Beynin elektriksel etkinliğinin dipol kaynakları şeklinde modellenmesi ve bu kaynaklara ait gerilim dağılımının bulunması
Başlık çevirisi mevcut değil.
- Tez No: 46290
- Danışmanlar: PROF.DR. BİNGÖL YAZGAN
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: EEG, Dipol kaynağı lokalizasyonu, iletken hacim, Beyin, Elektroensefalografi, İletkenlik, Brain, Electroencephalography, Conductivity
- Yıl: 1995
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
TÜRKÇE ÖZET
Özet (Çeviri)
Summary Determining the relationship between human evoked scalp potentials and underlying cortical sources is one of the great challenges in electroencephalography. In this thesis, a source localization method developed by Kavanagh, et. al. 1978 and refined by Ary. et al. 1981 is described. It is of great interest to be able to infer from multiple scalp recordings obtained from different derivations the distribution of the generators within the skull, responsible for different BEG phenomena. In its more specific form, the question of determining the place of intracranial sources of EEG phenomena implies solving the so-called inverse problem of volume conduction theory, which is to locate within a conductive medium the sources of electrical activity, given the distribution of electrical potentials at the surface enclosing the medium. The forward problem in EEG consists of finding the distribution of potentials at the scalp given the intracranial sources. To obtain an appropriate solution to both the inverse and the forward problem is not a simple task. Some of the limitations of this problem consists of a) the model of the source, and b) that of the volume conductor. a) Problems posted by the model source : In general the current generator can be modelled by several distributions. The most convenient one is the equivelant dipol source which is to be used throuhout the thesis. Aside from mere simplicity, the principal motivation that has led previous investigators to choose a current dipole source model is that it can be appropriate from a physical point of view. The exact expression for the potential due to a volume of discrete sources, such as might arise from the activity of a population of neurons, is an infinite series whose successively higher order terms decrease more rapidly for points distant from the sources. The net source in the head is assumed to be zero and thus the first or monopolar term is neglected. Then to a good approximation, the second term, the dipole term, suffices to determine the potential field at distances large compared to the maximum distance between the sources producing the field. In situations where this criterion is not met, the sources might be modelled by extended 2-dimensional dipole sheets with irregular surfaces. b) Problems posted by the model of the volume-conductor : In most solutions of the problems in electro-magnetoencephalograhy, thebrain and the different tissues of the head are modelled by concentric spheres. The investigators who have used the three or four spheres model agree that the effect of electrical inhomogenities is to attenuate and smear the pattern of scalp potentials. The formulation of the forward problem in the thesis begins with the governing equations. The problem first encounters the homogeneous model which is the one homogeneous sphere with uniform conductivity. For this approximation the Poisson equation is solved in spherical coordinates. (Figure SI) Şekil SL Coordinate system for the dipole in homogeneous model V oV0~V J, (SI) In this formula, <& is used for the potential field, cr is the conductivity of the medium, and Jf is the surface current density. The divergence of the surface current density gives the volume current density L. So the solution to the above formula is : 1 fivÇ*^ 4jhj J R (S2) The source function is determined to be a dipole, z=bR away from the origin on the z axis, with two opposite charhes that have a separation of 1 between each other. So the source function is given theoretically as : XIJv = -/0oV)8(y')[-8(W? + l-z') + SibR-z')'] (S3) The 1/R term in the above (S2) formula is expanded in spherical coordinates as : ^- = wI İ em-^-|^|p^(cose/)^(cose)coS[m(ş-^)] <S4) If the source is on the z axis then both 8' and <p' will be zero. Substituting (S3) and (S4) in (S2) gives the potential field distribution of a dipole on the surface of a homogeneous conducting medium : oo ®(R, 0, q» = -^- Z ^b^1 nmrPn(cos 0) (S5) «=1 Here the dipole is taken as in a radial direction. If it is taken tangential to the surface, which also means paralel to the x axis then the formula becomes : oo <*> = i 2 ^f^ WJkcoS0)cos(cp) (S6) Superemposing (S5) and (S6) gives the distribution of a dipole with certain eccentricity from the origin on the z axis, having both radial and tangential components : O(2?,0,<p) = -^£ ^L&w-I[«mrP“(cos0)+m^(cos0)cos(<p)J (87) H=l In the thesis, the solution for inhomogeneous media is also given. As previously mentioned, the real head can be modelled by four concentric spheres starting from the most inner one : brain, cerebrospinal fluid, skull, and the scalp. In my thesis I used the three concentric spheres model, because the conductivity of the brain and the cerebrospinal fluid is almost the same. The solution to this phenomena is the expansion of (S7) to two more surrending spheres with different conductivities. This is a boundary value problem, and the governing equations with their boundary conditions can be given as below : xn^1 = 4510ı 2 F»(cos6) n=\ n{bR) n-l rn+l +Anrn (S8) ^^i^cose^-HC^] (S9) V3 = ^ £ F”(coSe)[^-+^«] (S10) The boundary conditions for the above potentials are 1) a)r = r1->V1 = V2, v 3^ 3F2 i 9r 3rJr=ri 2) a)r = r2->F2 = F3 âF2 3^3 b) ©2-^-03^^2 3) ^-U=0 Using all the information given above, the potential field distribution on the surface of the third sphere which symbolized the scalp is determined : 3 n=\ %{2n+Y)2 I nmrPn(cos 0) + m^P"(cos 0) cos(<p) J (Sll) The next chapter hi the thesis is the simulation of these distributions with different values of mT and mt. Of course, the assumption in this equation is that the dipole is located on the z axis, and its components are in the xz plane. For a more realistic approach, the source function can be evaluated to be located anywhere inside the brain sphere; in this case the first sphere. xiuŞekil S2. Inhomogeneous three sphere model of the head The simulation studies are done using the programs MCAD v 2.5 and SURFER v. 4.2. The Legendre polynomilas that are seen in the equations are calculated for 1 < cos(6) ^ 0 in 50 points. Also the degree of rotation from the x axis known as cp is calculated in 50 points. xiv
Benzer Tezler
- Görsel uyarılmış potansiyellerin optimal filtrelenmesi
Optimal filtering of visual evoked potentials
SENİHA ÖZLEM ŞAMLI TÜRKKAN
Yüksek Lisans
Türkçe
1992
Elektrik ve Elektronik Mühendisliğiİstanbul Teknik ÜniversitesiDOÇ. DR. MEHMET KORÜREK
- Yalıtkan maddelerde elektriksel delinme dayanımının yapay sinir ağları ile belirlenmesi
Determination of electrical breakdown strength of solid insulating materials with artificial neural networks
MELİKE OĞUZ
Yüksek Lisans
Türkçe
2001
Elektrik ve Elektronik Mühendisliğiİstanbul Teknik ÜniversitesiDOÇ.DR. ÖZCAN KALENDERLİ
- Tek kanallı mikroelektrodlarla aksiyon potansiyellerinin kaydı ve analizi
Design of a single-channel micropipette amplifier for recording and analysis of action potential
KADİR TÜRK
Yüksek Lisans
Türkçe
1998
Elektrik ve Elektronik MühendisliğiKaradeniz Teknik ÜniversitesiElektronik Mühendisliği Ana Bilim Dalı
YRD. DOÇ. DR. TEMEL KAYIKÇIOĞLU