Beynin elektriksel etkinliğinin dipol kaynakları şeklinde modellenmesi ve bu kaynaklara ait gerilim dağılımının bulunması

Abstract

Beynin elektriksel etkinliğini ölçerek, beyindeki herhangi bir hastalığı teşhis eden, veya beynin çeşitli durumlardaki çalışmasını incelemek için bu elektriksel etkinliği ölçen branşa elektroensefalografi denir. Bu tezde, nöronları senkronize olarak çalıştığı düşünülen beynin bir bölgesindeki elektriksel etkinlik, eşdeğer bir dipol şeklinde modellenmiş ve bu akım kaynağına yönelik gerilim dağılımının kafa derisindeki görüntüsünün teorik olarak hesaplanması yapılmıştır. Kafa konsantrik, farklı iletkenliklerde, üç küre şeklinde modellenmiş ve belli bir eksantritesi olan bir dipol kaynağının üçüncü küre yüzeyinde yaratacağı gerilim dağılımı, sınır koşulları aracılığıyla belirlenmiştir. Farklı dipol bileşenlerine dair gerilim dağılımlarının simülasyonları yapılmış, böylelikle, farklı eksantritelerde bulunan dipollerin gerilim dağılımlarının kafanın iletke bölgeleri tarafından nasıl etkilendiği gösterilmiştir.

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, the brain 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.