GRADUATE SCHOOL OF BIOMEDICAL ENGINEERING
Computational Models of Electroconvulsive Therapy and Transcranial Direct Current Stimulation for Treatment of Depression
Siwei Bai
Dissertation submitted in fulfillment of the requirements for the degree of Doctor of Philosophy
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'3,/~ .3/~rJ. .. . COPYRIGHT STATEMENT 'I hereby grant lhe Unwersity of New South Wales or its agents the righ1 to arcllive and to make available my thesis Of dissertation In whole or part in the Unll/ersity libraries in all forms of medta now or here after known. subject to the provisions of the Copyright Act 1968. I retain all proprietary nghts, such as patent rights. I also retain the right to use in future works (such as articles or Docks) all or part of this thests or aissertation I also authorise Univers~y Microfilms to use the 350 word abstract of my thesis In Dissertation Abstract International (this is applicable to doctoral theses only) I have either used no substantial portions of copyright material in my thesis or I have obtained permission to use copyright material: where permission has not been granted I have applied/will apply for a partial restriction of the digital copy of my thesis or dissertation ' Signed ...... ~ ...... Date .. l ~~~}/~.' L ...... AUTHENTICITY STATEMENT 'I certiiy thal the Library deposit digital copy js a direct equivalent of (he Final officially approved version of m·y thesis. No emendation of content has occurred and if there are any minor variations in formatting, they are the resuH of the conversion to digital format.' Signed ...... _ fu...... ~ ...... d/o~/.U/~ Data ...... ···-··· .Z...... ,...... The Brain — is wider than the Sky — For — put them side by side — The one the other will contain With ease — and You — beside — The Brain is deeper than the sea — For — hold them — Blue to Blue — The one the other will absorb — As Sponges — Buckets — do — The Brain is just the weight of God — For — Heft them — Pound for Pound — And they will differ — if they do — As Syllable from Sound — — Emily Dickinson i Acknowledgements As the ending of this latest stage of my educational journey approaches, it is a great pleasure to reminisce about these bygone bittersweet days, and give respect to the kind people who shared with me this journey. Above all, it would not have been possible to write this doctoral thesis without the help, support and patience of my principal supervisor, A/Prof. Socrates Dokos, not to mention his advice and unsurpassed knowledge in the field of computational modelling. The invaluable advice and support from my co-supervisor, Prof. Colleen Loo, has been of great significance throughout the tenure of my PhD candidature, for which I am extremely grateful. I would like to acknowledge the financial, academic and technical support of the University of New South Wales and its staff, particularly in the University International Postgraduate Award that provided the necessary financial assistance for this research. I also owe sincere and earnest thankfulness to the Graduate School of Biomedical Engineering, where I spent one of the most precious four-year periods in my life, for their indispensable support and assistance since the beginning of my postgraduate work in 2009, especially the current Head of School, Prof. John Whitelock, who kindly chaired my annual review panel and offered me many constructive suggestions. I am most grateful to Dr. Elizabeth Tancred and A/Prof. Pascal Carrive for their benevolent support and encouragement during my study of the neuroanatomy course. I would like to offer my gratitude to Prof. Caroline Rae and Dr. John Geng from Neuro- science Research Australia for their support in acquiring and processing the magnetic resonance imaging data, and to Dr. Angelo Alonzo and Dr. Donel Martin for their assistance in determining electrode placements for transcranial direct current stimula- ii tion. Amongst my fellow postgraduate students in the Graduate School of Biomedical Engineering, the guidance I received from Dr. Amr Al Abed and Dr. Andrew Sims in finite element analysis, as well as the help from Mr. Umar Ansari in the troubleshoot- ing of LATEX problems, has been extremely valuable. Moreover, I am obliged to many others of my friends and colleagues — Huaying Chen, Tianruo Guo, Jane Li, Anjali Sheahan, Bill Cheng, Hamza Toor, Brandon Bosse, Adrian Bradd, Yisang Guo, Stig Schnell, etc. — for their support and encouragement throughout. For any errors or inadequacies that may remain in this work, of course, the responsibility is entirely my own. Last, but by no means least, I would like to thank my parents for their endearing love and unequivocal support as always, for which my mere expression of thanks does not suffice. iii Abstract Electroconvulsive therapy (ECT) and transcranial direct current stimulation (tDCS) are two important forms of transcranial electrical stimulation in clinical psychiatry. They have shown impressive therapeutic results in the treatment of major depression and other psychiatric disorders. The aim of this thesis was to develop novel computational models of ECT and tDCS to assist in the further understanding of these two brain- stimulation techniques, to explore possible refinements and improvements in treatment efficacy. Head models of three different subjects were reconstructed from corresponding computed tomography (CT) or magnetic resonance imaging (MRI) scans. One was a low-resolution model rendered from a set of CT scans, incorporating skull conductivity anisotropy. The other two were high-resolution models reconstructed from MRI scans, with one incorporating white matter conductivity anisotropy. In both high-resolution models, several brain cortical regions of interest were segmented and defined; these are known to be involved in therapeutic or adverse stimulation outcomes. In one set of simulations, these structural head models were taken to be passive volume con- ductors, to investigate the effect of various electrode montages on the distribution of current density or electric field within the head. Results showed that current distribu- tion in the brain was highly dependent on the electrode placement on the scalp. For example, when simulating three different right unilateral (RUL) ECT montages, the non-conventional montages with an electrode on the forehead appeared to have supe- riority over conventional RUL, because stimulation strength was stronger in regions believed responsible for the treatment efficacy, such as the anterior cingulate gyrus, and was weaker in regions that have been speculated to exert adverse effects, such as iv the hippocampus. In addition, a continuum active model of neural excitation was also developed to simulate direct activation of the brain following an ECT stimulus. This model was integrated into the passive head model to investigate the influence of different electrode placements, as well as the time-dependent effects of ECT stimulus parameters on brain activation. For instance, when the stimulus pulse width was reduced, maximum current density was unchanged but the spatial extent of activation was reduced. Moreover, results showed that stimulus frequency influenced the stimulus efficiency, that is, of all the brain neurons that were able to be directly activated by a single pulse, 80%, 10% and 0% were capable of being activated by both of two consecutive pulses with frequencies of 60 Hz, 90 Hz and 120 Hz, respectively. v Abbreviations In alphabetical order: 2D two-dimensional 3D three-dimensional ACC anterior cingulate cortex AH amygdala and hippocampus AP action potential BA Brodmann area BDF backward differentiation formula BF bifrontal BFC bias field corrector BSE brain surface extractor BT bitemporal CB cerebellum CSF cerebrospinal fluid CT computed tomography DBS deep brain stimulation vi DC direct current DLPFC left dorsolateral prefrontal cortex DT-MRI diffusion tensor MRI EC extracephalic ECT electroconvulsive therapy EEG electroencephalography E-field electric field FA fractional anisotropy FE finite element FES functional electrical stimulation FF-RUL frontofrontal RUL fMRI functional MRI FP-RUL frontoparietal RUL GABA γ-aminobutyric acid GM gray matter HD-tDCS high-definition tDCS HH Hodgkin-Huxley LTD long-term depression LTP long-term potentiation MDD major depressive disorder MP membrane potential vii MRI magnetic resonance imaging NIfTI Neuroimaging Informatics Technology Initiative NMDA N-Methyl-D-aspartate OCC occipital OFC orbitofrontal cortex PVC partial volume classifier PW pulse width ROI region of interest rTMS repetitive transcranial magnetic stimulation RUL right unilateral SO supraorbital SP-RUL supraorbital-parietal RUL tACS transcranial alternating current stimulation tDCS transcranial direct current stimulation tES transcranial electrical stimulation TMP temporal TMS transcranial magnetic stimulation TP-RUL temporoparietal RUL TRD treatment-resistant depression tRNS transcranial random noise stimulation WM white matter viii Contents Acknowledgements i Abstract iv Abbreviations vi Table of Contents ix List of Figures xiv List of Tables xvii I Background and Methods 1 1 Introduction 3 1.1 Motivation ...... 3 1.2 Thesis aims and contributions ...... 4 1.3 Thesis overview ...... 5 1.4 Publications ...... 5 2 Background 7 2.1 Depressive disorders ...... 7 2.2 Electroconvulsive therapy ...... 8 2.3 Transcranial direct current stimulation ...... 14 2.4 Anatomy of the human head ...... 19 ix 2.5 Bioelectric principles ...... 26 2.5.1 Volume conductor theory ...... 26 2.5.2 Ionic models of excitable cells ...... 28 3 Computational Models of Transcranial Electrical Stimulation 32 3.1 Early analytical models ...... 32 3.2 Numerical models ...... 34 3.2.1 FE spherical models ...... 35 3.2.2 Low-resolution models with coarse realistic anatomy ..... 38 3.2.3 High-resolution anatomically accurate head models ...... 39 3.3 Summary ...... 44 4 Development of Novel Computational Models of Transcranial Electric Stim- ulation 47 4.1 Reconstruction of low-resolution head model ...... 47 4.1.1 Image segmentation ...... 47 4.1.2 Finite element mesh generation ...... 48 4.2 Reconstruction of high-resolution head models ...... 50 4.2.1 Image segmentation ...... 50 4.2.2 Finite element mesh generation ...... 55 4.3 Tissue conductivities ...... 55 4.3.1 Skull conductivity ...... 56 4.3.2 White matter conductivity anisotropy ...... 58 4.4 Passive volume conductor model ...... 60 4.5 Active excitable tissue model of brain ...... 63 II Results and Discussion 67 5 ECT Simulations with Low-resolution Head Model 69 5.1 ECT stimulus configuration ...... 69 5.1.1 Electrode placements ...... 69 x 5.1.2 Stimulus Parameters ...... 70 5.2 Data analysis ...... 71 5.3 Results ...... 71 5.3.1 Anisotropic skull BF simulation ...... 71 5.3.2 Anisotropic skull BT simulation ...... 73 5.3.3 Anisotropic skull TP-RUL simulation ...... 75 5.3.4 Variation in stimulus parameters ...... 76 5.4 Discussion ...... 78 5.4.1 Model Formulation ...... 78 5.4.2 Comparison of three ECT electrode placements ...... 80 5.4.3 Effects of variations in stimulus amplitude and pulse width . . 83 5.4.4 Model limitations ...... 84 6 ECT Passive Volume Conductor Simulations in the High-resolution Head 86 6.1 Computational settings and data analysis ...... 86 6.1.1 Boundary conditions for volume conductor solver ...... 86 6.1.2 Electrode placements ...... 87 6.1.3 Data analysis ...... 90 6.2 Results ...... 90 6.2.1 Healthy subject head model with white matter isotropy .... 90 6.2.2 Healthy subject head model with white matter anisotropy . . . 95 6.2.3 Depressive subject head model ...... 100 6.3 Discussion ...... 105 6.3.1 ECT electrode montages and clinical implications ...... 105 6.3.2 Model validation and limitations ...... 106 7 ECT Brain Activation Simulations using a High-resolution Head 109 7.1 Model settings and data analysis ...... 109 7.1.1 Model setup ...... 109 7.1.2 Data analysis ...... 110 7.2 Results ...... 111 xi 7.2.1 Variation in ECT stimulus frequency ...... 111 7.2.2 Variation in ECT pulse type ...... 114 7.2.3 Variation in ECT pulse width and amplitude ...... 117 7.3 Discussion ...... 117 7.3.1 Effects of ECT stimulus frequency ...... 118 7.3.2 Effects of ECT pulse type ...... 120 7.3.3 Effects of ECT stimulus pulse charge ...... 122 7.3.4 Model implications and limitations ...... 123 8 tDCS Volume Conductor Simulations with High-resolution Head Geome- try 125 8.1 Model settings and data analysis ...... 125 8.1.1 Boundary conditions for volume conductor model ...... 125 8.1.2 Electrode placements ...... 126 8.1.3 Data analysis ...... 127 8.2 Results ...... 130 8.3 Discussion ...... 139 8.3.1 Clinical implications of electrode montages ...... 139 8.3.2 Model validation and limitations ...... 141 9 Conclusions and future work 144 9.1 Thesis contributions ...... 144 9.2 Future work ...... 145 Bibliography 148 Appendices 176 A MATLABR Script for Conductivity Tensor Import 177 B Rotation Transformation of a Rectangular Cuboid 181 xii C Formulation of Ion Currents 184 xiii List of Figures 2.1 ECT treatment ...... 9 2.2 Typical ECT electrode montages...... 11 2.3 The current profile of a conventional ECT stimulus...... 12 2.4 Transcranial direct current stimulation...... 15 2.5 10-20 system EEG electrode placements...... 18 2.6 The current profile of a typical tDCS stimulus...... 19 2.7 A human skull...... 21 2.8 Shape and location of major dural reflections...... 22 2.9 A human brain...... 23 2.10 Brodmann’s areas...... 24 2.11 A ventricular system...... 26 2.12 Derivation of Equation 2.4...... 28 3.1 The geometry of the three-layered sphere model...... 33 3.2 Coronal slice of E-field in a sphere ECT model...... 37 3.3 High-resolution model from Datta et al...... 40 3.4 E-field distribution in the anisotropic head model from Lee et al. . . . 45 4.1 Segmentation of low-resolution realistically shaped head model. . . . 49 4.2 Segmentation of HEAsub head model...... 53 4.3 Segmentation of DEPsub head model...... 54 4.4 Frontal and lateral view of the shoulder-extended HEAsub model. . . 55 4.5 Fibres of white matter shown after FSL computation...... 60 xiv 4.6 Comparison between constant current and constant voltage boundary conditions...... 62 4.7 Active neural single-compartment model defined within the 3D brain region...... 64 5.1 Biphasic ECT stimulus current waveform...... 70 5.2 Extracellular current density magnitude in the brain of three conven- tional electrode placements...... 72 5.3 Time course of direct neuronal excitation induced by BF ECT. .... 73 5.4 Simulated MPs in the brain with three conventional electrode placements. 74 5.5 Simulated MPs at four different locations in the brain for BF ECT. . . 74 5.6 Snapshots of neuronal excitation in BT and TP-RUL ECT simulations. 75 5.7 Snapshots of neuronal excitation in TP-RUL ECT model with different PW...... 76 5.8 MP of the brainstem region (medulla) in TP-RUL ECT during biphasic stimulation...... 77 5.9 Snapshots of neuronal excitation in BT ECT model and TP-RUL ECT models...... 77 5.10 Extracellular current density magnitude on the brain surface with isotropic skull model...... 80 5.11 Brainstem activation with the extended medulla...... 83 6.1 Five electrode placements tested on HEAsub head model...... 88 6.2 Five electrode placements tested on DEPsub head model...... 89 6.3 Brain E-field magnitude distribution in the HEAsub WM isotropic model. 92 6.4 Brain E-field magnitude distribution in the HEAsub WM isotropic model in two coronal slices...... 93 6.5 Brain E-field magnitude distribution in the HEAsub WM isotropic model in two horizontal slices...... 94 6.6 Brain E-field magnitude distribution in the HEAsub WM anisotropic model...... 96 xv 6.7 Brain E-field magnitude distribution in the HEAsub WM anisotropic model in two coronal slices...... 97 6.8 Brain E-field magnitude distribution in the HEAsub WM anisotropic model in two horizontal slices...... 98 6.9 E-field magnitude distribution in the DEPsub model...... 101 6.10 E-field magnitude distribution in the DEPsub model in two coronal slices.102 6.11 E-field magnitude distribution in the DEPsub model in two horizontal slices...... 103 7.1 Average MP over the first two cycles for three different stimulus fre- quencies...... 112 7.2 ECT stimulus waveform and MP within activated region with different stimulus frequencies...... 113 7.3 Average MP over the first two cycles with stimuli of different pulse type.115 7.4 ECT stimulus waveform and MP within activated region with different pulse directionality...... 116 8.1 tDCS electrode placement part 1...... 128 8.2 tDCS electrode placement part 2...... 129 8.3 E-field magnitude distribution in the whole brain with various tDCS montages part 1...... 131 8.4 E-field magnitude distribution in the whole brain with various tDCS montages part 2...... 132 8.5 E-field magnitude distribution in the brain in two coronal slices part 1. 134 8.6 E-field magnitude distribution in the brain in two coronal slices part 2. 135 8.7 E-field magnitude distribution in the brain in two horizontal slices part 1.136 8.8 E-field magnitude distribution in the brain in two horizontal slices part 2.137 B.1 Vector rotation...... 182 xvi List of Tables 4.1 +ScanFE mesh parameters for VHsub ...... 48 4.2 Mesh statistics of head models...... 49 4.3 Segmentation parameters for the BrainSuite toolboxes ...... 51 4.4 +FE mesh parameters of high-resolution models ...... 56 4.5 Tissue conductivities ...... 57 4.6 Skull conductivity anisotropy ...... 57 4.7 White matter conductivity anisotropy ...... 60 5.1 ECT stimulus parameters ...... 70 6.1 Average brain regional E-fields in the ‘HEAsub’ model with WM isotropy (V/m) ...... 95 6.2 Average brain E-fields in the ‘HEAsub’ model with WM anisotropy (V/m) ...... 99 6.3 Relative E-field difference with and without WM anisotropy (%). . . . 100 6.4 Average brain regional E-fields in the ‘DEPsub’ model (V/m) ..... 104 7.1 ECT stimulus parameters ...... 110 7.2 Average HH membrane potentials for various ECT stimulus modes + frequencies...... 111 7.3 Effect of ECT stimulus frequency on ROI activation for two activation modes ...... 114 7.4 Effect of stimulus type on ROI activation for two activation modes . . 117 7.5 Effects of stimulus pulse width and amplitude on ROI activation . . . 118 xvii 8.1 Average E-field magnitude for all tDCS configurations (mV/cm) . . . 138 8.2 Average E-field magnitude in the ACC (mV/cm) ...... 138 C.1 Parameter values for active brain tissue ...... 185 C.2 Initial values for active brain tissue ...... 185 xviii Part I Background and Methods 1 I felt a Funeral, in my Brain, And Mourners to and fro Kept treading – treading – till it seemed That Sense was breaking through – And when they all were seated, A Service, like a Drum – Kept beating – beating – till I thought My Mind was going numb – And then I heard them lift a Box And creak across my Soul With those same Boots of Lead, again, Then Space – began to toll, As all the Heavens were a Bell, And Being, but an Ear, And I, and Silence, some strange Race Wrecked, solitary, here – And then a Plank in Reason, broke, And I dropped down, and down – And hit a World, at every plunge, And Finished knowing – then – — Emily Dickinson 2 Chapter 1 Introduction 1.1 Motivation Major depressive disorder (MDD) is one of the most common psychiatric disorders, having a high rank among the main causes of illness-related disability [1]. Electro- convulsive therapy (ECT) has been an important strategy in the treatment of various psychiatric disorders including MDD, and there is now great interest in investigating other brain stimulation techniques for therapeutic neuromodulation or neurostimula- tion. Two prominent methods involving transcranial electrical stimulation (tES): tran- scranial direct current stimulation (tDCS) and ECT, have been significant in clinical practice and research. ECT delivers a train of alternating electric pulses into the brain via electrodes placed onto the scalp, producing a generalised seizure [2]. tDCS, a non- invasive form of brain stimulation, adopts a relatively low magnitude, non-convulsive constant DC current through patch electrodes placed against the head [3]. It is worth noting that tES has also involved a type of repetitive transcranial electrical stimulation, which is used to evoke motor potential for intraoperative monitoring [4]. Decades of empirical research and clinical experience have led to the emergence of novel brain stimulation techniques and improvements in existing brain stimulation techniques, but the mechanisms underlying how variations in treatment technique can lead to different efficacies and side effects (especially in ECT) are poorly understood. Imaging studies have provided some important information on the effects of tES on 3 cerebral blood flow and metabolism, but these give indirect evidence of patterns of neuronal depolarisation. Additionally, the difficulty in carrying out functional imaging during application of large transcranial currents precludes the complete characterisa- tion of electrical activation of the brain during the therapy. With the rapid maturation of mathematical and computational modelling tech- niques, a proliferation of modelling studies on brain stimulation have been published, which have provided useful information on current distribution profiles in the head. However, much information is still missing, necessitating further model refinements and development in several key areas, including incorporation of active neural excita- tion and detailed anatomical features. 1.2 Thesis aims and contributions The aims of this thesis were to develop accurate computational models to assist in the analysis of mechanisms underlying ECT and tDCS. Major contributions of this thesis were: 1. a low-resolution head model was reconstructed from computed tomography (CT) scans, incorporating skull anisotropic electrical conductivity; 2. two different high-resolution head models were reconstructed from correspond- ing magnetic resonance imaging (MRI) scans, with careful segmentation of a three-layer skull in both models, and the incorporation of white matter (WM) anisotropic electrical conductivity in one head model; 3. a systemic comparison of the effects of various simulated ECT and tDCS elec- trode montages used or proposed in existing clinical studies; 4. a continuum active ionic formulation was developed to represent bulk properties of excitable neurons in the brain, and was incorporated into the head models to simulate direct brain activation during ECT. This facilitated the simulation of the effects of various stimulus parameters on the spatial extent of brain activation. 4 1.3 Thesis overview This thesis describes the development of computational models to simulate transcranial current flow and/or brain activation during ECT and tDCS. The thesis chapters are structured as follows: Chapter 2 provides background knowledge on MDD, and the two types of tES — ECT and tDCS. It also provides basic outlines of the gross anatomy of the human head and bioelectric principles. Chapter 3 provides a comprehensive review of existing computational models of tES, including their contributions and shortcomings. Chapter 4 details the development of computational head models for ECT and tDCS simulations. Details regarding electrical properties of head tissues and computa- tional boundary conditions are also included in this chapter. Chapter 5 presents simulated comparisons among three conventional ECT elec- trode montages from a low-resolution model incorporating active brain tissue. Chapter 6 presents simulated comparisons among three conventional and two novel ECT electrode montages in two high-resolution models, with one model incor- porating WM anisotropy. Chapter 7 presents results of varying ECT stimulus parameters using a high- resolution head model with WM anisotropy incorporating active brain tissue. Chapter 8 explores a systemic comparison of various tDCS electrode montages which have been utilised or proposed in existing clinical studies using the high-resolution head model with WM anisotropy. Chapter 9 summarises the main contributions and conclusions of this thesis, and proposes some directions for future development. 1.4 Publications Below is a list of journal publications and referred conference proceedings resulting from the work of this thesis: 5 1. Bai S, Loo C, Al Abed A, Dokos S. A computational model of direct brain exci- tation induced by electroconvulsive therapy: Comparison among three conven- tional electrode placements. Brain Stimulation. 2012; 5(3), 408–421. 2. Bai S, Loo C, Dokos S. Effects of electroconvulsive therapy stimulus pulsewidth and amplitude computed with an anatomically-realistic head model. In: Con- ference Proceedings IEEE Engineering in Medicine and Biology Society, 2012 (accepted). 3. Bai S, Loo C, Geng G, Dokos S. Effect of white matter anisotropy in modeling electroconvulsive therapy. In: Conference Proceedings IEEE Engineering in Medicine and Biology Society, 2011; p. 5492-5495. 4. Bai S, Loo C, Dokos S. Electroconvulsive therapy simulations using an anatomically- realistic head model. In: Conference Proceedings IEEE Engineering in Medicine and Biology Society, 2011; p. 5484-5487. 5. Bai S, Loo C, and Dokos S. A computational model of direct brain stimulation by electroconvulsive therapy. In: Conference Proceedings IEEE Engineering in Medicine and Biology Society, 2010; p. 2069–2072. 6 Chapter 2 Background 2.1 Depressive disorders As a term in daily use, depression is usually considered synonymous with a low mood or feeling sad. But as a mental disorder, depression refers to a wide variety of psychic and somatic syndromes in addition to these emotions [1]. According to the Diagnostic and Statistical Manual of Mental Disorders [5], in order to diagnose MDD, five (or more) of the nine symptoms characterising depression must be present concurrently during a 2-week period, with the core symptom being a depressed mood and/or a loss of interest in usually enjoyable activities. Depressive disorder is one of the most common psychiatric disorders. The lifetime prevalence of depression for adults in most countries varies within the range 8–12%, reaching up to 16.9% in the US [6]. In Australia, the statistics in 2007 revealed that the 12-month prevalence rate was 4.1% [7]. The disorder is common across different cultures. For example, at least 5% of individuals were found to have suffered from depression in China [8]. It is predicted that the prevalence of depression will increase in the coming years [9], and by 2020 MDD will be the second most frequent illness in industrialised countries [1]. MDD has a high rank amongst the main causes of illness-related disability. Patients with depression generally suffer from insomnia, an inability to maintain healthy relationships with friends and family, an inability to work and pessimism about the future [9]. In addition, existing studies also show that around 7 20% of patients with MDD eventually committed suicide [9, 10]. The etiology of depression is still far from being completely understood, but it most likely consists of factors which are contributing to the neuronal changes seen in affected individuals [1,11]. Studies on the anatomical and physiological basis of MDD suggested that deficiencies of neurotransmitters, damage to neurons and a loss of con- nectivity were primarily found in the limbic structures, reward circuits, hypothalamus and the anterior temporal cortex [12, 13]. Hypotheses regarding deficiencies in the monoamine or neuroendocrine systems have been proposed [1,11]. In addition, stress- ful, disruptive life events which arouse negative emotions may also trigger episodes of depression [1]. The most common treatments for MDD are psychotherapy, adjustment of life fac- tors where possible, and anti-depressant pharmacotherapy [1]. Although antidepres- sant treatment is mainly used in patients with severe depression, at least one third of these patients fail to respond to standard interventions [14, 15], which is gener- ally recognised as treatment-resistant depression (TRD). Patients undergoing TRD are more likely to develop other psychiatric disorders and disabilities, and have a higher suicide risk [16, 17]. One established treatment for TRD is ECT [18]. 2.2 Electroconvulsive therapy ECT involves the passage of serial alternating electric pulses through the brain via electrodes placed on the scalp, producing a generalised tonic-clonic seizure [2], as shown in Figure 2.1. It has been known to be one of the most effective treatments for TRD, with remission rates ranging from 20% to 80% depending on the treatment technique [1,18]. It is also used as a treatment for patients with other severe psychiatric disorders including bipolar disorder, psychosis and schizophrenia. In the United States, the rates of ECT use per annum are up to 80 patients per 10,000 people [19]. The annual rate of ECT use in Victoria, Australia, is up to 40 per 100,000 people [20], whereas in Asia, including Hong Kong, the rate is less than 5 per 100,000 people [21]. Though exact rates may vary between countries, ECT remains an essential treatment 8 Figure 2.1: A patient receiving ECT treatment, with various monitoring and stimulating electrodes. Reproduced from Fink [22]. option for severe depression throughout the world. Introduced by the Budapest psychiatrist Ladislas Meduna in the 1930s, convulsive therapy was initially induced chemically by pentylenetetrazol [23]. Yet this therapy was a frightening procedure for patients, and was complex to administer. Electric stim- uli were hence resorted to as an alternative to seizure induction. In 1938, the first ECT on a human patient was successfully performed by Ugo Cerletti and Lucio Bini [23]. At that time, due to muscular convulsions in ECT, bone fracture was a principal risk of the treatment, and therefore patients had to be restrained by a sheet over the chest and abdomen. Thanks to the introduction of muscle relaxant in the 1950s, the prob- lem of motor convulsions was thereafter eliminated [22, 23]. Thereafter, ECT steadily gained in popularity, but concerns regarding side effects of the treatment remained. 9 In the 1950s, following the discovery of successful novel medications to treat psychi- atric diseases, the use of ECT was gradually reduced by the mid-1960s [1, 22, 23]. Nevertheless, the problem of TRD and other medication-resistant disorders remained. Thus ECT has continued to be used in clinical practice, with a particularly role as a highly effective treatment for depressive patients who were unresponsive to antide- pressants [24]. Two task forces were formed in 1975 and in 1990 by the American Psychiatric Association, in order to study and promote the use of ECT [25, 26]. By the mid-1990s, the role of ECT as a secondary (and even as a primary) treatment for severe psychiatric disorders was firmly established [22, 23]. During modern ECT, the patient is under anesthesia and breathing is controlled by an anaesthetist (known as anesthesiologist in US) with high concentrations of oxy- gen provided. Physiological characteristics of the patient are also monitored, includ- ing heart rate, blood pressure, blood oxygen levels, muscle activity and brain activ- ity [2, 22, 27]. The electric current stimulus is delivered through flat round electrodes, usually 5 cm in diameter, conventionally applied either bilaterally (bitemporal, known as BT, and bifrontal, known as BF), or unilaterally on the right (right unilateral, known as RUL) [2, 22], as shown in Figure 2.2. The electrodes are usually attached to the scalp, and electrolyte gel is used to increase the conductance of the skin-electrode interface. The degree of treatment efficacy as well as side effects is dependent on elec- trode configuration. RUL ECT has been shown to cause less short-term memory loss than BT ECT, but is less clinically effective when given at the same electrical dose rel- ative to seizure threshold [28, 29]. Alternatively, some (but not all) studies have found that BF ECT causes fewer memory side effects than BT ECT [30–33]. In terms of the stimulus waveform, a series of alternating brief pulses with a pulse width (PW) of 0.5– 2 ms is typically adopted, as shown in Figure 2.3. Sometimes, ultrabrief pulses having a PW less than 0.5 ms are used, since clinical studies using ultrabrief-pulse protocols have reported similar efficacy to brief-pulse ECT with fewer side effects [34–36]. The amplitude of the stimulus is conventionally kept at 800 or 900 mA, and the energy level of the stimulus, a.k.a the stimulus ‘dose’, is commonly individualised according to the patient’s age [37] or seizure threshold [38], which is the minimal level of energy 10 Figure 2.2: Typical electrode montages used in clinical ECT application: bifrontal (BF), bitemporal (BT) and right unilateral (RUL). ‘A’ and ‘B’ are labels for the separate electrodes in each montage. required to initiate a seizure. The stimulus dose can be calculated from the following equations: Q = A × PW, (2.1) N = 2 × f × D, (2.2) Q = Q × N. (2.3) Eq. 2.1 calculates the total charge delivered by a single pulse Q , where A is the amplitude of the stimulus. Eq. 2.2 calculates the total number of pulses N delivered in one session, where f is the pulse-pair frequency, and D is the duration of stimulus. Eq. 2.3 calculates total electric charge Q, or stimulus dose. The parameters of a typical ECT stimulus waveform are also shown in Figure 2.3. Even though a number of studies have been dedicated to elucidating the mecha- nisms underlying ECT, knowledge of its neurobiological basis is still inconclusive. It has been proposed that it is the biochemical and physiological consequences of the seizure which are responsible for the therapeutic effects of ECT [1]. ECT-induced seizures trigger the release of neurotransmitters and neurohormones, induce neuroplas- ticity and initiate anticonvulsant effects that terminate the seizure [22, 39]. However, the exact causes of efficacy, as well as the adverse effects of ECT, have yet to be dis- covered. There is evidence that different electrode montages (BT, BF, RUL) differ in their therapeutic and neurocognitive effects [28–30]. These different electrode mon- tages initially activate different sites of the brain due to the direct effect of the stimulus, 11 Figure 2.3: The current profile of a conventional ECT stimulus. A, PW , f and D are the amplitude, pulse width, pulse-pair frequency and duration of the stimulus, respectively. and this may be important in determining efficacy outcomes and side effects [40]. As revealed in electroencephalography (EEG) and imaging studies, different selective fo- cal networks may be activated by different forms of ECT [41–44]. This finding also adds evidence to the hypothesis regarding direct activation. As a result of these uncer- tainties, mechanisms underlying ECT efficacy are still a topic of active study. The death rate for ECT is extremely low: about 1 per 10,000 patients [27]. The cognitive side effects of ECT, however, are of such significance as to be given serious consideration in the treatment process. These effects include transient confusion, as well as anterograde and retrograde amnesia, with the latter being most persistent. It has been suggested that the confusion and the anterograde amnesia typically disap- pear soon after ECT, but retrograde amnesia may persist several months with often incomplete recovery [1,27,45]. Other adverse effects of ECT include headaches, mus- cle ache, fatigue, nausea, and vomiting. In addition, ECT may also interfere with the patient’s cardiac rhythm and induce arrhythmia [1, 45]. In seeking to improve the efficacy and reduce the adverse effects of the treatment, continual efforts have been made to refine ECT since its nascency, including changing the stimuli from sine wave to brief pulse and ultra-brief pulse waveforms [46–49], the introduction of new electrode configurations (RUL [50, 51] and BF [52]), as well as seizure threshold titration to provide individualised dosage [38]. Even to this day, studies are conducted to explore potentially important stimulus parameters to improve 12 ECT, such as electrode placement, amplitude, PW, frequency and stimulus duration [53, 54]. In 1994, a left anterior right temporal electrode placement was proposed, in the hope of interfering less with cognitive behaviour [55]. As shown in Figure 2.3, the conventional ECT stimulus is a train of biphasic (bidi- rectional) pulses. There had been early studies that reported that the use of monophasic (unidirectional) pulses had the benefits of lower seizure threshold, better efficacy and less adverse effects [56–60], but their results were inconclusive due to the possible influence of other stimulus parameters in those studies. Nonetheless, the findings of recent repetitive transcranial magnetic stimulation (rTMS) studies [61–66] compar- ing biphasic and monophasic stimuli have rekindled interest in the use of monophasic stimuli. A novel form of ECT, focal electrical administered seizure therapy, which combines unidirectional stimulation with a novel electrode configuration, has there- after been investigated [67–69]. In the quest for an appropriate RUL montage, d’Elia [70–72] originally proposed three different placements: temporoparietal RUL (TP-RUL) which is widely accepted today, frontofrontal RUL (FF-RUL) and supraorbital-parietal RUL (SP-RUL). While FF-RUL may not be preferred due to the likelihood of high current shunting due to the short inter-electrode distance, SP-RUL is still a potential treatment approach. The rationale for this alternative electrode placement is that stimulation of the hippocam- pus would be minimised compared to the TP-RUL placement, thus possibly resulting in a lesser risk of memory loss. This was one of the original electrode placements considered for RUL ECT [70, 71] but was abandoned in favour of the TP-RUL place- ment which is now known as the d’Elia placement, because it was more difficult to elicit seizures in some patients with the SP-RUL placement. This reflects the prevalent treatment methodology at the time, when ECT was given with fixed parameter settings (using machines where the voltage rather than current was set), instead of electrical dosing being determined for each individual, based on empirical estimation of his/her seizure threshold. The combination of the fixed dosing method (without adjustment for individual seizure threshold or electrode placement), and use of constant voltage rather than constant current machines, meant occasional treatment sessions in which seizures 13 were not elicited. Given that resistance is higher with the SP-RUL placement than the TP-RUL placement, missed seizures were more common with the former [70, 71], leading to the gradual widespread adoption of the TP-RUL placement. Many clini- cal ECT centres now titrate each individual’s seizure threshold and give RUL ECT at a dose relative to the individual’s threshold. Further, modern ECT machines deliver a constant current, varying the voltage to accommodate the patient’s impedance. Thus, it is now possible to induce effective seizures with the SP-RUL placement. It is possible that efficacy and cognitive outcomes may be superior with this placement compared to the commonly used d’Elia placement, but this has been minimally investigated. On the other hand, alternative methods of stimulation have also been investigated, in the hope of finding a new approach having the same efficacy, but with fewer side effects. These include rTMS, magnetic seizure therapy, tDCS, vagus nerve stimulation, and deep brain stimulation (DBS). Of these techniques, tDCS has perhaps the greatest potential for translation into clinical practice, as it involves a relatively simple, non invasive and economical procedure. To date, though the effect size and speed of action of rTMS and tDCS are still not comparable to those of ECT [1, 45]. While these approaches offer promise for the future, ECT continues to play a significant role in the acute treatment of TRD and other severe psychiatric disorders. 2.3 Transcranial direct current stimulation A constant direct current (DC) is a flow of electrical charge whose magnitude and di- rection remains unchanged. tDCS is a noninvasive form of brain stimulation which employs a relatively low magnitude, non-convulsive constant DC current targeted to the cerebral cortex through patch electrodes against the head [3], as shown in Figure 2.4. Side effects include slight itching at the electrode site, and sometimes skin irrita- tion/burn, headache, fatigue and nausea [73]. It has been increasingly investigated over the past few years as a potential candidate for the treatment of psychiatric disorders. Historically, the inception of weak electrical current stimulation began in the late 18th century, when Giovanni Aldini reported successful treatment of a melancholic 14 Figure 2.4: Transcranial direct current stimulation. patient with application of DC to the head [74]. Since the 1960s, systemic studies were undertaken to investigate the effects of tDCS on depression, using experimental protocols fundamentally different from those in use today [3]. A pilot study with anodal tDCS, employing two frontal electrodes bilaterally with a third one on the leg, reported that anodal tDCS improved the mood of subjects in half of all cases [75]. Although beneficial effects of tDCS in the treatment of depression were reported in some subsequent studies [76–80], others failed to find any significance [81]. Overall, these studies provided inconsistent findings, presumably due to limitations in protocol designs, due to stimulation technique and validation of the treatment [3,74]. As a result of the development of ECT, and later the discovery of effective neuropsychiatric drugs, tDCS was progressively abandoned. The turning point happened in the late 1990s, when it was discovered that weak di- rect currents were able to penetrate the skull and stimulate the vestibular system [82], and that TMS could directly test cortical motor area excitability by using induced motor-evoked potentials as a marker [83]. Evidence was thus provided in a later study that weak DC could maintain its ability to influence brain excitability [84], and this 15 finding was soon substantially confirmed and expanded in another study in 2000 [85]. Recently, preliminary antidepressant efficacy has been shown in double-blinded, sham- controlled studies [86–89]. Furthermore, a comparison between tDCS and antidepres- sant medication showed that tDCS had similar but faster beneficial effects compared to pharmacological treatment [90]. tDCS is performed with a DC generator delivering a constant current. A poten- tiometer is embedded in series with the DC source to adjust for the desired current, whose amplitude usually ranges from 0.5–2 mA [4]. The current is applied via two relatively large rubber electrodes attached to the scalp with saline-soaked sponges. No metallic electrodes are used, to avoid electrochemical polarisation [91]. The size of the electrodes is usually 25–35 cm2 in area, with large electrodes to avoid skin burns [92]. Skin preparation is often performed to reduce impedance [91, 93]. In contrast to ECT, the current density in the brain following tDCS is to too low to induce direct neuronal firing [3, 94]. Therefore, it has been speculated that tDCS may somehow modulate the firing rate of cortical neurons, i.e. the cortical excitability. The findings of several pharmacological studies have suggested that tDCS exerts its effects on cortical excitability mainly by depolarising or hyperpolarising the membrane poten- tials of cortical neurons [95,96]. In addition, as indicated by imaging and EEG studies, tDCS can also induce widespread effects throughout the brain as well as changes in brain synchronisation, including activation via interneuronal circuits [97, 98]. The current in tDCS flows in a single direction, from the anode (positively charged electrode), to the cathode (negatively charged electrode). Thus, based on the func- tioning electrode that is placed over the targeted cortical area, tDCS is classified into ‘anodal’ or ‘cathodal’ [3]. These two types of tDCS appear to have different effects on cortical excitability. Studies have suggested that anodal tDCS enhances the activity of neurons, whereas cathodal tDCS suppresses it [85,99,100]. An increase in regional blood flow was also reported in the anodally stimulated region in a recent imaging study [101]. Another study on tDCS reported that the concentration of γ-aminobutyric acid (GABA, an inhibitory neurotransmitter) decreased after anodal tDCS, whereas those of both GABA and glutamate (an excitatory neurotransmitter) decreased after 16 cathodal tDCS [102]. However, the exact cause of this phenomenon is still unknown. It can be interpreted either as a result of glutamatergic neurons depolarised by an- odal stimulation and hyperpolarised by cathodal stimulation, or as a consequence of GABAergic neurons hyperpolarised by anodal stimulation and depolarised by cathodal stimulation [85,94,102]. Another hypothesis is that since cortical neurons are oriented perpendicularly to the cortical surface, an inward electric field under the anode can hyperpolarise their dendrites but depolarise their axons, and thus this mode of stim- ulation is excitatory. In comparison, an outward electric field under the cathode can hyperpolarise the axons but depolarise the dendrites, thus suppressing the excitabil- ity [103, 104]. Nevertheless, a very weak DC (< 0.5 mA) was found to result in reduced excitability in anodal tDCS but elevated excitability in cathodal tDCS [84]. In addition, weak DC can only selectively influence cortical interneurons, but a strong stimulus intensity can also modify the excitability of pyramidal cells [103, 105, 106]. Therefore, precise mechanisms on how tDCS exerts its modulation effects on cortical excitability are yet to be clarified. In modern tDCS studies on the treatment of depression, the electrode montage is commonly anodal stimulation to the left dorsolateral prefrontal cortex (DLPFC), which means the anode is placed over the F3 electrode site on a 10-20 system EEG cap (see Figure 2.5) [3]. As it has been demonstrated that in depressive patients, left DLPFC is hypoactive while right DLPFC is hyperactive [107], the therapeutic rationale is thus to restore the balance between left and right DLPFCs. However, this rationale is still hypothetical [108]. The cathode, often named the ‘reference electrode’, is generally placed on the contralateral side of the head. It has also been suggested that an extra- cephalic reference electrode may be more efficacious, since it can increase the focality of tDCS by avoiding the confounding effects due to opposite polar electrodes on the head [109, 110]. The duration of the stimulus in tDCS usually lasts for 10–20 minutes per session, with the current amplitude kept at a constant value [3]. The current is commonly ramped up and down, as shown in Figure 2.6, at the beginning and the end of the treatment, to reduce cutaneous sensation and avoid retinal phosphenes [91]. In order 17 Figure 2.5: 10-20 system EEG electrode placements. Nasion and inion are two anatomical landmarks for the positioning of EEG electrodes. Adapted from Malmivuo and Plonsey [111]. to achieve after-effects, it is necessary to stimulate for at least 3 minutes at an intensity of 1 mA with an electrode size of 35 cm2, or at least 5 minutes at 0.6 mA with the same electrode size [85]. N-Methyl-D-aspartate (NMDA)-receptors appear to be a vital factor of this after-effect, since an NMDA antagonist can eliminate the after-effect of both anodal and cathodal tDCS [95]. On the contrary, an NMDA agonist can prolong this after-effect [112]. It is generally believed that greater stimulus durations can lead to longer lasting effects, but recent data contradicts this by showing that there appears to be an upper limit for the stimulus duration to sustain the excitatory after-effects from anodal stimulation, with cathodal stimulation expected to exhibit a similar pattern [92]. In modern tDCS studies, a sham technique is commonly utilised to produce effective blinding [3, 91], for example constituted of 10 seconds of ramping and 30 seconds of stimulus at a fixed current amplitude. As both the mechanism and efficacy of tDCS are still under exploration, further studies need to be devoted to various aspects of tDCS, such as the optimal electrode montage and the optimal stimulation protocol to achieve maximum efficacy. In the meantime, two variations of tDCS are also under investigation: transcranial random noise stimulation (tRNS) and transcranial alternating current stimulation (tACS) [92]. The former adopts a random noise signal with no DC offset, whose amplitude val- 18 Figure 2.6: The current profile of a typical tDCS stimulus. A and tstim are the stimulus amplitude and the actual stimulus duration, respectively, and tramp is the duration of the current ramping up/down. ues follow a normal distribution with 99% within ±500 μA. The frequency spectrum of the signal is 0.1–640 Hz, and its sampling rate is 1280 samples per second. It was discovered that tRNS possessed at least the same therapeutic potential as anodal tDCS, without the polarity effect [113]. It has been reported that with tACS, utilising a sinusoidally oscillating current with no DC offset at a low frequency (≤50 Hz), a measurable efficacy can hardly be detected, presumably due to a very weak current intensity (0.4 mA) [114]; however, at 140 Hz and 1 mA intensity, it appears to be at least as effective as anodal tDCS and tRNS at the same intensity and duration [115]. 2.4 Anatomy of the human head The scalp, bordered by the face anteriorly and the neck laterally and posteriorly, covers the vault of the skull [116]. It consists of five layers. The topmost layer is skin, in which sabaeceous glands and hair follicles are embedded. The layer below is connective tissue, a layer of fat and fibrous tissue that contains blood vessels and nerves. The third layer is a fibrous sheet, and the fourth layer is loose areolar tissue. The bottommost layer is pericranium, which covers the surface of the skull [116,117]. The face includes the skin at the topmost layer, followed by connective tissue with blood vessels and nerves, and finally muscles controlling facial expression and mastication [116]. The skull is the skeletal structure of the head, comprised of the cranium and mandible (shown in Figure 2.7), both of which join at the temporomandibular joint. The cranium, 19 separated by the sutures, consists of 8 cranial bones that enclose the brain, and 13 facial bones [116, 117]. The highest point of the skull is the vertex, which is the midpoint of the mid-sagittal line over the head between the nasion (identified as the center of the depression at the root of the nose) and the inion (identified as the most prominent point of the external occipital protuberance). The foramina in the skull allow entry of the blood vessels and exit of the nerve fibres (and the spinal cord at the foramen magnum) [118]. The skull is typically made up of three layers: compact bone as the outermost and innermost layers, with a spongy bone layer in between. The compact bone layer is hard and dense, and is usually of fixed thickness throughout the cranium. In comparison, the spongy bone is a lighter and porous layer that is more vascular and contains bone marrow, with uneven thickness in the cranium [119,120]. The skull also contains paranasal sinuses, which are air spaces lined by mucous membranes that help to reduce the weight of the skull [116, 119]. The brain is wrapped in protective membranous coverings known as meninges: the dura mater, arachnoid and pia mater [122]. The dura mater is a tough, white, fibrous connective tissue that adheres to the inner surface of the skull. At several places the inner dural layer folds into the cranial cavity, and thus forms dural reflections, as shown in Figure 2.8. The venous sinuses, into which the cerebral veins drain, can be found inside some edges of these dural reflections. The arachnoid is attached to the inner surface of the dura mater, and the pia mater directly covers the brain [119, 122]. The cerebrospinal fluid (CSF) fills the subarachnoid space, a narrow space between the arachnoid and the pia mater, and provides buoyancy to the brain. It enters the venous circulation through small invaginations of the arachnoid called arachnoid villi [122]. The brain, as shown in Figure 2.9, consists of three parts: the forebrain, midbrain and hindbrain [122]. The hindbrain is made up of the medulla oblongata, pons and cerebellum (CB). The former two, together with the midbrain, form the brainstem, which contains important respiratory and cardiovascular centers and is thus vital to life. The CB is attached to the posterior of the pons. It is significant in the maintenance of equilibrium and the coordination of voluntary movement. The forebrain consists of the telencephalon, i.e. cerebrum, and the diencephalon. The latter, located in front of the 20 Figure 2.7: The lateral and frontal surfaces of the human skull. Adapted from Netter [121]. 21 Figure 2.8: Shape and location of major dural reflections — falx cerebri and tentorium cerebelli. Adapted from Nolte [122]. midbrain, includes the thalamus and the hypothalamus. The thalamus is an important relay station that distributes information to the cerebral cortex through projection fibres in the WM, whilst the hypothalamus is the central control center for the maintenance of homeostasis [119, 122]. The cerebrum is formed by two cerebral hemispheres joined by a massive bundle of WM termed the corpus callosum [122]. Each hemisphere contains a sheet of gray matter (GM) at the top, known as the cerebral cortex. The cortex is the site where the highest level of neural processing occurs. It ranges from 2.5–4 mm in thickness and contains 10–20 billion neurons [122]. It is highly folded, and thus it has a large surface to volume ratio. The grooves in the cortex are called sulci, and the bumps between the sulci are known as gyri. The basic pattern of sulci and gyri is similar in all human brains. Based on some sulci which act as important landmarks, the cortex can be divided into five lobes [119, 122, 123], as shown in Figure 2.9: 1. Frontal lobe: located anterior to the central sulcus. It contains the primary motor cortex and Broca’s motor speech area (in the dominant hemisphere). 2. Temporal lobe: located inferior to the lateral sulcus. It includes the primary 22 Figure 2.9: The lateral surface (upper row) and medial cut surface (lower row) of the human brain. Adapted from Nolte [122]. auditory cortex, primary olfactory cortex and Wernicke’s receptive speech area (in the dominant hemisphere). It also contains the hippocampus, which serves as the center for memory consolidation. The amygdala, which plays a primary part in emotional responses, is also located in this lobe. 3. Parietal lobe: situated between the central and parieto-occipital sulci. It contains the primary somatosensory cortex. Wernicke’s area also extends up into this lobe in the dominant hemisphere. 4. Occipital lobe: located posterior to the parieto-occipital sulcus. It is entirely dedicated to vision. 5. Insula: buried in the depths of the lateral sulcus. There are two main types of neurons in the cortex: stellate cells, which act as in- terneurons, and pyramidal cells [122]. Based on the pattern of cellular lamination, the cortex can be divided into the neocortex which has six layers and occupies 90% of 23 Figure 2.10: Brodmann’s areas defined on the divided human cerebral cortex. Taken from Nolte [122]. the cortex, the archicortex which forms the hippocampus and has three layers, and the paleocortex in the olfactory areas. The stellate cells are usually predominantly in the superficial layer of the cortex, whereas the pyramidal cells are mostly in the deeper layer [122, 123]. Based on the cytoarchitectural organisation of neurons in the cortex, the cortex can be divided into 52 areas, each called a Brodmann area (BA) [122], as shown in Figure 2.10. These constitute a widely accepted mapping system. Cortical areas are specialised for different functions. Broadly speaking, the cere- bral cortex can be divided into [122, 123]: 1. Motor areas: related to movement. Lesions can result in paralysis or a form of apraxia. 2. Primary sensory areas: receive discrete sensory input. Each contains a map of its 24 specific sensory input and is involved in the initial perception and localisation of particular sensory stimuli. Lesions may cause loss in specific sensory perception. 3. Association areas: mediate higher levels of information processing. They can be subdivided into unimodal and multimodal association areas. Unimodal as- sociation areas are located adjacent to primary sensory areas, and receive infor- mation specifically related to that particular sensory modality. Lesion can result in a form of agnosia. Multimodal association areas integrate information from multiple regions of the cortex, and are related to high-level perceptual and in- tellectual functions. An important association area, the prefrontal cortex, which is a major part of the reward circuit, is concerned with the executive functions of the brain: planning, insight, foresight and personality. The prefrontal cor- tex includes the DLPFC (BA9, BA10 and BA46) and orbitofrontal cortex (OFC: BA11) [122, 124]. 4. Limbic areas: includes the hippocampus and the amygdala as two central com- ponents, as well as the anterior cingulate cortex (ACC: BA24, BA32 and BA33). Beneath the cortex is a thick layer of WM. It is made up of three types of fibre: projection fibres which link the cortex in both directions with subcortical structures such as the thalamus, brainstem and spinal cord, commissural fibres that connect parts of the two hemispheres, and association fibres that interconnect cortical neurons in the same hemisphere [122, 123]. Embedded within the WM, masses of GM, known as basal ganglia, perform an important role in the control of movement [122]. A large cavity known as the lateral ventricle is present in each hemisphere. It consists of an an- terior horn, a body, a posterior horn, an inferior horn and an atrium where the body and the posterior and inferior horns meet. The lateral ventricle communicates on each side with the third ventricle in the diencephalon through the interventricular foramen. The third ventricle then connects to the fourth ventricle between the pons and CB through the cerebral aqueduct in the midbrain, with a narrow central canal in the medulla at- tached to the fourth ventricle. These cavities thus form the ventricular system of the brain [122], as shown in Figure 2.11. CSF is secreted mainly by the choroid plexus 25 Figure 2.11: The shape and position of the ventricular system in the brain, seen from the left (A), front (B), above (C) and below (D). Adapted from Nolte [122]. in the ventricles, and enters the subarachnoid space through the median and lateral apertures of the fourth ventricle [122]. The blood supply to the brain drains from both the internal carotid artery and the vertebral arteries [119, 122]. The branches of the internal carotid artery provide blood for rostral parts of the brain and form the anterior circulation, whereas those of verte- bral arteries supply the caudal regions of the brain and constitute the posterior circula- tion. The two circulation networks then form an anastomotic system of arteries at the base of the brain which is referred to as the Circle of Willis [119, 122, 123]. 2.5 Bioelectric principles 2.5.1 Volume conductor theory Bioelectromagnetism is the study of electric, magnetic and electromagnetic phenom- ena arising from living cells, tissues or organisms. In the field of bioelectromagnetism, biological tissues are generally considered as ‘volume conductors’, in which the in- 26 ductive component of the impedance is neglected, and resistances, capacitances and batteries are distributed throughout a three-dimensional (3D) region [111]. In the low-frequency band, in which the frequency of internal bioelectric events lies, capacitive and electromagnetic propagation effects can be neglected [125, 126], implying that bioelectric currents and voltages in living tissues can be considered as stationary [127], known as the quasi-static approximation. A recent modelling study by Bossetti et al. [128] investigated the difference in neural activation between solv- ing the quasi-static field approximation and solving the full inhomogeneous Helmholtz equation using square-pulse current stimuli. They found that for commonly used stim- ulus parameters, the exact solution for the potential (including capacitive tissue effects) can be well-approximated by the quasi-static case. Given the relatively low values of permittivity and magnetic permeability in living tissue, the quasi-static approximation can therefore be employed in computational head models. Within an infinitesimal homogeneous volume conductor of side lengths Δx, Δy and Δz and electric conductivity σ, we assume there exists a source of current with volumetric current density of i Amperes per unit volume (see Figure 2.12). Assuming an electric field (E-field) of strength E established throughout the conductor, the net current flow out of the conductor, as a result, must satisfies ∇ · J = i, (2.4) where J is the current density generated by the E-field (see Figure 2.12). Based on Ohm’s law, it satisfies J = σE. (2.5) Under the quasi-static condition, the E-field E is defined as the gradient of the electric potential ϕ, that is E = −∇ϕ. (2.6) Therefore, Equation 2.4 can be rewritten as ∇ · (−σ∇ϕ)=i. (2.7) Equation 2.7 is known as Poisson’s equation. 27 Figure 2.12: Derivation of Equation 2.4. J is a vector field representing the current density and i is the scalar volumetric current source within the cube. Jx, Jy and Jz are the scalar components of J on the corresponding Cartesian axes x, y and z. Δx, Δy and Δz are the corresponding edge lengths of the cube. In Equation 2.7, i is a description of non-conservative current that represents bio- electric activity arising from the intracellular domain of excitable cells [111]. There- fore, outside the region of excitable cells, i is zero. In a typical passive volume con- ductor model, where tissue excitability is ignored, i is zero. Thus, Equation 2.7 can be written as ∇ · (−σ∇ϕ)=0. (2.8) Equation 2.8 is known as Laplace’s equation. 2.5.2 Ionic models of excitable cells Nerve cells and muscle fibres are known as excitable cells, which indicates that their cell membranes are capable of generating transient all-or-none electrochemical im- pulses as a result of stimulation, conducting these impulses along the membrane [111, 122]. The voltage difference across the cell membrane is known as the membrane po- tential (MP). The MP vm is defined as the difference between intracellular potential vi 28 and extracellular potential ve, i.e., vm = vi − ve. (2.9) At rest, The MP is held at a relatively stable negative value, known as the rest- ing potential. The resting potential is maintained predominantly by two mechanisms: 1) the Na+/K+-ATPase, also known as the sodium-potassium exchange pump, which exchanges two potassium ions (K+) from the extracellular space with three sodium ions (Na+) from the intracellular space, resulting in a net loss of positive charge from the intracellular space; and 2) transmembrane potassium-selective leak channels which allow a slow facilitated diffusion of K+ out of the cell. When excitable cells are under stimulation, their MP undergoes change. There are two types of stimulation: excitatory or depolarising, which results in the MP becoming more positive, and inhibitory or hyperpolarising, which leads to an increase in the magnitude of the negative resting MP. If the stimulus is not strong enough to cause the MP to reach threshold, the membrane behaviour is subthreshold and passive. However, if the stimulus is sufficient and the MP is able to reach threshold, an overshoot in the MP can thus be recorded, known as the action potential (AP). As such, the cell is activated. This activation is then capable of propagating along the axon in both directions from the stimulus site. The conduction velocity depends on geometrical and electrical properties of the axon. Numerous mathematical models have been proposed to simulate the behaviour of excitable cells. They range from simple resistant-capacitance models which simulate subthreshold behaviour to complex ionic models which include multiple ionic currents, from single-cell models to multi-compartmental cable-like models [111]. Of these, the simple mathematical model proposed by Hodgkin and Huxley represents one of the most influential attempts in simulating the activation of neurons. Despite its simple form with only four ionic current components, this model is still able to accurately simulate many membrane properties. The Hodgkin-Huxley (HH) model was based on results of their voltage-clamp ex- periments on squid giant axons [129]. In this model, the total current im across the 29 membrane is composed of four components: dv i = i + i + i +C m , (2.10) m Na K L m dt + + where iNa, iK and iL represent Na ,K and leakage currents respectively. The last component in Equation 2.10 is the capacitive current, in which Cm represents the mem- brane capacitance per unit area. The leakage current refers to non-specific ions, and is mainly constituted from chloride ions (Cl−). These ionic currents were given by the following equations: iNa = gNa(vm −VNa) , iK = gK(vm −VK) (2.11) iL = gL(vm −VL) + + where VNa, VK and VL are the reversal potentials for Na ,K and leakage currents, respectively, and gNa, gK and gL are the corresponding membrane conductances, which describe the ionic permeability of the membrane. Reversal potentials in Equation 2.11 are defined by the Nernst equation: ion = −RT ci , Vion ln ion (2.12) zF co where R, T and F are the gas constant, absolute temperature and Faraday’s constant, respectively, Vion and z are the reversal potentials and valence of the ion in question, ion ion respectively, and ci and co are the respective ion concentrations in the intra- and extracellular spaces. Since the positive direction of membrane currents and Nernst voltages is chosen to be from intra- to extracellular, VNa has a positive value, whereas VK and VL are negative. Based on the results of voltage-clamp experiments, membrane conductances of Na+ and K+ are functions of MP and time, whereas the leakage conductance is fixed. In the HH model, gNa and gK are expressed in terms of gating variables which control the state of ionic channels: 3 4, gNa = GNam hgK = GKn (2.13) + + where GNa and GK are the maximum membrane conductances for Na and K , re- 30 spectively, and m, h and n are gating variables satisfying dm = α (1 − m) − β m dt m m dh = α (1 − h) − β h . (2.14) dt h h dn = α (1 − n) − β n dt n n In Equation 2.14, α and β are transfer rate coefficients from one state to the other; m and 1 − m are the fractions of Na+ channels in the open and closed state, respectively; h and 1 − h are the fractions of Na+ channels in the non-inactivating and inactivating state, respectively; n and 1 − n are the fractions of K+ channels in the open and closed state, respectively. The transfer rate coefficients are in turn functions of the MP. 31 Chapter 3 Computational Models of Transcranial Electrical Stimulation This chapter presents a critical review of existing computational modelling studies of transcranial electric stimulation, including their advantages and disadvantages, to highlight the need for novel approaches to tES modelling. 3.1 Early analytical models Analytical models, as opposed to numerical models, are mathematical models de- scribed by analytic functions. While analytic models can provide concise previews of system behaviour, they are more suitable for simple geometries as the analytic func- tions can be very complicated in more complex structures. In comparison, numeri- cal models use computational approximation techniques to simulate physical systems. The latter are mostly applied to complex realistic geometries, but in order to acquire accurate results, there is often the need to undergo many iterative calculations. The early stage tES models are often referred to as analytic models [130], although in the calculation of electrical potential they adopted Legendre polynomials to solve differential equations. One such model was developed by Rush and Driscoll in 1969 based on the reciprocity theorem, and was initially used to determine the sensitivity of EEG leads to the location and orientation of the source [131]. It was then applied to 32 Figure 3.1: The geometry of the three-layered sphere model, and its fit to a human head. Reproduced from Rush and Driscoll [132]. investigate current distribution in the brain as a result of stimulus currents from scalp electrodes [132–135], as well as magnetic stimulation from a coil electrode [133, 134, 136]. The model was comprised of a simple geometry of three concentric spherical lay- ers, representing the scalp, the skull and the brain, and each layer was assumed to be homogeneous with isotropic conductivity. The dimensions of the spheres were fit to a human head, as shown in Figure 3.1. For the electrical conductivities, it was suggested that a ratio of about 1/80 for skull versus scalp (and brain) yielded the best fit between the model results and potentials measured within an electrolytic tank containing a half- skull [132]. The tES electrodes were placed according to particular montages under in- vestigation, but there was no clear information on the size of the electrodes [132–135]. The generated electrical potential was expressed as a series of Legendre polynomi- als, and the current density in the brain was calculated as the product of the potential gradient multiplied by brain conductivity. These models, though simple, provided some useful preliminary information re- garding current profiles inside the head [132–135]. Due to the high resistivity of the skull, only a small portion of the injected current could reach the brain [132,133,135]. When the distance between the electrodes was closer, this shunting effect became stronger [132, 135]. This, however, may not be universally true in a realistic head 33 model, due to the complexity of current pathways as a result of complex geometry and electrical properties of realistic head structures [137]. The models also suggested that the E-field in the brain was insensitive to the electrical properties and geometrical structures of the tissues, but was controllable by proper placement of electrodes [133]: the former conclusion was proved erroneous in later studies [137–140]. Despite the fact that only a small percentage of current could penetrate the skull, it was still able to affect all parts of the brain [135]. The area directly under the electrodes was found to have maximal current density, and this density dropped rapidly as the distance from the electrodes increased [133,135]. This observation, however, was challenged by later models which included the geometry of cortical foldings [139]. A comparison mod- elling study between electrical and magnetic stimuli suggested that electrical stimu- lation produced both radial and tangential components, and thus it had the ability to stimulate neurons on the surface that are oriented radially as well as neurons within the sulci which are oriented tangentially. It was also suggested that electrical stimulation produced a more diffuse field compared to magnetic stimulation, because the skull had little influence on the magnetic stimulation [134]. Overall, due to the simplistic nature of these models, they were unable to provide more insights into the features of tES, and some of their findings were later challenged by studies in more realistic models. 3.2 Numerical models With the rapid increase of computational performance, numerical methods have been increasingly applied to simulate almost every physical, chemical and biological pro- cess. For models expressed in partial differential and integral equations, the finite element (FE) method is one of the most popular numerical approaches for solving the models. One of the advantages of the FE method is that it can offer the most desirable approximation when dealing with complex geometries and boundaries compared with other techniques such as finite-difference scheme. 34 3.2.1 FE spherical models Similar to the early analytical models, these FE models also comprised several con- centric spheres representing different compartments of the human head. However, the number of layers in the model varied among the studies with three layers (scalp, skull and brain) remaining the basic structure [141, 142]. A four-sphere head model was developed by adding a shell representing CSF between the skull and brain [143, 144]. By separating the innermost sphere into two concentric spheres to represent GM and WM on top of the four-sphere version, a five-sphere model was described [145, 146]. The dimensions of these spheres were either based on the original Rush-Driscoll sphere model [141,142,144] or on measurements from subjects [143,145,146]. Electrodes on the head were modelled as an extrusion from the surface of the outermost sphere, and were assigned with conductivities corresponding to the electrode materials [141–146]. An inward current boundary condition was applied to the anode, and a potential ground was applied to the cathode, with all external boundaries set as electrically insulat- ing [143]. Again, similar to their predecessors, these models were criticized for their over simplification of the head geometry. In reality, the human head has an irregular ge- ometry and various substructures can alter local electrical impedance, including the orbits, the acoustic meatus and the paranasal sinuses in the skull, as well as the cortical folding and the ventricles of the brain. Some tissues in the head, like WM, also ex- hibit anisotropic conductivity. It has been shown in later modelling studies that due to these complexities, the field distribution is altered greatly, exhibiting greater local non- uniformity in E-field (or current density) [137–140]. Therefore, in order to enhance the accuracy of the E-field simulations, improving the anatomical accuracy of the head models is necessary. In spite of this, these simplified sphere models are still beneficial for making ini- tial evaluations of the effects of different electrode configurations. Electrode config- uration has always been critical in improving electrical brain stimulation protocols. Using these sphere models, the studies simulated bipolar and multi-polar (more than one anode or cathode in use) configurations [141, 144–146]. In Faria et al. [144], 35 the EEG 10-10 system was adopted to mark the placements of the electrodes. Datta et al. [143] also conducted simulations with ring configurations, which utilized one or two ring electrodes enclosing an electrode in the center. These modelling studies demonstrated that when the distance between electrodes was increased, the amount of current shunted on the scalp was reduced. Hence more current was injected into the brain, which led to increased stimulation of deeper structures. Nevertheless, stimulus focality was compromised because stimulated areas in the brain also correspondingly expanded [141, 143, 144]. The studies which investigated multi-polar configurations indicated that the use of multiple anodes and one cathode in cathodal tDCS could en- hance the focality of stimulation [141, 144]. One major contribution of these studies is that they introduced the concept of ‘equivalent current’ [142, 143], identified as the amount of injected current under dif- ferent electrode configurations in order to maintain a constant E-field magnitude (or current density) at the same target point. The idea is based on the hypothesis that effi- cacy is contingent on stimulation of critical cerebral sites above a certain threshold: in order to achieve the efficacy, a threshold strength of E-field has to be reached. Miranda et al. [142] thus investigated an assumption in tDCS studies, that ‘the ratio of the in- jected current to the electrode area (I/A) determines the magnitude of the stimulation effect’. They found out that the ‘equivalent current’ was not in a linear relationship with the area of electrode: in order to keep a constant current density at the target point, the I/A ratio with a small electrode had to be tuned to higher values than that with a larger electrode. In addition, the ‘equivalent current’ is also useful in quantify- ing the shunting effect among various electrode configurations. And since the degree of shunting is different, it might not be appropriate to maintain the total injected current at a constant value in actual practice with different electrode configurations [143]. Another contribution of these modelling studies is that they also quantitatively pre- sented the extent of focality as well as brain activation [53, 144–146]. Focality was calculated by the percentage of brain volume (and surface area) that was exposed to the E-field magnitude (or current density) within 50% of its maximum power [144–146]. Deng et al. [145] examined the influence of DBS devices inside a patient while receiv- 36 Figure 3.2: Coronal slice of E-field relative to neuronal activation threshold for (a) bitemporal ECT, (b) bifrontal ECT, (c) right unilateral ECT and (d) focal electrical administered seizure therapy. The outlines suggests the projected locations of the electrodes. Adapted from Deng et al. [146]. ing ECT by calculating the extent of focality. They found that the E-field distribution was altered due to the presence of DBS devices. They thus recommended that ex- amination should be performed on the integrity of a DBS device, and that electrode placements and stimulus strength ought to be adjusted so as to avoid undesirable out- comes. The extent of brain activation was quantified by the percentage of brain volume with E-field magnitudes exceeding the neuronal activation threshold [53, 146]. The neuronal activation threshold defined the lowest E-field strength required to elicit supra- threshold depolarisation, obtained from empirical data from TMS studies. This thresh- old was also subject to the shape and PW of a stimulus [53,146]. Although the adoption of a neuronal activation threshold may offer some insights into the relationship between the activated brain region and stimulus parameters, it cannot simulate the transient be- havior of the cellular membrane potential, and thus it is unable to investigate the out- comes of varying pulse frequency and duration of an applied stimulus. Furthermore, there is a discrepancy between the estimated areas directly activated based on mod- els using a predefined threshold (shown in Figure 3.2) [146], and areas of activation demonstrated in empirical studies by means of imaging during the stimulus [42–44]. Nevertheless, with this method, Peterchev et al. [53] demonstrated in a review on ECT stimulus parameters that lowering the stimulus amplitude could effectively reduce the volume of activated brain tissue and achieve better focality, highlighting an aspect of ECT stimulation that is often overlooked in the adjustment of stimulus parameters. 37 3.2.2 Low-resolution models with coarse realistic anatomy The last decade of the twentieth century saw rapid improvements in human body vi- sualisation and modelling techniques, which allowed the construction of head mod- els with the ability to represent not only anatomical structure, but also individual patient-specific features [147]. However, due to limitations in computational tools, a model with a comprehensive resemblance of head structure was too large to be used in practical simulations at that time. A ‘simple yet exact’ model of the head was thus adopted [147], i.e., a low-resolution realistically shaped model, whose geometry is non-spherical and realistically shaped but still largely lacks anatomical accuracy, particularly in the compartments that represent the brain structures [140, 147–154]. These low-resolution models were created either by constructive solid geometry de- scription of a head geometry [147], or by extracting the information from a MRI head scan [140, 148–154]. Due to the absence of cortical foldings, ventricles and tissue anisotropy, local non-uniformity of E-field distribution was still not reproducible in the models [137–139]. Therefore, the contribution of these models remains limited. A few modelling studies using low-resolution realistically shaped models have been completed by a group from Boston, USA [140, 152–154]. Their FE model was generated by computer-aided design rendering of an MRI head scan. In their tDCS study, they investigated several electrode montages used in clinical research [140]. Consistent with previous studies that used spherical geometries, the current density magnitude varied significantly across tissue compartments, and the maximum corti- cal current density was substantially lower than maximum scalp current density due to current shunting. Moreover, the models with different electrode sizes demonstrated that greater shunting occurred with smaller electrodes, which is in accordance with Miranda et al. [142]. However, by varying the electrode placement, they reported that the distance between electrodes was a less significant factor on cortical current density magnitude than overall relative location of electrodes on the scalp [140]. The results showed that the cortical current density magnitude was smaller when the electrodes were placed on regions of the scalp with more curvature, and that the cortical current density magnitude was found to be maximum for the montage with the two electrodes 38 being very close while over a location on the cortex with minimal curvature. This is contradictory to what was reported in the sphere models [132,133,135,141,143,144], and thus suggests the advantage of head models employing more realistic geometry. Another contribution of these models was that they were also used to explore the effects of TMS and tDCS in the presence of brain pathology [140, 153, 154]. Wagner et al. [153] initially made a comparison of TMS-induced current density distribution between healthy and stroke head models. Similar comparisons were then made for tDCS current density distribution [140] and TMS for a model with brain atrophy [154]. These models of brain pathology were made by altering the anatomical geometry and electrical conductivity of the brain tissue from the healthy head model. The results showed that the current distribution was significantly altered for stimulation close to the lesion, and the authors suggested that such perturbation in clinical practice may interfere with the treatment outcome, and even pose a danger to patients. The effect of tDCS on stroke was later expanded by a follow-up modelling study using a high- resolution anatomically accurate head model [155]. 3.2.3 High-resolution anatomically accurate head models As noted above, recent modelling studies have showed that E-field distribution is sen- sitive to the geometrical properties of the head model, especially for the brain compart- ments. For instance, several studies have reported that the shunting effects of highly conductive CSF leads to local non-uniformities of current density throughout the brain surface [138,139,156,157]. As a consequence, instead of on the gyri nearest the elec- trode, the maximum E-field is found at localized ‘hot spots’ with some at the base of the sulci [139]. It has also been demonstrated that the ventricular system of the brain can result in preferential current flow due to its higher conductivity [155]. Thus, more and more tES modelling studies have turned to high-resolution anatomically accurate models. These head models were reconstructed from MRI scans of a healthy subject or the patient of interest, with truncation of the model at varying levels below the base of the brain. One research group in New York, USA, has performed a substantial number of 39 Figure 3.3: A: Segmented compartments of the head - scalp, skull, CSF and brain; B.1: FE model using a7×5cm2 rectangular pad configuration; C.1: FE model using a 4×1 ring electrode configuration. The red and blue electrodes represent the anode and cathode, respectively. Adapted from Datta et al. [138]. studies using high-resolution anatomically accurate models. They were the first to dis- cuss in detail the influence of CSF on the distribution of E-field in 3D models [138], al- though similar results were presented earlier with two-dimensional (2D) models [156]. In the same study, they also compared two electrode configurations using a 3D model, as shown in Figure 3.3, and in agreement with previous studies using simpler geome- tries [141, 143, 144], the multi-electrode configuration (4×1) was shown to provide a significant improvement in spatial focality [138]. They also simulated head-tissue tem- perature changes during tDCS using the same head model combined with a bio-heat transfer equation [158], and their results indicated that conventional tDCS protocols merely caused negligible tissue-temperature increments, which failed to explain the occasional skin irritation and skin burn while tDCS was delivered [73]. One important role of these detailed computational models is to identify further re- finements of the stimulation approach which may lead to improved clinical outcomes. These approaches can then be tested empirically in clinical trials. tDCS is reported to enhance rehabilitation training in patients with neuropsychiatric conditions [94]. However, patients with traumatic brain injury or decompressive craniectomy may of- 40 ten have skull defects or skull plates. Datta et al. [159] conducted a comprehensive modelling study on how skull defects may influence the effects of tDCS. They consid- ered two types of skull defects, two types of skull plates, two defect locations relative to the electrodes, as well as various defect sizes. The results indicated that due to the highly resistive nature of the skull, a defect in the skull provided a preferential pathway for current flow to concentrate in the brain. Generally speaking for a small defect, as the size of the defect increases, the maximum cortical E-field increases. Further in- creases in defect size after a certain threshold will lead to the gradual decrease in the peak E-field. Furthermore, the position of electrodes relative to the defect site is also critical to the distribution of the E-field: a small to moderate skull defect directly under the electrode can focus the current to the sub-cortical area, with important clinical and safety implications [159]. tDCS, as well as other brain-stimulation techniques, has shown some promise in pain reduction [160–162]. The effect on pain perception of tDCS was thus investi- gated in two separate studies which combined both computer simulation and clinical trials [163, 164]. One was a pilot study, which examined the effect of high-definition tDCS (HD-tDCS), a modified form of tDCS, to the target site delivered by a single elec- trode, either anode or cathode, surrounded by four ‘return’ electrodes (4×1 rings), so that stimulation at sites other than the target site was minimized [163]. As mentioned previously, tDCS with multiple electrodes can result in focality of current distribution restricted to within the ring perimeter, hence implying improved efficacy. These pre- dictions from modelling were compared with the results of clinical trials, which found that although HD-tDCS showed some impact on pain threshold, the results were still inconclusive. Hence, the clinical applicability of HD-tDCS is yet to be established. The other study compared the influence of three tDCS electrode montages, and the results of experiments and computer simulations together suggested that stimulation of the prefrontal cortex is most beneficial for pain relief [164]. It has been proposed that brain-stimulation treatments should be customized in or- der to provide clinical flexibility and individualized therapy. In addition, any lesion or individual anatomical variation in brain morphology has the ability to alter the current 41 flow [140]. Therefore, an individualized model reconstructed from the MRI scan of the patient of interest, in order to obtain a precise representation of the lesion, is a fea- sible way to predict the possible outcome of treatment. In Datta et al. [155], four tDCS montages with fixed ‘active’ electrode placement but with varied ‘return’ electrode placements were investigated. E-field spatial profiles in the four models were found to be different, with diverse peak values, which indicated that even though the ‘active’ electrode placement remained unchanged, the ‘return’ electrode still exerted impact on the current pathway in the brain. In the same paper, the authors also demonstrated that the influence on current flow was still prominent even when both electrodes were placed away from the lesion [155]. Halko et al. [165] in their paper tested the relation- ship between tDCS induced current flow, which was predicted by computer simulation, and changes in functional activation, which was assessed by functional MRI (fMRI), in a patient with a lesion in the visual cortex. The authors found only partial agreement between the E-field profile and change in fMRI signal, which was located at the ipsile- sional occipital pole. One source of variation may be that the fMRI data was collected before and after stimulation, whereas modelling predicted current density during stim- ulation. Furthermore, fMRI data is also likely to reflect the effects of indirect activation of remote neurons by synaptic transmission, and thus activation maps are unlikely to correspond exactly with current density maps. Moreover, in this study, the effects of sham tDCS could not be distinguished from active tDCS from the fMRI data [165], using a passive volume conductor model. A model that incorporates fast and slow transmembrane kinetic behaviours, with the latter representing long-term synaptic po- tentiation/depression, is desired in order to differentiate between the influence of sham and active stimulation, as well as to compare the different effects of tDCS and tRNS as well as tACS. Sadleir et al. [166] presented a head model with very detailed segmentation, and performed a comparison of tDCS-induced current within various structures in the head. They noted that the orbit and the optic nerve might act as a preferential pathway for current flow into the brain when the electrodes were placed near the forehead, even though phosphenes were not reported with the same montage [91]. However, they 42 appeared to have mistaken a portion of the bone marrow as part of brain tissue 1, which may have resulted in errors in simulation depending on the assigned conductivity [166]. Similar to Sadleir et al. [166], Parazzini et al. [167, 168] also presented a head model with very detailed segmentation, but with more extensive conductivity assignments. In their results, the 99th percentile of the amplitude of E-field and current density in a given brain structure was chosen to be the ‘peak’ value, in order to avoid computational instability. The threshold area was defined as ‘the percentage of surface area where the amplitude of E-field and current density was greater than 70% of its 99th percentile’ [167]. This definition of the threshold area was similar to that of the brain activation extent mentioned earlier; however, the threshold for the brain activation extent was based on the neuronal activation threshold obtained from empirical data in TMS studies [53,146], whereas the threshold of Parazzini et al. [167] appeared to have been chosen arbitrarily. In addition to the geometrical factors of the head model, the electrical properties of head tissue compartments are also an important factor in the accuracy of simulations. It has been demonstrated in isotropic conductivity models that the skull and WM exerted a significant influence on the E-field (or current distribution) in the brain [132, 133, 166]. In reality, several head tissue structures are known to exhibit highly anisotropic electrical conductivity, including the WM, in which water molecules and ions can flow more easily along the fibre tracts than transverse to these [169,170]. On a whole-tissue scale, the skull also exhibits anisotropic conductivity, due to its three-layered structure — a low-resistance spongiform layer between two high-resistance layers [169, 170]. Compared to isotropic models, the anisotropic skull was shown to act as an important barrier to current flow, and therefore a stronger stimulus was required in the model to achieve similar E-field strength at the same target region [171–173]. The E-field spatial profile was more diffuse inside the brain due to the WM anisotropy, with shifted or no 1Fig. 2 of the Sadleir et al. [166] demonstrated the current density distribution in the brain in a series of horizontal slices, with all other head tissues been masked out of the images. From slices 51–75, the long thin structures next to the frontotemporal lobe bilaterally belong to the bone marrow of skull. This structure is often mistaken for brain tissue by automatic segmentation software due to the similarity in pixel intensity shown in MRI scans. 43 clear peak magnitude [156, 171–173]. Nevertheless, the skull in those models was one homogeneous compartment with anisotropic conductivity. In actuality, the skull consists of three layers, and thus a replacement with a three-layered structure may add to the accuracy of the simulation [174]. In Lee et al. [137], the authors simulated several ECT electrode placements using a high-resolution model with WM anisotropy, as shown in Figure 3.4. They quantified the difference between isotropic and anisotropic models using a statistical measure of relative errors. Adding to what has been reported earlier, WM in anisotropic mod- els displayed a strong attraction to current along the fibres when the current flow was partially aligned with the fibre orientation, whereas higher E-field magnitudes were generated due to current flowing transversely to the fibre orientation. Depending on the electrode placement, the difference between isotropic and anisotropic results var- ied, but the difference was typically greater for brain regions further away from the electrodes [137]. 3.3 Summary The geometric complexity of existing computational models of tES varied from sim- ple concentric spherical models to high-resolution models derived from individual MRI scans. Also, electrical properties varied from three or four major isotropic com- partment conductivities to multiple conductivity assignments incorporating anisotropic conductivity. The level of model accuracy mainly depends on the available computa- tional resources, as well as the nature of the problem being investigated. Although high complexity is not always demanded, a model with reasonable anatomical details is still necessary to obtain accurate simulations. These details include cortical folding on the brain surface, the ventricles in the brain, WM anisotropic conductivity, as well as the foramina on the skull, especially the optic canals for the optic nerves. These details are of prime importance when the variation across individualized models is taken into consideration, which, however, was rarely considered in existing studies, until recently. Existing models of tES are mostly passive volume conductor simulations. And 44 Figure 3.4: The E-field distribution in the anisotropic head model for BL (bitemporal), BF (bifrontal), RUL (right unilateral) and FEAST (focal electrical administered seizure therapy) electrode configura- tions. Columns from left to right show horizontal, coronal and sagittal slices, respectively. ‘L’ indicates the left side of the head. Reproduced from Lee et al. [137]. 45 yet, in order to grasp a better understanding of the mechanism of tDCS and ECT, a passive model unable to mimic the slow transmembrane kinetic behaviors is not opti- mal. The adoption of motor threshold in the passive models may offer some insights into the relationship between the modulated/activated brain region and the stimulus amplitude. However, the incorporation of a continuum active neural model would be highly desired, as the effects of alteration in dynamic stimulus parameters such as pulse frequency and pulse width can be explored. Such a model would hopefully re- veal the correlation of brain modulation/activation and the release and dissipation of neurotransmitters. The incorporation of an active model of brain excitation, along with realistic anatomical features and conductance anisotropy, is one of the main contribu- tions of this thesis to tES modelling. 46 Chapter 4 Development of Novel Computational Models of Transcranial Electric Stimulation 4.1 Reconstruction of low-resolution head model 4.1.1 Image segmentation Axial CT scans (1 mm × 1mm× 1 mm) of a male human head were obtained from the U.S. National Library of Health (Male Visible Human Project, USA). The NIH visible human dataset consists of a series of cryosection images and CT scans from both male and female single subjects. The CT images were truncated to the level of cervical vertebra 4, and then imported to ScanIP (Simpleware Ltd., UK) for registration and segmentation. After the registration, the slices were firstly downsampled to a resolution of 3 mm × 3mm× 3 mm, to reduce total element count and increase the computational effi- ciency. Using a floodfill algorithm based on upper and lower intensity threshold values, the skull was initially segmented. Using a combination of the floodfill algorithm and manual painting, GM and WM of the brain along with the CB and brainstem were then extracted as a single entity and assigned to a brain mask. Due to the reduction in image 47 Table 4.1: +ScanFE mesh parameters for VHsub Parameter Name VHsub Mesh type smoothed Max curvature 0.50 Max iterations 2 Min quality target 0.20 Target max grid size 8 × 8 × 8 Elements type All tets resolution, cortical foldings were unable to be represented. A CSF mask was manually reconstructed using the morphological filter ‘Erode’ applied to the brain mask, to re- duce the region by 1 pixel in every direction. A mask for scalp and subdermal muscle tissues was then generated. However, the thresholds around the jaw region were man- ually adjusted due to artifacts caused by dentures. The mask for paranasal sinuses was subsequently extracted. Each mask was then individually filtered and smoothed using a recursive Gaussian filter, a low-pass spatial filter that is typically adopted to reduce image noise and decrease detail levels [175]. Finally, any remaining blank voxels were manually assigned to the most appropriate neighbouring mask. 4.1.2 Finite element mesh generation Segmented masks were exported to +ScanFE (Simpleware Ltd., UK) to generate a tetrahedral mesh. +ScanFE offered the +FE Grid algorithm, a fast and robust meshing algorithm for generating tetrahedral mesh elements [175]. Mesh parameters chosen are listed in Table 4.1, and all masks were meshed simultaneously to ensure proper contact areas across mask boundaries. The resulting mesh model is shown in Figure 4.1, with mesh statistics listed in Table 4.2 (column 2). The tetrahedral mesh was then imported into the COMSOL Multiphysics (COMSOL AB, Sweden) FE solver. The model was named as ‘VHsub’ for further reference. 48 Figure 4.1: Segmentation of low-resolution realistically shaped head model: a. cross-section of whole- head mesh; b. scalp mask; c. skull mask; d. paranasal sinuses mask; e. CSF mask; f. brain mask. Table 4.2: Mesh statistics of head models. In this table, mean element size was calculated by dividing the integral of element size over mesh volume, and mean element quality was determined by dividing the sum of element quality over mesh volume. In COMSOL, the element size was evaluated as the maximum edge length of each element, and element quality, ranging from 0 to 1, was determined based on the geometry of the element—aregular tetrahedron exhibited a quality of 1. Mesh quality was given √ 72 3V by the formula q = / , where V denotes the volume of a tetrahedral element, and ( 2+ 2+ 2+ 2+ 2+ 2)3 2 h1 h2 h3 h4 h5 h6 the h’s the edge lengths. Low-resolution High-resolution Parameter Name VHsub HEAsub HEAsub-extended DEPsub Number of elements 1,219,127 959,698 996,622 1,425,526 Mean element size (mm) 4.91 7.34 8.51 6.45 Mean element quality 0.781 0.548 0.550 0.476 49 4.2 Reconstruction of high-resolution head models 4.2.1 Image segmentation Two different high-resolution computational head models were reconstructed from hu- man subjects. One subject was a healthy 35-year-old Asian male volunteer, whose MRI head scan was truncated at the level of cervical vertebra 6, named as ‘HEAsub’. The other was a Caucasian female in her 40’s who suffered from depressive disorder, named as ‘DEPsub’: her scan was truncated at the level of the atlas-axis, i.e., cervical vertebrae 1-2. T1-weighted MRI scans of both subjects were obtained from Neuro- science Research Australia. The scans were sagittally oriented with voxel resolution of1mm× 1mm× 1 mm. Head tissue masks were obtained using a combination of automated and manual segmentation software. Automated mask generation was performed using BrainSuite, an open-source package from the Laboratory of NeuroImaging at the University of Cal- ifornia, Los Angeles [176]. It integrates a suite of image processing tools specialised for brain segmentation from T1 MRI scans. The procedure for brain segmentation was: skull stripping based on edge detection between the cortical surface and skull using the Brain Surface Extractor (BSE) toolbox, non-uniformity correction using the Bias Field Corrector (BFC) toolbox to apply a uniform intensity throughout the same structure, tissue classification using the Partial Volume Classifier (PVC) toolbox and tissue labelling following a built-in volumetric registration to a pre-labelled brain atlas using the Cerebrum Labeling toolbox, followed by the generation of brain masks. De- pending on the quality of the MRI scan, the parameters in each toolbox were chosen differently for the two sets of scans, as listed in Table 4.3, with all parameters within the recommended range. Thus, tissue compartments including skin, skull, CSF, GM and WM were generated from the MRI data. These segmentation tools were designed to accurately distinguish brain tissues from other tissues in the head, and yet segmentation errors were present in other tis- sue masks. Therefore, manual correction was necessary to improve the accuracy of the segmentation. The segmented masks were exported from BrainSuite as grayscale 50 Table 4.3: Segmentation parameters for the BrainSuite toolboxes Toolbox Parameter Name HEAsub DEPsub Diffusion iterations 0 1 Diffusion constant 25 30 BSE Edge constant 0.6 0.6 Erosion size 1 1 Histogram 12 12 Sample 16 16 Control point 36 64 BFC Spline stiffness 0.0001 0.0001 Lower limit 0.8 0.9 Higher limit 1.2 1.1 PVC Spatial prior 0.02 0.05 Linear convergence 0.01 0.01 Cerebrum labelling Wrap convergence 100 100 Wrap level 5 5 51 images, and imported into ScanIP (Simpleware Ltd., UK) for manual correction and further processing, using a combination of segmentation algorithms mentioned earlier. The five original masks were hence divided into more compartments: • masks representing eyes, paranasal sinuses, larynx and cervical vertebrae were separated from the skin and skull, as shown in Figures 4.2a and 4.3a. In addition, the major foramina of the skull were included in the skull mask, including the superior orbital fissure, optic canal, foramen ovale and foramen magnum; • the skull was divided into the cranium and jaw. The cranium was then subdivided into three layers, with spongy bone tissue as the middle layer, and compact bone tissue as the outermost and innermost layers. The jaw was considered compact. These skull compartments are shown in Figures 4.2b and 4.3b; • the brain masks consisted of GM, WM, CB (with brainstem) and the cervical spinal cord (SC), as well as the ventricular system which was later assigned to the CSF mask; • several regions of interest (ROIs) in the brain, considered important in tEC ther- apeutic or adverse effects, were further segmented from the GM mask as shown in Figures 4.2c and 4.3c. The ACCs, amygdalae and hippocampi (AHs) were manually segmented based on their anatomical location. The DLPFCs and the OFCs were extracted from the GM mask using the 3D editing toolbox in ScanIP. Finally, any remaining blank voxels were manually assigned to the most appropriate neighbouring mask. To examine the effect of an extracephalic clinical electrode montage used in some tDCS studies [177,178], a synthetic upper torso was added onto the segmented ‘HEA- sub’ head. 80 pixels were padded to the scan in both +Y and -Y directions, and 25 pixels in the +Z direction. Subsequently, the upper torso was manually painted in Sca- nIP up to the level above the axilla, as shown in Figure 4.4. The generated head model was named ‘HEAsub-extended’ for future reference. 52 Figure 4.2: a): Segmentation of ‘HEAsub’ head: skin, eyes, paranasal sinuses (with larynx), skull (including compact bone tissue and spongy bone tissue), vertebrae, CSF and brain. b): Segmentation of skull: compact bone tissue and spongy bone tissue. c): Detailed segmentation of the brain, including defined regions for white matter (WM), grey matter (GM), anterior cingulate cortex, (ACC), dorsolateral prefrontal cortex (DLPFC), orbitofrontal cortex (OFC), amygdala and hippocampus (AH), cerebellum (CB, with brainstem), and cervical spinal cord (SC). ‘l’ and ‘r’ denote the left and right sides of the brain respectively. 53 Figure 4.3: a): Segmentation of ‘DEPsub’ head: skin (including the eyes), paranasal sinuses (with larynx), skull (including compact bone tissue and spongy bone tissue), vertebrae, CSF and brain. b): Segmentation of skull: compact bone tissue and spongy bone tissue. c): Detailed segmentation of the brain, including defined regions for white matter (WM), grey matter (GM), anterior cingulate cortex, (ACC), dorsolateral prefrontal cortex (DLPFC), orbitofrontal cortex (OFC), amygdala and hippocampus (AH), cerebellum (CB, with brainstem), and cervical spinal cord (SC). ‘l’ and ‘r’ denote the left and right sides of the brain respectively. 54 Figure 4.4: Frontal and lateral view of the shoulder-extended HEAsub model. To respect the subject’s privacy, the eyes of the model are hidden. 4.2.2 Finite element mesh generation Two meshing algorithms were available in the +FE module of ScanIP (v4.3): +FE Grid and +FE Free. +FE Free utilizes a free-tetrahedral meshing algorithm for remeshing the surfaces extracted from the +FE Grid mesh, which is initially gen- erated, with the remeshed surfaces then filled with tetrahedral elements using an Ad- vancing-Front/Delaunay tetrahedralisation technique [175, 179]. Compared to +FE Grid, +FE Free is a slower process; however, it provides more control over the num- ber of elements in the generated mesh. The +FE Free meshing algorithm was thus selected to generate the tetrahedral mesh elements for the high-resolution head models. The mesh parameters (see Table 4.4) were adjusted so that a relatively coarse mesh was generated to ensure computa- tional efficiency. Resulting mesh statistics of the head models are listed in Table 4.2. The meshes were then imported into the COMSOL Multiphysics FE solver (v3.5 and v4.2). 4.3 Tissue conductivities Most compartments of the head models were considered to be electrically homoge- neous and isotropic, except the skull and WM. Since the paranasal sinuses are air- 55 Table 4.4: +FE mesh parameters of high-resolution models HEAsub & HEAsub-extended DEPsub Resolution 1.5 mm × 1.5 mm × 1.5 mm 1 mm × 1mm× 1mm Compound coarseness -30 -42 Target min edge length (mm) 3.9 3.44 Max edge length (mm) 9.6 8.56 Target max error (mm) 0.15 0.10 Surface change rate 50 80 Internal change rate 30 80 Target no. of elements across a layer 0.75 0.58 Quality optimisation cycles 5 7 filled spaces, their electrical conductivity was set to zero. The conductivity of CSF has been accurately measured as 1.79 S/m [180]. Conductivities of the scalp, skull (generic isotropic) and brain (except WM), were assigned mean values from multiple studies [169, 181–184]. Similarly, conductivities of compact and spongy bones were also averaged from several studies [185–187]. The conductivity of WM was taken from Wolters et al. [188]. All conductivity values are listed in Table 4.5. The conductivities of the eyes and the synthetic torso were assigned to the scalp conductivity. 4.3.1 Skull conductivity The skull is known to exhibit anisotropic electrical conductivity, as a result of its three- layer structure [189]. In the ‘VHsub’ head model, the skull was assigned to only a single layer exhibiting anisotropic conductivity. Radial and circumferential conductiv- ity values of the skull were determined using the volume constraint method of Wolters et al. [188], which retained the geometric mean of eigenvalues between the isotropic and anisotropic cases, and thus the ‘volume’ of the conductivity tensor σ, i.e. 4 4 πσ σ 2 ≡ πσ3 , (4.1) 3 r c 3 iso 56 Table 4.5: Tissue conductivities Compartment Electrical Conductivity (S/m) Scalp 0.41 Eyes 0.41 Sinus 0 Skull (generic isotropic) 0.013 CSF 1.79 Brain (except WM) 0.31 WM (generic isotropic) 0.14 Vertebrae 0.013 Synthetic torso 0.41 Skull (compact bone) 0.006 Skull (spongy bone) 0.028 Table 4.6: Skull conductivity anisotropy Skull Model Electrical Conductivity (S/m) Generic isotropic σiso 0.013 Radial anisotropic σr 0.0028 Circumferential anisotropic σc 0.028 where σiso is the generic isotropic skull conductivity value, σr and σc are the radial and circumferential anisotropic values respectively, with σr : σc = 1 : 10. Values of these skull conductivities are given in Table 4.6. The radial direction within the skull was determined from the spatial gradient G (Gx,Gy,Gz) of a boundary distance variable u defined as the distance from any point to the outer boundary of the skull. This spatial gradient of the boundary distance vari- able was available throughout the skull thickness through custom in-built processing functions of the finite element solver, which was defined using: G = ∇u, (4.2) 57 The orthogonal matrix of unit eigenvectors S (l, m, n) of the anisotropic conduc- tivity tensor σ was thus calculated at every point in the skull based on the following equations: G l = |G| , l · m = 0 (4.3) l × m = n as they defined a set of mutually perpendicular vectors. |G| in Equation 4.3 represents the magnitude of the vector G. The anisotropic conductivity tensor σ at every point in the skull was then calculated from σ = S diag(σr,σc,σc) S , (4.4) where S is the transpose of S. However, since the skull consists of three layers, a low resistance spongiform layer between two high-resistive layers, replacement with a three-layered structure may be more accurate [169,174]. Therefore, in both ‘HEAsub’ and ‘DEPsub’ head models, the skulls were separated into three layers — compact bone as the outermost and innermost layers, and a spongy bone layer in between. Each layer was electrically homogeneous and isotropic. Their conductivities are given in Table 4.5. 4.3.2 White matter conductivity anisotropy WM in the brain is known to exhibit highly anisotropic electrical conductivity [169, 170], as water molecules and ions inside and outside nerve fibres can flow more easily along the fibre tracts than transverse to them. Following the assumption that the electric conductivity tensor shares the same eigenvectors as the water diffusion tensor [190], the latter can be measured using diffusion tensor MRI (DT-MRI). The linear rela- tionship between the conductivity and diffusion tensors has been experimentally vali- dated [191, 192]. Modelling studies on the EEG have suggested that WM anisotropic conductivity greatly influences the estimated dipole source [188, 193–195]. Several simulation studies on tES have also shown that E-field distribution inside the brain is altered after the incorporation of WM conductivity anisotropy [137, 156, 171–173]. 58 Hence, WM with anisotropic conductivity should be incorporated in computational head models whenever possible. DT-MRI was performed only on the ‘HEAsub’ head, in 61 gradient directions. The slices were axially oriented with voxel resolution of 2.5 mm × 2.5 mm × 2.5 mm. All scans were initially registered to the T1 structural scan in Amira (Visage Imaging GmbH, Germany) using its affine registration algorithm. The open-source software FSL, developed by the FMRIB Analysis Group of University of Oxford, was chosen for diffusion tensor calculation using the probabilistic tracking algorithm using its FDT diffusion toolbox [196–198]. Two separate files that contained b-values and b-matrices for all gradient directions were required as input for the diffusion tensor calculation. The former summarises the sensitivity to diffusion for each gradient direction, whereas the latter reflects the attenuation effect in x, y and z for each gradient direction [199]. In addition, the input also required a 3D Neuroimaging Informatics Technology Initiative (NIfTI) image file of the ROI, i.e., the brain region, and a four-dimensional (4D) NIfTI image file that combined all 61-direction scans. Eigenvectors and fractional anisotropy (FA) were then calculated, with the latter being widely used to denote the degree of anisotropy: typically greater than 0.45 for WM [200]. The fibre tracks computed in FSL are shown in Figure 4.5. Similar to the skull anisotropy from Equation 4.4, the conductivity tensor of WM, σ, was calculated from: σ = S diag(σl,σt,σt) S , (4.5) where S is the orthogonal matrix of unit eigenvectors obtained from the WM diffusion tensor, and σl and σt are the assigned conductivities longitudinal and transverse to the fibre directions respectively, with σl : σt = 10 : 1 [170, 189]. σl and σt were calcu- lated using the volume constraint method [188], which retained the geometric mean of conductivity eigenvalues and thus the ‘volume’ of the conductivity tensor, i.e. 4 4 πσ σ 2 ≡ πσ3 , (4.6) 3 l t 3 iso where σiso is an assigned generic isotropic WM conductivity. The values of WM con- ductivity used are shown in Table 4.7. Following the diffusion tensor calculation, the 59 Figure 4.5: Fibres of white matter shown after FSL computation. Fibre tracks in red, green and blue rep- resent the fibres running perpendicular to sagittal plane, coronal plane and horizontal plane, respectively. ‘S’: superior, ‘I’: inferior, ‘A’: anterior, ‘P’: posterior, ‘L’: left and ‘R’: right. Table 4.7: White matter conductivity anisotropy White Matter Model Electrical Conductivity (S/m) Generic isotropic σiso 0.14 Longitudinal anisotropic σl 0.65 Transverse anisotropic σt 0.065 calculated conductivity tensors of data points in the DT-MRI scans were then linked to their individual coordinates. This process was performed using MATLABR (The Mathworks, USA), and the script is given in Appendix A. Only fibre conductivity data having a strong anisotropy signal (FA ≥ 0.45) were exported. 4.4 Passive volume conductor model All volume compartments in the head models were considered as passive volume con- ductors, except the brain regions in most ECT simulations. In the passive regions, electric potential ϕ was given by Equation 2.8: ∇ · (−σ∇ϕ)=0. As noted earlier, 60 the equation represents a quasi-static approximation, valid even for commonly used square-wave stimulus currents having high frequency components [128]. The boundary conditions were: • active electrode boundary: normal component of inward current density set to Jn, where I J = , (4.7) n area of electrode with I defined as the applied stimulus current waveform (in Amperes); • return electrode boundary: normal component of inward current density set to −Jn; • all other external boundaries treated as electric insulators, i.e., zero normal com- ponent of current density, unless specified, which will be mentioned in Chapters 6, 7 and 8. A ground reference (zero electric potential) was placed in the passive model in the specific locations mentioned in Chapters 6 and 8; • continuous current density (i.e., flux continuity) across all interior boundaries. It should be noted that Equation 4.7 was the simplest means to represent a constant current mode of stimulation, as utilised by clinical ECT stimulators. A slightly more realistic boundary condition would be to employ a constant voltage across each elec- trode, allowing the current density to be non-uniform across the electrode area. In this case however, additional processing is required at each time instant to determine the correct electrode voltage which constrains the stimulus current to the desired value. Preliminary simulations using a simplified spherical head model, as shown in Figure 4.6, suggest that both types of boundary condition yield similar brain activation pro- files. Therefore, the inward current density from Equation 4.7 was chosen as the elec- trode boundary condition. The current stimulus waveform I depends on the application in question, and will be discussed further in corresponding chapters. Electrodes patched onto the scalp were defined mathematically. Electrode geome- tries of interest, with uniformly distributed normal component of current density, were formulated depending on the shape and size of the electrodes. A 3D electrode ‘mask’ was first defined according to: 61 Figure 4.6: Comparison between constant current and constant voltage boundary conditions. a) Model geometry made up of three concentric spheres, with dimensions identical to that of Miranda et al. [141] — rscalp = 9.2 cm, rskull = 8.5 cm and rbrain = 8.0 cm. The sphere highlighted in red represents the brain. The electrodes were placed across opposite poles of the outermost sphere as discs of radius 2.5 cm. b) Extracellular current density in the sphere representing the brain. c) Activation in the ’brain’ att=3ms and 5 ms, computed using the excitable tissue model of Section 4.5. The stimulus was delivered at t = 1 ms, at a duration of 1 ms 62 • ECT electrode: a sphere of radius 2.5 cm with the center at targeted positions. • tDCS electrodes: a rectangular cuboid with dimensions at 5 cm × 7cm× 5cm (or with a different size depending on the montage). A rotation transformation was applied to the block to ensure that the orientation of the intersected boundary fit the electrode placements in clinical trials. Details on the rotation transforma- tion are found in Appendix B. Scalp electrodes were thus defined as the intersectional boundary between the electrode ‘mask’ and the scalp. The surface area of each electrode was determined by numerical integration of the intersected boundary, and was ensured to be similar to the known area of the corresponding physical electrode. The ragged edges of some electrodes reflected the resolution of surface mesh grids. 4.5 Active excitable tissue model of brain A continuum model based on the HH formulation of neural ion currents [129] was in- corporated into the brain compartment to simulate excitation arising from transcranial current stimulation in Chapters 5 and 7. The ionic continuum model, consisting of intracellular and extracellular voltage domains, is schematically shown in Figure 4.7. At each point within the brain, the neural membrane potential vm, defined as the difference between intracellular potential vi and extracellular potential ve, satisfies ∂v C m + i = i , (4.8) m ∂t ion m where Cm is the membrane capacitance of the neuron per unit membrane area, im is the total membrane current per unit membrane area, and iion is the total ionic current per unit area, detailed in Appendix C. In this neural model, the intracellular potential vi is resistively tied to a resting po- tential Vr. This constraint represents the effect of coupling between the neural soma and the more remote dendritic and axonal regions in the neuron, restricting the intra- cellular potential from floating freely with the extracellular potential. vi and im are 63 Figure 4.7: Active neural model defined within the 3D brain region. At each point, two domains are abstractly defined to represent the intracellular and extracellular potentials vi and ve respectively. These domains occupy the same overlapping 3D geometric space representing the whole brain. iion represents the ionic membrane current flowing across the soma membrane, Vr denotes a fixed resting potential, resistively tied to the intracellular potential via a conductance gr . Cm is the membrane capacitance per unit membrane area and vm the transmembrane potential. im is the total membrane current per unit membrane area, which includes ionic and capacitive components. 64 connected through the equation: im = gr (Vr − vi), (4.9) where gr is a conductance governing the extent of coupling between vi and the ‘resting’ intracellular potential Vr in the more remote regions of the neuron. The lower the gr value, the smaller the extent of spatial neuronal activation in the brain, since the intracellular potential is not as strongly tied to Vr. A trial and error process was used to select the appropriate gr value in order to approximately match the spatial extent of BF activation obtained from the SPECT imaging study of Blumenfeld et al. [42]. Due to differences in the head geometry and electrical conductivities of skull and brain, different gr values were used for VHsub and HEAsub models, as shown in Table C.1. This was so that both models matched the SPECT imaging data in terms of the spatial extent of brain activation. Traditional computational neural models are multi-compartment representations which effectively tie the intracellular compartment to adjacent intracellular compart- ments, leading to a cable-type model of a propagating action potential. However, when modelling the spatial extent of activation in the brain, it is clear that neurons do not directly activate adjacent neurons, except through synaptic connections. Use of a stan- dard bidomain equivalent formulation, as used for example in cardiac tissue, would necessitate setting the equivalent averaged intracellular conductivity to zero in order to prevent cable-like propagation, since adjacent neurons are not intracellularly con- nected. However, setting the intracellular conductivity to zero would mean that no extracellular stimulus can activate the neurons, since the intracellular potential would be free to float so that the transmembrane collage is maintained always at its resting level. The scope of this thesis was not to model the spread of excitation through neural networks in the brain (seizure), but rather the spatial extent of direct neural activa- tion due to transcranial current flow. The continuum description given here should not be confused with the standard bidomain model, in which the intracellular spaces of elements are effectively connected through an intracellular conductivity tensor [201]. Instead, the intracellular spaces of neurons defined at every point in the formulation of this thesis remain non-communicating. Connection to adjacent intracellular compart- 65 ments is effectively implemented by gr, which couples each cellular compartment to a fixed distal intracellular potential. The single-compartment neuron model was linked to the extracellular potential of the brain ve by Poisson’s equation (Equation 2.7, non-zero volume current source): ∇ · (−σbrain∇ve)=βim, (4.10) where β is a parameter specifying the surface-to-volume ratio of the neurons within the continuum representation of the brain. The extracellular potential ve in Equation 4.10 was enforced to be continuous with the electric potential ve of Equation 2.8 at the boundaries between active (i.e. brain) and passive domains, as was the current density (i.e. conservation of current). β was calculated from existing data [202] using the following expression: 4πr2 β = n , (4.11) Vbrain/Nn where rn is the radius of the soma, Nn is the total number of neurons in the brain, and Vbrain is the volume of the brain. Values of parameters used in the continuum neural description are listed in Table C.1. 66 Part II Results and Discussion 67 “Hope” is the thing with feathers — That perches in the soul — And sings the tune without the words — And never stops — at all — And sweetest — in the Gale — is heard — And sore must be the storm — That could abash the little Bird That kept so many warm — I’ve heard it in the chillest land — And on the strangest Sea — Yet — never — in Extremity, It asked a crumb — of me. — Emily Dickinson 68 Chapter 5 ECT Simulations with Low-resolution Head Model 5.1 ECT stimulus configuration 5.1.1 Electrode placements In order to investigate the effect of scalp electrode placement in ECT, three typical configurations used in clinical practice were simulated; each utilising two electrodes placed on the scalp, as shown earlier in Figure 2.2: • BF placement: each electrode (A and B) was placed 5 cm superior to the lateral angle of the eye; • BT placement: each electrode (A and B) was placed on each side of the scalp 3 cm superior to the midpoint of a line connecting the external ear canal with the lateral angle of the eye; • TP-RUL placement (RUL montage in Figure 2.2): one electrode (B) was placed in the temporal position (as described above in BT placement) on the right side of the scalp, and the other electrode (A) placed just right of the vertex of the head. 69 Table 5.1: ECT stimulus parameters Electrode Stimulus Stimulus Frequency Configuration Amplitude PW (mA) (ms) (Hz) BF ECT 800 1 120 BT ECT 800 1 120 TP-RUL ECT 800 1 120 BT ECT 500 1 120 TP-RUL ECT 800 0.6 120 Figure 5.1: Biphasic stimulus current waveform with 800 mA amplitude, 1 ms PW and 120 Hz fre- quency used in the simulations. The effects of variations in stimulus parameters were investigated by changing the amplitude or PW of the waveform. 5.1.2 Stimulus Parameters Clinical ECT conventionally utilizes a biphasic brief-pulse, square-wave stimulus cur- rent [203]. The modelled stimulus current waveform is shown in Figure 5.1, where the stimulus is retained as biphasic, with anodic-first stimulation applied to electrode A (Figure 2.2). Two pulses of a 120 Hz stimulus train were delivered, and the time between anodic and cathodic onset was set to half the stimulus period, or 4.17 ms. The effects of variations in stimulus parameters were also investigated, with combinations of parameters modelled listed in Table 5.1. A total of five simulations were undertaken. 70 5.2 Data analysis The models were solved using the segregated numerical solver in COMSOL (v3.5), on a Windows 64-bit workstation with 24 GB RAM utilising 4 processors. To solve the time-dependent equations, a variable-step backward differentiation formula (BDF) scheme was utilised with an absolute error tolerance set to 10−5. It took ∼ 60 hours to solve for a 10-millisecond duration simulation. In this chapter, the direct excitation of the brain due to transcranial current appli- cation during ECT was simulated using the VHsub model. The analysis focused on comparing the magnitude of current density with the spatial extent of brain activation, as electrode placement, stimulus amplitude and PW were varied. 5.3 Results 5.3.1 Anisotropic skull BF simulation Extracellular current distribution The magnitude of the current density on the surface of the brain at 0.4 ms following ECT stimulus onset is shown in Figure 5.2 (left panel). Peak current densities of around 15 A/m2 are seen immediately beneath the electrodes. A moderate current density less than 5 A/m2 flowed through the temporal and parietal lobes, but there was little current flowing into the occipital area and the brainstem. Brain activation The simulated time course of brain excitation following application of a BF ECT stim- ulus is shown in Figure 5.3, with side view plots showing the spatial extent of activa- tion on the brain surface along with coronal section plots showing the spatial depth of activation into the brain. The anodic stimulus pulse was delivered from t =1mstot = 2 ms. After the stimulus and prior to t = 3 ms, the brain region near electrode A (Figure 2.2) was hyperpolarised, and that near electrode B was depolarised, as shown in Figure 5.4. 71 Figure 5.2: Extracellular current density magnitude in the brain at 0.4 ms following ECT stimulus onset in simulations of three conventional electrode placements: bifrontal ECT (BF), bitemporal ECT (BT) and right unilateral ECT (TP-RUL). At t = 3 ms, APs with overshoots over 40 mV were initiated on the cortex beneath electrode B, corresponding to maximum current density magnitude on each side of the cortex, as shown in Figure 5.3. The spatial extent of brain activation transiently expanded in the frontal region. At t = 4 ms, the excited region nearly reached its maxi- mum spatial extent, with an activated depth approximately 1.5 cm beneath the cortical surface. At t = 5 ms, the activated region had ceased to expand, and most excited areas were in their late repolarisation phase. Between t =6msandt = 7 ms, most of the post-activated region (beneath electrode B) had begun to hyperpolarize due to the sec- ond pulse, while the contralateral side of the brain began to depolarize. At t = 9 ms, the brain region beneath electrode B had begun its slow recovery from hyperpolarisation, while the excited region on the contralateral side reached its maximum spatial extent, with part of this region beginning to recover. Figure 5.3 indicates that once activation was initiated, there appeared to be slight spread of activation up to a maximal spatial extent, before the entire brain recovered to resting levels. For this, and all other active simulations in this thesis, this spread did not extend beyond a maximal region, and was due to edges of the activated region being more distant from the electrodes. The resulting lower current density at the distal edges required longer times for the local membranes to charge to threshold. This is also indicated by Figure 5.5, which shows the MPs at four different locations in the brain 72 Figure 5.3: Time course of direct neuronal excitation induced by BF ECT, with side view plots showing the extent of activation on the brain surface (top panels) and coronal section plots showing the depth of activation into the brain (bottom panels). The dashed line on the upper left surface plot denotes the position of the coronal plane. The colorbar represents the neuronal MP within the brain. for BF ECT. A, B and C were located within the activated region, with A nearest the region of maximum current density, B farther and C farthest away, while D was taken outside the region but close to the edge. 5.3.2 Anisotropic skull BT simulation Extracellular current distribution ECT simulation of BT electrode placement resulted in an increase in the maximum current density relative to that of the BF electrode configuration (see Figure 5.2, middle panel). Peak current densities reaching 20 A/m2 occurred on the temporal cortical surfaces, directly beneath the electrodes. There was also a moderate current density magnitude less than 5 A/m2 flowing through the remainder of the brain surface. Brain activation A large region in the temporal and lateral-frontal lobes was directly excited, as shown in Figure 5.6. In comparison with the BF simulation (Figure 5.3), the size of the excited region under BT electrodes was marginally larger, although the depth of activation was still comparable (around 1.3 cm beneath the cortical surface). 73 Figure 5.4: Simulated MPs on brain surface beneath each electrode for bifrontal ECT (BF), bitemporal ECT (BF) and right unilateral ECT (TP-RUL) electrode placements. In these panels, dashed lines represent the MP at sites under electrode ‘A’ of Figure 2.2, whilst solid lines represent sites beneath electrode ‘B’. Figure 5.5: Simulated MPs at four different locations in the brain for BF ECT. A, B and C are plotted within the activated region, with A nearest the region of maximum current density, B is more peripheral than A, with C being the most peripheral near the edge of the maximal extent of spatial activation. D was taken outside the activated region but close to its edge. 74 Figure 5.6: Snapshots of neuronal excitation in BT and TP-RUL ECT simulations at maximal brain excitation for each stimulus pulse, with side view plots showing the extent of activation on the brain surface (upper panels) and coronal section plots showing the depth of activation into the brain (lower panels). The dashed lines on the surface plots denote the position of the coronal plane. The colorbar represents neuronal MP within the brain. 5.3.3 Anisotropic skull TP-RUL simulation Extracellular current distribution In the anisotropic TP-RUL simulation, the transcranial current was found to be con- centrated in the right temporal and parietal lobes, as shown in Figure 5.2 (right panel). Two values for peak current density magnitudes were observed: 26 A/m2 on the pari- etal surface, and 18 A/m2 on the surface of right temporal lobe. Brain activation Compared to BT electrode placement, the spatial size of the excited temporal region was similar, but the location was slightly altered (see Figure 5.6). For the BT electrode configuration, the excited region occurred on the dorsal surface of the temporal and lateral-frontal areas, whereas for TP-RUL placement, direct activation was inferior to- wards the base of the right temporal lobe, even though both BT and TP-RUL shared the same temporal electrode placement (electrode B). Furthermore, Figure 5.7 illustrates that in TP-RUL ECT, a section of the brainstem (medulla) was also excited by the first 75 Figure 5.7: Snapshots of neuronal excitation in TP-RUL ECT model for stimulus PWs of 1 ms (left) and 0.6 ms (right). The colorbar represents neuronal MP within the brain. The brainstem was activated when the stimulus PW was 1 ms, as shown by the arrow. pulse. The resulting AP initiated in the brainstem is shown in Figure 5.8 (solid line), which indicates that the onset of the AP was delayed by 3 ms relative to the stimulus (stimulus onset at t = 1 ms). 5.3.4 Variation in stimulus parameters Change in amplitude By reducing the amplitude of the current stimulus by almost half to 500 mA, the max- imum current density in the brain was reduced to 10.5 A/m2, nearly half of when the stimulus was 800 mA. Due to the decrease in current density, depolarisation to thresh- old took longer, and the spatial extent of the excited brain region (both the surface area on the cortex and the depth of penetration) decreased and became more focal, as shown in Figure 5.9). The maximum depth of excitation was significantly less than 1 cm at 500 mA pulse amplitude, compared to 1.3 cm at 800 mA. Change in pulse width By reducing the stimulus PW to 0.6 ms, the depolarisation time to threshold was also longer than that of the default 1 ms PW, and the excited brain volume was also more focal (see Figure 5.9). This was similar to the effect of reducing the pulse amplitude, despite the fact that the current density magnitude in the brain remained unchanged 76 Figure 5.8: MP of the brainstem region (medulla) in TP-RUL ECT during biphasic stimulation. Each phase of stimulation had a PW of 1 ms (solid line) or 0.6 ms (dashed line). The stimulus was cathodic first with respect to the right temporal lobe electrode B. Figure 5.9: Snapshots of neuronal excitation in BT ECT model (for 1 ms PW and 500 mA amplitude) and TP-RUL ECT models (under 0.6 ms PW and 800 mA amplitude) at maximal brain excitation after the first pulse, which was cathodic with respect to the right temporal lobe electrode B. The side view plots (upper panels) show the extent of activation on the brain surface, and the coronal section plots (lower panels) show the depth of activation into the brain. The dashed lines on the surface plots denote the position of the coronal plane. The colorbar represents neuronal MP within the brain. 77 compared to the 1 ms PW. In addition, depolarisation in the brainstem region was not sufficient to trigger an AP, as shown in Figure 5.8 (dashed line). 5.4 Discussion The simulations presented in this chapter represent a major advance in the field of ECT modelling in two major respects: 1) the model incorporated direct neuronal activation of the brain by transcranial currents, and 2) the effect of stimulus current parame- ters and electrode scalp placement on direct brain activation can be readily investi- gated. These simulations were all performed using an anatomically realistic, albeit low-resolution, head model. The major advantage of modelling neuronal activation, as opposed to simulating passive volume current flow, is that it allows the investigation of dynamic effects such as altered stimulus PW on brain activation. The effect of changing PW, for example, cannot be demonstrated in a passive volume conductor model, since the current den- sity and electric field remain unchanged during the stimulus. If desired, the model described in this chapter could also be extended to investigate the dynamic effects of longer stimulus trains or other types of transcranial stimulation. 5.4.1 Model Formulation The computational model presented used a novel approach to incorporate excitable ionic neural elements into the whole brain, utilising a continuum active neural model based on HH kinetics to characterize excitable brain tissue. As an alternative, logical gating neural network models are very popular in brain-machine interface applications, but these are discrete cellular automaton models which are difficult to implement over large spatial regions such as the entire brain [204, 205]. Numerous compartmental models have also been proposed to simulate neural activation induced by electromag- netic fields, using the concept of an activation function equal to the second spatial derivative of extracellular potential along the neural axon [206, 207]. Activation is deemed to occur when the activation function is great than zero. Although this concept 78 was used to simulate volume of brain activation in deep-brain stimulation, it requires knowledge of axonal direction and uses linear approximation to represent non-linear, dynamic neuronal activation. Furthermore, the activation function method cannot be used to simulate the effects of dynamic stimulus parameters such as pulse width and frequency. The model formulation described here represents the first to incorporate excitable ionic neural elements into a whole head model to simulate the direct spatial activation of the brain. Nonetheless, it should be acknowledged that parameters gr and β have been fitted to only a single image data set [42], and that further imaging studies are necessary to fully validate this novel formalism of direct brain activation. Since propagation of activation (i.e. seizure) was not incorporated into the model, the simulations revealed only brain regions that were directly stimulated by the tran- scranial current. The latencies in activation times shown in the results (Figures 5.3 and 5.5) indicate the strength of activation in a given region of the brain. The time course of activation shown is not an example of propagation, since the spread of excitation was limited in its spatial extent and did not encompass the whole brain. The passive spread in spatial extent was due to the stimulus strength-duration relationship for activation — neurons further away required more time to charge to threshold, since the stimulus strength (current density) in these regions was lower. As noted in Chapter 4, the value for gr in this neuronal continuum model was cali- brated based on BF ECT image data using single photon emission computed tomogra- phy (SPECT) [42]. With this gr value, the simulation results of BT ECT and TP-RUL ECT were similar in the spatial extent of activated brain region with the corresponding SPECT imaging studies, including the findings that BT ECT led to activation mainly in the temporal region, and TP-RUL ECT induced activation in the right fronto-temporal regions as well as the parietal cortex [42–44]. The adjustment of gr affected the degree of both depolarisation and hyperpolarisation; however, compared to its depolarisation effect, it exerted a relatively smaller influence on the degree of hyperpolarisation. 79 Figure 5.10: Extracellular current density magnitude on the brain surface at 0.4 ms following ECT stimulus onset in simulations of the BT montage with isotropic skull conductivity. 5.4.2 Comparison of three ECT electrode placements Results of the three ECT models (using 1 ms PW and 800 mA amplitude) suggest that for all electrode placements, maximum current density in the brain was found on the cortical surface directly beneath the electrodes, consistent with previous find- ings [135, 140, 150]. Some studies found that maximum current density occurred be- tween electrodes rather than under the electrodes for unilateral or asymmetric electrode montages [53, 143], but in these simulations the electrodes were placed much more closely together than the d’Elia placement used for TP-RUL ECT in this model. The simulated current density magnitudes are about three-fold lower than results from previous modelling studies using similar stimulus current strengths [151], likely due to the fact that an anisotropic conductivity was incorporated into the skull. To verify this, a simulation without skull anisotropy was carried out with the BT mon- tage, as shown in Figure 5.10, finding that maximum current density in the brain was indeed consistent with these previous studies [151]. A separate modelling study on transcranial current stimulation found that in order to maintain the same current den- sity magnitude in the brain, the stimulus had to be roughly three times stronger in an anisotropic skull model compared to the isotropic case [172], consistent with the simulation results presented here. Activated brain regions were found to be highly correlated to current density mag- nitude (and thus the induced electric field) within the brain: the earliest activation was at the site of maximum current density beneath the return electrode. The simulations 80 also found that at maximal brain activation, penetration of activation into the brain was less than 2 cm, i.e. 10–15% of overall brain width. Thus modelling of active neuronal depolarisation suggests that ECT only directly excites a limited region of the brain be- neath each electrode and its vicinity, with the excitation unable to penetrate very deep into the brain. The simulation results also showed that scalp electrode configuration is a major determinant of current density within the brain, and conversely, the size and location of the brain region directly-activated by ECT. The BF electrode configuration results in the lowest current densities within the brain (Figure 5.2), likely due to the thicker portion of the skull beneath the BF electrodes as well as the closer distance between electrodes in this configuration. As a result of both these factors, more current is shunted across the low-resistance scalp pathway, with less current penetrating into the brain. In regards to the TP-RUL and BT configurations, the distance between electrodes is lower for TP-RUL, however in this montage the relatively thin layers of skin and bone beneath the vertex electrode allows greater current penetration into the brain than that of BT (Figure 5.2). The difference in current density distribution for the three electrode placements with a stimulus of the same amplitude is consistent with clinical observations that TP- RUL ECT has the lowest seizure threshold [33, 35, 208, 209]. In the TP-RUL ECT model, a high current density is found near the motor cortex, which is thought to have the lowest seizure threshold of all cortical areas [210]. This would explain observa- tions that seizure threshold with TP-RUL ECT is reduced by a factor of two to three compared to BT ECT [35]. It could also explain findings from clinical trials that TP-RUL ECT needs to be given at a higher dose relative to seizure threshold than BT and BF ECT to achieve comparable efficacy [28–30,33]. This may be partly due to the fact that TP-RUL ECT mainly stimulates the right rather than bilateral frontotemporal areas; noting that this brain region is considered to play a key role in mediating the effects of antidepressant treatments [211]. However, another consideration is that with TP-RUL ECT a stimulus of relatively lower intensity is required to induce a seizure (due to the proximity of the 81 vertex electrode to the motor cortex and the low seizure threshold of the latter), but to achieve levels of frontotemporal stimulation comparable to that found with BT and BF ECT, the stimulus then needs to be increased to a higher multiple of seizure threshold. Maximum current density in the frontotemporal region differs by only about 25% between BT and BF ECT, when both are modelled with an identical stimulus. This is consistent with clinical reports that BF ECT may have a similar or slightly reduced efficacy compared to BT ECT [30–33]. The simulation results for BF and BT ECT also confirm previous models and neuroimaging studies showing reduced temporal lobe stimulation with BF ECT, which would explain the reduced memory side effects reported in some studies [31, 33, 212]. It is interesting to note that for BT and TP-RUL ECT, the location and extent of di- rect brain activation at the common right temporal electrode site differed slightly. For the same electrical stimulus amplitude, maximum current density in the frontotemporal region was reduced and the area of neural excitation was more inferior. These differ- ences need to be investigated with higher resolution anatomical models, e.g. those based on MRI brain scans, before their clinical significance can be assessed. In TP-RUL ECT, the brainstem region was directly activated by the stimulus, which did not occur in the bilateral electrode configurations. In order to test whether this ac- tivation was due to a ‘boundary effect’ resulting from removal of the spinal cord, the brainstem was extended into a cervical cord in a test model. It was found that the ac- tivation in the brainstem was still preserved only with TP-RUL placement, as shown in Figure 5.11. Simulations suggest that in TP-RUL ECT, the current density in the vicinity of the brainstem is sufficient to elicit activation of this region. This concurs with recent unexpected findings that TP-RUL had larger effects on heart rate than bi- lateral forms of ECT, with BT ECT in turn having greater heart rate effects compared to BF ECT [213–215]. Direct effects on heart rate during the ECT stimulus likely arise from direct stimulation of vagus nerve nuclei in the brainstem. From an earlier com- putational study which suggested that charge density at the brainstem would be greater with BT than TP-RUL ECT [135], it was predicted that BT would have the greater effects on heart rate, but found empirically that this was not the case. Nevertheless, as 82 Figure 5.11: Comparison of TP-RUL and BT montages in brainstem activation with the medulla ex- tended into a cervical spinal cord. shown later in Figure 7.1 in Chapter 7, the activation in the medulla was less obvious in a high-resolution model, but since the frontal part of CB as well as the pons are seen to be activated, the vagus nerve arising from the medulla and its nuclei may as well be affected by the ECT stimulus. 5.4.3 Effects of variations in stimulus amplitude and pulse width Recent studies have provided evidence that ECT with ultrabrief PWs can reduce cogni- tive side effects, while maintaining useful efficacy [34–36,216]. It has been suggested that due to less energy and charge transfer in briefer pulses, a narrower band of tis- sue may be stimulated, minimising the activation of non-targeted brain tissue with its associated side effects [53, 68]. Simulation results in this chapter indicated that the activated region was more focal for a briefer PW, supporting this hypothesis. There- fore, direct activation of the brain is not only correlated to current density magnitude, but also to the net charge transfer delivered by transcranial electrodes into the brain, underscoring the importance of stimulus PW. In addition, results showed that with a PW of 0.6 ms, the brainstem region was only passively stimulated with a subthreshold response (see Figure 5.8). This result may explain the diminished adverse cardiac ef- fects when TP-RUL ECT was given with ultrabrief pulses (0.3 ms) compared to brief pulses (1 ms) [213, 215]. Conventionally, the stimulus amplitude in ECT is fixed at 800 or 900 mA [203]. Among all possible stimulus parameters, the current amplitude has not been varied in 83 recent ECT studies. Results of this chapter showed that lowering the stimulus ampli- tude reduced both the volume of brain tissue that was directly stimulated (the cortical surface area and the depth of penetration), as well as the induced current density, which was proportional to the amplitude of the ECT current stimulus. This suggests that ma- nipulation of the stimulus amplitude may offer as much, or even greater potential, than varying PW for optimising the ECT stimulus to minimize cognitive side effects. The significance of stimulus amplitude has been overlooked and merits further testing in clinical trials. Further, given the differences in maximum current densities found when electrode placement is altered but stimulus amplitude is kept constant, it may be useful to vary stimulus amplitude when titrating seizure threshold to account for differences in elec- trode placement. Current clinical practice involves varying the number of stimuli (by altering pulse frequency and train duration) to compensate for differences in induced current density. A better approach would be to adjust the current density achieved (which is proportional to neural excitation, as shown by the results) by varying stim- ulus amplitude, an approach also suggested by other investigators [53]. Use of lower stimulus amplitudes may be particularly relevant for BT ECT, which the results showed had the highest maximum induced current density in the temporal region (relevant for memory effects) for stimuli of the same amplitude, and where cognitive, especially memory, impairment, remains a concern [35]. 5.4.4 Model limitations Due to the poor resolution of the CT images used and additional downsampling, the gray and white matters were defined as one brain compartment, the gyri/sulci were not incorporated into the anatomical structure of the brain, and the CSF layer had to be artificially defined. Investigations have shown that the complex geometry of the brain and regional differences in conductance can produce local non-uniformities of current density through the CSF [138]. The skull in the model was one homogeneous compartment with anisotropic conductivity. However, since the skull consists of a low resistance spongiform layer between two high-resistive layers, replacement with a 84 three-layered structure may be more accurate [169, 174]. In addition, the white matter also exhibits anisotropic conductivity due to axonal fibre orientation [169,189]. These anatomical and conductive details may form a significant source of error. 85 Chapter 6 ECT Passive Volume Conductor Simulations in the High-resolution Head 6.1 Computational settings and data analysis 6.1.1 Boundary conditions for volume conductor solver All head compartments were simulated as volume conductors using Laplace’s equa- tion, as in Equation 2.8. The boundary conditions were: • active electrode boundary (electrode A): inward current density set to Jn, and the total injected current I was fixed at 800 mA; • return electrode boundary (electrode B): inward current density set to −Jn; • distributed resistance boundary (at the base of the neck): outward current flow jn, which is calculated by σ · ϕ j = , (6.1) n d where σ is the conductivity of the tissue at the base of the neck and ϕ is the electric potential at this bottom boundary. d is a specified equivalent distance from the bottom boundary to electric ground. This boundary condition is based 86 on the fact that a small proportion of the stimulus current may still be able to flow out of the base of the neck into the torso, and thus an electric insulating boundary condition would not be physically realistic. It was assumed that the reference electrode was placed on the upper chest, similar to Figure 2.1, and thus d was taken as 3 cm and 6 cm in the HEAsub and DEPsub models, respectively; • ground (zero electric potential) at a set point on the lower boundary of the neck; • all other external boundaries were assigned as electric insulators (zero normal component of current density); • continuous current density across all interior boundaries. 6.1.2 Electrode placements Three conventional configurations used in clinical ECT, mentioned in Chapter 5, as well as two new electrode placements were simulated: each utilising two electrodes placed on the scalp, as shown in Figures 6.1 and 6.2: • BF placement: as described in Chapter 5; • BT placement: as described in Chapter 5; • TP-RUL placement: as described in Chapter 5; • SP-RUL placement: one electrode (B) was placed 5 cm superior to the midpoint of the arcus superciliaris on the right, and the other electrode (A) placed near the vertex, the same as electrode A in TP-RUL placement; • Frontoparietal RUL (FP-RUL) placement: one electrode (B) was placed 5 cm superior to the lateral angle of the right eye, the same as electrode B in BF place- ment, and the other electrode (A) placed near the vertex, the same as electrode A in TP-RUL placement. This placement was modelled as a variation of the originally proposed SP-RUL placement — compared to the latter, the frontal electrode is slightly more lateral, avoiding the thick skull bones at the frontal pole. 87 Figure 6.1: Five electrode placements tested on HEAsub head model: bifrontal (BF) placement, bitem- poral (BT) placement, temporoparietal right unilateral (TP-RUL) placement, frontoparietal right unilat- eral (FP-RUL) placement and supraorbital-parietal right unilateral (SP-RUL) placement. ‘A’ and ‘B’ are labels for the separate electrodes in each placement. To respect the subject’s privacy, the eyes of the model are hidden. 88 Figure 6.2: Five electrode placements tested on DEPsub head model: bifrontal (BF) placement, bitem- poral (BT) placement, temporoparietal right unilateral (TP-RUL) placement, frontoparietal right unilat- eral (FP-RUL) placement and supraorbital-parietal right unilateral (SP-RUL) placement. ‘A’ and ‘B’ are labels for the separate electrodes in each placement. To respect the subject’s privacy, the eyes of the model are hidden. 89 6.1.3 Data analysis The models were solved using the segregated numerical solver in COMSOL (v3.5) on a Windows 64-bit workstation with 24 GB RAM utilising 4 processors. To solve the stationary equations, a direct linear solver was utilised with an absolute error tolerance set to 10−5. It took ∼ 20 minutes to solve for the simulation. Simulation results were analysed by comparing the difference in the E-field distri- bution in the brain among different electrode montages and different head models. The analysis also focused on comparing the average E-field magnitude E in several ROIs in the brain. The average E-field was calculated using the following equation: |E| dV E = V , (6.2) dV V where |E| is the magnitude of the E-field in the ROI in question, and represents V a volume integral over this region. Note that the denominator integral is simply the volume of the ROI. In addition, the effect of WM anisotropy was investigated by calculating the relative percentage difference in E between models with and without WM anisotropy, using the following equation: − = Eaniso Eiso × , dE 100% (6.3) Eiso where dE is the difference in E, Eaniso and Eiso are the E in WM anisotropic and isotropic models, respectively. 6.2 Results 6.2.1 Healthy subject head model with white matter isotropy Figure 6.3 shows the E-field magnitude profile over the surface of the whole brain of the HEAsub model for all five different ECT montages, and Figures 6.4 and 6.5 show the brain E-field magnitude in various coronal and horizontal slices, respectively. Similar to the results of Chapter 5, the regions directly beneath the electrodes exhib- ited a greater E-field magnitude compared to the remainder of the brain: however, the 90 maximum E-fields were not found on the gyri, but at the base of the sulci. A high E-field magnitude was found primarily in both frontal lobes in the BF model. The BT placement resulted in a more widely distributed current, which was mainly concen- trated bilaterally on the lateral frontal and temporal lobes. The BT current also spread ventrally, with significant E-field presented in the CB and brainstem. For the three RUL models, all of their E-field profiles presented right-side predom- inance characteristics. The current in the TP model appeared to largely spread over the right side of the brain, with higher E-fields on the frontal, temporal and parietal lobes, as well as the anterior part of the CB and brainstem. In the FP placement how- ever, current was concentrated primarily in the frontal and parietal lobes of the right hemisphere, largely sparing the temporal lobe. In the SP montage, high E-fields were also found in the frontal and parietal lobes of the right hemisphere, but the current also shifted towards the medial part of both hemispheres. That is, in SP, the medial part of the left frontal lobe exhibited a higher E-field than the other two RUL montages. Table 6.1 lists the average regional E-field magnitude for all five ECT montages in the HEAsub model with WM isotropy. As shown in the table, the overall E-fields in both hemispheres were quite similar under both bilateral montages, whereas the right hemisphere magnitude was significantly greater than that in the left under the three RUL montages. The average E-field magnitude in the CB (and brainstem) was higher in BT and TP than in the other three montages. All montages induced a strong E-field in the DLPFC. Those montages with a frontal electrode (including SP) resulted in a relatively stronger E-field in the right DLPFC. The BT configuration exhibited the highest average E-field magnitude in the OFC. In the ACC, the average E-field was significantly higher in all three RUL mon- tages than that of the bilateral montages, with the SP model being the highest. In terms of the hippocampus, those montages having a temporal electrode resulted in a rela- tively high E-field in this region. A comparable E-field was found bilaterally for BT, whereas the E-field magnitude was much higher in the right hemisphere with the TP montage. 91 Figure 6.3: Brain E-field magnitude distribution in the HEAsub WM isotropic model for various ECT montages: bifrontal (BF), bitemporal (BT), temporoparietal right unilateral (TP-RUL), frontoparietal right unilateral (FP-RUL) and supraorbital-parietal right unilateral (SP-RUL). The leftmost, middle and rightmost columns feature the lateral view from the right, the frontal view and the top view, respectively. 92 Figure 6.4: Brain E-field magnitude distribution in the HEAsub WM isotropic model in two coronal slices for various electrode montages: bifrontal (BF), bitemporal (BT), temporoparietal right unilateral (TP-RUL), frontoparietal right unilateral (FP-RUL) and supraorbital-parietal right unilateral (SP-RUL). Dashed lines indicate locations of coronal slice planes. 93 Figure 6.5: Brain E-field magnitude distribution in the HEAsub WM isotropic model in two horizontal slices for various electrode montages: bifrontal (BF), bitemporal (BT), temporoparietal right unilateral (TP-RUL), frontoparietal right unilateral (FP-RUL) and supraorbital-parietal right unilateral (SP-RUL). Dashed lines indicate locations of horizontal slice planes. 94 Table 6.1: Average brain regional E-fields in the ‘HEAsub’ model with WM isotropy (V/m) Compartment BF BT TP-RUL FP-RUL SP-RUL Left hemisphere 46.05 54.05 41.50 38.42 41.90 Right hemisphere 43.29 50.34 67.22 61.80 62.55 CB 23.32 39.82 39.53 30.95 30.95 Left DLPFC 91.99 70.06 34.06 39.58 48.43 Right DLPFC 90.59 66.68 71.67 88.07 94.91 Left OFC 78.84 79.98 29.75 30.34 36.54 Right OFC 80.15 80.68 62.03 54.75 60.62 Left ACC 36.98 33.14 59.65 58.51 67.20 Right ACC 35.72 31.31 66.04 62.82 70.80 Left hippocampus 44.38 64.69 42.47 36.14 37.25 Right hippocampus 42.97 62.04 59.06 49.84 49.69 6.2.2 Healthy subject head model with white matter anisotropy Figure 6.6 shows the E-field in the HEAsub model with WM anisotropy. In general, the E-field distribution in the anisotropic model was similar to the isotropic model with the same montage. However, local non-uniformities in the E-field were more prominent in the anisotropic model. Figures 6.7 and 6.8 present the E-field magnitude distribution in coronal and hor- izontal slices, respectively. As shown in these figures, the E-field in the anisotropic model exhibited inhomogeneous regions of greater current concentration compared to the isotropic case where the electric field was more uniformly distributed. Regions exhibiting a high E-field magnitude match the sites where major fibres in the brain are located, including the corpus callosum and the internal and external capsules. A list of regional E-fields in the brain for the WM anisotropic model is given Table 6.2. The pattern revealed by the average E-field magnitude with WM anisotropy mostly agrees with that found in the isotropic models. However, the differences in the ROI magnitudes between different montages are not the same as that of the isotropic model. Table 6.3 compares the average E-field magnitude between isotropic and anisotropic 95 Figure 6.6: Brain E-field magnitude distribution in the HEAsub WM anisotropic model for various ECT montages: bifrontal (BF), bitemporal (BT), temporoparietal right unilateral (TP-RUL), frontoparietal right unilateral (FP-RUL) and supraorbital-parietal right unilateral (SP-RUL). The leftmost, middle and rightmost columns feature the lateral view from the right, the frontal view and the top view, respectively. 96 Figure 6.7: Brain E-field magnitude distribution in the HEAsub WM anisotropic model in two coro- nal slices for various ECT montages: bifrontal (BF), bitemporal (BT), temporoparietal right unilateral (TP-RUL), frontoparietal right unilateral (FP-RUL) and supraorbital-parietal right unilateral (SP-RUL). Dashed lines indicate locations of coronal slice planes. 97 Figure 6.8: Brain E-field magnitude distribution in the HEAsub WM anisotropic model in two horizon- tal slices for various ECT montages: bifrontal (BF), bitemporal (BT), temporoparietal right unilateral (TP-RUL), frontoparietal right unilateral (FP-RUL) and supraorbital-parietal right unilateral (SP-RUL). Dashed lines indicate locations of horizontal slice planes. 98 Table 6.2: Average brain E-fields in the ‘HEAsub’ model with WM anisotropy (V/m) Compartment BF BT TP-RUL FP-RUL SP-RUL Left hemisphere 51.45 61.97 50.25 46.00 49.61 Right hemisphere 48.83 57.83 81.71 73.35 74.47 CB 27.45 47.28 46.33 35.34 35.09 Left DLPFC 101.83 77.43 36.31 43.10 53.06 Right DLPFC 100.36 70.13 72.96 88.90 99.80 Left OFC 81.66 90.79 32.40 30.77 37.89 Right OFC 83.20 93.68 89.17 65.04 70.89 Left ACC 56.11 49.10 80.58 74.93 83.49 Right ACC 61.18 52.47 91.34 80.38 86.09 Left hippocampus 59.03 91.44 59.72 46.85 47.26 Right hippocampus 56.26 85.09 95.67 67.70 63.90 models in terms of relative difference. As can be seen from the table, the differences in each ROI varied among the electrode montages. RUL montages in general exhib- ited greater difference in the E-field magnitude over both hemispheres. The difference in both DLPFC and OFC regions was relatively small, the largest being 10.77% with BF on the right and 43.75% with TP on the right, while the corresponding smallest differences were 0.94% with FP on the right and 1.42% with FP on the left. In com- parison, the relative difference in the ACC was much more significant, the maximum being 71.27% with BF on the right and the minimum 21.60% with SP also on the right. Meanwhile, the differences in this region with the three RUL montages were all lower than that with the bilateral montages. The largest and smallest differences found in the hippocampus were 62.00% with TP on the right and 26.89% with SP on the left, which were also significant. If looking at each montage individually, the regions with the highest relative difference were the ACC and the hippocampus with all montages. 99 Table 6.3: Relative E-field difference with and without WM anisotropy (%). Percentage difference is relative to the isotropic case according to Equation 6.3. Compartment BF BT TP-RUL FP-RUL SP-RUL Left hemisphere 11.72 14.65 21.09 19.73 18.39 Right hemisphere 12.80 14.90 21.56 18.70 19.05 CB 17.68 18.74 17.23 14.17 13.37 Left DLPFC 10.70 10.51 6.63 8.89 9.76 Right DLPFC 10.77 5.17 1.79 0.94 5.15 Left OFC 3.58 13.52 8.92 1.42 3.67 Right OFC 3.80 16.10 43.75 18.78 16.95 Left ACC 51.71 48.16 35.09 28.08 24.24 Right ACC 71.27 67.60 38.30 27.96 21.60 Left hippocampus 32.99 41.35 40.64 29.64 26.89 Right hippocampus 30.93 37.16 62.00 35.82 28.61 6.2.3 Depressive subject head model A third set of simulations was performed on the DEPsub high-resolution head model. As with the HEAsub model, this model also incorporated a three-layer skull, but did not include WM anisotropy. Figure 6.9 shows the E-field magnitude profile in the whole brain of the DEPsub model for all five different ECT montages, and Figures 6.10 and 6.11 show the E-field magnitude distribution for the coronal and horizontal slices, respectively. The E-field magnitude distribution in the DEPsub model is quite similar to that of the correspond- ing isotropic HEAsub model, with some minor differences, such as the current in the SP-DEPsub model tended to extend to posterior part of the right temporal lobe. This was presumably due to differences in the head geometries of the models. Table 6.4 lists the average E-field magnitude for all five ECT montages in the DEP- sub model. As with the HEAsub models, the E-fields in both hemispheres were quite similar in the two bilateral montages, whereas the difference between right and left was significant with the RUL montages. The average E-field magnitude in the CB (includ- 100 Figure 6.9: E-field magnitude distribution in the DEPsub model for various ECT montages: bifrontal (BF), bitemporal (BT), temporoparietal right unilateral (TP-RUL), frontoparietal right unilateral (FP- RUL) and supraorbital-parietal right unilateral (SP-RUL). The leftmost, middle and rightmost columns feature the lateral view from the right, the frontal view and the top view, respectively. 101 Figure 6.10: E-field magnitude distribution in the DEPsub model in two coronal slices for various electrode montages: bifrontal (BF), bitemporal (BT), temporoparietal right unilateral (TP-RUL), fron- toparietal right unilateral (FP-RUL) and supraorbital-parietal right unilateral (SP-RUL). Dashed lines indicate locations of coronal slice planes. 102 Figure 6.11: E-field magnitude distribution in the DEPsub model in two horizontal slices for various electrode montages: bifrontal (BF), bitemporal (BT), temporoparietal right unilateral (TP-RUL), fron- toparietal right unilateral (FP-RUL) and supraorbital-parietal right unilateral (SP-RUL). Dashed lines indicate locations of horizontal slice planes. 103 Table 6.4: Average brain regional E-fields in the ‘DEPsub’ model (V/m) Compartment BF BT TP-RUL FP-RUL SP-RUL Left hemisphere 53.64 58.74 52.25 50.82 58.28 Right hemisphere 54.97 58.51 85.08 79.69 80.99 CB 24.32 43.47 53.66 37.63 38.61 Left DLPFC 104.84 82.70 55.18 63.06 79.48 Right DLPFC 107.91 82.48 93.52 108.95 119.49 Left OFC 96.73 101.22 42.51 49.39 61.71 Right OFC 97.85 92.92 76.68 81.95 97.43 Left ACC 36.59 32.73 64.51 63.58 78.29 Right ACC 41.20 36.40 66.77 71.56 82.35 Left hippocampus 68.47 95.90 49.33 41.29 47.75 Right hippocampus 66.54 93.32 88.67 79.48 75.36 ing brainstem) was also very high in BT and TP, with the magnitude being higher with the TP montage, unlike the HEAsub model which had a slightly greater magnitude with the BT montage. In terms of the E-field in the various ROIs, the pattern was similar to the HEAsub model. Those montages with a frontal electrode still exhibited high field strengths on right DLPFC, but the montage that induced the strongest E-field in this region was the SP with the DEPsub model, as against BF with the HEAsub model. Unlike the HEAsub model, BF and SP induced the highest average E-field strength in right OFC. In regards to the ACC, the case was similar to the HEAsub model: the average E-field magnitude was significantly higher in all three RUL montages than that in bilateral montages, and the magnitude in the SP model was the highest. 104 6.3 Discussion 6.3.1 ECT electrode montages and clinical implications The unilateral ECT electrode configuration is commonly placed on the right side of the head. Since for the majority of people, the left hemisphere of the brain is the dom- inant side for the control of speech and memory, a RUL montage will thus exert less effect on verbal memory [217]. RUL ECT montages have been shown to significantly reduce confusion and memory disturbance after the treatment, compared to the tradi- tional bilateral montage, namely the BT electrode configuration [28,29,218,219]. It is assumed that a smaller amount of electric current is delivered into the brain in unilat- eral montages [135], especially in the hippocampi, which are associated with memory consolidation. In the previous chapter, it was demonstrated that BT ECT directly acti- vated the temporal lobes bilaterally, whereas TP ECT activated only the right lobe. But since that head model was at a low resolution, the effect of ECT on the hippocampi could not be determined. The results from the high resolution models of this chapter showed that mean E-field throughout the brain with TP ECT was not necessarily less than BT ECT, however the E-field in the hippocampi, especially in the left hippocam- pus, was stronger with the BT montage. This finding mostly agrees with what Lee et al. [137] reported in their modelling study. The simulations confirmed that among the three conventional montages (BF, BT and TP), BF ECT generated stronger E-fields in the anterior portion of the head in gen- eral, especially in prefrontal structures, than the other two montages. Furthermore, BT ECT resulted in higher E-field magnitudes in the frontal part of both hemispheres than TP ECT. Surprisingly, the ACC with TP ECT had the highest average E-field mag- nitude among these three configurations. It is commonly believed that abnormalities with the ACC are an important part of the depression circuit model [13,220]. Evidence has shown that focal stimulation via DBS targeted at the subcallosal cingulate gyrus, a subdivision of ACC, eased abnormal network activity and exerted an antidepressant effect [221,222]. Therefore, the strong E-field in the ACC may be part of the reason for the efficacious antidepressant outcome with TP ECT. In addition, BF ECT produced 105 the least amount of E-field strength in the brainstem, which may explain recent findings that BF ECT had less effects on heart rate than both BT ECT and TP ECT [213–215], since the brainstem is known to be involved with cardiac regulation due to the presence of vagal nuclei. As mentioned earlier in Chapter 2, the conventional RUL montage is TP, first pro- posed by d’Elia [219]. Simulation results of this chapter confirm that among the three RUL montages, the two montages with a frontal electrode — FP and SP, produced stronger E-fields in the DLPFC and ACC, both of which are considered to play im- portant roles in the depression network [13]. In addition, both FP ECT and SP ECT generated a lower E-field strength in the hippocampi, as well as in the CB and brain- stem, compared to TP ECT. The simulation results of this chapter thus indicate that frontal placements may be better candidates for a RUL montage — i.e., provide sim- ilar efficacy with lesser memory impairment. It may appear from the results that SP ECT holds an advantage over FP ECT, but since the frontal electrode in the SP mon- tage is placed more medially on the frontal bone than FP, the electric impedance of SP is higher (calculated impedances for the FP and SP montages in the HEAsub WM anisotropic model are 158.88 Ω and 168.01 Ω, respectively). According to Ohm’s law, as the impedance increases, the voltage must increase to keep a constant current out- put. As a result, the delivery of high voltage through a high impedance montage may lead to the possibility of skin burn, or more likely, due to voltage limiting associated with modern ECT devices as a safety precaution, to the failure of an effective stimulus being delivered [53, 223]. 6.3.2 Model validation and limitations As is pointed out by Lee et al. [137], validation of computer simulations of E-field distribution in the brain with experiments remains a challenge, because of the diffi- culty in obtaining data in vivo. One option available is to compare simulation results with existing studies. Using a high-resolution head model, Lee et al. [137] reported median E-field values in the whole brain for the three conventional ECT montages to be around 200 V/m, which is about 4 times the average E-field magnitude obtained in 106 the simulations here. The reason for this discrepancy may be their choice of high skull conductivity of 0.0132 S/m, which was more than twice as much as the compact bone conductivity here. Another study was conducted by the same group using concentric- sphere models, with maximum cortical E-field values for the three montages reported of this chapter ranged between 210–250 V/m [146], similar to the maximum E-fields obtained here. In addition, by rescaling the current used in another tDCS modeling study [155] to 800 mA, the maximum E-field value in the brain can be extrapolated to be around 300 V/m, which is also consistent with the simulation results of this chapter. The results of this chapter demonstrated that the incorporation of WM anisotropy greatly altered the E-field distribution inside the brain, in agreement with previous simulation studies [137, 156, 171–173, 188]. Unlike the relatively uniform E-field dis- tribution found in WM isotropic models, the distribution in the anisotropic model ex- hibited a highly non-uniform pattern. Due to a higher conductivity along the fibre tracts, the current flow largely followed the fibre direction in the WM anisotropic mod- els. However, the local elevated E-field magnitude in the anisotropic model was not necessarily due to an increased current flow along the tracts. As suggested by Lee et al. [137], when current is driven to flow perpendicular to the fibres, a high E-field magnitude can also be produced due to the high impedance direction. This scenario was highly obvious in the internal capsule with the BT montage, as shown in Figure 6.8. In addition, it appears that deep brain structures, such as the ACC and hippocam- pus, are more influenced by the WM anisotropy. A similar conclusion was also drawn from several existing comparison studies on various forms of brain-stimulation tech- niques [137,188,224]. Therefore, WM conductivity anisotropy plays an important role in accurate investigation of ECT effects on deep brain structures, and such anisotropy should be incorporated into computational head models of transcranial stimulation wherever possible. In regards to skull thickness, a previous study found no association between skull thickness and EEG alpha power [225]. However, there was significant correlation be- tween EEG activity and skull thickness at frontal sites, but as the electrode moved posteriorly, the correlation became insignificant [225]. Several studies have looked 107 at skull resistivity at various locations. Law [226] measured skull resistivity over the upper surface of a human adult skull, obtaining values between 1,360–21,400 Ω · cm. Tang et al. [227] found a resistivity within a similar range, and reported an inverse correlation between skull resistivity and thickness. Therefore, it is possible that skull thickness may contribute to individual variability when discussing ECT clinical out- comes. A modelling study using a spherical head model investigated the effect of anatomical variability, and found that skull thickness had a great influence on the ECT- induced maximum E-field magnitude and the size of the stimulated brain volume [228]. Computer modelling may be a useful tool for identifying the optimal placement of treatment electrodes in patients with significant skull inhomogeneities, eg skull defect due to prior trauma, where ECT is required, Nevertheless, the extent to which such anatomical variabilities can be captured by the segmentation tools (and in the end be preserved in the reconstructed model), re- mains a critical problem. Due to low signal intensity produced by bony structures in MRI, it is not an easy task to distinguish the skull from surrounding structures, espe- cially from the paranasal sinuses since skull and air have overlapping signal intensi- ties [229]. In MRI scans, intensity non-uniformities within the same tissue, caused by inter-individual variation in magnetic susceptibility, as well as inhomogeneous mag- netic fields during MRI acquisition, prevent a clear distinction and accurate separation between different tissues [176,229]. In addition, uncertainties about the exact size and location of ROIs in the brain also contribute to the inaccuracies of the simulation results and discrepancies between various models [130, 137]. The DTI data have highly non- linear characteristics, and therefore, a simple interpolation of individual components of fibre conductivity tensors may compromise the accuracy of data interpretation. More- over, imperfect alignment between reconstructed structures and conductivity tensors also adds to the likelihood of introducing errors into final results. 108 Chapter 7 ECT Brain Activation Simulations using a High-resolution Head 7.1 Model settings and data analysis 7.1.1 Model setup The electrode configuration used was TP-RUL with the HEAsub model with WM anisotropy, as shown in Figure 6.1. The boundary conditions for the volume con- ductor solver were the same as in Chapter 6, except that the total injected current I had a time-dependent waveform, whose parameters are detailed below, and that brain compartments including GM, WM and CB were simulated using the ionic continuum model described in Section 4.5. A total of seven combinations of stimulus parameters were investigated. The ‘con- trol’ stimulus mode was carried out with biphasic (bidirectional) pulses of 800 mA amplitude, 1 ms PW and 60 Hz frequency, with a latency of 1 ms before the first pulse was delivered. The time between anodic and cathodic onset was set to half the stimulus period, i.e., 8.33 ms. All other stimulus modes were named after the parameter distinct to the ‘control’ mode, as listed in Table 7.1, where ‘uni’ indicates the pulses in the stimulus were monophasic (unidirectional). All models were simulated for a total of three full periods. The biphasic current stimulus waveforms were anodic-first applied 109 Table 7.1: ECT stimulus parameters Stimulus Mode Direction Amplitude PW Frequency No. of Cycles (mA) (ms) (Hz) control bi 800 1 60 3 90-Hz bi 800 1 90 3 120-Hz bi 800 1 120 3 temporal uni 800 1 120 3 vertex uni 800 1 120 3 0.5-ms bi 800 0.5 60 3 400-mA bi 400 1 60 3 to electrode A (Figure 6.1). For the models with monophasic stimuli, the ‘tempo- ral’ model referred to anodic-stimulation applied to electrode A, whereas the ‘vertex’ model referred to anodic-stimulation applied to electrode B. 7.1.2 Data analysis The models had over 6×106 degrees of freedom, and were solved in COMSOL (v3.5) using the segregated numerical solver on a Windows 64-bit workstation with 24 GB RAM utilizing 4 processors. To solve the time-dependent equations, a variable step BDF scheme was utilised with an absolute error tolerance set to 10−3. It took approx- imately 144 hours to solve for one simulation with a three-cycle-long stimulus. The simulation data were analyzed by calculating the average MP over two full cycles of stimuli. Two types of activation modes were defined to assist in quantifying the extent of brain activation: the primary mode of activation (mode 1), was defined as that in which one AP was initiated per full stimulus cycle, whilst the secondary mode of activation (mode 2) was at least one AP generated every two full stimulus cycles. The average MPs of the two activation modes over two full cycles for each frequency, listed in Table 7.2, were approximated in MATLABR by solving the ionic HH equations with the same parameters as in the models. These values were used as thresholds for post-processing simulation results in COMSOL. The brain regions 110 Table 7.2: Average HH membrane potentials for various ECT stimulus modes + frequencies. These defined membrane potential threshold values for determining the stimulus modes of each brain region. Frequency Mode 1 Mode 2 (Hz) (mV) (mV) 60 -55.93 -57.57 90 -51.75 -56.38 120 -46.34 -55.59 with average MPs greater than these thresholds were considered as mode 1 and mode 2 activated regions, respectively, and the extent of brain activation was measured by following equation: V |MP ≥ threshold activation extent = ROI × 100%, (7.1) VROI where VROI denotes the volume of the ROI, and VROI|MP ≥ threshold represents the volume of activated ROI. And thus, in a two-cycle analysis, the fraction under mode 2 can be considered as activated by the first cycle, whereas the fraction under mode 1 can be seen as activated by both cycles. 7.2 Results 7.2.1 Variation in ECT stimulus frequency The average MP in the brain over the first two cycles under various stimulus frequen- cies is shown in Figure 7.1, with side view (top row) and top view (mid row) plots showing the extent of activation on the brain surface along a horizontal section (bottom row) plots showing the spatial depth of activation into the brain. Figure 7.1 suggests that when only the frequency of the stimulus varies, the brain region activated by the current shares a similar size. Figure 7.2b illustrates the simulated transmembrane po- tentials at the same right temporal location in the brain close to the cortical surface for the three different stimuli, showing that both 60 Hz and 90 Hz stimuli managed to initiate an AP at every cycle, whereas 120 Hz only initiated an AP at every other 111 Figure 7.1: Average MP over the first two cycles for three different stimulus frequencies corresponding to 60 Hz (control), 90 Hz and 120 Hz. The rows of the figure show the right side view (top row), top view (mid row) and horizontal section (bottom row). The dashed line on the upper/left surface plot denotes the position of the horizonal plane. cycle; moreover, the third AP in the 90-Hz model shows obvious fatigue (i.e., reduced overshoot) in comparison to the first two. Table 7.3 shows the effect of stimulus frequency in several ROIs. The size of these regions under activation mode 2 are comparable; however, the size of mode 1 activated regions varies significantly among the three types of stimuli. No brain region was under mode 1 activation in 120-Hz model. Only a relatively small volume in each ROI was under mode 1 activation with the 90-Hz model, and the size of the whole brain under activation mode 1 was less than 10% of that under mode 2. But in the simulation with the ‘control’ stimulus, the size of mode 1 activated regions was much larger, being almost comparable to that of mode 2, especially for regions closer to the electrodes. 112 Figure 7.2: (a) ECT stimulus waveform and (b) MP within activated right temporal region. Each stimu- lus phase was of frequency 60 Hz (solid line), 90 Hz (dashed line) or 120 Hz (violet dash-dotted line). The stimulus was cathodic first with respect to the right temporal lobe electrode B. 113 Table 7.3: Effect of ECT stimulus frequency on ROI activation for two activation modes Stimulus Mode Control 90-Hz 120-Hz Activation Mode 1 2 1 2 1 2 Activated Volume (%) Whole brain 21.24 27.26 2.39 28.84 0 26.38 Right hemisphere 44.19 52.80 7.88 53.45 0 49.89 Right OFC 96.61 99.89 6.58 94.97 0 96.74 Right DLPFC 8.79 24.62 0.01 26.93 0 23.28 Right ACC 16.62 24.04 0 26.85 0 27.43 Right AH 3.17 27.06 0.13 29.09 0 20.3 CB 1.71 6.86 0.01 8.31 0 4.50 Surface Area (%) Whole Brain 40.06 46.67 9.85 48.21 0 44.78 7.2.2 Variation in ECT pulse type Due to the nature of the monophasic pulse stimulus, only the area under one electrode was activated, whereas the other electrode induced inhibition in the region beneath it, as shown in Figure 7.3 for the ‘temporal’ model. Furthermore, every alternate pulse, as illustrated in Figure 7.4b, caused a sub-threshold depolarisation instead of hyper- polarisation, as in the control (biphasic stimulus) model, and thus an elevated average MP can be found in the brain region under electrode B in the monophasic model, as demonstrated in Figure 7.3. As can be seen from Figure 7.3 and Table 7.4, the volume of activated brain region was greatly reduced compared to ‘control’ in the monophasic model. Regarding the ROIs, regions that were closer to the cathode were less affected: for the ‘temporal’ model, the OFC and DLPFC were least affected, and the AH and CB were moderately influenced, especially the size of their mode 2 activated region, whilst the ACC was not activated in the monophasic model. For the ‘vertex’ model, among all ROIs, only the ACC was activated. 114 Figure 7.3: Average MP over the first two cycles with stimuli of different pulse type, with right side view (top row) and top view (mid row) plots showing the extent of activation on the brain surface, and horizontal section plots (bottom row) showing the depth of activation into the brain. The dashed line on the upper/left surface plot denotes the position of the horizonal plane. 115 Figure 7.4: a ECT stimulus waveform and (b) MP within activated right temporal region. Each stimulus phase was of type biphasic (solid line) or monophasic (dashed line). The stimulus was cathodic first with respect to the right temporal lobe electrode B. 116 Table 7.4: Effect of stimulus type on ROI activation for two activation modes Stimulus Type Control (Biphasic) Temporal (Monophasic) Vertex (Monophasic) Activation Mode 1 2 1 2 1 2 Volume (%) Whole Brain 21.24 27.26 6.09 7.16 12.43 14.36 Right Cerebrum 44.19 52.80 17.73 20.04 23.38 25.56 Right OFC 96.61 99.89 95.39 98.56 0 0 Right DLPFC 8.99 24.62 8.89 14.67 0 0 Right ACC 16.62 24.04 0 0 10.25 15.64 Right AH 3.17 27.06 2.25 18.85 0 0 CB 1.71 6.86 1.65 3.19 0 0 Surface Area (%) Whole Brain 40.06 46.67 11.97 13.44 24.80 27.55 7.2.3 Variation in ECT pulse width and amplitude Another set of simulations were performed by altering the stimulus PW and magnitude. Table 7.5 shows that by reducing either the PW or the amplitude by half, the volume of directly activated regions (mode 1 or 2) reduced significantly, particularly for ROIs furthest from the electrodes. Both AH and CB were not directly activated when either PW or amplitude was reduced by half. In addition, the reduction of activated mode 1 regions was more prominent than that of mode 2. Since the total charge delivered by a single pulse in the latter two models was the same (i.e., product of amplitude and PW), the size of the activated region was similar for both stimulus types. Nevertheless, the activated region in the 0.5-ms model was still slightly larger than that of the 400-mA model. 7.3 Discussion This chapter simulated the direct excitation of the brain due to transcranial current application during ECT, using a high-resolution anatomically-accurate model, with the incorporation of WM anisotropy and a three-layered skull. The analysis focused 117 Table 7.5: Effects of stimulus pulse width and amplitude on ROI activation Stimulus Mode Control 0.5-ms 400-mA Activation Mode 121212 Volume (%) Whole Cerebrum 21.24 27.26 6.32 11.02 5.59 10.40 Right Cerebrum 44.19 52.80 17.03 27.30 16.75 24.85 Right OFC 96.61 99.89 22.40 57.47 17.89 54.02 Right DLPFC 8.79 24.62 0.01 0.60 0.01 0.42 Right ACC 16.62 24.04 0.01 0.10 0 0 Right AH 3.17 27.06 0000 CB 1.71 6.86 0000 Surface Area (%) Whole Brain 40.06 46.67 18.06 25.76 16.75 24.85 on comparing the spatial extent of direct neuronal activation in the brain as the stimulus parameters were varied. 7.3.1 Effects of ECT stimulus frequency When a train of ECT stimulus pulses is delivered to the brain, cumulative neuronal activation occurs such that when a sufficient number of pulses are given, a seizure is triggered. Thus the total number of delivered pulses in an ECT stimulus train is believed to be a key parameter for seizure induction [2, 53]. However, the simulation results of this chapter suggest that the above statement may not be completely precise. The above does not take into account the number of effective pulses in the stimulus train which elicit significant physiological changes, such as neuronal depolarisation. In these models, although a similar cortical volume was activated with all three ECT frequencies, the characteristics of the activation were different. Hence, the efficiency of the stimulus train under different frequencies varied. In the 120-Hz model, of all the brain neurons that were able to be directly activated by one full cycle, none were activated by the second of two consecutive cycles. Hence 118 for a stimulus of this frequency, the number of efficient pulses is likely to be only 50% of the total pulse number. In the 90-Hz model, the size of the whole brain under activation mode 1 was less than 10% of mode 2, suggesting that in the first two cycles of this stimulus train, the efficiency of the second cycle is only around 10% of the first one. In addition, the slight reduction in MP overshoot for the third AP indicates that the activation pattern may be more complex if given a long stimulus train. In comparison, when a stimulus with 60 Hz frequency was delivered, the efficiency of the second cycle was almost 80% of the first. A similar trend was found in the ROIs for all three frequencies. Therefore, of the three frequencies modelled, the 60 Hz train appears the most efficient for cortical activation. The likely reason why a smaller volume (or none) of the cortical region was under activation mode 1 compared to mode 2, was that the neurons were still in their refrac- tory state when subsequent pulses were delivered. The refractory period in neurons is typically around 3–5 ms [2, 122], with some even longer than 5 ms [230]. During the refractory period, the AP is either unable to be initiated (absolute refractory period), or requires much higher stimulus energy to be initiated (relative refractory period). The single-compartment neurons in our continuum model have a similar refractory period. Furthermore, neurons further away from the electrodes required more time to charge to threshold, as the current density in these regions was lower [40], increasing their latency of activation. When a subsequent pulse was delivered, neurons further away were still within their refractory period, and hence the stimulus was insufficient to elicit an AP. Consequently, a stimulus train of lower frequency was able to provide sufficient time for neurons to fully recover, which led to a high efficiency in AP generation. In reality, the duration of the refractory period varies between types of neurons, and the frequency-efficiency relationship would thus be more complex. Modern ECT studies have shown that stimuli with lower pulse frequencies have a higher efficiency for triggering seizure than high frequency stimulus trains [231]. In addition, lower frequencies have been demonstrated to require a smaller number of pulses to induce seizure [232, 233]. An early animal experiment on cortical electrical stimulation to compare seizure induction among stimuli with frequencies from 10 to 119 300 Hz, found that the 60-Hz stimulus was the most efficient in triggering seizure [234]. Our simulation results concur with these observations, since the ECT-induced seizure presumably resulted from accumulation of repetitive activation at or near the region of seizure onset [2, 235], 7.3.2 Effects of ECT pulse type A limited number of ECT and repetitive-TMS studies found that a monophasic stimu- lus train is capable of enhancing stimulus efficiency [61–66, 69], as well as leading to the reduction of seizure threshold [69]. Two monophasic pulses in one stimulus cycle delivered to a presumed region of seizure onset, compared to only one pulse of that polarity in one cycle of a biphasic stimulus, would presumably be twice as efficient as a biphasic train. However, this is not strictly the case, owing to the existence of neuronal refractory period, as discussed above. Results showed that when a second pulse in one cycle of monophasic stimulation was delivered, a slight depolarisation occurred because the neuron was still refractory. However, in comparison with the hyperpolarisation caused by the reversed pulse po- larity in a biphasic stimulus, the elevation in MP induced by the second pulse of the monophasic train still provided facilitation of cortical activation and energy accumu- lation. Thus, it is possible to induce a seizure with lower charge using a monophasic stimulus train. By choosing a stimulus frequency which allows neurons to recover between pulses, a significant reduction in seizure threshold is possible. A critical aspect that needs to be taken into consideration in monophasic stimula- tion, is the polarity of the electrode. When a conventional biphasic stimulus is adopted, both electrodes alternate as the anode and the cathode during the stimulus train. How- ever, when a monophasic stimulus is employed, the anode and the cathode are spatially defined and not interchangeable during the entire stimulus, and thus have a fixed po- larity. Evidence from functional electrical stimulation (FES) is that under the cathode dur- ing electrical stimulation, the neuronal membrane is depolarised, while conversely, hy- perpolarisation occurs under the anode [236]. However, studies using tDCS show that 120 anodal tDCS is able to enhance the activity of neurons, whereas cathodal tDCS sup- presses their activity [85, 99, 100]. One explanation for this phenomenon is that weak direct current may selectively influence cortical interneurons, while a strong stimulus intensity may also modify the excitability of pyramidal cells [103, 105, 106]. Because inhibitory interneurons make up a much larger percentage of the cortical interneurons than excitatory interneurons [237], the predominant effect of anodal tDCS may be overall excitation through hyperpolarisation of inhibitory interneurons, while cathodal tDCS results in overall inhibition by depolarising inhibitory neurons. As ECT employs a much stronger current than tDCS, the pyramidal cells are thus thought to be excited by the cathode (or the negative pulse), and to be inhibited by the anode (or the positive pulse) where a monophasic stimulus is used. Results have shown an increased focality in the area of direct neuronal activation with a monophasic stimulus, which exerts its effect as a result of fixed polarity. Stim- uli with alternating polarity are able to directly activate brain regions under both elec- trodes, whereas stimuli with fixed polarity only directly excite neurons beneath the cathode. Even though ECT induces a ‘generalised’ tonic-clonic seizure, the brain re- gion directly activated by the electrical stimulation affects clinical, EEG and imaging outcomes, as demonstrated when electrode placement is varied [235]. Thus, the ability to selectively activate one brain region predominantly, by use of a monophasic stimu- lus, rather than the obligatory activation of two brain regions as occurs with a biphasic stimulus, may be advantageous, if the preferential site of activation for therapeutic effects is known. The simulation results of this chapter, which adopted RUL placement, showed that compared to biphasic stimulation, cathodal stimulation on the right temple activated the OFC and DLPFC similarly, with some variation in the AH and CB, and no direct activation of ACC. This indicates that the temporal electrode exerts a greater effect on the OFC, DLPFC and AH, whereas the vertex electrode leads to ACC activation. All these areas — OFC, DLPFC, AH and ACC — have been implicated in the pathophysi- ology of depression [12,13,107]. Thus the combination of a monophasic stimulus and variation in electrode placement, with use of active neuronal modelling to elucidate 121 the interaction of these factors, may lead to refinement of the ECT stimulus through selective activation of key regions, while avoiding direct stimulation of areas that may lead to cognitive impairment. In addition, it has been concluded in previous modelling studies that the high E-field (or activation) in the motor cortex under RUL configura- tion may be the reason why this montage has the lowest seizure threshold [40, 137]. It can therefore be speculated that monophasic RUL ECT with cathodic-stimulation applied to vertex electrode may result in a lower seizure threshold. 7.3.3 Effects of ECT stimulus pulse charge In titrating an individual patient’s seizure threshold, stimuli of increasing electrical charge are delivered until a generalised seizure occurs. Similarly, increases in cur- rent dosage during a course of ECT treatment typically involve delivery of stimuli of increasing overall charge. As discussed above, some studies have examined the effi- ciency of increasing the pulse frequency in order to achieve higher levels of charge. Pulse amplitude, on the other hand, has typically not been manipulated in setting dose treatment levels. The product of amplitude and PW for a single pulse is the total pulse charge. A computational modelling study of transcranial electrical stimulation with unilateral electrode placement estimated that the stimulus intensity threshold for motor activation was 175 to 269 mA, corresponding to PWs of 1 to 0.05 ms [238], which may suggest that conventional ECT with 800 mA amplitude and 1 ms PW delivers a level of charge substantially more than that needed for cortical neuronal activation. Several studies have shown that by keeping the same stimulus dose (total electric charge), the schemes using lower pulse charge with greater number of pulses can be as effective as (if not more than) those using higher pulse charge with less pulses, and with fewer side effects [35, 239, 240]. The reduction of pulse charge, either by reduction in amplitude or in PW, leads to a decrease in size of the activated ROIs, especially in mode 1, which in turn has implications to seizure induction as well as therapeutic and adverse effects. The extent of reduction in activation volume was different for the various ROIs: the effect was more pronounced in ROIs further from the electrodes. Thus, being the farthest away 122 from both electrodes, the hippocampus and CB were not activated at all in both ‘re- duction’ models. ACC and DLPFC activation were also greatly reduced, but were still activated, and OFC was least affected as it was close to the temporal electrode. Simi- larly, the reason why the ACC was less influenced than the AH is that it was relatively close to the vertex electrode. Hence, in BT ECT where the vertex electrode is missing, reducing the PW to 0.3 ms may result in an inactive ACC, which could explain why ultrabrief BT ECT was not found to be as effective as ultrabrief RUL ECT [35]. However, it is currently not known which of PW or amplitude is the more impor- tant or efficacious parameter to modulate in clinical ECT. Research is thus needed to investigate this matter, in order to arrive at an optimal ECT paradigm. In terms of neuronal activation, the relation of PW and amplitude of a rectangular pulse required to elicit neuronal firing, known as the strength-duration relationship, can be described with a hyperbolic formula of the form of t A = A × (1 + cx ), (7.2) rb PW where A is the amplitude of the pulse; Arb is the rheobase, the minimum amplitude with long PW to reach the firing threshold; tcx is the chronaxie, the PW when the amplitude is equal to twice the rheobase [241]. This formula suggests that ideally, the directly activated volume should be equal whenever the pulse charge is the same. However, simulation results show that, although the size of activated ROIs in both 0.5-ms and 400-mA models were very similar, a slightly greater reduction in activated volume occurred when the amplitude was altered. These differences may be important when stimulating near vital structures, which are important for efficacy and/or adverse cognitive effects. 7.3.4 Model implications and limitations As mentioned in Chapter 5, the computational model of this chapter, which incor- porated excitable ionic neural elements into the brain, represents a novel approach in simulating ECT. However, because seizure (propagation of activation) was not in- corporated into the model, simulations revealed only those regions that were directly 123 stimulated by the transcranial current, which is presumably the region of seizure onset. By using this whole head model, it was feasible to simulate the direct spatial activation of the brain under various combinations of ECT stimulus parameters, and to report the differences among these combinations, which has not yet been conducted in previous modelling studies. A major limitation of these models is that they were computationally expensive to solve. For a single simulation with a three-cycle-long stimulus, it required approx- imately six days to solve, making it unrealistic to complete a simulation with a full stimulus train consisting of hundreds of pulses. Another limitation is that it is dif- ficult to validate simulation results, since there exists no adequate empirical data for comparison. The difficulty in carrying out functional imaging during the instant of ap- plication of large transcranial currents precludes the complete characterization of the direct activation of the brain during the therapy. As mentioned in Chapter 6, limitations in image segmentation and computational tools can affect the precision of the recon- structed anatomy, and therefore, the size of ROIs may be in error. There also exists some uncertainty in the precise electrical properties of the compartments in the model due to a wide range of tissue conductivity values reported, especially those of the skull and WM compartments. In addition, the HH formulation of the neuronal AP represents a simple model of activation, chosen for computational expediency. If desired, more complex ionic models may be used in future. Nevertheless, the ECT model described here provides useful implications for clinical research, and represents a novel approach in simulating direct brain activation in ECT. 124 Chapter 8 tDCS Volume Conductor Simulations with High-resolution Head Geometry 8.1 Model settings and data analysis 8.1.1 Boundary conditions for volume conductor model All head compartments in the tDCS simulations were formulated as passive volume conductors using Laplace’s equation, as in Equation 2.8. The boundary conditions were: • active electrode boundary (anode): inward current density set to Jn, and the total injected current I wasfixedatDClevelof1mA; • return electrode boundary (cathode): inward current density set to −Jn; • ground (zero electric potential) at the bottom boundary of the synthetic (ex- tended) torso; • all other external boundaries were assigned as electric insulators (zero normal component of current density); • continuous current density across all interior boundaries. 125 8.1.2 Electrode placements A total of eleven tDCS electrode montages were simulated using the HEAsub model with WM anisotropy, as shown in Figures 8.1 and 8.2. Most of these montages have been reported or are known to be under current clinical investigation. The electrode placements of these montages are described as follows: • F3-supraorbital (F3-SO) [86, 87, 242–244]: both electrodes were 7 cm × 5cm rectangular pads. The anode was placed over the F3 electrode site on a 10-20 system EEG cap, as shown in Figure 2.5, with the long axis of the pad pointing towards the vertex. The cathode was placed above the arcus superciliaris on the right, with the long axis of the pad parallel to the horizontal plane. • F3-F8 [89]: both electrodes were 7 cm × 5 cm rectangular pads. The anode was placed at the same location as in F3-SO. The cathode was placed over the F8 electrode site of the EEG cap system, with the bottom edge of the pad 4–5 mm lower than the eye socket, and the long axis of the pad was perpendicular to the horizontal plane. • sF3-F8: The anode was placed at the same location as in F3-F8, but the size of the anode pad was 4 cm × 4 cm. The cathode was the same as in F3-F8. • F3-F4-1 [245–248]: both electrodes were 7 cm × 5 cm rectangular pads. The anode was placed at the same location as in F3-SO, and the cathode was placed over the F4 electrode site on a 10-20 system EEG cap, with the long axis of the pad also pointing towards the vertex. • F3-F4-2: both electrodes were 7 cm × 5 cm rectangular pads, and were placed at the same sites as in the F3-F4-1 configuration, but the orientations of both electrodes were perpendicular to those in F3-F4-1. • F3-extracephalic (F3-EC) [177]: both electrodes were 7 cm × 5 cm rectangular pads. The anode was placed at the same location as in F3-SO, and the cathode was placed on the right shoulder. 126 • sF3-EC: The anode was placed at the same location as that of F3-EC, but the size of the pad was 4 cm × 4 cm. The 7 cm × 5 cm cathode was placed in the same location as in the F3-EC configuration. • Temporal-extracephalic (TMP-EC): both electrodes were 7 cm × 5 cm rectan- gular pads. The anode was placed between the F3 and T3 EEG positions, with the long axis of the pad in parallel to the line connecting F3 and T3. The cathode was placed on the right shoulder. • Supraorbital-occipital (SO-OCC): The anode wasa7cm× 5 cm rectangular pad, placed above the arcus superciliaris on the left, with the long axis of the pad parallel to the horizontal plane. The cathode was a 10 cm × 10 cm square pad placed over the inion. • Supraorbital-cerebellum (SO-CB): The anode wasa7cm× 5 cm rectangular pad, placed at the same position as that in the SO-OCC configuration. The cath- ode was a 10 cm × 5 cm rectangular pad, with the top edge 2–3 mm below the inion, and the long axis of the pad parallel to the horizontal plane. • Supraorbital-extracephalic (SO-EC) [75]: two circular anodes of diameter of 0.5 inch (1.27 cm) were placed above the arcus superciliaris on both sides, with the cathode the same as for the F3-EC configuration. 8.1.3 Data analysis The models were solved using the segregated numerical solver in COMSOL (v4.2) on a Windows 64-bit workstation with 24 GB RAM utilizing 4 processors. To solve the stationary equations, a direct linear solver was utilized with an absolute error tolerance set to 10−5. It took ∼ 20 minutes to solve for the simulation. The data of these models were analyzed by comparing the difference in the E-field distribution in the brain between different electrode montages. In addition, the average E-field magnitude E was also calculated in several ROIs in the brain using Equation 6.3. 127 Figure 8.1: tDCS electrode placement part 1: F3-supraorbital (F3-SO), F3-F8, sF3-F8, F3-F4-1 and F3-F4-2. The red and blue electrodes represent the anode and cathode, respectively. To respect the subject’s privacy, the eyes of the model are hidden. 128 Figure 8.2: tDCS electrode placement part 2: F3-extracephalic (F3-EC), sF3-EC, temporal- extracephalic (TMP-EC), supraorbital-occipital (SO-OCC), supraorbital-cerebellum (SO-CB) and supraorbital-extracephalic (SO-EC). The red and blue electrodes represent the anode and cathode, re- spectively. To respect the subject’s privacy, the eyes of the model are hidden. 129 8.2 Results Figures 8.3 and 8.4 show the E-field magnitude profile in the whole brain for all eleven tDCS electrode montages from three different views. The five montages that utilized the F3 anode and a contralateral cephalic cathode (F3-SO, F3-F8, sF3-F8, F3-F4-1 and F3-F4-2), in comparison to the other six montages, resulted in current concentrating predominately in the frontal lobes of the brain. However, among these five electrode configurations, the difference in E-field distribution between lateral and medial parts of the right frontal lobe in the F3-SO model was most prominent, indicating that the cathode on the right SO shifted the current towards the medial part of the right frontal lobe. A smaller electrode on the F3 position (sF3-F8) did not seem to show much gross effect on the E-field distribution, compared to the F3-F8 montage. Among the seven montages having the anode at the F3 position, both EC mod- els presented a more uniformly and widely distributed current in the whole brain, es- pecially in the ventral part (despite a predominance in the left hemisphere), but the E-field magnitude in the frontal lobe appeared weaker than that in the other four mon- tages. Similar to the ‘F8’ pair, F3-EC and its smaller-anode version did not show much difference on gross E-field distribution. Similar to F3-EC, the four montages utilising the TMP or SO anode also showed a broad E-field distribution. However in the EC montages, a higher concentration of current was found towards the ventral part of the brain, whereas in SO-OCC, the current tended to be concentrated in the dorsal part. In addition, similar to F3-EC montage, the E-field magnitude was stronger in the left hemisphere than that in the right for the TMP-EC, SO-OCC and SO-CB configurations, whereas the current was distributed almost evenly on both hemispheres with SO-EC. Figures 8.5 and 8.6 show the E-field profile in two coronal slices of the brain for all nine tDCS electrode montages, and Figures 8.7 and 8.8 show the E-field profile in two horizontal slices. As can be seen on these figures, among the five montages with the F3 anode and a contralateral cephalic cathode, the E-field magnitude in F3-SO was weaker in the posterior part of the right frontal lobe, and the current in F3-F8 and sF3-F8 shifted inferiorly in the right hemisphere. 130 Figure 8.3: E-field magnitude distribution in the whole brain with different tDCS montages part 1: F3-supraorbital (F3-SO), F3-F8, sF3-F8, F3-F4-1 and F3-F4-2. The leftmost, middle and rightmost columns feature the lateral view from the left, the frontal view and the top view, respectively. 131 Figure 8.4: E-field magnitude distribution in the whole brain with different tDCS montages part 2: F3- extracephalic (F3-EC), sF3-EC, temporal-extracephalic (TMP-EC), supraorbital-occipital (SO-OCC), supraorbital-cerebellum (SO-CB) and supraorbital-extracephalic (SO-EC). The leftmost, middle and rightmost columns feature the lateral view from the left, the frontal view and the top view, respectively. 132 Among the seven montages using the F3 anode, those montages with a contralateral EC cathode produced a strong E-field predominantly in the left hemisphere, especially in the dorsal part, and diffusing into the ventral region and the right hemisphere. A similar pattern was also found in TMP-EC, SO-OCC and SO-CB montages, with a slightly weaker E-field in the ventral part of the brain for SO-OCC. Table 8.1 shows the average E-field magnitude for all eleven tDCS montages. The distance between the anode and the cathode in F3-SO was relatively short, which could lead to a high shunting of electric current across the scalp. As a result, the E-field mag- nitudes for the left and right hemispheres, and CB were the smallest among all elec- trode montages. For those montages with bilateral cephalic electrodes, the magnitudes of left and right hemispheres were similar. However for F3-EC, sF3-EC, TMP-EC, SO-OCC and SO-CB, the magnitude difference between left and right hemispheres was quite obvious, which can also be seen in Figures 8.3 and 8.4. Since SO-OCC, SO-CB and all EC models shared a higher current distribution in the ventral part of the brain compared to the five montages with the F3 anode and a contralateral cephalic cathode, a higher average E-field magnitude in the CB was found in these five models. In terms of the E-field magnitude in several ROIs related to depression circuits, in the left DLPFC, the montages with the F3 anode and a contralateral cephalic cathode had a higher average E-field magnitude, whereas in the right DLPFC, only F3-F8, sF3-F8 and both F3-F4 montages resulted in average E-fields over 1.10 mV/cm. The magnitude difference between left and right DLPFCs was significant in F3-SO, sF3- F8, F3-EC, sF3-EC, TMP-EC, SO-OCC and SO-CB, compared to the other electrode configurations, with a higher average E-field in the left DLPFC. The average E-field magnitude in the OFC was similar among all configurations expect the TMP-EC, and the magnitude in the left and right OFCs was almost identical for TMP-EC, SO-EC and both F3-F4 montages. In F3-F8 and sF3-F8, the E-field was greater in the right OFC, whereas in F3-SO, F3-EC, sF3-EC, SO-OCC and SO-CB, the E-field was greater in the left OFC. In terms of the ACC, a higher average E-field was found in the right ACC than in the left. Among all electrode montages, the E-field magnitude was higher in F3-EC and all four SO montages. 133 Figure 8.5: E-field magnitude distribution in the brain in two coronal slices part 1: F3-supraorbital (F3-SO), F3-F8, sF3-F8, F3-F4-1 and F3-F4-2. Dashed lines indicate locations of coronal slice planes. 134 Figure 8.6: E-field magnitude distribution in the brain in two coronal slices part 2: F3-extracephalic (F3-EC), sF3-EC, temporal-extracephalic (TMP-EC), supraorbital-occipital (SO-OCC), supraorbital- cerebellum (SO-CB) and supraorbital-extracephalic (SO-EC). Dashed lines indicate locations of coronal slice planes. 135 Figure 8.7: E-field magnitude distribution in the brain in two horizontal slices part 1: F3-supraorbital (F3-SO), F3-F8, sF3-F8, F3-F4-1 and F3-F4-2. Dashed lines indicate locations of horizontal slice planes. 136 Figure 8.8: E-field magnitude distribution in the brain in two horizontal slices part 2: F3-extracephalic (F3-EC), sF3-EC, temporal-extracephalic (TMP-EC), supraorbital-occipital (SO-OCC), supraorbital- cerebellum (SO-CB) and supraorbital-extracephalic (SO-EC). Dashed lines indicate locations of hori- zontal slice planes. 137 Table 8.1: Average E-field magnitude for all tDCS configurations (mV/cm) Compartment F3-SO F3-F8 sF3-F8 F3-F4-1 F3-F4-2 F3-EC sF3-EC TMP-EC SO-OCC SO-CB SO-EC Left hemisphere 0.67 0.79 0.80 0.72 0.74 0.93 0.93 0.85 0.93 0.89 0.74 Right hemisphere 0.55 0.77 0.76 0.67 0.69 0.69 0.67 0.56 0.75 0.73 0.73 CB 0.33 0.50 0.51 0.38 0.40 0.83 0.82 0.80 0.77 0.89 0.79 Left DLPFC 1.36 1.24 1.34 1.32 1.32 1.10 1.16 0.73 1.06 1.05 0.97 Right DLPFC 1.05 1.16 1.15 1.24 1.24 0.75 0.73 0.48 0.80 0.83 1.00 Left OFC 0.96 0.97 1.03 0.93 0.96 1.08 1.11 0.71 1.05 1.16 1.19 138 Right OFC 0.83 1.37 1.37 0.92 0.95 1.02 1.01 0.75 0.88 1.01 1.18 Left ACC 0.75 0.79 0.78 0.76 0.77 0.90 0.85 0.57 0.91 0.93 1.02 Right ACC 0.75 1.04 1.00 0.80 0.81 1.15 1.09 0.73 1.09 1.15 1.12 Table 8.2: Average E-field magnitude in the ACC (mV/cm) Compartment F3-SO F3-F8 sF3-F8 F3-F4-1 F3-F4-2 F3-EC sF3-EC TMP-EC SO-OCC SO-CB SO-EC ACC 0.75 0.92 0.89 0.78 0.79 1.03 0.98 0.65 1.01 1.04 1.07 8.3 Discussion 8.3.1 Clinical implications of electrode montages A number of tDCS studies have reported positive effects on depressive disorder pa- tients [88,249]. However, it is still unclear which areas of the brain should be targeted in order to achieve anti-depressant efficacy. Most anti-depression tDCS protocols se- lected DLPFC as their potential target by placing the anode on F3 [86,87,89,177,242– 248], for it has been demonstrated that in depressive patients, the left DLPFC is hy- poactive while right DLPFC is hyperactive [107]. Yet in depressive patients, apart from the DLPFC, other areas have also been found to be pathologically altered, including the ACC [13]. DBS treatment targeted at the subcallosal cingulate cortex, a subdivi- sion of the ACC, has shown anti-depressant efficacy [221,222]. In addition, deficiency in the monoaminergic system has also been found in depressive patients [249]. Since monoaminergic nuclei in subcortical regions have projections into the prefrontal cor- tex, particularly DLPFC and OFC, modulation of the monoaminergic system can thus be achieved through network effects by modulating neural activity in the prefrontal cortex. Most clinical studies have shown that anodal tDCS stimulation enhances perfor- mance in cognitive tests, whereas cathodal tDCS suppresses cognitive performance [85, 99, 100]. Thus the rationale for tDCS studies with the anode on F3 is to up- regulate neuronal activity in the left DLPFC. Our simulations results suggest that among all tDCS montages investigated, anodal stimulation on F3 indeed produced a significant high E-field strength in the left DLPFC, especially when the cathode was placed cephalically on the contralateral side. In addition, an F3 anode with a smaller size effectively strengthened the focus of current in the left DLPFC, as well as in the left OFC, and increased the difference in E-field strength between the left and right DLPFCs. This effect was more prominent with the F8 cathode than with the con- tralateral EC cathode. It also decreased the E-field magnitude in remote regions, thus enhancing the focality of tDCS, in agreement with the findings of Parazzini et al. [167]. It is apparent that the E-field strength in the left DLPFC is dependent on the posi- 139 tion of the anode. But the decision on where to place the cathode is also an important factor in determining the resulting stimulus effect on the DLPFC. In early modelling studies with a spherical head model, results suggested that increasing the distance be- tween electrodes reduced the shunting across the skin, increasing the current into the targeted brain area [132, 133, 141]. However, Moliadze et al. [178] reported a signifi- cant decline in motor evoked potentials when they compared left M1-contralateral EC with left M1-contralateral forehead simulations. As clearly demonstrated by the results of this chapter, among all F3 montages when the cathode was placed on F8 or extra- cephalically, the average E-field magnitude in the left DLPFC decreased, especially for the F3-EC montage. This is in line with a case study by Bikson et al. [250]. In contrast, although the inter-electrode distance in F3-SO and F3-F4-2 was closer than F3-F4-1, their resulting E-field strengths in the left DLPFC were still comparable. It is possible that by moving the electrodes further apart, more alternate pathways are provided for the current flow. As shown in the figures displaying E-field magnitude, montages with a more inferior cathode exhibited greater currents passing into the ven- tral part of the brain, thus reducing the stimulus strength in the dorsal part. This was also demonstrated by the relatively high value in OFC E-field magnitude with the EC montages. Nevertheless, Martin et al. [177] in an open-label pilot study found that patients, af- ter receiving F3-EC tDCS, showed a significant reduction in depressive symptoms with greater initial treatment response, in comparison to F3-F8 tDCS. Figure 8.4 showed that the montages with a contralateral EC cathode indeed led to a more widespread current distribution in the brain than those montages with a contralateral cephalic cath- ode. It has been suggested that a widespread current flow induced by the use of EC electrodes can exert effect on brain regions embedded within the hemispheres [251]. When trying to compare the average E-field magnitude in the left and right ACCs, the value in the right ACC with all montages was found to be greater than that in the left. This was likely caused by segmentation error, or by channelling of current through the CSF (or sagittal superior sinus, which is included in CSF mask) due to the close dis- tance between the left and right ACCs. Therefore, an overall average E-field strength 140 was also calculated and listed in Table 8.2. Among all F3 montages, the average E- field magnitude in the ACC was found to be comparably higher in F3-EC and sF3-EC than the other montages, which thus supported the hypothesis and may explain why F3-EC exhibited greater anti-depressant efficacy than F3-F8 in the open-label study. In addition to F3-EC, the three montages with an SO anode also produced a sig- nificant E-field effect in the ACC. This was probably because the shunting effect of the CSF channelled current through the medial surface of the brain. Moreover, TMP- EC produced the lowest E-field strength in the DLPFC, OFC and ACC, as a result of inferiorly-placed electrodes. In regards to the F3-F8 montage, most studies consider the F8 area as neutral re- gion [249]. This, however, may be incorrect, since the results of this chapter clearly demonstrated that the E-field strength in the right OFC was significantly higher in F3- F8 and sF3-F8 than the other tDCS montages. This may explain why in Boggio et al. [87] the authors found OCC-F8 was still able to induce a larger effect than sham tDCS. 8.3.2 Model validation and limitations As mentioned in Chapter 6, validation of computer simulations of E-field distribution in the brain with experimental data remains a challenge. Nevertheless, the simulation results of this chapter are in line with other modelling studies. Parazzini et al. [167] reported a median E-field magnitude of 3.3 mV/cm in the cortex using the left M1- right SO configuration: which was about five times as much as the average E-field value found here. This is probably due to our adoption of a three-layer skull in the HEAsub model, which could decrease current flow into the brain. In addition, Bik- son et al. [250] found a peak cortical E-field value of 4.4 mV/cm in simulations of a healthy subject with left M1-contralateral forehead tDCS. Datta et al. [155] simulated the head of a stroke patient, and found a peak value at 3.6 mV/cm with the left M1- contralateral shoulder montage. Those studies, however, assumed a higher value of skull conductivity than the three-layer skull used in this chapter. As mentioned earlier, limitation in image segmentation and associated software 141 can affect the accuracy of the reconstructed anatomical geometry. As a result, the calculation of average E-field in brain ROIs may be in error. There also exists some uncertainty in electrical properties of compartments in the head model due to the wide ranging values of tissue conductivities reported, especially those from the skull and WM compartments. Halko et al. [165] in a case report used fMRI to investigate the relationship between simulated tDCS current flow and changes in brain activation. The authors found only partial agreement between the E-field profile and change in the fMRI signal. A possi- ble explanation may be that a simple volume conductor model, as used in this chapter, is unable to represent the transmembrane kinetic behaviours of neuromodulation due to tDCS. For the same reason, the effect of sham tDCS is also unable to be distinguished from active tDCS using a passive volume conductor model. An improved model incor- porating fast and slow transmembrane kinetic behaviours, with the latter representing long-term synaptic potentiation or depression, is desired in order to differentiate be- tween the influence of sham and active stimulation, as well as to compare the different effects of tDCS, tRNS and tACS. FES studies show that during electrical stimulation, there is neuronal depolarisa- tion under the cathode, with hyperpolarisation under the anode [236]. However, most clinical studies have shown that anodal tDCS stimulation enhances performance in cognitive tests, whereas cathodal tDCS suppresses cognitive performance [85,99,100]. One challenge in modelling transmembrane kinetic behaviours induced by tDCS is to find an appropriate way of representing this behaviour. One proposed mechanism is that the axons of inhibitory interneurons are hyperpolarised by anodal stimulation and depolarised by cathodal stimulation [85, 94, 102]. This could account for the observed action of tDCS, since inhibitory interneurons account for 20% of all cortical neurons, while excitatory interneurons represent only 2–3% of the neocortex [237]. A study on the effect of tDCS on cortical neurotransmitters revealed that GABA concentration decreases after anodal tDCS, whereas both GABA and glutamate decrease after catho- dal tDCS [102]. This finding partially agrees with the above mechanism. However, another proposal is that because the neurons in the cortex are oriented perpendicularly 142 to the cortical surface, an E-field aligned in the dendrite-axonal direction, known as the orthodromic direction, will lead to depolarisation of the soma. On the contrary, an E-field in the antidromic direction, i.e., from the axon to dendrites, will hyperpolarise the soma [103, 104, 252]. Many existing computational models simulating the tran- sient effect of electrical or magnetic field stimulation on cortical cells are based on this hypothesis [252–256], as supported by in-vitro experiments [257, 258]. Another challenge in modelling is to include the long-term effects of tDCS. De- pending on the stimulus duration, the effect of tDCS may extend well beyond the stimulus period [94]. For example, a tDCS session with a stimulus duration of 5 or 7 minutes was shown to induce an after-effect that lasted for less than 5 minutes, whereas a session extending to 9–13 minutes exhibited an after-effect lasting for 30–90 min- utes [99]. It is believed that long-term potentiation (LTP) and long-term depression (LTD) of synaptic transmission induced by tDCS, accounted for the long-term after- effect [3, 96]. LTP refers to a prolonged enhancement of synaptic transmission [259], and was first discovered in the hippocampus of anaesthetised rabbits in the early 1970s, induced by concurrent depolarisation of pre- and postsynaptic neurons [260]. In con- trast, LTD refers to a persistent suppression of synaptic behaviour [259]. Many com- putational models, mainly categorised into phenomenological and biophysical models, have been developed to assist in the understanding of pre- and postsynaptic behaviors in LTP and LTD [261]. Inclusion of LTP/LTD in our head model, will provide more insights into the behaviour of tDCS. This was, however, beyond the scope of this thesis. 143 Chapter 9 Conclusions and future work 9.1 Thesis contributions This thesis aimed to develop a series of computational models to assist in the un- derstanding of ECT and tDCS. It has provided two major contributions to existing modelling studies of brain stimulation. Firstly, this work described a novel computational approach to simulate direct exci- tation of the brain during the ECT stimulus. For the three conventional ECT electrode placements with a low-resolution head, the model was able to simulate brain activa- tion, showing differences in the maximum current densities induced as well as the brain regions directly activated by the ECT stimulus. For instance, the conventional TP-RUL montage was shown to exert a high influence on the brainstem compared to the other two conventional ECT montages. Additionally, this thesis was the first sim- ulation study to investigate the dynamic effects of ECT stimulus parameters on brain activation. Results showed that when PW was reduced, maximum current density was unchanged but the spatial extent of direct brain activation was reduced. Similarly, a reduction in stimulus amplitude led to reductions in both induced current density and the spatial extent of neural excitation. This suggests that the size of the brain region di- rectly activated has important implications for cognitive impairment, and that reducing the stimulus amplitude may be an important strategy for further improving cognitive outcomes. Moreover, pulse train frequency influenced the stimulus efficiency, that is, 144 the spatial extent resulting from subsequent pulses was affected by stimulus frequency — a low frequency can enhance stimulus efficiency. Secondly, a systemic comparison of the effects of various ECT and tDCS electrode montages was also simulated. Results showed that current distribution in the brain was highly related to electrode placement on the head. In terms of ECT, three conventional and two new montages were included in the comparison, and results demonstrated that the two new RUL montages generated a high E-field strength in the prefrontal region as well as in the ACC, also producing a relatively small influence on the hippocampus, CB and brainstem. This suggested that these new montages may be superior to TP- RUL which is widely used in clinical practice today. Regarding tDCS, all electrode montages investigated in this study have been utilised or proposed in existing clini- cal studies. Results showed that montages with the anode in the F3 position indeed generated a comparably high E-field strength in the left DLPFC, but the presence of a contralateral EC cathode led to a decrease in E-field in comparison with other F3 montages having a contralateral cephalic cathode. In addition, an EC electrode or an electrode at the back of the head was capable of producing a more widely distributed current, and to result in a higher E-field strength in deep brain regions as well as in the CB. In addition, this thesis also made a contribution by investigating the effect of WM conductivity anisotropy, as well as that of different head geometries. It thus demon- strated the importance of subject-specific models, as well as the significance of incor- porating WM anisotropy. 9.2 Future work The task of experimentally validating the computer simulations on E-field or current distribution in the brain remains a challenging task, due to the difficulty of measuring the relevant data in vivo. Over the past few years, a new imaging technique known as current density imaging (CDI) has been steadily developing. CDI is a technique using MRI to obtain measurements of current density vectors inside a conducting medium, 145 following application of an external stimulus to the medium during image acquisition [262]. Thus in future, it may be possible to directly validate the field distribution inside the brain with a current density vector map readily measured from CDI. Regarding the active neural continuum model formulated in this thesis, since the parameters used were tuned and verified based on limited imaging studies [42–44], additional experimental data are necessary for further justification and development of this 3D model of brain activation. In addition, the HH model has a relatively simple formulation with only three ionic currents. With the presence of more comprehensive excitable-cell models, a more sophisticated model should be considered in future for an improved representation of the transient behaviour of the neuronal membrane. As is noted in Chapter 5, the network effect of activation propagation was not incorporated in this continuum model. However, the seizure, as mentioned in Chapter 2, is generally believed to also have a therapeutic effect in the treatment of ECT, and therefore, a seizure model with adequate network connections between different regions in the brain may add more insights into the understanding of ECT. Moreover, the release and slow diffusion of neurotransmitters and neurohormones inside the brain may also be included to complement of the model in future. In terms of tDCS simulations, a computational model which incorporates trans- membrane kinetics, with a fast term representing the immediate polarsing effect of the neuronal membrane and a slower term characterising the LTP/LTD of synapses, is de- sired and should be developed in future, in order to differentiate between the influence of sham and active stimulation, as well as to compare the different effects of tDCS and its variations. The models presented in this thesis could also serve as the basis for patient-specific modelling of transcranial stimulation, where individualized models of heads could be reconstructed from MRI structural scans. 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Because only DTI with FA >=fathre are % considered white matter region, pixels with FA < fa thre % should be considered as gray matter (FA = 0). dti FA = load nii(’dti FA.nii’); dti fa = flipdim(dti FA.img,2); dti fa(dti fa < fa thre) = 0; % Operation of V1. First assign the eigenvectors where 177 %FA< fa thre with 0. The vector system has already been % trasformed into spherical coordinate system, which means the % magnitude of the vectors maintains as 1 (unit vectors). dti V1 = load nii(’dti V1.nii’); dti v11 = flipdim(dti V1.img(:,:,:,1),2); dti v12 = flipdim(dti V1.img(:,:,:,2),2); dti v13 = flipdim(dti V1.img(:,:,:,3),2); dti v11(dti fa < fa thre) = 0; dti v12(dti fa < fa thre) = 0; dti v13(dti fa < fa thre) = 0; %Operation of V2 dti V2 = load nii(’dti V2.nii’); dti v21 = flipdim(dti V2.img(:,:,:,1),2); dti v22 = flipdim(dti V2.img(:,:,:,2),2); dti v23 = flipdim(dti V2.img(:,:,:,3),2); dti v21(dti fa < fa thre) = 0; dti v22(dti fa < fa thre) = 0; dti v23(dti fa < fa thre) = 0; %Operation of V3 dti V3 = load nii(’dti V3.nii’); dti v31 = flipdim(dti V3.img(:,:,:,1),2); dti v32 = flipdim(dti V3.img(:,:,:,2),2); dti v33 = flipdim(dti V3.img(:,:,:,3),2); dti v31(dti fa < fa thre) = 0; dti v32(dti fa < fa thre) = 0; dti v33(dti fa < fa thre) = 0; 178 % Generation of coordinates in a/x, b/y and c/z axes using % ’meshgrid’. Be aware that the directions ofa&bshould % match the destination: for example, ifa&bare % [0:.0025:.135] & [0:.0025:.2375], respectively. % The notations of ’a’ & ’b’ should be swapped in the code as % ’[b,a,c] = meshgrid(0:.0025:.2375, 0:.0025:.135, 0:.0025:.2375)’. % This resulted in three 96x55x96 matices. It can be replaced by % ’[a,b,c] = ndgrid(0:.0025:.2375, 0:.0025:.135, 0:.0025:.2375)’. [b,a,c] = meshgrid(0:.002:.254, 0:.002:.254, 0:.002:.178); % Used only when the padded scan and structures were imported space = 1.5e−3; %m, sampling rate pad = 80; %padding c = c+space∗pad; %padding in Z direction % The eigenvalue of the conductivity in S/m sigma ev = diag([0.65,0.065,0.065]); % Calculate conductivity for each individual data point, and % save them separately with their coordinates for future % interpolation in COMSOL. sigmaxx = []; sigmaxy = []; sigmaxz = []; sigmayy = []; sigmayz = []; sigmazz = []; for i = 1:(size(dti fa,1)∗size(dti fa,2)∗size(dti fa,3)) if dti fa(i) > fa thre E = [dti v12(i),dti v22(i),dti v32(i);... dti v13(i),dti v23(i),dti v33(i);... dti v11(i),dti v21(i),dti v31(i)]; 179 sigma t=E∗sigma ev∗E’; sigmaxx = [sigmaxx; a(i), b(i), c(i), sigma t(1,1)]; sigmaxy = [sigmaxy; a(i), b(i), c(i), sigma t(2,1)]; sigmaxz = [sigmaxz; a(i), b(i), c(i), sigma t(3,1)]; sigmayy = [sigmayy; a(i), b(i), c(i), sigma t(2,2)]; sigmayz = [sigmayz; a(i), b(i), c(i), sigma t(3,2)]; sigmazz = [sigmazz; a(i), b(i), c(i), sigma t(3,3)]; end end dlmwrite(’sigmaxx.txt’,sigmaxx,’delimiter’,’\t’); dlmwrite(’sigmaxy.txt’,sigmaxy,’delimiter’,’\t’); dlmwrite(’sigmaxz.txt’,sigmaxz,’delimiter’,’\t’); dlmwrite(’sigmayy.txt’,sigmayy,’delimiter’,’\t’); dlmwrite(’sigmayz.txt’,sigmayz,’delimiter’,’\t’); dlmwrite(’sigmazz.txt’,sigmazz,’delimiter’,’\t’); 180 Appendix B Rotation Transformation of a Rectangular Cuboid In 3D, a rotation is a transformation in space that can be expressed as the movement of a rigid body at a specified angle θ around a fixed unit vector axis u, as shown in Figure B.1. Given a vector eo(eox,eoy,eoz), once a rotation is performed, the vector becomes en(enx,eny,enz). Since the rotation axis u is perpendicular to the plane on which eo and en lie, these three vectors thus have the relationship: u = eo × en. (B.1) The corresponding scalar components of u are eoyenz − eozeny ux = un eozenx − eoxenz uy = , (B.2) un eoxeny − eoyenx uz = un where un = |eo||en|sinθ. (B.3) The rotation angle θ is − e · e θ = cos 1 o n . (B.4) |eo||en| 181 Figure B.1: Vector eo is rotated anticlockwise around an axis u at an angle θ, becoming en. The rotation matrix R, which is used to perform a rotation in Euclidean space and satisfies en = Reo, (B.5) can thus be written as θ + 2( − θ) ( − θ) − θ ( − θ)+ θ cos ux 1 cos uxuy 1 cos uzsin uxuz 1 cos uysin = ( − θ)+ θ θ + 2( − θ) ( − θ) − θ , R uxuy 1 cos uzsin cos uy 1 cos uyuz 1 cos uxsin ( − θ) − θ ( − θ)+ θ θ + 2( − θ) uxuz 1 cos uysin uyuz 1 cos uxsin cos uy 1 cos (B.6) or as R = Icosθ + sinθ[u]× +(1 − cosθ)uu , (B.7) where I is the identity matrix, u is the transpose of u, and [u]× is the cross product − 0 uz uy matrix of u, given by [u]× = uz 0 −ux , such that for any vector v, [u]×v = u × v. −uy ux 0 Equation B.7 is also known as Rodrigues’ rotation formula. Given a rectangular cuboid with its centre at C (xo,yo,zo), it can be defined in 182 Euclidean space as x − xo ∈ [−L/2,L/2] , y − yo ∈ [−D/2,D/2] (B.8) z − zo ∈ [−H/2,H/2] where L, D, H are the length, depth and height of the cuboid, respectively. After a rotation transformation is applied, the coordinates of any point in the cuboid xn is thus ⎛ ⎞ − ⎜x xo⎟ ⎜ ⎟ = ⎜ − ⎟, xn R⎝y yo⎠ (B.9) z − zo r1,1 r1,2 r1,3 where x, y and z are original coordinates, and R = r2,1 r2,2 r2,3 is the rotation matrix r3,1 r3,2 r3,3 from B.6. Therefore, we have xn = r1,1(x − xo)+r1,2(y − yo)+r1,3(z − zo) , yn = r2,1(x − xo)+r2,2(y − yo)+r2,3(z − zo) (B.10) zn = r3,1(x − xo)+r3,2(y − yo)+r3,3(z − zo) which can be used to express the position of a translated and rotated electrode ‘mask’ on the scalp. 183 Appendix C Formulation of Ion Currents In the HH ionic formulation of the neural action potential [129], the total ionic current per unit membrane area iion, comprised of sodium iNa, potassium iK and leakage iL membrane currents, is given by 3 4 iion = gNam h(vm −VNa)+gKn (vm −VK)+gL (vm −VL), (C.1) where gNa, gK and gL are maximum membrane conductances for iNa, iK and iL, respec- tively; VNa, VK and VL are reversal potentials for iNa, iK and iL, respectively; and m, n and h are gating variables satisfying dm = α (1 − m) − β m dt m m dn = α (1 − n) − β n (C.2) dt n n dh = α (1 − h) − β h dt h h with α,β rates (in s−1) given by: ( + ) −( + ) α = 100 v m 35 β = vm 60 m −( + ) m 4000exp 1 − exp vm 35 18 10 ( + ) −( + ) α = 10 v m 50 β = vm 60 . n −( + ) n 125exp (C.3) 1 − exp vm 50 80 10 −( + ) α = vm 60 β = 1000 h 70exp h −( + ) 20 + vm 30 1 exp 10 Values of parameters used are listed in Table C.1, with initial values of variables in Table C.2. The equations and parameters presented here have been adjusted from the 184 Table C.1: Parameter values for active brain tissue Parameter Value 2 Cm 1 μF/cm 2 gNa 120000 μS/cm 2 gK 36000 μS/cm 2 gL 300 μS/cm VNa 55 mV VK -72 mV VL -49.387 mV rn 5 μm 9 Nn 50 × 10 3 Vbrain 1500 cm β 1.04 × 104 m−1 Vr -60 mV 2 gr (VHsub) 20 μS/cm 2 gr (HEAsub) 15 μS/cm original HH formulations [129] to yield a resting potential of -60 mV and outward currents corresponding to hyperpolarization of the membrane. Table C.2: Initial values for active brain tissue Parameter Initial Value vm -60 mV m 0.0529 n 0.3177 h 0.5961 185