Brain Topography

, Volume 9, Issue 3, pp 191–202 | Cite as

A four sphere model for calculating the magnetic field associated with spreading cortical depression

  • Ranjith S. Wijesinghe
  • Norman Tepley
Article

Summary

In our previous model, we ascertained that the large amplitude waves (LAWs), reported by Barkley and coworkers (1990) in time series magnetoencephalography (MEG) recordings from migraine patients, could be simulated and compared with the recorded signals using a simple plane volume conductor model (Tepley and Wijesinghe 1996). In this paper, we model LAWs using the help of more complicated yet reliable four-sphere model. This mathematical model furthermore assumes that the LAWs arise from propagation of Spreading Cortical Depression (SCD) across a sulcus and these simulated signals are more similar to the recorded signals than the ones we obtained from our previous model. SCD propagates slowly across the cortex in all species in which it has been observed. In our model, current dipoles represent the excitable neurons in the cortex and magnetic fields created by these individual dipoles are calculated using a four-sphere model. The magnetic field arising from the excited area of cortex is obtained by summing the fields due to these individual dipoles. Sulci shapes are represented by simple mathematical formulae.

Key words

Magnetoencephalography Spreading cortical depression Current dipole Migraine Volume conduction model 

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References

  1. Barkley, G.L., Tepley, N., Moran, J.E., and Welch, K.M.A. DC-MEG studies of migraine patients and controls. In: Baumgartner, C, Deecke, L., Stroink, G., Williamson, S.J., eds. Biomagnetism: Fundamental Research and Clinical Applications. Amsterdam: Elsevier-IOS Press, 1995: 70–74.Google Scholar
  2. Barkley, G.L., Tepley, N., Moran, J.E., and Welch, K.M.A. Blinded analysis of MEG studies in migraine, New advances. In: Clifford, R.F., ed. Headache Research 3, Smith-Gordon, 1994: 69–72.Google Scholar
  3. Barkley, G.L., Tepley, N., Nagel-Leiby, S., and Moran, J.E., Simkins, R.T., Welch, K.M.A. Magnetoencephalographic Studies of Migraine. Headache 1990, 30: 428–434.Google Scholar
  4. Bures, J., Buresova, O., and Krivanek, J. The Mechanism and Application of Leao's Spreading Depression of Electorencephalography Activity. New York, Academic Press, 1974.Google Scholar
  5. Cuffin, B.N. Eccentric sphere models of the head. IEEE Trans on Biomedical Eng BME 1991, 58: 871–878.Google Scholar
  6. Cuffin, B.N., and Cohen, D. Magnetic fields of a dipole in spherical volume conductor shapes. IEEE Trans on Biomedical Eng BME 1977, 24: 372–381.Google Scholar
  7. Cuffin, B.N., and Cohen, D. Comparison of the magnetoencephalogram and electroencephalogram. Electroenceph. and Clinical Neurophys. 1979, 47: 132–148.Google Scholar
  8. Geselowitz, D.B. On the Magnetic Field Generated Outside an Inhomogeneous Volume Conductor by Internal Current Sources. IEEE Trans on Biomedical Eng Mag-6 1970, 2: 346–347.Google Scholar
  9. Leao, A.A.P. Spreading depression of activity in the cerebral cortex. J Neurophysiol 1944, 7: 379–390.Google Scholar
  10. Leao, A.A.P., and Morrison, R.S. Propagation of Spreading Depression J Neurophysiol 1945, 8: 33–45.Google Scholar
  11. Nunez PL. Localization of brain activity with Electroencephalography. In: Sato, S., ed. Advances in Neurology. New York: Raven Press, 1990: 39–65.Google Scholar
  12. Tepley, N., and Wijesinghe, R.S. A Dipole Model for Spreading Cortical Depression. Brain Topography 1996, 8: 211–219.Google Scholar
  13. Wijesinghe, R.S., Gielen, F.H., Wikswo, J.P. A model for compound action potentials and currents in a nerve bundle I: the forward calculation. Annls. Biomed. Eng. 19: 43–72, 1991.Google Scholar

Copyright information

© Human Sciences Press, Inc. 1997

Authors and Affiliations

  • Ranjith S. Wijesinghe
    • 2
  • Norman Tepley
    • 1
  1. 1.Dept. of PhysicsOakland UniversityRochesterUSA
  2. 2.Department of NeurologyK-11, Henry Ford HospitalDetroitUSA

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