Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Reserved Physical Symbols and Quantities
- Abbreviations
- 1 Introduction
- 2 Charges, Currents, Fields, and Potentials in the Brain
- 3 Neural Dynamics
- 4 Volume-Conductor Theory
- 5 Conductivity of Brain Tissue
- 6 Schemes for Computing Extracellular Potentials
- 7 Spikes
- 8 Local Field Potentials (LFPs)
- 9 Electroencephalography (EEG)
- 10 Electrocorticography (ECoG)
- 11 Magnetoencephalography (MEG)
- 12 Diffusion Potentials in Brain Tissue
- 13 Final Comments and Outlook
- Appendix A Frequency-Dependent Length Constant
- Appendix B Derivation of the Current-Dipole Approximation
- Appendix C Electric Stimulation
- Appendix D Derivation of the Point-Source Equation for Anisotropic Medium
- Appendix E Statistical Measures
- Appendix F Fourier-Based Analyses
- Appendix G Derivation of Formulas for Population Signals
- Appendix H Equations for Computing Magnetic Fields
- Appendix I Derivation of the MC+ED Scheme
- References
- Index
4 - Volume-Conductor Theory
Published online by Cambridge University Press: 30 May 2024
- Frontmatter
- Dedication
- Contents
- Preface
- Reserved Physical Symbols and Quantities
- Abbreviations
- 1 Introduction
- 2 Charges, Currents, Fields, and Potentials in the Brain
- 3 Neural Dynamics
- 4 Volume-Conductor Theory
- 5 Conductivity of Brain Tissue
- 6 Schemes for Computing Extracellular Potentials
- 7 Spikes
- 8 Local Field Potentials (LFPs)
- 9 Electroencephalography (EEG)
- 10 Electrocorticography (ECoG)
- 11 Magnetoencephalography (MEG)
- 12 Diffusion Potentials in Brain Tissue
- 13 Final Comments and Outlook
- Appendix A Frequency-Dependent Length Constant
- Appendix B Derivation of the Current-Dipole Approximation
- Appendix C Electric Stimulation
- Appendix D Derivation of the Point-Source Equation for Anisotropic Medium
- Appendix E Statistical Measures
- Appendix F Fourier-Based Analyses
- Appendix G Derivation of Formulas for Population Signals
- Appendix H Equations for Computing Magnetic Fields
- Appendix I Derivation of the MC+ED Scheme
- References
- Index
Summary
The standard two-step scheme for modeling extracellular signals is to first compute the neural membrane currents using multicompartment neuron models (step 1) and next use volume-conductor theory to compute the extracellular potential resulting from these membrane currents (step 2). Here, we present the volume-conductor theory used in step 2. The neural output from step 1 can be represented in terms of (i) a set of point sources, (ii) a set of line sources, (iii) a current-source density, or (iv) one or several current dipoles. We derive equations for the extracellular potential under the approximations (i–iv), discuss the validity and applicability of the different approximations, and explain how they are related. We also discuss how to model the effects that the electrode itself can have on the measured extracellular potential.
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- Electric Brain SignalsFoundations and Applications of Biophysical Modeling, pp. 79 - 104Publisher: Cambridge University PressPrint publication year: 2024