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Title of Thesis

Syed Arif Kamal
Institute/University/Department Details
University of Karachi/ Department of Physics
Number of Pages
Keywords (Extracted from title, table of contents and abstract of thesis)
space-time representation, electrocortical activity, hypothalamus, electrical activity, brain, magnetoencephalogram, brain waves, neurology

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 (Cramer’s 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 moiré fringe topography for the study of neurological disorders is discussed

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726.06 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents
65.16 KB
2 1 Physiology Of The Brain 1
140.11 KB
  1.1 Introduction 2
  1.2 The Human Brain 3
  1.3 Regions Of Cortical Surface 3
  1.4 The Neuron 8
  1.5 Electrical Activity Of The Brain 15
  1.6 Electrocortical Activity 19
3 2 Brain Waves A Resonance 20
73.25 KB
  2.1 The Phenomenon Of Standing Waves 21
  2.2 Standing Waves In Physical Systems 24
  2.3 EEG As A System Of Standing Waves 27
4 3 Mathematical Preliminaries 29
77.49 KB
  3.1 Transformations 30
  3.2 Lorentz Transformations 31
  3.3 Four-Vectors 34
  3.4 Similarity Transformation 36
  3.5 Tensors And Determinants 36
5 4 Global Electrocortical Activity 39
80.57 KB
  4.1 Linear Model 40
  4.2 Covariant Model 44
  4.3 Generalization Of The Covariant Model 47
6 5 Group Structure Of The Covariant Model 49
58.71 KB
  5.1 The State Transition Matrix 50
  5.2 Determinant Of Transition Matrix 51
  5.3 Group Structure 53
  5.4 Brain Death As Identity Of The Group 54
7 6 Effects Of Weak Magnetic Fields 56
41.09 KB
  6.1 Introduction 57
  6.2 Weak Magnetic Fields 57
  6.3 Effects On Frequencies 59
  6.4 Generalized Potential 60
8 7 Generalized Coupling In The Covariant Model 61
49.32 KB
  7.1 Need For Generalized Coupling 62
  7.2 Methematical Description 62
  7.3 Predictions 64
9 8 Moire Techniques In Neurology 67
72.61 KB
  8.1 Introduction 68
  8.2 The Moiré Technique 69
  8.3 Applications 74
  8.4 Study Of Neurological Disorders 74
  8.5 Scope Of Moiré Techniques 75
10 9 Conclusions And Discussion 76
210.36 KB
  9.1 Bibliography 81
  9.2 Appendics 88
  9.3 Appendics- A 89
  9.4 Appendics-B 91
  9.5 Appendics-C 95
  9.6 Vita 101