Pakistan Research Repository


Syed, Arif Kamal (1989) SPACE-TIME REPRESENTATION IN THE BRAIN. PhD thesis, University of Karachi, Karachi.



Wright and Kydd have developed a linear model of global electrocortical activity and its control by lateral hypothalamus. Their model rests on drastic simplifications and bypasses issues of cell-to-cell coupling, details of anatomy etc. Moreover, it does not take into account of the magnetic fields which are generated when there is a motion of charges. In the covariant description the equations for the time variation of potentials of segments of dendritic trees are written in the commoving frames of the signals. When these equations are transformed into the laboratory frame a magnetic vector potential appears along with the electrostatic potential. This model, therefore, offers a possible explanation of magnetoencephalogram (MEG). Essential theoretical features of this covariant model may be summarized as: (a) Elcetrocoritical recordings reflect the transformed spatial average of cortical potentials (b) The telecephalon is assumed to be a linear wave medium with regard to the gross wave potentials although the under-lying microscopic interactions may be extremely non-linear. (c) Closed and constant boundary conditions lead the linear waves to generate activity at a large number of resonant frequencies are clustered about certain central values (Cramers Central Limit Theorem). (e) Ascending inhibitory systems act partly to damp resonant activity and partly as a source of noise like driving signals (f) An electrical potential in a commoving frame of the signal transforms as four-potential in the laboratory frame The group structure of this model is also explored. By block diagonalization a nonsingular matrix is constructed from the state transition matrix. This forms a group whose identity corresponds to the physiological state commonly known as brain death. Further, the effects of weak magnetic fields on this covariant model are considered. A method to calculate the ratio of components of signal velocities is proposed and a gauge transformation is suggested for the electrical potential. In the presence of weak magnetic field frequencies are modified, but damping coefficients and coupling constants remain essentially unchanged. A generalized coupling is suggested in which potentials are also effected by rate of change of neighboring potentials are also effected by rate of change of neighboring potentials. In the presence of weak magnetic fields the effect of generalized coupling on the frequencies is calculated. In the end use of moir fringe topography for the study of neurological disorders is discussed

Item Type:Thesis (PhD)
Uncontrolled Keywords:space-time representation, electrocortical activity, hypothalamus, electrical activity, brain, magnetoencephalogram, brain waves, neurology
Subjects:Physical Sciences (f) > Physics(f1)
ID Code:1074
Deposited By:Mr. Muhammad Asif
Deposited On:20 Dec 2006
Last Modified:04 Oct 2007 21:04

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