## 2 State-of-the-Art
### Forward Problem  
To solve the EEG forward problem, three main configurations are required--(a) the head and source models (i.e., the location of the solution points in the brain), (b) the electrode alignment on the head model, and (c) the Leadfield matrix using the channel locations in relation to the anatomical information of the head model. As such, the solution's accuracy highly depends on the efficient generation and composition of the above. The basic components and the flow of processes are shown in Figure 1.  
Regarding the creation of the head model, the integration of anatomical data has rendered earlier widely adopted spherical head models outdated [14]. Converting MRI images into head models is a time-consuming process with a high computational cost, and this procedure presents optimal results in terms of localization accuracy. Nevertheless, subject-specific MRI recordings are not always available, requiring the head model to be constructed through computational methods. In this regard, however, it is important to emphasize that the sophistication of the head models does not display a linear trend with ESI localization, leading to high implementation complexity (e.g., inclusion of skull spongiosa) to demand significant computational resources, with little to no significant impact in spatial accuracy [15, 16]. The most common methods utilized for head-modeling are the boundary element methods (BEMs), finite difference methods (FDMs) and the finite element methods (FEMs) [17, 18, 19, 20]. The Projective Method (PM) (that incorporates the mathematical descriptors of surfaces, such as Fourier descriptors, and dimensionality reduction methods, such as Principal Component Analysis), is also well established, albeit less common [21, 22]. Of note is that for PM, in contrast with the aforementioned methods, the time required to extrude the head model and the computational resources is drastically reduced, but with lower spatial resolution [23]. Regarding the frequently employed algorithms, FEM and FDM provide more analytical outcomes and can tackle inhomogeneity problems, which is vital if the head model requires the modeling of anisotropic properties of white matter and the skull. On the other hand, BEM presents lower computational time and accuracy in comparison to the FEM and FDM, being unable to treat inhomogeneous and nonlinear problems. Even though the FEM approach provides a more well-established detailed model, since it incorporates more than the three standard head tissues, its universal implementation has been hamstrung due to its computational needs and lack of open-source tools incorporating a complete FEM approach. However, the Fieldtrip-SimBio pipeline has been recently introduced, providing an integrated EEG forward problem solution, while employing an FEM-created head model [24]. On this premise, it should also be noted that subject-specific MRIs are not always possible to be recorded. For this reason, an averaged (standardized) volume conductor model using the ICBM 152 anatomical template and the FEM (\"The New York Head\") was created, showing promising results in ESI, compared to other standardized FEM and BEM approaches [25]. While FEM effectiveness is shown to be comparable with analytical solutions [26], adverse issues could occur due to skull leakage effects (i.e., the inhomogeneity of skull thickness), which could lead the implemented model to present similar properties to a simple three-layer sphere model [27]. In order to overcome this inconsistency, different FEM approaches are used, deviating from the standard continuous Galerkin-FEM method (CG-FEM) by creating a mixed or discontinuous Galerkin-FEM utilizing the subtraction approach [28, 29]. Evidence suggests that this solution combines the benefits from both approaches, decreasing the skull leakage effect [19]. Furthermore, using analytical expressions combined with the subtraction approach, the accuracy of the forward problem solution was increased compared to other numerical approaches with similar computational costs [30].