The scalp and skull conductivities (σsc, σsk respectively) are determined from Electrical Impedance Tomography (EIT) data using the Gauss-Newton method (GN). Our best estimates of σsc and σsk are 0.58 S/m and 0.008 S/m respectively. It is necessary to use the true head geometry

McCann, Hugh

Ouypornkochagorn, Taweechai

Polydorides, Nick

Carleton University's Institutional Repository

10 SESSION 2. POSTER SESSION IIn Vivo Estimation of the Scalp and Skull Conductivity  Taweechai Ouypornkochagorn, Nick Polydorides and Hugh McCann University of Edinburgh, Edinburgh, UK, t.ouypornkochagorn@sms.ed.ac.uk  Abstract: The scalp and skull conductivities (?sc, ?sk respectively) are determined from Electrical Impedance Tomography (EIT) data using the Gauss-Newton method (GN). Our best estimates of ?sc and ?sk are 0.58 S/m and 0.008 S/m respectively. It is necessary to use the true head geometry.   1 Introduction Although many authors have reported in vivo values for ?sc and ?sk, most of them refer only to particular regions of the head. For example, it is reported in [1] that ?sc in a selected region is 0.43 S/m, and in [2-4] that ?sk in various regions is in the range 0.0078-0.0801 S/m. In EIT, where the whole head is modelled, it is typical to set all regions of each tissue to a single conductivity value. Here we determine ?sc and ?sk by comparing experimental EIT data with such a model. Our approach is to fit a geometrically accurate head model having two unknowns, ?sc and ?sk, to a set of real measurements by performing a few iterations of the Gauss-Newton method to regress the measurement into the model. The GN formula to evaluate ? is shown in (1) where ? is [?sc;?sk], J is the 2-parameter Jacobian, Vmeas is the measurement vector, and Vi is the model prediction for ?i, and i is the iteration index.  ? ? ? ?imeasTTii VVJJJ ??? ?? 11 ??   (1) 2 Methods Three measurement trials on a single human subject were carried out on three different dates. EIT measurements were recorded at 100 frames per second with 32 electrodes. Three head models (called Model1, 2, and 3) having 338k, 396k, and 53k elements respectively were used. Model 1, the geometrically accurate head model for the subject, was available from MRI scans. In this model, both isotropic and anisotropic (?radial: ?tangential ratio of 1:10) skull conductivities were implemented for comparison. The sensitivity of the method to various effects was tested and found to be small: by simulation, the dependence of the results on electrode shape and position, and on contact impedance, was found to be small, of order 1%; experimentally, the results obtained from multiple installations on the same subject on different days also varied by about 1%. By carrying out a large number of simulations with a wide variety of conductivity values for CSF, grey matter and white matter, and studying the resulting correlation with scalp and skull conductivity results, we conclude that there is no significant dependence of our results upon the accuracy of the CSF, grey matter and white matter conductivity values. Equation (1) was employed to evaluate ? with 15 iterations (both ? are finally converged). The estimated ?sc and ?sk are 0.58 S/m and 0.008 S/m, respectively, for both the isotropic and anisotropic versions of Model1 (see table). Compared to the reported values [1], ?sc is significantly larger, while ?sk is at the low end of the range of previously reported values [2-4]. It should be noted that the ? values determined here are effectively from the whole head, in contrast to the small selected regions used in [1-4]. The surface plot of the error term in our iteration procedure is shown in Fig.1, showing a distinct trough in the region of the preferred values. The dependence on ?sc is weak in the range 0.4-0.8 S/m, while being much more strongly dependent on ?sk in the region 0.008-0.010 S/m.  Table: The evaluated ? (S/m)1 and prediction relative error1   Model1 (reference) Model2 Model3 Isotropic Anisotropic Isotropic Isotropic ?scalp 0.58?.026 0.58?.026 0.23?.007 0.45?.019 ?skull .008?.0005 .008?.0005 .017?.0011 .006?.0007 Err. 0.28?.008 0.28?.008 0.32?.005 0.33?.012 1 The value represents in the format of mean±standard deviation   Figure 1: The relative error from the variation of ?sc and ?sk  The evaluated ? values from Model2 and 3, non-subject specific models, are different to Model1 and the errors are higher. The estimation from Model3 is closer to that from Model1, probably since their geometry is quite similar (despite the relatively poor mesh refinement of Model3). Model2 is geometrically different to both of the other models; even when it was scaled to the same size as Model1, the estimated ?sc and ?sk values are 0.29 and 0.0137 S/m, close to the results in the table.   3 Conclusions We find that the determination of the scalp and skull conductivities by using EIT are strongly dependent on the true head geometry, necessitating the use of subject-specific anatomical scans, by MRI and CT. The results obtained using such a subject-specific model are consistent with values in the literature [5,6].  References [1] Burger, H. C., Milaan J. B. Acta Medica Scandinavica CXIV, 1943 [2] Akhtari, M., et al. Brain Topography 14(3): 151-167, 2002 [3] Hoekema, R., et al. Brain Topography 16(1): 29-38, 2003 [4] Tang, C., et al. IEEE Trans on Biomedical Engineering, 55(9): 2286-2292, 2008 [5] Gonçalves, S. I., et al. IEEE transactions on Biomedical Engineering, 50(6):754:767, 2003 [6] Baysal, U., Haueisen J., Physiol. Meas. 25:737-748, 2004 0.20.40.60.80.010.020.030.040.050.40.60.811.2Scalp (S/m)Skull (S/m).003.008.013.018.023.028.033.038.043.0480.2 0.4 0.6 0.8?Scalp (S/m)Best ??Skull (S/m)Proceedingsof the15th International Conference onBiomedical Applications ofELECTRICAL IMPEDANCETOMOGRAPHYEdited by Andy Adler and Bartłomiej GrychtolApril 24-26, 2014Glen House ResortGananoque, OntarioCanadaThis document is the collection of papers accepted for presentation at the 15th International Conference onBiomedical Applications of Electrical Impedance Tomography.Each individual paper in this collection: c© 2014 by the indicated authors.Collected work: c© 2014 Andy Adler and Bartłomiej Grychtol.All rights reserved.Cover design: Bartłomiej GrychtolPhoto credit: c©1000 Islands Photo Art Inc. / Ian CoristinePrinted in CanadaISBN 978-0-7709-0577-4Systems and Computer EngineeringCarleton University, 1125 Colonel By DriveOttawa, Ontario, K1S 5B6, Canadaadler@sce.carleton.ca+1 (613) 520-2600www.eit2014.org

In Vivo Estimation of the Scalp and Skull Conductivity

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In Vivo Estimation of the Scalp and Skull Conductivity

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