handling,thus it has been developed more and more for brain imaging.But,BEMT is a typical nonlinear and highly ill-posed inverse problem,so its accuracy,resolution and reconstruction efficiency have limitations which hinder the clinical application of BEMT.Therefore,focusing on the existing problems in BEMT,this thesis uses computational electromagnetic methods and artificial neural network(ANN)schemes to improve the computational accuracy and efficiency of forward and inversion methods of BEMT and promote the clinical applications of BEMT.First,the fast volume integral equation inversion method is proposed for 3-dimensional MRI-based electrical properties tomography(MREPT).The volume integral equations are employed as the governing equations of MREPT to avoid assuming the electrical properties of biological tissues are locally homogeneous and significant errors along boundaries.Meanwhile,the stabilized biconjugate-gradient fast Fourier transform(BCGS-FFT)method is used to iteratively solve the forward problem of MREPT and the variational Born iterative method(VBIM)combined with the conjugate-gradient fast Fourier transform(CG-FFT)method is utilized to compute the inverse problem of MREPT for reducing computation time and memory.Numerical results have demonstrated that the proposed fast volume integral equation inversion method can reconstruct 3-dimensional MREPT for the high contrast human brain.Second,the mixed finite element method(Mixed FEM)based on scattered field is proposed for broadband full-wave simulations of bioelectromagnetism including BEMT.To overcome the low frequency breakdown problem which occurs in low frequency bioelectromagnetism,the mixed FEM imposes Gauss’ law to the scattered-field-based vector Helmholtz equation in the form of Lagrangian multiplier.Gauss’ law is regarded as the divergence free constraint condition for reducing the condition number of system matrix and eliminating singularity.Numerical results have demonstrated that the full-wave mixed FEM can solve the bioelectromagnetism problems of 3-dimensional complex human brain model from DC to microwave frequencies and perform stably regardless of frequencies.Finally,the ANN-based electromagnetic inversion method is proposed for high resolution 3-dimensional BEMT.Firstly,the semi-join back propagation neural network(SJ-BPNN)scheme is used to transfer the measured data into the preliminary images of electrical properties distributions about the human brain.Specially,using the semi-join strategy,SJ-BPNN can reduce computer memory and time compared with the traditional full-join back propagation neural network.Then,U-Net is employed to further enhance the imaging quality of output from SJ-BPNN.Moreover,to avoid the time-consuming and uneconomical training process in brute-force fitting,the brain imaging training strategy incorporating the a priori information of the human brain is employed to generate a reasonable and economical training dataset for reducing learning tasks and improving reconstruction accuracy.Numerical experiments have indicated the proposed inversion method based on ANN can reconstruct high resolution 3-dimensional electrical properties distributions of the human brain efficiently and accurately on a workstation.