A Model for Frequency Dependence of Conductivities of the Live Human Skull M. Akhtari*, H.C. Bryant*, D. Emin*, W. Merrifield + , A.N. Mamelak $> , E.R. Flynn < , J.J. Shih^ ~ , M. Mandelkern # , A. Matlachov ! , D.M. Ranken ? , E.D. Best ? , M.A. DiMauro*, R.R. Lee % , and W.W. Sutherling $> Summary: A mathematical model (σ(ω) ≈ Αω α , where, σ≡ conductivity, ω =2πf ≡ applied frequency (Hz), A (amplitude) and α (unitless) ≡ search pa- rameters) was used to fit the frequency dependence of electrical conductivities of compact, spongiosum, and bulk layers of the live and, subsequently, dead human skull samples. The results indicate that the fit of this model to the experimental data is excellent. The ranges of values of A and α were, spongiform (12.0-36.5, 0.0083-0.0549), the top compact (5.02-7.76, -0.137-0.0144), the lower compact (2.31-10.6, 0.0267-0.0452), and the bulk (7.46-10.6, 0.0133-0.0239). The respective values A and α for the respective layers of the dead skull samples were (40.1-89.7, -0.0017-0.0287), (5.53-14.5, -0.0296 - -0.0061), (4.58-15.9, -0.0226-0.0268), and (12.7-25.3, -0.0158-0.0132). Key words: Skull; Conductivity; Model; MEG; EEG. Introduction MagnetoEncephaloGraphy (MEG), ElectroEnceph- aloGraphy (EEG) and combined MEG-EEG (Baillet et al. 1999; Diekman et al. 1998; Fuchs et al. 1998) are noninvasive techniques for investigation and localiza- tion of intracranial current sources and regions of neuronal activities. Source reconstruction with these techniques can be used for pre-surgical planning near the central sulcus (Alberstone et al. 2000; Sobel et al. 2000; Ebersole 1999; Simos et al. 1999; Baumgartner et al. 1998; Nakamura et al. 1998; Akhtari et al. 1994; Gallen et al. 1993; Sutherling et al. 1988a; Wood et al. 1988), localiza- tion of interictal spike and epileptic activity (Ishibashi et al. 2002; Pataraia et al. 2002; Hisada et al. 2000; Michel et al. 1999; Silva et al. 1999; Wheless et al. 1999; Diekmann et al. 1998; Sutherling et al. 1991; Sutherling et al. 1990; Barth et al. 1989; Sutherling et al. 1988b; Rose et al. 1987; Sutherling et al. 1987; Ricci et al. 1985), investigation of cognitive and functional processes (Bastiaansen et al. 2001; Herrmann et al. 2000; Tendolkar et al. 2000; Tesche and Karhu 2000; Breier et al. 1999a,b; Hari and Fross 1999; Pantev et al. 1999; Papanicolau et al. 1999; Ribary et al. 1999; Simos et al. 1999; Huotilainen et al. 1998; Volkmann 1998; Buchner et al. 1995; Sutherling et al. 1992; Pantev et al. 1989; Wood et al. 1985; Romani et al. 1982), the study of various brain disorders (Kasai et al. 2002; Berendse et al. 2000; Hurley et al. 2000; Reite et al. 1999; Sperling et al. 1999), and many other applications. MEG and EEG source reconstruction techniques use dipole and extended source models for localization of ce- rebral activity (Kincses et al. 1999; Mosher and Leahy 1998; Sarvas 1987; Stock 1986). The model of the volume conductor significantly affects localization accuracy (van den Broek et al. 1998; Stinstra and Peters 1998). Several mathematical and geometrical models of the human cra- nium as a volume conductor have been developed to cor- relate extracranially measured magnetic fields (MEG) * Department of Physics and Astronomy, The University of New Mexico, Albuquerque, NM, USA. + Huntington Medical Research Institutes, Pasadena, CA, USA. ^ Department of Neurology, The University of New Mexico School of Medicine, Albuquerque, NM, USA. ~ Department of Neurosciences, The University of New Mexico School of Medicine, Albuquerque, NM, USA. # Department of Physics, University of California at Irvine, Irvine, CA, USA. $ Epilepsy and Brain Mapping Program, Huntington Memorial Hospital, Pasadena, CA, USA. ! Physics Division, Los Alamos National Laboratory, Los Alamos, NM, USA. % Department of Radiology, VA Medical Center, Albuquerque, NM, USA. < Senior Scientific, Albuquerque, NM, USA. > Huntington Hospital, Pasadena, CA, USA. ? Scientific Software Engineering, Los Alamos National Labora- tory, Los Alamos, NM, USA. Accepted for publication: June 25, 2003. Supported By NIH Grant 20806. Correspondence and reprint requests should be addressed to Massoud Akhtari PhD., 545 Westgate St., Pasadena, CA, 91103, USA. Copyright © 2003 Human Sciences Press, Inc. Brain Topography, Volume 16, Number 1, Fall 2003 (© 2003) 39