مدل‌سازی الکترومغناطیسی امواج مغزی بر اساس تحلیل تمام‌موج

نوع مقاله : علمی-پژوهشی

نویسندگان

1 دانشکده مهندسی برق و کامپیوتر- دانشگاه صنعتی نوشیروانی بابل

2 دانشکده علوم پایه– دانشگاه صنعتی نوشیروانی بابل

چکیده

در این مقاله با استفاده از مدل‌سازی الکترومغناطیسی نورون‌ها در مغز، امواج الکترومغناطیسی به صورت تمام‌موج استخراج شده‌اند. هم‌اکنون در تمام مراکز و کلینیک‌های  تحقیقاتی این کار به طور سنتی با استفاده از تقریب شبه‌استاتیک معادلات ماکسول در الکترومغناطیس انجام می‌شود ولی میزان خطای حاصل از این تقریب در نتایج نهایی بررسی نمی‌شود. این موضوع با توجه به افزایش حساسیت حس‌گرهای مدرن امروزی بیشتر جلب توجه می‌کند. در این مقاله ابتدا با مروری بر مبانی به‌کارگیری تقریب شبه‌استاتیک در تحلیل امواج مغزی، ابهاماتی راجع به شایستگی این تقریب در این مسئله مطرح شده و لزوم حل مسئله به صورت تمام‌موج بیان می‌شود. پس از آن میدان‌های حاصل از یک دوقطبی جریان واقع در مرکز کره‌ای با رسانایی معلوم توسط بسط توابع بسل و هنکل نوشته شده و با تئوری‌های پراکندگی در الکترومغناطیس، مسئله به صورت تمام‌موج حل می‌گردد. سرانجام منحنی معیار اختلاف نسبی (RDM) بین پاسخ شبه‌استاتیک و تمام‌موج برحسب فرکانس و رسانایی‌های مختلف رسم می‌شود. نتایج نشان می‌دهد که خطای حاصله با افزایش فرکانس رشد داشته و می‌تواند توسط حسگرهای مدرن آشکارسازی شود. از رهاوردهای مهم مدل‌سازی تمام‌موج، غنا بخشیدن به اطلاعات حاصل از مغزنگاری الکتریکی (EEG) و مغناطیسی (MEG) و در نتیجه استخراج الگوهای دقیقتری از فعالیت‌های مغز می‌باشد.

کلیدواژه‌ها


عنوان مقاله [English]

Electromagnetic Modeling of Brain Waves based on Full-wave Analysis

نویسندگان [English]

  • S. Samadi Gorji 1
  • B. Zakeri 1
  • Reza Khanbabaie 2
1 Faculty of Electrical and Computer Engineering, Babol Institute of Technology, Babol, Iran
2 Faculty of Physics, Babol Institute of Technology, Babol, Iran,
چکیده [English]

In this paper by electromagnetic modeling of neurons in brain, the brain waves have been derived in a full-wave way. Now, in all clinics and research centers, traditionally, it has been done by using the quasi-static approximation of the Maxwell equation in electromagnetic. However, the error rate resulting from the approximation has not been studied upon the final results. This issue becomes more noticeable due to increasing the sensitivity of today's modern sensors. In this paper, first, with an overview of the basics of applying quasi-static approximation in the analysis brain waves, ambiguities about the suitability of this approximation are presented and the necessity of full-wave solution of the problem is expressed. Then, in the simplest form, the electromagnetic fields aroused from a current dipole where is located in the center of a sphere with known conductivity is written in terms of Bessel and Hankel function expansion; and the problem has been solved in a full-wave way by using of scattering theories in electromagnetic. Finally, the curve of relative difference measure (RDM) between quasi-static and full-wave solution has been drawn in terms of frequency conductivity. One of the important achievements of full-wave modeling is enriching the information resulted from EEG and MEG and consequently extracting more accurate patterns from brain activities.

کلیدواژه‌ها [English]

  • Brain Waves
  • Quasi-static Approximation
  • Full-wave Analysis
  • Bioelectromagnetics
  • EEG
  • MEG
[1]      محمدعلی گنجعلی و وحید شالچیان، « استخراج الگوهای فضایی طیفی از سیگنال‌های الکتروانسفالوگرام برای تشخیص اختلال شناختی خفیف»، مجله مهندسی برق دانشگاه تبریز، دوره 48، شماره 4، صفحه 1752-1741، زمستان 1397.
[2]      T. Ito, H. Otsubo, H. Shiraishi, K. Yagyu, Y. Takahashi, Y. Ueda, F. Takeuchi, K. Takahashi, S. Nakane and S. Kohsaka and S. Saitoh, “Advantageous information provided by magnetoencephalography for patients with neocortical epilepsy,” Brain and Development, vol. 37, no. 2, pp. 237-242, 2015.
[3]      J. Ebersole, “EEG voltage topography and dipole source modeling of epileptiform potentials,” In Ebersole JS, Pedley TA (Eds), Current practice of clinical electroencephalography. Philadelphia: Lippincott Williams and Wilkins, pp. 732-752, 2003.
[4]      C. Plummer, A. S. Harvey and M. Cook, “EEG source localization in focal epilepsy: where are we now?,” Epilepsia, vol. 49, no. 2, pp. 201–218, 2007.
[5]      M. Hämäläinen, R. Hari, R. J. Ilmoniemi, J. Knuutila and O. V. Lounasmaa, “Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain,” Reviews of Modern Physics, vol. 65, no. 2, pp. 413–497, 1993.
[6]      B. B. Andrei, “Brain's magnetic field: a narrow window to brain’s activity,” Electromagnetic field and the human body workshop, Technion, December 2010.
[7]      مرتضی به‌نام و حسین پورقاسم، «شناسایی صرع بر اساس بهینه‌سازی ویژگی‌های ادغامی تبدیل هارتلی با مدل ترکیبی MLP و GA همراه با استراتژی یادگیری ممتیک»، مجله مهندسی برق دانشگاه تبریز، دوره 45، شماره 4، صفحه 67-51، زمستان 1394.
[8]      J. Vorwerk, J. Cho, S. Rampp, H. Hamer and T. R. Knösche and C. H. Wolters, “A guideline for head volume conductor modeling in EEG and MEG,” NeuroImage, vol. 100, pp. 590-607, 2014.
   [9]      C. H. Wolters, A. Anwander, X. Tricoche, D. Weinstein and M. A. Koch and R. S. Macleod, “Influence of tissue conductivity anisotropy on EEG/MEG field and return current computation in a realistic head model: a simulation and visualization study using high-resolution finite element modeling,” NeuroImage, vol. 30, no. 3, pp. 813-826, 2006.
[10]      J. de Munck and B. van Dijk and H. Spekreijse, “Mathematical dipoles are adequate to describe realistic generators of human brain activity,” IEEE Trans Biomed. Eng. vol. 35, no. 11, pp. 960–966, 1988.
[11]      S. Supek and C. J. Aine, Magnetoencephalography from Signals to Dynamic Cortical Networks, Springer press, 2012.
[12]      D. Geselowitz, “On bioelectric potentials in an inhomogeneous volume conductor,” Biophys Journals, vol. 7, no. 1, pp. 1–11, 1967.
[13]      J. Malmivuo, “Comparison of the properties of EEG and MEG in detecting the electric activity of the brain,” Brain topography, vol. 25, no. 1, pp. 1-19, 2012.
[14]      Barnard and I. Duck and M. Lynn, “The application of electromagnetic theory to electrocardiology: I. derivation of the integral equations,” Biophysics Journals, vol. 7, no. 5, pp. 443–462, 1967.
[15]      D. Brenner, J. Lipton and L. Kaufman and S. Williamson, “Somatically evoked magnetic fields of the human brain,” Science, vol. 199, no. 4324, pp. 81–83, 1978.
[16]      J. Sarvas, “Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem,” Physics in Medicine & Biology, vol. 32, no. 1, pp. 11–22, 1987.
[17]      M. Z. Koubeissi and N. J. Azar (Editors) “Epilepsy Board Review a Comprehensive Guide”, (chap. 23: Magnetoencephalography and Magnetic Source Modeling), pp. 301-307, Springer press, New York, NY, 2017.
[18]      T. V. Zakharova and P. I. Karpov, and V. M. Bugaevskii, “Localization of the activity source in the inverse problem of magnetoencephalography,” Computational Mathematics and Modeling, vol. 28, no. 2, pp. 148-157, 2017.
[19]      J. D. Jackson, Classical Electrodynamics, 3rd ed., Wiley Press, 1999.
[20]      B. N. Cuffin and D. Cohen, “Magnetic fields of a dipole in special volume conductor shapes,” IEEE Transactions on Biomedical Engineering, vol. 4, pp. 372–381, 1977.
[21]      R. Ilmoniemi and M. S. Hamalainen and J. Knuutila, “The forward and inverse problems in the spherical model,” Proceedings of Biomagnetism: applications and theory journal, Pergamon, New York, pp. 278–282, 1985.
[22]      L. Heller, D. van Hulsteyn, “Brain stimulation using electromagnetic sources: theoretical aspects,” Biophysics Journal, vol. 63, no. 1, pp. 129–138, 1992.
[23]      Y. Petrov, “Anisotropic spherical head model and its application to imaging electric activity of the brain,” physical review, vol. 86, pp. 1-13, 2012.
[24]      J. O. Nieminen and M. Stenroos, “The magnetic field inside a layered anisotropic spherical conductor due to internal sources,” Journal of Applied Physics, vol. 119, no. 2023901, pp. 1-12, 2016.
[25]      R. Plonsey and D. B. Heppner, “Considerations of quasi-stationarity in electrophysiological systems,” The Bulletin of mathematical biophysics, vol. 29, no. 4, pp. 657-664, 1967.
[26]      H. B. Dang and A. C. Maloof and M. V. Romalis, “Ultrahigh sensitivity magnetic field and magnetization measurements with an atomic magnetometer,” Applied Physics Letters, vol. 97, no. 15:151110, 2010.
[27]      H. J. Scheer, T. Fedele and G. Curio and M. Burghoff, “Extension of non-invasive EEG into the kHz range for evoked thalamocortical activity by means of very low noise amplifiers,” Physiological measurement, vol. 32, no. 12, p. N73, 2011.
[28]      T. Fedele, H. J. Scheer, M. Burghoff and G. Curio and R. Körber, “Ultra-low-noise EEG/MEG systems enable bimodal non-invasive detection of spike-like human somatosensory evoked responses at 1 kHz,” Physiological measurement, vol. 36, no. 2, pp. 357-368, 2015.
[29]      S. L. Gratiy, G. Halnes, D. Denman, M. Hawrylycz, C. Koch and G. T. Einevoll and C. A. Anastassiou, “From Maxwell’s equations to the theory of current‐source density analysis,” European Journal of Neuroscience, vol. 45, no. 8, pp. 1013-1023, 2017.
[30]      R. Albanese and P. B. Monk, “The inverse source problem for Maxwell’s equations,” Inverse Problems, vol. 22, no. 3, pp. 1023–1035, 2006.
[31]      T. Kuiken, Stoykov, M. Popovic and M. Lowery and A. Tafflove, “Finite element modeling of electromagnetic signal propagation in a phantom arm,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 9, no. 4, pp. 346–354, 2001.
[32]      C. Bedard and A. Destexhe, “Macroscopic models of local field potentials and the apparent 1/f noise in brain activity,” Biophysics Journal, vol. 96, no. 7, pp. 2589–2603, 2009.
[33]      R. F. Harrington, Time-Harmonic Electromagnetic Fields, IEEE Press series on Electromagnetic Wave Theory, p. 287, 2001.
[34]      C. A. Balanis, “Advanced Engineering Electromagnetics,” John Wiley & Sons, Inc., 2nd edition, 2012.
[35]      T. Ito, H. Otsubo, H. Shiraishi, K. Yagyu, Y. Takahashi, Y. Ueda, F. Takeuchi, K. Takahashi, S. Nakane and S. Kohsaka and S. Saitoh, “Advantageous information provided by magnetoencephalo-graphy for patients with neocortical epilepsy,” Brain and Development, vol. 37, no. 2, pp. 237-242, 2015.
[36]      J. Meijs, O. Weier and M. J. Peters and A. V. Oosterom, “On the numerical accuracy of the boundary element method,”
IEEE transactions on biomedical engineering, vol. 36, no. 10, pp. 1038–1049, 1989.