Calculation of the electromagnetic fields of spherical head model by using Dyadic Green's function and analysis of matching media layer

In this study, the calculation of electromagnetic fields in the spherical head model and the effects of a matching media (MM) layer. Matching medium represents a layer which locates between head and free space and has a different dielectric properties from free space. The problem can be summarized that solving the electromagnetic field problem by using Dyadic Green's Functions (DGF) of all the layers of 5-layered spherical head model whose last layer is free space; after that, analyzing the effects of a MM which is located on the surface of this head model. At the first stage of the study, literature research is done and previous studies about the topic are analyzed. First of all, the literature research about the solution of the electromagnetic field problem of a spherical system by using DGFs is examined and lots of studies that suggest a solution of electromagnetic field problem of a 2-layered dielectric sphere and 𝒩-layered spherical systems. After that, the research about the usage of MM is made and some reference studies are found. Some of them are Transmission Line Model (TLM) and Stroke Detection (SD) of 2D Head Model. By using the values of these studies, some comparisons are obtained and the results are analyzed. In these studies, the dielectric properties, such as permeability and permittivity of MM are suggested. Both of the values of these studies are examined. After the analysis of the reference studies, the problem is approached step by step. First of all, the techniques of the calculation of electromagnetic fields by using DGF and the usage of these techniques on a spherical head model are examined. In this stage, just the solution which is about 2-layered dielectric sphere and a coefficient calculation of this solution are done. For this case, the x-directed dipole is layered on z-axis in free space. Three electromagantic field calculations are done. One of them is inside the dielectric sphere, and two of them are outside of the sphere (between the dipole-dielectric sphere and between dielectric sphere-infinite). Thereafter, suggested equations for extending the problem to 𝒩-layered sperical systems are analyzed. The coefficient calculations, DGF and electric field obtainments for all of the layers of spherical head model are described step by step. After the general expressions of obtainment of electromagnetic fields for 𝒩-layered spherical head model, firstly 2-layered case is examined and coefficient calculation is done for 2-layered case. The results of this calculation are comparised to the results of the 2-layered dielectric sphere which is studied in the previous examination. The results show that two techniques are compeletely overlapped. After this confirmation, firstly in a 6-layered spherical system, x-directed dipole is located on z-axis in the outwardly second layer as a MM (located between skin and free space) and the calculation of electromagnetic field problem is done step by step. In this case, 40 coefficients and 6 xx different DGFs are calculated. There are as much DGF calculation as layer number (for this case, there are 6 layers and 6 DGF functions). After that, the calculation of 5-layered system is examined by considering the dielectric properties of the MM are equal to the dielectric properties of the free space. Secondly, the x-directed dipole is located on z-axis at the inwardly second layer of the 6-layered spherical system . For this case, there are 40 coefficients and 6 different DGFs calculated. The outwardly second layer is accepted as a MM and electromagnetic field calculation is done step by step. Similarly, for this case, 5-layered system is examined by accepting the dielectric properties of the MM are equal to the dielectric properties of free space. For all of the cases, the geometries of the problems are shown in proper figures. At the third stage of the study, the electromagnetic field values of 5-layered and 6-layered spherical head model, which are obtained using IES Method, are compared the values that are obtained before. In the IES method, the spherical head is modeled as a sphere with hundreds of cells. The electromagnetic field calculation is done by using special integral equations. The layers of the spherical head model are suggested from inward to outward as a brain, cerebrospinal fluid (CSF), bone tissue, skin and free space. The MM layer is located between skin and free space. The purpose of this comparison is the confirmation of the method of a calculation of 𝒩-layered spherical head model. The confirmation is done for four case. Firstly, MM layer is not used, the x-directed dipole is located on z-axis at the free space and the numerical results of electromagnetic fields are calculated both in the brain and free space (very close to the surface of the head). Secondly, MM layer is located between the skin and free space and x-directed dipole is located on z-axis at the MM layer. The observation points are located in the brain and outside the head samely. The same calculation is done by using IES method with and without MM layer. The results are compared each other (seperately in the brain and outside the head). Thirdly, when MM layer is not used, the x-directed dipole is located on z-axis at the free space and numerical results of electromagnetic fields are calculated both in the brain and free space (very close to the surface of the head). Finally, MM layer is located between the skin and free space and x-directed dipole is located on z-axis at the MM layer. The observation points are located in the brain and outside the head. The same calculation is done by using IES method with and without MM layer. The results are compared each other for this case too (seperately in the brain and outside the head). For these four cases, all of the results are almost overlapped. Against to this confirmation, the 𝒩-layered spherical head model calculation method is used for all of the numerical examinations until the end of the study. At the fourth stage, the dielectric properties of MM are examined. Especially, two suggested dielectric properties are analyzed. The layers of the spherical head model are suggested from inward to outward as a brain, CSF, bone tissue, skin and free space. The MM is located between skin and free space. The x-directed electric dipole is located on z-axis at the MM layer. The imaginary part of the relative permittivity is changed and for all of the cases, the observation point is located at the brain layer. In this study, besides the suggested relative permittivity values, free space and some other relative permittivity values are observed. After the examination, the proper dielectric values of MM are used until the end of the study. At the fifth stage, the variation of the electromagnetic field values are investigated with and without MM. The layers of the spherical head model are suggested from inward to outward as a brain, CSF, bone tissue, skin and free space. The MM is located between skin and free space. First of all, the x-directed dipole is located on the z-axis xxi in free space and the observation is done in brain, CSF and skin layers. After that, a MM layer is located between skin and free space, the x-direxted dipole is located on z-axis in MM layer and the same observation is done again for this case. The results are compared to each other (seperately for skin, CSF and brain layers). The proper relative permittivity value of MM that is examined in previous stage is used. The electromagnetic field values for the case with MM are observed as larger than the elecromagnetic field values for the case without MM. Secondly, for the same case, the non-proper relative permettivity value of MM is used to calculate the electromagnetic fields inside the head. The values which are calculated with MM layer are observed as much smaller than the values for the case without MM layer. Against to this result, the proper relative permittivity value is proven again. Finally, the x-directed dipole is located on the z-axis in CSF layer and the observation is done in the outside of the head, bone tissue and brain. After that, a MM layer is located between skin and free space, the x-directed dipole is located on z-axis in MM layer and the same observation is done again for this case. The results are compared to each other (seperately brain, bone tissue and outside of the head). At the next stage, some additional analyses and results are shared such as the investigation of the variation of electromagnetic field values by considering the variation of r and the solution of the problem in polar coordinates. First of all, the 𝜃 and 𝜑 values are accepted as constant and the changing of electromagnetic field is observed. Secondly, electromagnetic field calculation is done in polar coordinated. In this analysis, 𝑥 is accepted as constant, 𝑦-axis and 𝑧-axis are changed in an interval. This analysis is examined for both a 5-layered spherical head model and 6-layered spherical head model with MM between skin and free space. For the 5-layered case, the electric dipole is located at the outside of the head. Beside this, for the 6-layered case, the electric dipole is located at MM layer. The calculation is done for 400 cells and the numerical results are shared. The inferences, the limitations of the problem and the suggestions about the study for the future are mentioned at the conclusion of the study.