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Title of Thesis

Nasiruddin Khan
Institute/University/Department Details
University Of Karachi/ Department of Mathematics
Number of Pages
Keywords (Extracted from title, table of contents and abstract of thesis)
electrodynamics, brain, electro cortical activity, electrocortical waves, electroencephalograms (eeg), neuroscience, neurons

Biological background to understand the brain system and the electrical activity has been discussed. A linear model of global electro cortical activity developed by wright and kydd is described. The model proposed that the properties of the electrocortical waves be clearly distinguished from the microscopic and nonlinear interactions which underlie them. This model is generalized to include magnetic fields

Covariant model of global electro cortical activity is developed by considering telencephalonic structures as mass of linked oscillators generating activity with a number of resonant modes. Equations for the signals are written in the commoving frame and then transformed into the laboratory frame. The state transition matrix is obtained in the presence of electric and magnetic fields. Generalized coupling dependent on both the electrical potentials and their rate of change is introduced in covariant model of global electro cortical activity. First order shift in frequencies is obtained. A condition of impedance matching relates the coupling parameters and damping coefficients

Effects of perturbing fields are described. Effects of weak magnetic fields are considered on a covariant model of global electro cortical activity. A method to calculate the ratio of components of signal velocities is given. Effects of weightlessness and acceleration are described. Weightlessness has very small effects on electroencephalograms (EEG)

EEG is a signal resulting from registration of the changes of electrical potentials accompanying the brain activity. Simulation techniques has been tried to understand the underlying phenomenon. A Pascal procedure has been developed to emulate the results of Wright and Kydd’s description of power spectra

Group structures of transition matrix suggest a possible link between the identity of the group and the phenomenon of brain death. Physiological implications of the theory are discussed

Download Full Thesis
882.62 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents 0
50.57 KB
2 1 Neuroscience 1
127.94 KB
  1.1 Introduction 1
  1.2 Brain 2
  1.3 Neurons 3
  1.4 Electrical Activity Of The Brain 6
  1.5 Electrocortical Activity 8
3 2 Global Electro Cortical Activity 10
130.99 KB
  2.1 General View 10
  2.2 Linear Model Of Electro Cortical Activity 11
  2.3 Covariant Formulation Of Electro Cortical Activity 17
  2.4 Generalized Coupling Model Of Electro Cortical Activity 23
4 3 Perturbation Effects In Electro Cortical Activity 30
103.44 KB
  3.1 Introduction 30
  3.2 Weak Stationary Electric And Magetic Fields 31
  3.3 Weak Linearly Time Dependent Electromagnetic Fields 35
  3.4 Gravitational Field Effects 35
5 4 Modling And Simulation 46
90.44 KB
  4.1 Introduction 46
  4.2 A Field Theoretic Approach 48
  4.3 Simulation Of EEG 51
  4.4 Simulation Of Power Spectra 57
6 5 Conclusion 59
74.34 KB
  5.1 Symmetry Properties Of Transition Matrix 59
  5.2 Physiological Impects 63
  5.3 The Limitations And The Speculations 66
7 6 Appendices 69
461.26 KB
  6.1 Appendix-A 69
  6.2 Appendix-B 81
  6.3 Appendix-C 92
  6.4 Appendix-D 112
8 7 References
55.75 KB