Influence of tissue resistivities on neuromagnetic fields and electric potentials of the head

Influence of Tissue Resistivities on Neuromagnetic Fields and Electric Potentials Studied witha Finite Element Model of the HeadJens Haueisen,*Ceon Ramon,Member,IEEE,Michael Eiselt,Hartmut Brauer,Member,IEEE,and Hannes NowakAbstract—Modeling in magnetoencephalography(MEG)and electroencephalography(EEG)requires knowledge of the in vivo tissue resistivities of the head.The aim of this paper is to examine the influence of tissue resistivity changes on the neuromagnetic field and the electric scalp potential.A high-resolutionfinite ele-ment method(FEM)model(452162elements,2-mm resolution) of the human head with13different tissue types is employed for this purpose.Our mainfinding was that the magneticfields are sensitive to changes in the tissue resistivity in the vicinity of the source.In comparison,the electric surface potentials are sensitive to changes in the tissue resistivity in the vicinity of the source and in the vicinity of the position of the electrodes. The magnitude(strength)of magneticfields and electric surface potentials is strongly influenced by tissue resistivity changes, while the topography is not as strongly influenced.Therefore, an accurate modeling of magneticfield and electric potential strength requires accurate knowledge of tissue resistivities,while for source localization procedures this knowledge might not be a necessity.Index Terms—Biological tissues,conductivity,electroenceph-alography,finite element methods,magnetoencephalography.I.I NTRODUCTIONT HE in vivo resistivity values of the different tissues of the human head are needed for forward and inverse modeling in magnetoencephalography(MEG)and electroen-cephalography(EEG).There are studies which show that even within simple spherical volume conductors inhomogeneities close to sources can significantly affect the measured MEG and EEG[27],[28].Other studies investigated the ratio of conductivities with the help of spherical models(see e.g., [1],[25])and with compartmental boundary element methodManuscript received January26,1996,revised April2,1997.This work was partly supported by the German ministry of education and research, (BMFT)under project01ZZ9104.The work of C.Ramon was supported by the National Science Foundation under Grant BCS-9209938and the University of Washington under the Graduate School Research Fund.Asterisk indicates corresponding author.*J.Haueisen is with Biomagnetisches Zentrum,Friedrich-Schiller-Universit¨a t Jena,Philosophenweg3,Jena07740Germany(e-mail: haueisen@biomag.uni-jena.de).C.Ramon is with the Center for Bioengineering,University of Washington, Seattle,WA98195USA.M.Eiselt is with the Institut f¨u r Pathologische Physiologie,Friedrich-Schiller-Universit¨a t Jena,Jena07740Germany.H.Brauer is with the Technische Universit¨a t Ilmenau,Institut f¨u r Allgemeine und Theoretische Elektrotechnik,Ilmenau98684Germany.H.Nowak is with Biomagnetisches Zentrum,Friedrich-Schiller-Universit¨a t Jena,Jena07740Germany.Publisher Item Identifier S0018-9294(97)05352-4.(BEM)models(see,e.g.,[13]).A more recent systematic investigation of conductivity changes using BEM models and simplified geometries for certain brain inhomogeneities also found significant effects on the magnitude of magneticfields and electric potentials[14].A major drawback of all these studies is the limited inclusion of realistic inhomogeneities as they are present within the human head.Also the number of compartments and subsequently the number of conductivities used is usually very limited.Some studies do also use relative conductivity values(compartment ratios)only,since pure MEG and pure EEG modeling with compartmental models (BEM or spheres)does not need absolute conductivity val-ues.For combined MEG/EEG analysis absolute conductivity values are necessary.The aim of this study is to quantify how different tissue resistivities change the solution of the forward problem in MEG and EEG modeling.We employ a high-resolution FEM model(22mm)of the human head with13tissue types which has been used and validated previously[12]. Recently,studies have been published on the influence of tissue resistivities and on estimating tissue resistivities for the human torso using FEM[5],[6],[15],[16],but to our knowledge no such studies have been performed so far for the human head.II.M ETHODSA.FEM Volume Conductor ModelingOur FEM head model construction and solution technique is described in detail elsewhere[12].A brief summary is given here.The human head model was constructed out of 128sagittal magnetic resonance imaging(MRI)scans with a slice thickness of2mm.Based on these scans a semiautomatic tissue classifier was used to distinguish between the different tissue types in the head.The13different tissue types which were used to describe the conductivities in the human head are given in Table I.Fig.1shows the upper part of a MRI scan and the corresponding FEM model cross section(classified slice).The model used for the computations presented here extended to the chin[12].A large scalefinite element mesh was generated by connecting all slices.This leads to a uniform grid of452162hexahedral elements with a voxel resolution of22mm.Based on this grid a linear system of equations was set up and solved iteratively by means of the successive over-relaxation(SOR)method.The relaxation0018–9294/97$10.00©1997IEEEFig.1.Slice with classified tissues (top)and corresponding MRI scan (bottom).Original size was 5122512pixel,the bottom portions were cut off.The classified slice represents the FEM model cross section.In the classified slice different tissue types are represented by different gray values.The origin of the coordinate system is at the lower left corner of the first slice.The dipole points into z direction (into the drawing plane).factor,was set to be 1.0.A fixed valuefor.With the last 200iterations a smoother error distribution was reached.Convergence of the solution was ensured by two criteria:first the L2norm of the system matrix of the linear system of equations had to drop below 1.0E-13V,and second,the potential difference had to decrease continuously during the iteration process.The limit values for the L2norm were found by comparing the calculated magnetic fields of a test dipole for each model at different values for the L2norm.If the magnetic field did not change anymore in the first five significant digits the limit value for the L2norm was chosen.The electric surface potentials were computed from the node potentials on the surface of the scalp.The current density was calculated in the middle of each element from the adjacent node potentials.The magnetic field was computed in a sampling plane(15 1.25cm)located at a distance of 1.2cm above the head.The surface potentials were computed on the scalp close to the position of the dipole(13coordinatefrom anterior toposterior,50%of the mean value.Only in the caseof widely varying values in the literature were other bounds chosen.Even though not all the literature written on resistivity values has been cited,the range of the chosen lower and upper bounds represents a good approximation for all the resistivity values which can be found in the literature.Moreover,most of the data were taken from animal experiments.Thus,applying those values to the human head already incorporates a species-dependent approximation.Therefore,all mean values used were rounded off.Resistivity also depends on frequency and temperature.Thus,only resistivity values measured at or near body tem-perature and at low frequencies (dc–100kHz)were taken into account.A summary of how the resistivity values in Table I were estimated is given in [11].All resistivity values areinHAUEISEN et al.:TISSUE RESISTIVITIES ON NEUROMAGNETIC FIELDS AND ELECTRIC POTENTIALS729TABLE IIR ELATIVE S ENSITIVITY OF M AGNETIC F IELDS TO C HANGES IN THE R ESISIVITY OF H UMAN H EAD T ISSUES T YPES A CCORDING TO(3)FOR THE C HOSEN L OWER ANDU PPER B OUNDS IN THE FEM M ODEL.N OTE THAT THE R ELATIVE S ENSITIVITY D EFINITION M AKES THE V ALUES D IRECTLY C OMPARABLE FOR ALL TISSUESC.Analysis of Field and Potential ChangesFor a complete description of the effects observed we applied three different types of analysis.First we used a relative sensitivity measure in order to make all tissue re-sistivity changes directly comparable.This was necessary because of the different percentage in resistivity changes for each tissue.However,the relative sensitivity measure does not distinguish between the two types of possible changes in the magneticfield and electric potential profiles,namely the topography and the scaling(magnitude)of the profiles.The distinction between these two types is important because their implications are quite different.A change in the magnitudeofaccording toDSM(1)where summation goes over all samplingpointsis the magneticfield at meanresistivity.Similarly we defined the deviation of scaling forelectric potentials(DSE)withDSEis the relative sensitivity of thetissue,the meanresistivity fortissue,and the lower or upper resistivityvalue.and the magneticfield at the lower or upper resistivityvalue.The summation is over all points in the sampling plane.The relativesensitivity,,gives a measure of the changesof the magneticfield due to the changes in the resistivity.Since it is scaled by absolute values of theresistivity,thestronger is the influence of that particular tissueresistivity.corresponds to no influence.For the calculation of thesensitivity of the surface potentials due to resistivity changesthe magneticfield in(3)is replaced by the electric potential.All analysis was performed with the help of PV-Wave(VisualNumerics,Boulder,CO).III.R ESULTSOur mainfindings are that the magneticfields are sensitiveto tissue resistivity changes in the vicinity of the source,andthe electric potentials are sensitive to tissue resistivity changesin the vicinity of the source and the position of the electrodes.Tables II and III show the index of the relative sensitivitymeasure according to(3)for all tissues considered.We foundthat internal air,soft tissue,eye,blood,spinal cord,andcerebellum show no significant sensitivity for both magneticfields and electric potentials.Therefore,they were not includedin the following analysis using correlation coefficients anddeviation of scaling as defined in(1)and(2).In Table II weshow that the magneticfield is sensitive only to changes of theresistivity of tissues in the vicinity of the dipole[i.e.,cerebro-spinalfluid(CSF),gray and white matter].In comparison,inTable III we show the scalp electric surface potential to besensitive to tissue resistivity changes in the vicinity of the730IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING,VOL.44,NO.8,AUGUST1997TABLE IIIR ELATIVE S ENSITIVITY OF E LECTRIC S URFACE P OTENTIALS TO C HANGES IN THE R ESISTIVITY OF H UMAN H EAD T ISSUE T YPES A CCORDING TO(3)FOR THE C HOSENL OWER AND U PPER B OUNDS IN THE FEM M ODEL.N OTE THAT THE R ELATIVE S ENSITIVITY D EFINITION U SED M AKES THE V ALUES D IRECT C OMPARABLE FOR ALL TISSUESFig.2.Surface plot of the electric surface potentials at mean values(dotted lines)and for the electric potential when the resistivity of bone is changed to upper value(solid lines).dipole and the electrode position(i.e.,scalp,fat,bone,soft bone,CSF,and gray and white matter).Fig.2shows a surface plot for the electric potential at mean values(dotted)and for the electric potential when the resistivity of bone is changed to upper value(solid).Two main features are observable from Fig.2.First,the major difference between the two potential profiles is in scaling (magnitudes).The profile for bone upper resistivity is larger than that for the mean values.Second,there are small changes in the topography as can be seen,e.g.,in deviations of the lines around the zero line.These two different types of changes are quantified with the help of the correlation coefficient and the deviation of scaling in the next fourfigures.Figs.3and4show the correlation coefficients for the magneticfields and electric surface potentials,respectively. In general,all correlation coefficients are in between0.98 and1.0.This means that there are only small changes in the topography for all profiles.For magneticfields white and gray matter show the lowest correlation followed by CSF.For electric potentials gray matter shows the lowest correlation followed by CSF,white matter,bone,and scalp.This signifies that the electric potentials are most influenced by changes in the resistivities of tissues which lay between the source position and the electrodes on the scalp.The magneticfields are most influenced by changes in the resistivities of tissues close to the source position.Figs.5and6show the deviation of scaling for the magnetic fields(DSM)and scalp potentials(DSE),respectively.Again we observe the principal difference between magneticfields and electric potentials regarding the influence of tissue resis-tivity changes close to the source and close to the electrodes, as already found with the preceding two types of analysis. For magneticfields gray matter shows the highest deviation of scaling followed by CSF and white matter.For electric potentials bone shows the highest deviation of scaling followed by scalp,CSF,white matter,soft bone,fat,and gray matter. The value of DSE for bone upper bound is very high due to the high percentage of change of resistivity(refer to Table I).One interesting fact is the different sign in the deviation of scaling for the different tissues.For electric potentials the scaling increases when resistivity is increased for fat,muscle,scalp, and CSF,while scaling decreases when resistivity is increased for bone,soft bone,white,and gray matter.When resistivity is decreased the effect is of course vice versa.For magnetic fields the scaling decreases when resistivity is increased for CSF,gray,and white matter and,although one can observe only very small values for DSM in Fig.5,the scaling increases when resistivity is increased for all other tissues.IV.D ISCUSSIONThe magneticfield is most sensitive to changes in the resistivity of gray matter.This is to be expected because the dipolar source is located in the gray matter.The CSF and white matter show the next highest sensitivity after gray matter,since these are close to the gray matter.All other tissue resistivities have much lower sensitivity values.Thus, the magneticfield is only sensitive to the tissue resistivities in the volume surrounding the dipolar source.Because of this very clear result,we would expect that different dipole positions in the brain would also yield a high sensitivity of tissues close to the source and a low sensitivity away from the source.Depending on the position of the dipole in relation to CSF,gray,and white matter,one would expect some changes in the ratio of sensitivity of these three tissue types.ForHAUEISEN et al.:TISSUE RESISTIVITIES ON NEUROMAGNETIC FIELDS AND ELECTRIC POTENTIALS731 Fig.3.Correlation coefficients for the correlation of magneticfields at mean resistivity values and at lower or upper bound of theresistivity.Fig.4.Correlation coefficients for the correlation of electric surface potentials at mean resistivity values and at lower or upper bound of the resistivity.all other tissue types no substantial change is expected with different dipole positions in the brain.The strong sensitivity of the tissues close to the dipole location could possibly explain alterations in the MEG of patients with structural changes and hence resistivity changes in the cortex.The scalp shows the largest influence on the electric surface potentials in terms of sensitivity.It is assumed that the scalp resistivity is subject to much stronger changes than CSF,gray or white matter,sometimes even during one measurement session(e.g.,sweating).To assure and quantify the assumption of larger resistivity changes of the scalp,a study including resistivity measurements is necessary.The surface potentials are sensitive to all tissue types in between the source and the electrodes.For the source position in the motor cortex the tissues between the scalp and the brain are fat,bone,and soft bone.The sensitivity values of these three tissue types are considerably higher than the sensitivity values of muscle,soft tissue,or cerebellum which are away from the source and electrode position.Thus,it is assumed that for different source positions those tissues which are in between the source and the electrodes will show a high sensitivity value.For instance,for a source in the temporal lobe one would expect a higher sensitivity value of muscle than for the source in the motor cortex.The sensitivity values of blood are very low.They can be considered as zero within the given computational accuracy. The reason is that the modeling only includes the largest blood vessels.Therefore,the fraction of this tissue in the model is732IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING,VOL.44,NO.8,AUGUST1997Fig.5.DSM at mean resistivity values and at lower or upper bound of the resistivity.The maximum and minimum of the magneticfield at mean resistivities are 2.32pT and01.16pT.Fig.6.DSE at mean resistivity values and at lower or upper bound of the resistivity.The maximum and minimum of the electric potentials at mean resistivities are0.28mV and00.25mV.very low.Also,there is no large vessel in the vicinity of thesource.Thus,no significant change in the computed magneticfields and surface potentials is observed.Neither the magneticfield nor the surface potentials aresensitive to the change of the resistivity value of internal airfrom50000cm.Therefore,the value of50000cm,the lowervalue is8000cm(HAUEISEN et al.:TISSUE RESISTIVITIES ON NEUROMAGNETIC FIELDS AND ELECTRIC POTENTIALS733 bone resistivity will draw more volume currents from othersurrounding tissues.Increasing the already high mean value ofbone resistivity to the resistivity value of internal air(50000cm can already be considered as the value of a good insulator.Based on a BEM model using simple geometries,a paper by Huang et al.[14]suggested that the magneticfields and surface potentials should decrease when the source is close to a region with lower conductivity having a diameter of more ing our model,we found that for white matter an enhancement in resistivity leads to a decrease for both the magneticfield and the surface potentials,thus,confirming the results of the above study.For CSF,which has in the region of our source a“diameter”of less than20mm,we found a similar influence on the magneticfield as for white matter but an opposite type of behavior for the surface potentials.The high correlation coefficients(between0.990and1.0) suggest a minor influence of resistivity changes on the source localization procedures.Additionally,we checked the position of the minimum and maximum on the sampling plane for all field and potential profiles.For the magneticfields all maxima were at the same position,as well as all the minima except for those of gray upper,CSF lower,and white lower.The minimum for white lower was shifted by two sampling points (2cm)and that for the other two by one sampling point(1 cm).As for the electric potentials,all except the maximum of white lower(shifted one sampling point,0.6cm)were at the same location.The minima of gray lower,CSF lower,white upper,white lower,scalp lower,bone upper,and bone lower were shifted one sampling point(0.6cm).One principal limitation of this study is that it does not investigate different source positions within the brain.As discussed above,we do not expect that the major conclusion of this paper will change for different dipole positions.However, the values quantified in Tables II and III depend on the model geometry and the dipole direction.Previously,Ueno et al.[27] have shown that for a radial dipole in a spherical volume conductor with two different regions of resistivitiy thefield change can be quite dramatic,even reversing its sign.We believe that there are two reason why we did not observe such dramatic changes.First,we used a tangential dipole in a realistic volume conductor model and second,our resistivity changes were much smaller than those used by Ueno et al.[27].Also,with the modeling technique used it is not possible to exactly predict and quantify the changes introduced by different model geometries.Only rough qualitative predictions are possible.For instance one would expect a lower influence of CSF in other regions of the brain with less CSF close to the source.The reason is that there is a large area of CSF next to the dipole position for the model depicted(refer to Fig.1).This area extends throughout the gap between both hemispheres because the falx cerebri was not included into the FEM model.There are two reasons for this omission:first, our model resolution is2mm and the width of the falx cerebri is about1mm and second,the falx cerebri is not an absolute barrier for CSF.The dipole used was about5mm away from the position of the falx cerebri.There are several problems connected with the measurement of in vivo resistivities.First,there is an intersubject and intrasubject variability which can be related to age,diseases, environmental factors,and personal constitution[4].Second, there is no reliable method with which to accurately de-termine the in vivo resistivities of the human head tissues for each patient in today‘s science.The measurement of in vivo resistivities is problematic due to errors introduced by assumptions about the tissue structure,polarization effects, andfinite electrode resistance.For example intracellular and extracellular conductivities were investigated and modeled for skeletal muscles and a strong dependence on the electrode distance was found[10].Third,the tissue resistivity also differs between in vivo and in vitro measurements[21]and it obviously differs between dead and living tissue.Even small pertubations in the normal conditions of the living tissue caused by mechanical damage or chemical reaction can lead to significant changes in the resistivity profile within the tissues. Most of the studies on measurements of resistivity values were conducted about30years ago and the values obtained varied over a wide range(see,e.g.,[3],[4],[9],[24],and[26]). Since these publications,the concept of extracellular space has been investigated by Nicholson and colleagues(see,e.g., [8],[18]).It was found that the extracellular space occupies about20%of the cerebellum and that current which is passed through the brainflows through both neurons and glia.The lat-ter fact is especially important for the resistivity of brain tissue, since resistivity measurements are usually based on passing current through the brain(i.e.,also through neurons)and when recording EEG/MEG the neurons are the active generators and the volume currentflows outside the neurons through glia cells and extracellular space.Thus,in the brain we face a principal discrepancy between the conditions of recording EEG/MEG and measuring the tissue resistivity.The relative contributions of intracullular and extracellular resistivity to the apparent resistivity were investigated by Okada and colleagues [20].They found the apparent conductivity to be734IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING,VOL.44,NO.8,AUGUST1997V.C ONCLUSIONSFrom the results it can be seen that the magneticfield is sensitive only to changes of the resistivity of tissues close to the dipole position,while scalp electric surface potential is sensitive to all tissues close to the dipole and the electrode positions.The changes observed here will also show up in MEG or EEG measurements.The scaling(strength)of magneticfields and electric surface potentials is strongly influenced by tissue resistivity changes. 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B.Ranck,“Specific impedance of rabbit cerebral cortex,”Exp.Neurol.,vol.7,pp.144–152,1963.[23]Y.Rudy,R.Plonsey,and J.Liebman,“The effects of variation inconductivity and geometrical parameters on the electrocardiogramm, using eccentric spheres model,”Circ.Res.,vol.44,pp.104–111,1979.[24]S.Rush,J.A.Abildskov,and R.McFee,“Resistivity of body tissues atlow frequencies,”Circ.Res.,vol.12,pp.40–50,1963.[25]S.Rush and D.A.Driscoll,“Current distribution in the brain fromsurface electrodes,”Anesth.Analgesia,vol.47,no.6,pp.715–723, 1968.[26]H.P.Schwan and C.F.Kay,“Specific resistance of body tissues,”Circ.Res.,vol.4,pp.664–670,1956.[27]S.Ueno,K.Iramina,and K.Harada,“Effects of inhomogeneities incerebral modeling for magneto-encephalography,”IEEE Trans.Magn., vol.23,pp.3753–3755,1987.[28]S.Ueno,K.Iramina,H.Ozaki,and K.Harada,“The MEG topographyand the source model of abnormal neural activities associated with brain lesions,”IEEE Trans.Magn.,vol.22,pp.874–876,1986.[29] A.van Harreveld,T.Murphy,and K.W.Nobel,“Specific impedance ofrabbit’s cortical tissue,”Amer.J.Physiol.,vol.205,pp.203–207,1963.Jens Haueisen was born in Jena,Germany,in1966.He received the M.S.and the Ph.D.degrees inelectrical engineering from the Technical UniversityIlmenau,Germany,in1992and1996,respectively.He is currently a Research Associate at the Bio-magnetic Center,Friedrich-Schiller-University Jena,Germany.His research interests are in the numericalcomputation of bioelectromagneticfields and theanalysis of biomagnetic signals.。