Journal of Neuroscience Methods 185 (2009) 125���132 Contents lists available at ScienceDirect Journal of Neuroscience Methods j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j n e u m e t h Approximate average head models for EEG source imaging Pedro A. Vald��s-Hern��ndez a,���,1, Nicol��s von Ellenrieder b,1, Alejandro Ojeda-Gonzalez a, Silvia Kochen c, Yasser Alem��n-G��mez a, Carlos Muravchik b, Pedro A. Vald��s-Sosa a a Neuroimaging Department, Cuban Neuroscience Center, Havana, Cuba b Laboratory of Industrial Electronics, Control and Instrumentation, National University of La Plata, La Plata, Argentina c Epilepsy Center, IBCN - CONICET - University of Buenos Aires, Buenos Aires, Argentina a r t i c l e i n f o Article history: Received 28 July 2009 Received in revised form 1 September 2009 Accepted 1 September 2009 Keywords: Approximate head model Average Electrode measurement Thin Plate Spline BEM Lead field sLORETA MNI EEG Cuban Brain Mapping Project a b s t r a c t We examine the performance of approximate models (AM) of the head in solving the EEG inverse prob- lem. The AM are needed when the individual���s MRI is not available. We simulate the electric potential distribution generated by cortical sources for a large sample of 305 subjects, and solve the inverse prob- lem with AM. Statistical comparisons are carried out with the distribution of the localization errors. We propose several new AM. These are the average of many individual realistic MRI-based models, such as surface-based models or lead fields. We demonstrate that the lead fields of the AM should be calculated considering source moments not constrained to be normal to the cortex. We also show that the imperfect anatomical correspondence between all cortices is the most important cause of localization errors. Our average models perform better than a random individual model or the usual average model in the MNI space. We also show that a classification based on race and gender or head size before averaging does not significantly improve the results. Our average models are slightly better than an existing AM with shape guided by measured individual electrode positions, and have the advantage of not requiring such measurements. Among the studied models, the Average Lead Field seems the most convenient tool in large and systematical clinical and research studies demanding EEG source localization, when MRI are unavailable. This AM does not need a strict alignment between head models, and can therefore be easily achieved for any type of head modeling approach. �� 2009 Elsevier B.V. All rights reserved. 1. Introduction In Electromagnetic Source Imaging (ESI), the smallest source localization error is achieved when the physical properties of the head are modeled with the information provided by the individual���s Magnetic Resonance Image (MRI) (Huiskamp et al., 1999 Henson et al., 2009). However in some cases an MRI system is not available or EEG related studies with a large number of individuals make MR acquisition unpractical. In this work we are interested in finding the best possible approximation of the individual head model when the MRI-based head model is unknown. We quantify the performance of a head model by the error in the estimation of the source posi- tion. The value of this error would be helpful to decide in which situations an approximate model is acceptable. The simplest and worst approximate head model is a set of spheres representing the boundaries of different tissue domains of ��� Corresponding author at: Neuroimaging Department, Cuban Neuroscience Cen- ter, Ave 25, Esq. 158, #15202, PO Box 6412/6414, Cubanac��n, Playa, Havana, Cuba. Tel.: +53 7 208 4460 fax: +53 7 208 6707. E-mail address: multivac@cneuro.edu.cu (P.A. Vald��s-Hern��ndez). 1 Both authors contributed equally. the head with homogeneous physical conductivities (de Munck and Peters, 1993 Ermer et al., 2001). A further improvement is achieved by using realistically shaped head models based on standard MRIs, such as the average image provided by the Montreal Neurological Institute (ICBM-152), as proposed in (Fuchs et al., 2002). However the ICBM-152, as being an average of 9 parameter-based affine coregistered individual MRIs, presents a coarse level of anatomical detail. This compromises the accuracy of some volumetric piece- wise head modeling methods such as the Finite Element Method (FEM) (Wolters et al., 2006) and the Finite Difference Method (FDM) (Neilson, 2003). Alternatively finer detailed standard MRIs could be used, e.g. the average of 27 MRIs from a single individual in MNI space (MNI-27) (Collins et al., 1998), or the average of dif- ferent individual MRIs that have been nonlinearly coregistered to a common stereotaxic space (ICBM-452) (Mazziotta et al., 2001). However, these standard MRIs are far from being representative of a target population in the sense of shape since they are registered to the MNI space. No matter the level of anatomical detail achieved, a wrong shaped approximation is a major cause of localization errors in ESI, as shown in (von Ellenrieder et al., 2009). Therefore, reduc- ing the shape differences between the approximate and individual head models is a prime goal in improving the performance of the approximate head models in ESI. 0165-0270/$ ��� see front matter �� 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jneumeth.2009.09.005

126 P.A. Vald��s-Hern��ndez et al. / Journal of Neuroscience Methods 185 (2009) 125���132 The MNI-shape drawback has only been dealt with in (Darvas et al., 2006), where the ICBM-152 was warped to the individual space through a nonlinear Thin Plate Spline (TPS) transformation. This TPS was estimated by matching the predefined electrode posi- tions in the scalp of the ICBM-152 (the template) to those measured in the individual. The TPS head model has two problems: (1) the shape improvement is, by definition, more effective toward the scalp, inheriting the defects of the chosen template model (2) the individual electrode positions have to be measured manually (de Munck et al., 1991), or with a Polhemus device (Lamm et al., 2001) or by other methods (Le et al., 1998). In this paper, we propose new approximate head models that do not require the measurement of the electrode positions. These methods are also designed to be, from a statistical point of view, closer in shape to the individual unknown head model than the MNI-shaped and TPS head models. We are interested in reducing the localization error by modifying only the shape. Therefore, we work with head models consisting of a set of surfaces defining the boundary of nested homogeneous and isotropic compart- ments, as proposed elsewhere (H��m��l��inen and Sarvas, 1989 de Munck, 1992 Ermer et al., 2001 Fuchs et al., 1998, 2001, 2002 von Ellenrieder et al., 2009), thus adopting the Boundary Element Method (BEM) to solve the Forward Problem of the EEG (de Munck, 1992), i.e. the calculation of the lead field matrix. The first of our pro- posed approximate head model is an estimate of the shape centroid of the target population built with the head models defined from 305 MRIs drawn from the Cuban Human Brain Mapping Project. This head model is the closest in shape to all the individual head models. In Appendix A, we demonstrate that the simple surface element wise average can readily substitute for this head model. Therefore an estimate of the centroid head model is only eas- ily achievable for surface-based head models. This simple average concept cannot be extended straightforwardly to more heteroge- neous head models, such as FEM or FDT. The centroid estimate of these type of head models involves complicated inter-subject reg- istration pipelines (see for example, Guimond, 2000 Christensen et al., 2006 and Appendix A), requiring high dimensional nonlin- ear registration methods to achieve detailed images. Additionally, they are not easy to update with newer models. Therefore, as a new alternative, we investigate the use of the direct average of the lead fields of the subjects of the sample. This model only requires very simple transformations to align head models before calculating the lead fields and its use is computationally inexpensive. The Average Lead Field has to be calculated for predetermined electrode mon- tages. This is well suited for systematical studies involving a large sample of individuals. Further approaches are considered in this work such as partial head model averages clustered according to race, sex or head size of the individuals. With this we investigate whether the knowl- edge of these individual externals characteristics, which are easy to determine, can be used to decrease the source localization error. The first idea that would come into mind when the individual���s MRI head model is not available is using any head model at hand, which is equivalent to taking that defined from a random disparate subject. In fact some works in the literature used this approach, e.g. the Collins head in (Trujillo-Barreto et al., 2008). We also evaluate in this work how prejudicial this can be for ESI. We evaluate the improvement in the performance of all the pro- posed head models, and compare them with existing approaches in the literature, adapted to our dataset, i.e. the MNI-shaped model and its TPS version. Finally we also investigate a possible improve- ment by using a TPS transformation of the Average Surface model. We consider that this improvement should be considerable to make the measurement of electrode positions worthwhile. Without loss of generality, the algorithms for the EEG Inverse Problem are chosen to yield a null expected localization error when the individual MRI head models are used. In this way the local- ization error obtained when using an approximate head model will be caused only by its difference from the individual head models. 2. Materials and methods The head model we adopted has three parts: (1) the volume conductor model, representing the physical properties of the head, (2) the cortical surface, providing the possible location and orien- tation of the sources of the EEG and (3) the fiducials on the outer surface of the skin, which serve as guidelines to locate the positions of the electrodes (where the EEG is measured). The fiducials can include the electrode positions as is the case of the TPS-based head models. In this work we deal with the following hypothetical experimen- tal situation. Someone measures the scalp electrical potential in an individual without MRI. Since he/she wants to obtain the sources of the measured EEG he/she is forced to use an approximate head model for ESI. Using the fiducials as guidelines, an electrode set is placed on the approximate scalp in an attempt to reproduce the same anatomical locations where EEG was measured in the indi- vidual scalp. Then the forward problem and inverse problems of the EEG are solved. In this section we test the performance of several approximate head models in ESI. The test is done as follows. We simulated the expected elec- tric potential measurements generated by known sources. This is done with the individual���s MRI head model. Then we solve the inverse problem, i.e. source localization, using the approximate head model, and compare the estimated sources with the simu- lated ones by means of the localization error. This is carried out for a subset of 305 individuals of the Cuban Human Brain Mapping Project (CHBMP) in a leave one out statistical procedure, i.e. each subject is taken to simulate sources and EEG whereas the remain- ing 304 head models are taken to achieve the approximate model. This procedure yields 305 localization errors for each approximate head model. The CHBMP is composed by a large sample of subjects of the Cuban population, randomly selected from the Cuban National ID registry, who were submitted to neuropsychiatrical and neuropsy- chological tests. Those who were considered by experts as healthy subjects were included in the database, after informed consent. 2.1. MRI-based head models We adopted a layered model for the head, with three nested compartments of constant isotropic conductivity representing the brain, skull, and skin tissues. The electrical conductivity values are 0.33 S/m for the brain and skin and 0.022 S/m for the skull. The 1/15 skull/skin conductivity ratio is supported by recent studies (Oostendorp et al., 2000 Wendel and Malmivuo, 2006 Zhang et al., 2006). The shape of these layers was obtained from magnetic resonance images (MRIs) of the subjects. These MRIs were obtained using a Siemens Symphony 1.5 T system, consisting in a set of 3D MPRAGE T1-weighted images of dimensions 160 �� 256 �� 256, and 1 mm �� 1 mm �� 1 mm voxel size, TR = 100 ms, TE = 3.3 ms, and TI = 1100 ms. The images were segmented into brain, skull and skin using the best outcome, according to an expert���s criterion, between betsurf, a tool of the FSL software package (Jenkinson et al., 2005), and BrainSuite2 (Shattuck and Leahy, 2002). They yielded three sur- faces, characterized by tessellations (nodes and triangles), for each subject: inskull (brain/skull interface), outskull (skull/skin interface) and scalp (skin/air interface). However, we discarded the extracted inskulls for both softwares due to their very low quality, a conse-