Electromagnetic Field Modeling
`of
`Transcranial Electric and Magnetic Stimulation:
`Targeting, Individualization, and Safety of
`Convulsive and Subconvulsive Applications
`
`Zhi-De Deng
`
`Submitted in partial fulfillment of the
`requirements for the degree
`of Doctor of Philosophy
`in the Graduate School of Arts and Sciences
`
`COLUMBIA UNIVERSITY
`
`2013
`
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`© 2013
`Zhi-De Deng
`All rights reserved.
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`ABSTRACT
`
`Electromagnetic Field Modeling of Transcranial Electric and
`Magnetic Stimulation: Targeting, Individualization, and
`Safety of Convulsive and Subconvulsive Applications
`
`Zhi-De Deng
`
`The proliferation of noninvasive transcranial electric and magnetic brain stimulation tech-
`niques and applications in recent years has led to important insights into brain function and
`pathophysiology of brain-based disorders. Transcranial electric and magnetic stimulation
`encompasses a wide spectrum of methods that have developed into therapeutic interven-
`tions for a variety of neurological and psychiatric disorders. Although these methods are
`at different stages of development, the physical principle underlying these techniques is
`the similar. Namely, an electromagnetic field is induced in the brain either via current
`injection through scalp electrodes or via electromagnetic induction. The induced electric
`field modulates the neuronal transmembrane potentials and, thereby, neuronal excitability
`or activity. Therefore, knowledge of the induced electric field distribution is key in the
`design and interpretation of basic research and clinical studies. This work aims to delin-
`eate the fundamental physical limitations, tradeoffs, and technological feasibility constraints
`associated with transcranial electric and magnetic stimulation, in order to inform the de-
`velopment of technologies that deliver safer, and more spatially, temporally, and patient
`specific stimulation.
`Part I of this dissertation expounds on the issue of spatial targeting of the electric field.
`Contrasting electroconvulsive therapy (ECT) and magnetic seizure therapy (MST) config-
`urations that differ markedly in efficacy, side effects, and seizure induction efficiency could
`advance our understanding of the principles linking treatment parameters and therapeutic
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`outcome and could provide a means of testing hypotheses of the mechanisms of therapeu-
`tic action. Using the finite element method, we systematically compare the electric field
`characteristics of existing forms of ECT and MST. We introduce a method of incorporating
`a modality-specific neural activation threshold in the electric field models that can inform
`dosage requirements in convulsive therapies. Our results indicate that the MST electric
`field is more focal and more confined to the superficial cortex compared to ECT. Further,
`the conventional ECT current amplitude is much higher than necessary for seizure induc-
`tion. One of the factors important to clinical outcome is seizure expression. However, it is
`unknown how the induced electric field is related to seizure onset and propagation. In this
`work, we explore the effect of the electric field distribution on the quantitative ictal elec-
`troencephalography and current source density in ECT and MST. We further demonstrate
`how the ECT electrode shape, size, spacing, and current can be manipulated to yield more
`precise control of the induced electric field. If desirable, ECT can be made as focal as MST
`while using simpler stimulation equipment.
`Next, we demonstrate how the electric field induced by transcranial magnetic stimula-
`tion (TMS) can be controlled. We present the most comprehensive comparison of TMS coil
`electric field penetration and focality to date. The electric field distributions of more than
`50 TMS coils were simulated. We show that TMS coils differ markedly in their electric field
`characteristics, but they all are subject to a consistent depth–focality tradeoff. Specifically,
`the ability to directly stimulate deeper brain structures is obtained at the expense of induc-
`ing wider electric field spread. Figure-8 type coils are fundamentally more focal compared
`to circular type coils. Understanding the depth–focality tradeoff can help researchers and
`clinicians to appropriately select coils and interpret TMS studies. This work also enables
`the development of novel TMS coils with electronically switchable active and sham modes
`as well as for deep TMS. Design considerations of these coils are extensively discussed.
`Part II of the dissertation aims to quantify the effect of individual, sex, and age differ-
`ences in head geometry and conductivity on the induced neural stimulation strength and
`focality of ECT and MST. Across and within ECT studies, there is marked unexplained
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`variability in seizure threshold and clinical outcomes. It is not known to what extent the
`age and sex effects on seizure threshold are mediated by interindividual variation in neural
`excitability and/or anatomy of the head. Addressing this question, we examine the effect
`on ECT and MST induced field characteristics of the variability in head diameter, scalp
`and skull thicknesses and conductivities, as well as brain volume, in a range of values that
`are representative of the patient population. Variations in the local tissue properties such
`as scalp and skull thickness and conductivity affect the existing ECT configurations more
`than MST. On the other hand, the existing MST coil configurations show greater sensitivity
`to head diameter variation compared to ECT. Due to the high focality of MST compared
`to ECT, the stimulated brain volume in MST is more sensitive to variation in tissue layer
`thicknesses. We further demonstrate how individualization of the stimulus pulse current
`amplitude, which is not presently done in ECT or MST, can be used as a means of com-
`pensating for interindividual anatomical variability, which could lead to better and more
`consistent clinical outcomes.
`Part III of the dissertation aims to systemically investigate, both computationally and
`experimentally, the safety of TMS and ECT in patients with a deep-brain stimulation
`system, and propose safety guidelines for the dual-device therapy. We showed that the
`induction of significant voltages in the subcutaneous leads in the scalp during TMS could
`result in unintended and potentially dangerous levels of electrical currents in the DBS
`electrode contacts. When applying ECT in patients with intracranial implants, we showed
`that there is an increase in the electric field strength in the brain due to conduction through
`the burr holes, especially when the burr holes are not fitted with nonconductive caps.
`Safety concerns presently limit the access of patients with intracranial electronic devices
`to therapies involving transcranial stimulation technology, which may preclude them from
`obtaining appropriate medical treatments. Gaining better understanding of the interactions
`between transcranial and implanted stimulation devices will demarcate significant safety
`risks from benign interactions, and will provide recommendations for reducing risk, thus
`enhancing the patient’s therapeutic options.
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`Table of Contents
`
`1 Introduction
`1.1 Clinical and Research Trends in Neuromodulation . . . . . . . . . . . . . .
`1.1.1 Electroconvulsive Therapy . . . . . . . . . . . . . . . . . . . . . . . .
`1.1.2 Transcranial Magnetic Stimulation . . . . . . . . . . . . . . . . . . .
`1.1.3 Magnetic Seizure Therapy . . . . . . . . . . . . . . . . . . . . . . . .
`1.2 Approach and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`I Spatial Targeting of Electric Field
`
`2 Electric Field Strength and Focality in Clinical ECT and MST
`2.1
`Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2.2 Electric Field Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2.2.1 Finite-Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . .
`2.2.2 Head Model and Anatomical Parameters . . . . . . . . . . . . . . . .
`2.2.3 ECT Electrode and MST Coil Configurations . . . . . . . . . . . . .
`2.2.4 Electric Field Solution . . . . . . . . . . . . . . . . . . . . . . . . . .
`2.2.5 Magnetically-Induced Electric Field . . . . . . . . . . . . . . . . . .
`2.2.6 Electric Field Metrics
`. . . . . . . . . . . . . . . . . . . . . . . . . .
`2.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2.3.1 Electric Field Characterization . . . . . . . . . . . . . . . . . . . . .
`2.4 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`i
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`1
`3
`3
`6
`6
`7
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`10
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`2.4.1 MST Coil Model Validation . . . . . . . . . . . . . . . . . . . . . . .
`2.4.2
`Simulation Comparison with Intracerebral Field Recordings . . . . .
`2.5 Electric and Magnetically-Induced Electric Field . . . . . . . . . . . . . . .
`2.5.1 ECT vs. MST induced electric field . . . . . . . . . . . . . . . . . .
`2.5.2 Comparison of ECT Electrode and MST Coil Configurations
`. . . .
`2.5.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`3 Topographic Ictal EEG Correlates of Electric Field in ECT and MST
`3.1
`Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.2.1
`Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.2.2 ECT and MST Procedures
`. . . . . . . . . . . . . . . . . . . . . . .
`3.2.3 EEG Acquisition and Data Conditioning . . . . . . . . . . . . . . . .
`3.2.4 Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.2.5 Currrent Source Density and Power Analysis
`. . . . . . . . . . . . .
`3.2.6 Correlation with the Induced Electric Field . . . . . . . . . . . . . .
`3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.4.1 Differential Seizure Expression in ECT and MST . . . . . . . . . . .
`3.4.2 Electrophysiologically Correlates of Electric Field . . . . . . . . . . .
`3.4.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`4 Controlling Stimulation Strength and Focality in ECT
`4.1
`Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`4.2 Electric Field Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`4.2.1 ECT Electrode and MST Coil Configurations . . . . . . . . . . . . .
`4.2.2 Electric Field Characterization . . . . . . . . . . . . . . . . . . . . .
`ii
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`29
`30
`38
`38
`39
`41
`44
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`47
`47
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`4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`4.3.1 Effect of Inter-Electrode Spacing . . . . . . . . . . . . . . . . . . . .
`4.3.2 Effect of Electrode Geometry and Size . . . . . . . . . . . . . . . . .
`4.3.3 Effect of Current Amplitude . . . . . . . . . . . . . . . . . . . . . . .
`4.3.4 Circular Electrode Array ECT . . . . . . . . . . . . . . . . . . . . .
`4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`4.4.1 Role of Electrode Size, Geometry, and Inter-Electrode Spacing . . .
`4.4.2 Role of Current Amplitude . . . . . . . . . . . . . . . . . . . . . . .
`4.4.3 ECT Can be Made as Focal as MST . . . . . . . . . . . . . . . . . .
`4.4.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`4.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`5 Electric Field Depth–Focality Tradeoff in TMS
`5.1
`Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.2 Electric Field Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.2.1 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.2.2 Electric Field Characterization . . . . . . . . . . . . . . . . . . . . .
`5.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.4.1 Electric Field Depth–Focality Tradeoff . . . . . . . . . . . . . . . . .
`5.4.2
`Strategies for Controlling Electric Field Focality . . . . . . . . . . .
`5.4.3
`Strategies for Controlling Electric Field Depth . . . . . . . . . . . .
`5.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`6 Coil Design Considerations for Deep TMS
`6.1
`Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6.2 Electric Field Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6.2.1 Head Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6.2.2
`dTMS Coil Models . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`iii
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`99
`102
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`6.2.3 Electric Field Computation . . . . . . . . . . . . . . . . . . . . . . .
`6.2.4 Coil Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . .
`6.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6.3.1 Effect of Coil Size
`. . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6.3.2 Comparison of Coil Configurations . . . . . . . . . . . . . . . . . . .
`6.3.3 Timing of Coil Windings
`. . . . . . . . . . . . . . . . . . . . . . . .
`6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6.4.1
`Stimulation Strength, Depth, and Focality Tradeoffs . . . . . . . . .
`6.4.2
`Safety and Tolerability of dTMS . . . . . . . . . . . . . . . . . . . .
`6.4.3 Energy Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6.4.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`7 TMS Coil with Electronically Switchable Active and Sham Modes
`7.1
`Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`7.2 Sham Coil Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`7.2.1 Electric Field Computation . . . . . . . . . . . . . . . . . . . . . . .
`7.3 Switchable Figure-8 and Quadrupole Coils . . . . . . . . . . . . . . . . . . .
`7.3.1 Coil Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . .
`7.4 Comparison Electric Field Characteristics . . . . . . . . . . . . . . . . . . .
`7.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`7.5.1 Coil Performance Comparison . . . . . . . . . . . . . . . . . . . . . .
`7.5.2
`Implementation Considerations . . . . . . . . . . . . . . . . . . . . .
`7.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`II
`
`Individualization of Stimulus Strength
`
`141
`143
`144
`144
`152
`154
`157
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`159
`161
`162
`163
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`165
`165
`168
`168
`169
`169
`170
`172
`172
`173
`174
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`175
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`8 Effect of Anatomical Variability on Electric Field Characteristics in ECT
`and MST
`177
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`Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8.1
`8.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8.2.1 Parametric Head Model
`. . . . . . . . . . . . . . . . . . . . . . . . .
`8.2.2 ECT Electrode and MST Coil Configurations . . . . . . . . . . . . .
`8.2.3 Model of ECT in Rhesus Monkey . . . . . . . . . . . . . . . . . . . .
`8.2.4 Electric Field Characterization . . . . . . . . . . . . . . . . . . . . .
`8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8.3.1 Nominal Head Model
`. . . . . . . . . . . . . . . . . . . . . . . . . .
`8.3.2 Effect of Anatomical Variation . . . . . . . . . . . . . . . . . . . . .
`8.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8.4.1 Comparison between Electric and Magnetic Stimulation . . . . . . .
`8.4.2
`Impact of Anatomical Variation in ECT and MST . . . . . . . . . .
`8.4.3
`Sex-Related Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8.4.4 Age-Related Effects
`. . . . . . . . . . . . . . . . . . . . . . . . . . .
`8.4.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
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`184
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`9 Current Amplitude Adjustment in ECT and MST
`9.1
`Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`9.2 Role of Current Amplitude Individualization . . . . . . . . . . . . . . . . .
`9.3 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`199
`199
`200
`203
`
`III Safety of Device–Device Interactions
`
`10 TMS in the Presence of DBS Implants
`10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`10.1.1 Magnetic Forces on Metal Implants . . . . . . . . . . . . . . . . . . .
`10.1.2 Heating of Implants Due to TMS . . . . . . . . . . . . . . . . . . . .
`10.1.3 Device Electronic Damage . . . . . . . . . . . . . . . . . . . . . . . .
`v
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`10.1.4 Induced Electrode Currents . . . . . . . . . . . . . . . . . . . . . . .
`10.2 Measurement of TMS-Induced Voltages
`. . . . . . . . . . . . . . . . . . . .
`10.2.1 TMS-Induced Voltages in the DBS Leads
`. . . . . . . . . . . . . . .
`10.2.2 IPG Modes of Operation . . . . . . . . . . . . . . . . . . . . . . . .
`10.3 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`10.3.1 TMS-Induced Voltages in the DBS Leads
`. . . . . . . . . . . . . . .
`10.3.2 IPG Current–Voltage Characteristic . . . . . . . . . . . . . . . . . .
`10.3.3 Equivalent Circuit Model of the IPG . . . . . . . . . . . . . . . . . .
`10.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`10.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`11 ECT in the Presence of DBS Implants
`11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`11.2 FEM Models of DBS Electrode Anchoring . . . . . . . . . . . . . . . . . . .
`11.2.1 Head Model & ECT Electrode Configurations . . . . . . . . . . . . .
`11.2.2 DBS Electrode Entry and Anchoring . . . . . . . . . . . . . . . . . .
`11.2.3 Electric Field Simulation and Analysis . . . . . . . . . . . . . . . . .
`11.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`11.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`11.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`12 Thesis Contributions and Future Research Suggestions
`12.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`12.2 Suggestions for Future Research . . . . . . . . . . . . . . . . . . . . . . . . .
`
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`Bibliography
`
`Appendices
`
`A Finite Element Method
`A.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`A.2 Electromagnetic Model Equations . . . . . . . . . . . . . . . . . . . . . . . .
`A.2.1 General Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . .
`A.2.2 Static Solver Solver
`. . . . . . . . . . . . . . . . . . . . . . . . . . .
`A.2.3 Time-Harmonic Solver . . . . . . . . . . . . . . . . . . . . . . . . . .
`A.3 Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`A.4 Iterative Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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`B Coil Configuration Parameters
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`List of Figures
`
`1-1 Number of new published brain stimulation papers indexed on PubMed per
`year (2000–2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`1-2 Transcranial electric and magnetic stimulation . . . . . . . . . . . . . . . .
`1-3 Conceptual framework of the thesis . . . . . . . . . . . . . . . . . . . . . . .
`
`2-1 Simulation models of ECT electrode and MST coil configurations . . . . . .
`2-2 Recorded electric field waveforms and estimated axonal membrane potentials
`for ECT and MST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2-3 Simplified schematic diagram of a conventional biphasic magnetic stimulator
`2-4 Electric field strength relative to neural activation threshold for BL, BF,
`RUL, and FEAST ECT, and CIRC, CAP, and DCONE MST . . . . . . . .
`2-5 Electric field characteristics: maximum electric field, maximum electric field
`relative to neural activation threshold, electric field as a function of depth in
`the brain from the gray matter surface, and directly activated brain volume
`2-6 Comparison of measured and simulated electric field as a function of distance
`from the double cone coil center . . . . . . . . . . . . . . . . . . . . . . . . .
`2-7 Determination of head diamter in nonhuman primates . . . . . . . . . . . .
`2-8 Recorded electric field and simulation comparison, subject 1, BL ECT . . .
`2-9 Recorded electric field and simulation comparison, subject 1, RUL ECT . .
`2-10 Recorded electric field and simulation comparison, subject 1, LUL ECT . .
`2-11 Recorded electric field and simulation comparison, subject 2, BL ECT . . .
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`2-12 Recorded electric field and simulation comparison, subject 2, FEAST . . . .
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`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3-1 EEG electrode layout
`3-2 Wavelet decomposition with an iterated filter bank . . . . . . . . . . . . . .
`3-3 CSD power topography for patient M314, modality: MST, treatment 2 . . .
`3-4 Power topography for patient M314, modality: MST, treatment 2 . . . . . .
`3-5 CSD power topography for patient M317, modality: MST, treatment 2 . . .
`3-6 Power topography for patient M317, modality: MST, treatment 2 . . . . . .
`3-7 CSD power topography for patient M318, modality: ECT, treatment 2 . . .
`3-8 Power topography for patient M318, modality: ECT, treatment 2 . . . . . .
`3-9 CSD power topography for patient M318, modality: ECT, treatment 8 . . .
`3-10 Power topography for patient M318, modality: ECT, treatment 8 . . . . . .
`3-11 CSD power topography for patient M319, modality: ECT, treatment 2 . . .
`3-12 Power topography for patient M319, modality: ECT, treatment 2 . . . . . .
`3-13 CSD power topography for patient M320, modality: ECT, treatment 2 . . .
`3-14 Power topography for patient M320, modality: ECT, treatment 2 . . . . . .
`3-15 CSD power topography for patient M323, modality: ECT, treatment 2 . . .
`3-16 Power topography for patient M323, modality: ECT, treatment 2 . . . . . .
`3-17 CSD power topography for patient M323, modality: ECT, treatment 8 . . .
`3-18 Power topography for patient M323, modality: ECT, treatment 8 . . . . . .
`3-19 CSD power topography for patient M324, modality: ECT, treatment 2 . . .
`3-20 Power topography for patient M324, modality: ECT, treatment 2 . . . . . .
`3-21 CSD power topography for patient M325, modality: ECT, treatment 2 . . .
`3-22 Power topography for patient M325, modality: ECT, treatment 2 . . . . . .
`3-23 CSD power topography for patient M325, modality: ECT, treatment 8 . . .
`3-24 Power topography for patient M325, modality: ECT, treatment 8 . . . . . .
`3-25 CSD power topography for patient M326, modality: ECT, treatment 2 . . .
`3-26 Power topography for patient M326, modality: ECT, treatment 2 . . . . . .
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`3-27 CSD power topography for patient M326, modality: ECT, treatment 8 . . .
`3-28 Power topography for patient M326, modality: ECT, treatment 8 . . . . . .
`3-29 CSD power topography for patient M329, modality: ECT, treatment 2 . . .
`3-30 Power topography for patient M329, modality: ECT, treatment 2 . . . . . .
`3-31 CSD power topography for patient M329, modality: ECT, treatment 8 . . .
`3-32 Power topography for patient M329, modality: ECT, treatment 8 . . . . . .
`3-33 CSD power topography for patient M330, modality: ECT, treatment 2 . . .
`3-34 Power topography for patient M330, modality: ECT, treatment 2 . . . . . .
`3-35 CSD power topography for patient M331, modality: ECT, treatment 8 . . .
`3-36 Power topography for patient M331, modality: ECT, treatment 8 . . . . . .
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`4-1 Simulation models of parametrized ECT electrode and MST coil configurations 98
`4-2 Cross-sectional profiles of the electric field strength induced in the brain
`relative to neural activation threshold for the symmetric and asymmetric
`ECT electrode configurations at 2 cm and 15 cm inter-electrode spacing, as
`well as for DCONE MST . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`4-3 Effect of electrode configuration, size, inter-electrode spacing, and current
`amplitude on the electric field characteristics
`. . . . . . . . . . . . . . . . .
`4-4 Circular coil MST and circular electrode array ECT . . . . . . . . . . . . .
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`5-1 Simulation models of 52 TMS coil configurations . . . . . . . . . . . . . . .
`5-2 Induced electric field distribution on the brain surface by the 52 TMS coils
`5-3 Examples of electric field characterization for the double-cone, 90 mm circu-
`lar, and (c) MRI x- (or y-) gradient coils . . . . . . . . . . . . . . . . . . . .
`5-4 Electric field focality quantified by the half-value spread, S1/2, as a function
`. . . . . . . . . . . . . .
`of the half-value depth, d1/2, for the 52 TMS coils
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`5-5 Volume of the brain sphere region that is exposed to an electric field as
`strong as or stronger than half-maximum, V1/2, and area of brain surface
`region where the electric field is as strong as or stronger than half-maximum,
`A1/2, as a function of half-value depth . . . . . . . . . . . . . . . . . . . . .
`5-6 Electric field S1/2–d1/2 locus for the MagVenture MST twin coil for inter-loop
`opening angles ranging from 90° to 180° . . . . . . . . . . . . . . . . . . . .
`
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`6-1 Cutaway views of the crown and C-core coil models . . . . . . . . . . . . . .
`6-2 Simulation models of seven TMS coil configurations and the corresponding
`electric field distribution in the brain: Magstim 90 mm circular coil, Brain-
`sway H1 coil, crown coil, Magstim 70 mm figure-8 coil, Neuronetics iron core
`142
`figure-8 coil, Magstim double cone coil, and stretched C-core coil
`. . . . . .
`6-3 Crown and C-core coil performance as a function of target depth and coil size 150
`6-4 Relative performance of crown and C-core coils of various sizes for stimulation
`of targets at depths of 2–6 cm . . . . . . . . . . . . . . . . . . . . . . . . . .
`6-5 Optimal C-core coil angle γoptimal that minimizes the energy delivered to the
`coil for stimulation target depths of 2–6 cm . . . . . . . . . . . . . . . . . .
`6-6 Performance metrics of the seven TMS coil configurations for stimulation
`target depths of 2–6 cm . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6-7 Evaluation of pulse sequences for temporal summation . . . . . . . . . . . .
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`7-1 Simulations of TMS coils in active and sham mode: figure-8 coil, quadrupole
`coil with coplanar windings, and quadrupole coil with stepped windings . .
`7-2 Electric field characteristics of the figure-8, quadrupole coils (coplanar and
`stepped) in active and sham modes . . . . . . . . . . . . . . . . . . . . . . .
`7-3 Cortical electric field distributions of the figure-8 and quadrupole coils in
`active and sham modes
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`8-1 Simulation models of human and nonhuman primate ECT electrode and MST
`coil configurations
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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`8-2 Electric field characteristics of ECT and MST in the nominal head mode . .
`8-3 Electric strength and focality comparison between human and nonhuman
`primate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8-4 Sensitivity of ECT and MST electric field characteristics to head tissue thick-
`ness and conductivity variations . . . . . . . . . . . . . . . . . . . . . . . . .
`8-5 Lumped-circuit models of the electric field induced by ECT and MST . . .
`
`9-1 ECT and MST current amplitude adjustment to compensate for head tissue
`layer thickness and conductivity variations.
`. . . . . . . . . . . . . . . . . .
`
`10-1 Electromagnetic induction by TMS in a DBS system . . . . . . . . . . . . .
`10-2 Effective DBS circuit including the TMS induction voltage source . . . . . .
`10-3 Measurement of TMS-induced voltages . . . . . . . . . . . . . . . . . . . . .
`10-4 Induced IPG voltage and lead current with external voltage . . . . . . . . .
`10-5 IPG current–voltage characteristic in various modes of operation . . . . . .
`10-6 Equivalent IPG circuit model for externally-induced currents
`. . . . . . . .
`
`11-1 Three DBS electrode anchoring methods: ring and cap, linear 4-hole titanium
`microplate, and titanium burr-hole cover . . . . . . . . . . . . . . . . . . . .
`11-2 Coronal views of the simulated electric field distribution of BL, RUL and BF
`ECT with intact skull, and change of electric field strength relative to intact
`skull model for ring-cap, microplate, and burr-hole DBS electrode anchoring
`models.
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`11-3 The maximum electric field strength and stimulation focality for BL, RUL,
`and BF ECT with various DBS electrode anchoring methods
`. . . . . . . .
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`List of Tables
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`. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2.1 Head model parameters
`2.2 Estimated neural membrane depolarization factor and neural activation thresh-
`old . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`16
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`27
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`8.1 Nominal human and nonhuman primate head model parameters
`
`. . . . . .
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`Acknowledgments
`
`I have benefited enormously from the interaction and collaboration with many mentors, col-
`leagues, and friends; they have provided me with a well-rounded graduate school experience.
`Accordingly, I take this opportunity to express my appreciation to them all.
`Foremost, it is with immense gratitude that I acknowledge the guidance of my advisor,
`Professor Angel Peterchev. I have had the privilege of being his first doctoral student and
`we have accomplished a great deal in our collaboration. Over the years, Dr. Peterchev
`has guided my research directions and developed my abilities to study new and exciting
`problems. He has also tirelessly edited many drafts of my manuscripts, proposals, etc. This
`dissertation is incalculably better due to his valuable input and advice.
`I am indebted to Professor Sarah Lisanby, for recognizing the clinical significance of this
`work. She has cultivated an multidisciplinary environment in which engineers can work side
`by side with neuroscientists and psychiatrists to better understand the brain and develop
`novel technology for treating psychiatric disorders. This interdepartmental collaboration
`effort truly represents a synergy of professional specialties.
`I am appreciative of Professor Ken Shepard for serving as my co-advisor and dissertation
`sponsor.
`I would also like to acknowledge the other members of my defense committee,
`Professors Harish Krishnaswamy and Christine Fleming, for their enormous generosity in
`the midst of busy schedules and for their votes of confidence.
`This work has benefited more than I can account from the many helpful discussions
`with Drs. Andrew Krystal, Richard Weiner, Moacyr Rosa, Shawn McClintock, Mustafa
`Husain, and Stefan Götz. Special thanks to Dr. Bruce Luber for his big help, and, on
`critical occasions, emergency backup help. I offer grat