Progress in brain research, volume 222

There is now no denying the contribution that both noninvasive brain stimulation NIBS techniques including transcranial direct current tDCS, alternating current, and tran-scranial magnet

Mark Bear, Cambridge, USA.

Medicine & Translational NeuroscienceHamed Ekhtiari, Tehran, Iran

First edition 2015

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ISBN: 978-0-444-63546-4

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Mohamed Aboseria

Department of Biomedical Engineering, The City College of New York, CUNY,

New York, NY, USA

Devin Adair

Department of Biomedical Engineering, The City College of New York, CUNY,

New York, NY, USA

Steffen Angstmann

Danish Research Centre for Magnetic Resonance, Centre for Functional and

Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre,

Hvidovre, Denmark

Til Ole Bergmann

Department of Psychology, Christian-Albrechts-University, Kiel, Germany

Sven Bestmann

Sobell Department of Motor Neuroscience and Movement Disorders, UCL

Institute of Neurology, University College London, London, UK

Marom Bikson

Department of Biomedical Engineering, The City College of New York, CUNY,

New York, NY, USA

James J Bonaiuto

Sobell Department of Motor Neuroscience and Movement Disorders, UCL

Institute of Neurology, University College London, London, UK

Flavio Fr€ohlich

Department of Psychiatry; Department of Biomedical Engineering; Department of

Cell Biology and Physiology; Neuroscience Center and Department of Neurology,

University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

Warren M Grill

Department of Biomedical Engineering; Department of Electrical and Computer

Engineering; Department of Neurobiology, and Department of Surgery, Duke

University, Durham, NC, USA

Gesa Hartwigsen

Department of Psychology, Christian-Albrechts-University, Kiel, Germany

Damian Marc Herz

Danish Research Centre for Magnetic Resonance, Centre for Functional and

Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre,

Hvidovre, Denmark

Frances Hutchings

Interdisciplinary Computing and Complex BioSystems, School of Computing

Science, Newcastle University, Newcastle upon Tyne, UK

v

Marcus Kaiser

Interdisciplinary Computing and Complex BioSystems, School of ComputingScience, and Institute of Neuroscience, Newcastle University, Newcastle uponTyne, UK

Anke Karabanov

Danish Research Centre for Magnetic Resonance, Centre for Functional andDiagnostic Imaging and Research, Copenhagen University Hospital Hvidovre,Hvidovre, Denmark

Sobell Department of Motor Neuroscience and Movement Disorders,

UCL Institute of Neurology, University College London, London, UK

Asif Rahman

Department of Biomedical Engineering, The City College of New York, CUNY,

New York, NY, USA

Hartwig Roman Siebner

Danish Research Centre for Magnetic Resonance, Centre for Functional and

Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre,

Hvidovre, and Department of Neurology, Copenhagen University Hospital

Bispebjerg, Copenhagen, Denmark

Iris E.C Sommer

Department of Psychiatry, Brain Center Rudolf Magnus, University Medical

Center Utrecht, Utrecht, The Netherlands

Axel Thielscher

Danish Research Centre for Magnetic Resonance, Centre for Functional and

Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre,

Hvidovre, Denmark, and Biomedical Engineering Section, Technical University

of Denmark, Kongens Lyngby, Denmark

Jochen Triesch

Frankfurt Institute for Advanced Studies, Goethe University, Frankfurt, Germany

Dennis Q Truong

Department of Biomedical Engineering, The City College of New York, CUNY,

New York, NY, USA

Nico A.T van den Berg

Department of Radiotherapy, University Medical Center Utrecht, Utrecht,

The Netherlands

Yujiang Wang

Interdisciplinary Computing and Complex BioSystems, School of Computing

Science, Newcastle University, Newcastle upon Tyne, UK

Ulf Ziemann

Department of Neurology & Stroke, Hertie Institute for Clinical Brain Research,

Eberhard-Karls University Tu¨bingen, Germany

Christoph Zrenner

Department of Neurology & Stroke, Hertie Institute for Clinical Brain Research,

Eberhard-Karls University Tu¨bingen, Germany

vii Contributors

Computational neurostimulation in basic

and translational research

For a field that started with the application of a torpedo fish to the head for the

treat-ment of migraine (Kellaway, 1946; Priori, 2003), neurostimulation has come a long

way Where once the humble torpedo fish delivered uncontrolled electricity to the

head, neurostimulation devices are now engineered with sophistication and can

deliver current to any region of the brain with precision voltage control There is

now no denying the contribution that both noninvasive brain stimulation (NIBS)

techniques including transcranial direct current (tDCS), alternating current, and

tran-scranial magnetic stimulation (TMS) as well as invasive deep brain stimulation

(DBS) have made to improving our understanding of brain function and to helping

treat carefully selected patients

For example, DBS is now applied routinely for a growing number of neurological

and psychiatric disorders, and electrical stimulation therapies are established for use

in treating hearing loss (cochlear implants), with visual neurostimulation prosthetics

currently under development Several applications of transcranial NIBS techniques

have now made the transition into clinical use, while phase 2 and 3 clinical trials for

the application of NIBS are proliferating, and increasingly NIBS is also being used to

augment healthy brain function, including home use (Bikson et al., 2013)

Neurostimulation in basic and translational research therefore remains a dynamic

and innovative field However, one can also observe that the success and application

of different forms of neurostimulation has galloped ahead of our understanding of the

mechanisms through which electrical stimulation of the brain expresses its effects

On the one hand, many applications of invasive or noninvasive brain stimulation,

such as DBS or TMS, are now used widely for treatment of neurological and

psychi-atric disorders In these cases, not having a deeper understanding about the

underly-ing mechanism is acceptable if clinical benefits outweigh the possible concerns that

arise from any mechanistic ignorance On the other hand, ignorance delays progress

and may even lead to intellectual and research investment in dead ends For

appli-cations in basic and translational research, the dearth of understanding about key

aspects of neurostimulation seems much less acceptable Here, it leads to spurious

inference, promotion of simplistic ideas, or plain wrong assumptions/procedures,

and poses a hindrance to progressing forward beyond a peak of inflated expectations

into a mature field of research, technology, and clinical use (Bestmann et al., 2015)

Finally, side effects, even if subtle, may be less acceptable in healthy individuals

Using neurostimulation to improve brain function has several challenges

(Bestmann et al., 2015; de Berker et al., 2013) A deeper understanding of how

xv

behavioral changes unfold with brain stimulation would surely help address theseissues, spurn further innovation, and quell misuse.

The question then is: where should such a mechanistic insight come from? This isnot trivially answered, not least because there is not one form of neurostimulation.Invasive DBS, for example, is focused on a relatively small spatial scale of severalmillimeters, targets subcortical structures, commonly uses high-frequency(130 Hz) trains of short biphasic electrical pulses, and is exclusively applied insevere pathology By contrast, most forms of NIBS stimulate several square centi-meters of cortical tissue or even entire networks of the brain at once (Bestmannand Feredoes, 2013; Bestmann et al., 2015; de Berker et al., 2013) Pulsed stimula-tion techniques such as TMS are applied at frequencies rarely exceeding 50 Hz formore than a few pulses (Huang et al., 2005), whereas direct or alternating transcranialcurrent stimulation techniques apply low currents continuously for tens of minutes at

a time (Nitsche and Paulus, 2011) This panoply of ways to deliver stimulation plicates comparison of the resulting effects on physiology and behavior The fre-quent creation of superficial analogies based on concepts used for all types ofstimulation, such as changes in excitability, inhibition and excitation, plasticity,

com-or virtual lesions, should thus probably be avoided (Bestmann et al., 2015; deBerker et al., 2013) Another crucial point that is often ignored is that different types

of neurostimulation are predominantly investigated at very different levels of vation Drawing parallels between them is often unwarranted or simplistic For ex-ample, a lot of knowledge about the impact of DBS rests on direct recordings inanimals and novel developments that allow for recording directly from the vicinity

obser-of the stimulation electrode in humans These single neuron or local field potential(LFP) recordings starkly contrast with the level of observation for most of the NIBStechniques in humans, where behavioral and neuroimaging measures provide themainstay of inference on how stimulation expresses its effects As recently argued(Bestmann et al., 2015), even when data from invasive recordings in animals(e.g.,Ma´rquez-Ruiz et al., 2012; Rahman et al., 2013) complement current knowl-edge about the impact of stimulation in humans, the question remains how the effects

of neurostimulation at these different levels of observation ought to relate to oneanother

We argue that the field of neurostimulation is now at a stage where quantitativecomputational models must guide further progress Put simply, there is a strikingpaucity of quantitative models that span across levels of description and link dose

of stimulation through neurophysiology to behavior Computational tion, as envisaged here, is the use of mechanistic, quantitative models for understand-ing the physiological and behavioral consequences of neurostimulation Such modelsmust meet several requirements: first, they must be biologically and biophysicallygrounded in current knowledge This inevitably requires many assumptions withsufficient uncertainty about the specific parameters one should use to incorporatecurrent knowledge into a model Second, they must address the question at hand

neurostimula-at an approprineurostimula-ate level of description thneurostimula-at is suited to answer thneurostimula-at specific question.While they may draw upon knowledge (and other models) cast at lower or higher

xvi Preface

levels of description, the choice of model should be governed by the type of data the

model seeks to explain, and that one can obtain experimentally to inform the iterative

process between modeling and experimentation Third, models ought to provide

“mathematical/computational microscopes” (Moran et al., 2011) in that they can

probe unobservable or hidden processes and interactions in observed data Fourth,

and related, models should seek to explain what it is that the observed data actually

represent in terms of a task or computation that is carried out by a specific system

Fifth, and most pertinent to this volume, is the need to explain how the physiological

changes produced by stimulation ultimately influence or change cognition and

be-havior, in both health and disease The last point is unlikely to be achieved without

substantial progress on the other requirements, but because neurostimulation is used

to alter behavior and cognition, it should remain the ultimate goal Many important

issues merit discussion: what levels of description (microscopic

–mesoscopic–mac-roscopic) are most suited to address a specific question at hand; how realistic (i.e.,

complex) should models be and how should one trade-off biological realism with

model complexity and the possibility of overfitting; how generalizable across

indi-viduals and behaviors should models be? It is an exciting development that recent

work has initiated discussion on these issues and the possible role of different forms

of computational models for the field of neurostimulation (Bestmann et al., 2015;

Bikson et al., 2015; Bonaiuto and Bestmann, 2015; Frohlich, 2015; Grill, 2015;

Hartwigsen et al., 2015; Little and Bestmann, 2015; Moran, 2015; Neggers et al.,

2015; Rahman et al., 2015; Triesch et al., 2015; Wang et al., 2015)

Of course, substantial advances in the use of models for the field of

neurostimu-lation have already been made Perhaps the most advanced and accepted use of

models is in the field of DBS, where neural network models and simulations have

made substantial contributions to understanding how different waveforms and

stimulation regimes affect local firing (Grill, 2015; Little and Bestmann, 2015)

The contributions from this work have started to be applied in designing novel,

energy-efficient DBS stimulators In other fields of neurostimulation, particularly

the group of NIBS techniques, the use of models is in a much earlier stage of infancy

Here, the use of detailed head models and finite element methods to estimate current

flow through the brain based on individual MRI scans are most notable, and for tDCS

applications (Datta et al., 2013; Kuo et al., 2013) and TMS (Thielscher et al., 2011;

Windhoff et al., 2013) are now on the verge of becoming standard procedure

Yet, few models presently seek to explain the computations carried out by neural

circuits and how these are affected by stimulation, in the sense that they do address

what it is these circuits do and what the information they process reflects A simple

example may serve to illustrate this crucial point: if we were to understand a book

written in a foreign language, then simulations of current flow are analogous to

pre-dicting the distribution of ink on the pages; neural network models then attempt to

predict the patterns of letters on each page, and whether these patterns are influenced

by stimulation; but crucially, none of these tell us what those letters actually mean

If neurostimulation is seen as an attempt to edit the meaning of the letters of a book,

then understanding the meaning of the letters first seems crucial

The imminent issue that requires addressing is thus to develop quantitativemodels that span across these level of understanding, and make predictions abouthow different stimulation procedures culminate in behavioral changes including sideeffects The reason there is a need for such models is that they force us to formalizeour ideas about the physiological basis of brain stimulation, and constrain thepossible conclusions we might draw from observed data Such models can be used

to simulate data, under specific assumptions about the parameters of the model (e.g.,connectivity profiles), which are then compared to observed data Alternatively,generative models incorporate an expected (prior) distribution of parameter values(e.g., baseline firing rates of different types of neurons of a model) based on currentknowledge, and a so-called forward model that quantifies the probability that aspecific pattern of data (e.g., firing rates in STN neurons, evoked potentials inEEG recordings) results from the parameters of the model In principle, this allowsfor estimating the (posterior) probability for a specific parameter or set of parameters

of the model, given the data one actually observes experimentally

Regardless of the specific structure and modeling approach, models explicitly malize the hypotheses one might have about a mechanism and process, in this case howbrain stimulation influences neural circuits Common to all models that will be useful

for-to this debate is that their quantitative nature allows for comparing how the predictionsfrom a model hold up against data observedin vivo This illustrates the iterative loopthrough which modeling and experimentation inform one another

As Arthur C Clarke observed, “Any sufficiently advanced technology is guishable from magic,” and at this stage some of the results emerging from differentapplications of neurostimulation indeed seem magical It perhaps also seems thatsome magic is now much needed to develop computational models that will be able

indistin-to accurately explain how neurostimulation alters neural circuits with sufficientbiological realism to accurately predict behavioral outcome and side effects in indi-viduals resulting from these alterations Despite perhaps appearing quixotic at thisstage, the field must confront these challenges and should not be deterred from startingthe quest for such models The debate is not whether such models are needed, butrather that the field must seek consensus about what the appropriate models and levels

of description ought to be in order to help put the field of neurostimulation on a propermechanistic footing The advances in other fields of neuroscience are testament to howmodeling can help to understand complex processes in biology and stimulate novelquestions and hypotheses (Moran et al., 2011; Stephan et al., 2015) Computationalneurostimulation is in its infancy, but recent work is now initiating a much neededdebate and encouraging efforts into the development of appropriate models(Bestmann et al., 2015; Bikson et al., 2015; Bonaiuto and Bestmann, 2015;

de Berker et al., 2013; Frohlich, 2015; Grill, 2015; Hartwigsen et al., 2015; Littleand Bestmann, 2015; Moran, 2015; Rahman et al., 2015; Triesch et al., 2015;Wang et al., 2015) It is hoped that in the not too distant future, the developments thiswill spawn will make the current state of the field appear much like how using a fish onthe head to treat migraine does to us now

The EditorSven Bestmann

xviii Preface

Bestmann, S., Feredoes, E., 2013 Combined neurostimulation and neuroimaging in cognitive

neuroscience: past, present, and future Ann N.Y Acad Sci 1296, 11–30

Bestmann, S., de Berker, A.O., Bonaiuto, J., 2015 Understanding the behavioural

conse-quences of noninvasive brain stimulation Trends Cogn Sci 19, 13–20

Bikson, M., Bestmann, S., Edwards, D., 2013 Neuroscience: transcranial devices are not

play-things Nature 501, 167

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Rahman, A., 2015 Modeling sequence and quasi-uniform assumption in computational

neurostimulation Prog Brain Res 222, 1–24

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effects of tDCS through computational neurostimulation Prog Brain Res 222, 75–104

Datta, A., Zhou, X., Su, Y., Parra, L.C., Bikson, M., 2013 Validation of finite element model

of transcranial electrical stimulation using scalp potentials: implications for clinical dose

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tDCS: a neurophysiological study Brain Stimul 6, 644–648

Little, S., Bestmann, S., 2015 Computational neurostimulation for Parkinson’s disease Prog

Brain Res 222, 163–190

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xx Preface

Modeling sequence and

quasi-uniform assumption

in computational

neurostimulation

1

Marom Bikson1, Dennis Q Truong, Antonios P Mourdoukoutas, Mohamed

Aboseria, Niranjan Khadka, Devin Adair, Asif RahmanDepartment of Biomedical Engineering, The City College of New York, CUNY, New York, NY, USA

1 Corresponding author: Tel.: 212 650-6791, Fax: 212 650-6727;

e-mail address: bikson@ccny.cuny.edu

Abstract

Computational neurostimulation aims to develop mathematical constructs that link the

appli-cation of neuromodulation with changes in behavior and cognition This process is critical but

daunting for technical challenges and scientific unknowns The overarching goal of this review

is to address how this complex task can be made tractable We describe a framework of

se-quential modeling steps to achieve this: (1) current flow models, (2) cell polarization models,

(3) network and information processing models, and (4) models of the neuroscientific

corre-lates of behavior Each step is explained with a specific emphasis on the assumptions

under-pinning underlying sequential implementation We explain the further implementation of the

quasi-uniform assumption to overcome technical limitations and unknowns We specifically

focus on examples in electrical stimulation, such as transcranial direct current stimulation Our

approach and conclusions are broadly applied to immediate and ongoing efforts to deploy

computational neurostimulation

Keywords

Neuromodulation, Direct current, Computational models, Finite Element Model,

Quasi-uniform, Electrical stimulation

Computational neurostimulation (first formalized inBestmann et al., 2015) argues

that advancement of experimental and clinical interventions will be accelerated

through development of quantitative models linking stimulation dose to behavioral

and clinical outcomes But doing so requires significant technical sophistication and

Progress in Brain Research, Volume 222, ISSN 0079-6123, http://dx.doi.org/10.1016/bs.pbr.2015.08.005

assumptions To make the process tractable, we explain here how computational rostimulation can be divided into distinct steps that are implemented sequentially.The steps are distinct when they are assumed sequential, such that later steps donot need to inform earlier ones By conceptualizing computational neurostimulationinto discrete steps, the technical challenges and assumptions at each stage can beproperly addressed This review focuses on electrical neuromodulation of the cortex(invasive and noninvasive, electrical and magnetic), though the sequence describedhere generally applies to other targets and forms of neuromodulation with any energy(e.g., light, ultrasound) Specifically for electrical stimulation, we review the “quasi-uniform” assumption, initially made explicit in 2013 (Bikson et al., 2013a).The first step in electrical neuromodulation is the use of “forward models” to pre-dict current flow patterns through the head or brain target region The second step is

neu-to consider how current flow directly polarizes cell membranes and changes neuronalfiring rate Third, the consequences of cellular polarization on neuronal informationprocessing are modeled Fourth, these changes in neuronal processing are implicated

in changes in behavior or higher order cognitive function In aggregate, this processachieves the goal of computational neurostimulation: to quantitatively predict thecognitive or behavioral consequences of electrical stimulation for the purpose of un-derstanding and refining interventions In addition to considering these steps as se-quential, the application of the quasi-uniform assumption (defined below) makes thiscomplex process more tractable

The first step of predicting brain current flow is assumed to be independent ofbrain activity state or the response of activity to electrical stimulation Therefore,the first step of predicting current flow can be conducted ignoring brain neurophys-iology Indeed, this assumption is universal to brain stimulation modeling, (Warman

et al., 1992) spanning applications as diverse as deep brain stimulation (DBS), scranial magnetic stimulation (TMS;Esser et al., 2005), and transcranial direct cur-rent stimulation (tDCS), and both analytical and numerical approaches Whatever thelimitations of this assumption in relation to the physics of current flow (Bossetti

tran-et al., 2008) or activity-dependent changes in tissue conductivity, they are consideredrelatively minor

In the second step, the direct cellular polarization produced as a consequence ofcurrent flow (through a brain region of interest) is predicted, essentially independent

of brain activity This separation of the first and second steps dates back to the liest examples of electrical stimulation modeling, where analytical solutions wereused to predict current flow in homogenous media and the response of simple axonswas derived analytically This separation of steps persists even as more sophisticatednumerical techniques for predicting current flow and neuronal responses have devel-oped Thus, state-of-the-art computational neurostimulation efforts adopt this two-stage process Though the validity and limitations of this process has been questioned(Bossetti et al., 2008), it was generally concluded that any theoretical errors are mi-nor compared to other, the unknowns within each step itself Polarization can beused, for example, to predict resulting changes in firing rate either as a result of pac-ing by suprathreshold stimulation or changes in threshold by subthreshold

ear-2 CHAPTER 1 Modeling sequence and quasi-uniform assumption

stimulation It is understood that changes in activity secondary to polarization can

feedback to further change polarization and firing (e.g., polarization changes

oscil-lation activity which then changes firing;Rahman et al., 2013), but it is still possible

to predict the initial direct polarization—which serves to establish mechanisms and

causality

In the third step, the polarization of a population of cells by electrical stimulation

is used to predict change in neuronal information processing—this will change brain

state as well as be entirely determined by baseline brain state While brain state depends

on cognition and behavior, approaching this question from a systems level allows

analysis on a neuronal network scale Finally, these changes in network function

can be quantitatively linked to changes in performance or clinical symptoms

This multistep process is evidently rife with simplifications, unknowns, and

as-sumptions The sequential methodology is largely determined by the mechanics of

computer simulation (e.g., current flow models do not include active neuronal

net-works, neuronal networks models have membrane polarization as a parameter) and

existing constructs in neuroscience (e.g., a given neuronal network model is linked to

behavior) Making this modeling workflow rigorous and useful is precisely the goal

of computational neurostimulation research The quasi-uniform assumption is

ap-plied at the second step, with consequences throughout

Current flow prediction relies on relatively well-defined physical assumptions To

accurately predict brain current flow produced during stimulation, one needs to

spec-ify the (1) relevant aspects of the stimulation device, and (2) relevant tissue

proper-ties; below we consider the relevant features each case In this review, we focus on

electrical stimulation, but in any form of energy application where the physics are

well defined, then defining device and tissue properties should lead to

straightfor-ward prediction of energy dissipation in the body (Cho et al., 2010; Deng et al.,

2014; Ding et al., 2015; Jagdeo et al., 2012; Lee et al., 2015; Wu et al., 2012)

One of the most common and confounding mistakes in neuromodulation is to

as-sume that placing an electrode “near” a nominal target guarantees current flow to that

region In the case of noninvasive electrical stimulation, such as tDCS, this has led to

irrational assumptions such as that current is delivered to a brain regionsmaller than

the primary electrode and that the second electrode can simply be ignored Rather,

when two large scalp electrodes are used current must flowbetween electrodes

po-tentially influencing all intermediary regions, with a diffuse pattern determined by

the underlying tissues (Datta et al., 2009), and the position of the second electrode

even affects current under the first electrode (Bikson et al., 2010) With often

unin-tuitive current flow patterns, models are required (Seibt et al., 2015)

Even in the case of implanted electrodes (e.g., DBS), where increased targeting is

achieved by virtue of embedding an electrode near the target, oversimplistic

assump-tions about stimulation “near” targets should be avoided As summarized by

Cameron McIntyre (Arle and Shils, 2011): “The electric field generated by animplanted electrode is a three-dimensionally complex phenomenon that is distrib-uted throughout the brain While the fundamental purpose of neurostimulation tech-nology is to modulate neural activity with applied electric fields, historically, much

of the device design work and clinical protocols were primarily based on anatomicalconsiderations (i.e., stimulation of a specific brain nucleus) This approach was takenbecause logical hypotheses could be generated to relate the effects of selectivelystimulating a given nucleus to a behavioral outcome However, without consideringthe complete system of electrode placement in that nucleus, stimulation parametersettings, electrical characteristics of the electrode, and electrical properties of the sur-rounding tissue medium, it is impossible to determine if the stimulation effects will

be contained in that nucleus or if they will extend to surrounding brain regions.Therefore, the first step in predicting the effects of neurostimulation is to characterizethe voltage distribution generated in the brain.”

Forward models are therefore needed, and the first element that needs to be duced in computer simulations is dose The relevant aspects of stimulation that need

repro-to be reproduced is simply the “dose,” which as defined inPeterchev and colleagues(2012)as those features of the stimulation device and electrodes or coils that influ-ence the generation of current flow in the body For electrical stimulation, this is theelectrodes’ shape and location, and the waveform applied to each electrode For ex-ample, in DBS, dose is reflected in the location and configuration of the implantedelectrodes and the high-frequency pulse train applied to them While for tDCS, dose

is the position of the electrodes on the head and the intensity of direct current applied.For TMS dose is coil geometry, current applied to the coil, and position relative to thehead (Deng et al., 2014; Guadagnin et al., 2014) Given the well-defined stimulationdose, while there are some variations in how this is implemented (the simulationboundary conditions; Bikson et al., 2012; Saturnino et al., 2015), it is relativelystraightforward to reproduce the dose of stimulation in a computational forward model.Special care should be taken in voltage-controlled stimulation Current-controlled stimulation provides the benefit that electrode impedance does not distortstimulation waveform (Merrill et al., 2005), and for this reason the complex electrodeinterface does not need to be incorporated in current flow models The benefit pro-vided by using current-controlled stimulation in physical devices is, in this sense,transferred to models In contrast, simulating voltage control requires explicit con-sideration of the electrode interface (McIntyre et al., 2006) Current control is notwithout concerns in regard to nonideal performance (e.g., see ratcheting inMerrill

et al., 2005) and voltage limits inHahn et al (2013), but such issues can generally

be disregarded for current flow modeling For both current- and voltage-controlledstimulation, there are issues regarding electrochemical reactions at the electrode thatare important for safety and tolerability (Merrill et al., 2005), but can be consideredseparately from predictions of current flow

Other than defining dose, models of current flow must reproduce the relevant sue properties Here, the framework is well agreed-upon, if not the specific tissue

tis-4 CHAPTER 1 Modeling sequence and quasi-uniform assumption

parameters that should be used in any given case (Datta et al., 2013a; Opitz et al.,

2011; Schmidt et al., 2015; Wagner et al., 2014) The tissue properties are generated

in forward models by first dividing the anatomy into individual masks, such as gray

and white matter Then, electrical properties are assigned to each mask The

impor-tance of separating masks derives from the need to assign each mask its own

elec-trical properties While in principle this approach is well established, there are

significant unknowns and debate about which masks should be segmented and what

electrical properties (e.g., frequency-specific tissue conductivities) should be

assigned Masks may be synthetic (i.e., generic in a rendering software with

simpli-fied shapes;Wagner et al., 2007) or based on imaging from individuals (e.g., MRI,

CT;Datta et al., 2009; Lu and Ueno, 2013) Specific imaging sequences may provide

further insight into tissue properties, such as use of DTI to predict anisotropy

(Schmidt and van Rienen, 2012; Sweet et al., 2014)—though implementation is

not without debate (Diczfalusy et al., 2015; Shahid et al., 2014)

While there is a general trend toward increased model complexity (e.g., the

num-ber and detail of tissue masks), it is important to note that increased precision does not

necessarily translate to increased accuracy (Bikson and Datta, 2012) In some cases,

synthetic (abstracted) incorporation of preexisting information not evident in the

scans is needed (e.g., not resolved by scan contrast or not resolved full by scan

res-olution), for example, ensuring CSF continuity in transcranial stimulation models

(Datta et al., 2009) or an encapsulation layer in DBS (Butson et al., 2006) Relevant

tissue details will depend on the dose, for example, gyri-precise cortical

representa-tion is critical for tDCS (Datta et al., 2009) but not DBS Similarly, spinal anatomy

details may be critical for stimulation of the spine (Song et al., 2015), but not for

cor-tical microstimulation (Song et al., 2013) Ultimately, the validity of forward models

in informing clinical trial design relates to the specific questions being asked of them

If and how to individualize models, to account for variations in anatomy, remain

an open area of investigations (Dougherty et al., 2014; Edwards et al., 2013; Lee

et al., 2013; Opitz et al., 2015; Russell et al., 2013; Truong et al., 2013; Viskochil

et al., 1990) In some cases, interventions such as TMS, DBS, and ECT inherently

use individual dose titration, but the process is empirical In other cases, no

individ-ual dose titration is attempted, such as tDCS Models can inform both extremes

While naturally model accuracy will increase with consideration of individual

anat-omy, the open question is what benefits are provided for computational

neurostimu-lation (Pourfar et al., 2015) Will individualized models explain data from human

trials in a way explicitly not possible with nonindividualized models (Douglas

et al., 2015; Kim et al., 2013)? Or will individualized models result in a different

dose being applied in a human trial in a way that impacts outcomes (Edwards

et al., 2013)? If the answer to both questions is “no” then it is not evident the value

of individual models, especially given the cost One alternative is to rely on a

pre-existing head library to select a comparable anatomy or to warp prepre-existing

models—but these steps still require (potentially costly and complex)

subject-specific measurement and analysis Dealing with susceptible populations, such as

children (Gillick et al., 2014) or cases of brain injury (Datta et al., 2011), may nify the need for individual models.

mag-Various tools have been developed for computational modeling; spanning flows with varied engineering simulation packages (Huang and Parra, 2015), tostand-alone workflows (e.g., Matlab; SCIRun; Dannhauer et al., 2012; Windhoff

work-et al., 2013), to GUI-based simulation (Truong et al., 2014) In principle, the processinvolves exploring various montages (dose) with the goal of identifying a currentflow pattern that best supports the presumed mechanism of action or experimentalhypothesis (Wongsarnpigoon and Grill, 2012) However, how to select a “best” tar-get and consider collateral brain current flow (side effects) is an open question(Cheung et al., 2014; Fytagoridis et al., 2013) because the relationship between braincurrent flow patterns and cognition is complex One solution, which is implicitlyadopted in many reports though not made explicit, is the quasi-uniform assumption.Under the quasi-uniform assumption the electric field (or current density) in eachbrain region is assumed to predict the degree of polarization and neuromodulation(Bikson et al., 2013a) The quasi-uniform assumption is addressed in detail in thenext section

AND THE QUASI-UNIFORM ASSUMPTION

Significantly more complicated than the prediction of current flow patterns in thehead during stimulation is predicting the resulting neurophysiological and then cog-nitive/behavioral outcomes The second step in the sequential computational neuro-stimulation process is calculating the cellular polarization produced by the braincurrent flow patterns predicted in Step 1 While the theory for this is well established,the details of complete implementation can be a (intractable) burden in CNS stim-ulation The process of complete implementation is described, setting up the discus-sion of the utility of the quasi-uniform assumption alternative

The long-standing approach to model polarization response to electrical lation is to consider “which elements are activated” (Ranck, 1975)—where elementsrefer not only to which cells but which specific compartments of cells such as abranch of the dendrite, the soma, or a segment of the axon It is essential to appreciatethat separate compartment of a single neuron will respond different to electrical stim-ulation, even as the compartments interact Which elements respond will be highlydose (electrode position and stimulation waveform) dependent Regardless of down-stream actions, the primary response of the nervous system to current flow is typi-cally considered (foremost) polarization of neuronal membranes Understandingwhich neurons are polarizing, and which compartments within those neurons, is thusconsidered a critical substrate for a quantitative model of electrical stimulation Theanswer will evidently depend on the modality (dose) of stimulation, which regions ofthe nervous system receive significant current flow as a result, and the types of cells

stimu-in those regions

6 CHAPTER 1 Modeling sequence and quasi-uniform assumption

For computational neurostimulation, it is important to situate this second step in

the context of the series The first step generates current flow predictions that

meth-odologically do not consider neuronal morphology, except globally when it affects

gross resistivity such as gray versus white matter or white matter anisotropy In the

second step, this current flow pattern is “overlaid” on neurons (or other cells of

in-terest), explicitly considering their morphology and membrane biophysics—taking

current flow patterns and cell morphology/biophysics together provides the

informa-tion needed, in principle, to predict resulting membrane polarizainforma-tion in each

com-partment of each cell These polarizations are a quantity that can be used as an

input to the neuronal networks models in the third step, as membrane potential

(or a cell parameter of excitability) is often factored in network models

Alterna-tively, for suprathreshold approach, the second step can be used to predict which

neural elements are driven to fire action potentials (and with what periodicity/rate)

and this action potential rate information can be provided in the third step to a

network model where firing is a parameter A separate variation for subthreshold

stimulation is to predict the change in synaptic efficacy produced at a given synapse

by stimulation (Rahman et al., 2013), and provide this as a coupling parameter in to a

network model that considers synaptic coupling strength There may be still other

“cell level” parameters that can be transferred to a network model The decision

of what parameter(s) to carry forward from the second to third state depends on

hypothesis for mechanisms (what parameters considered relevant) and ultimately

the mechanics of the models (what parameters are applicable)

In those applications where suprathreshold pulses are used (such as DBS, TMS)

identification of cellular targets has focused on axons (Nowak and Bullier, 1998) In

the case of stimulation targeting the peripheral nervous system, axons evidently are a

unique target But also in the central nervous system they may represent the

struc-tures more sensitive to stimulation, in the sense they have the lowest threshold to be

driven to fire action potentials—specifically axon terminals For subthreshold

stim-ulation, such as produced by tDCS, attention has traditionally focused on

compart-ments other than axons Specifically, weak current produces a biphasic polarization

profile along the neuronal axis producing polarization of the soma and dendrites

(Bikson et al., 2004) However, ongoing research on subthreshold as refocused

at-tention on axon terminals (Arlotti et al., 2012; Rahman et al., 2013) brings cellular

targets more in line with suprathreshold

How does one predict the polarization produced in each compartment of every

cell, and in turn which specific neurons fire or how synaptic efficacy changes at each

connection? The theory for modeling neuronal polarization, and so action potential

generation, by electrical stimulation is well established but requires considering of

each neurons and its distributed segmented morphology and membrane biophysics at

each segment Specifically, the activating function (derivative of electric field) along

each neuronal compartment must be calculated and then the polarization of the entire

neuron solved, one unique neuron at a time In contrast to the PNS where relatively

uniform axonal bundles make this tractable, in the CNS the number and diversity of

cell types make this complex (McIntyre et al., 2007) The complexity is then

amplified when considered how stimulation of axons that are part of a complex andactive brain network results in an aggregate change of activity in the third step Thetraditional way to make this second-step process tractable in the CNS is some com-bination of reductionism (considering only a few type of homogeneous neurons in afew brain regions) and increasing complexity and speculation (since parameters arelargely unknown).

This approach can be daunting For example, in discussing cortical stimulation,Sergio Canavero concludes (Arle and Shils, 2011) “In the end, this discussion high-lights the extreme aspecificity of current cortical stimulation paradigms, since stim-ulation tends to affect the cortex across the board A first step would be complexityanalysis with closed-loop stimulation devices (e.g., the NeuroPace device for epi-lepsy control), but it is moot that this alone may circumvent the amazing intricacy

of cellular architecture Does cortical stimulation affect differentially positionedcells in the same way? Does a homogeneous wave of excitation create intracorticalconflicts (e.g., two self effacing inhibitions)? Should dendrites, soma, axon hillocks,nodes, internodes and unmyelinated terminals, all having different electrical proper-ties, be stimulated differentially? This is way beyond current technology When itcomes to details, the only currently feasible approach is to consider the cortex a sort

of black box, from which a net effect is sought through trial and error.”

One alternative to this complexity is the “quasi-uniform” assumption that sumes that regional polarization (as a global quantity) and even neuromodulation

pre-is predicted simply by local electric field (Bikson et al., 2013a) Under the uniform assumption, current flow models are used to predict regional electric fields,and these values in the brain are presented a representative of the aggregate likeli-hood a brain region will be polarized and so modulated Other postprocessingmethods to simplify visualizing of predicted activation maps have been proposed(Hartmann et al., 2015; Madler and Coenen, 2012)

quasi-The quasi-uniform assumption is not trivial because membrane polarizationhas long been linked to thechange in electric field along a cell, via the so-calledactivating function (see above), but it is precisely because of this dependence thattraditional approach depends on exhaustive cell-specific data Rather, the quasi-uniform approach considers that in a “soup” of noncompact, bending, and terminat-ing processes (axons, dendrites), the electric field may indicate maximal polarization(Arlotti et al., 2012; Rattay, 1986), while compact neuron polarization will also trackelectric field (Joucla and Yvert, 2009; Radman et al., 2009a) Straight axonal will besensitive to electric field when crossing resistive boundaries (Miranda et al., 2006;Salvador et al., 2011), and local terminations and bends will polarize with electricfield (Arlotti et al., 2012)

The possibility that nonneuronal cells, such as glia or endothelial cells, may betargets for stimulation remains an highly open but critical debate (Lopez-Quintero

et al., 2010; Pelletier and Cicchetti, 2014) and would require separate classes ofmodels Interestingly, the polarization of spheres (or spheroids; Kotnik andMiklavcic, 2000) is directly linked to electric field, making the quasi-uniform

8 CHAPTER 1 Modeling sequence and quasi-uniform assumption

assumption relevant to these cases Predicting clinical and behavioral outcomes

would still require coupling action on nonneural cells types to neurons

Finally, the quasi-uniform assumption helps support the concept of coupling

con-stant (also called polarization length) which can be defined as the amount of cell

membrane compartment polarization (in mV) per unit uniform electric field (in

mV/mm) The coupling constant (Bikson et al., 2004) is a powerful concept because

it can be readily quantified in experimental or neuron models (assuming a linear

sen-sitivity to low-intensity electric fields) and can be generalized to many types of

com-putational neurostimulation (Frohlich and McCormick, 2010) The coupling constant

may be waveform specific (e.g., AC fields;Deans et al., 2007)

CHANGES

The third step in computational neurostimulation is modeling active network

re-sponses to electric stimulation Warren Grill summarizes (Arle and Shils, 2011):

“Electrical activation of the nervous system has traditionally been thought of and

analyzed as a two-part problem The first part is determining, through measurement

or calculation, the electrical potentials (voltages) generated in the tissue by the

ap-plication of stimulation pulses [or other waveforms] The second part is determining,

again through measurement or calculation, and now, through imaging, the response of

neurons to the stimulation pulses (i.e., to the voltages imposed in the tissue) However,

recent progress highlights the need to add a third part to this problem—the network

effects of stimulation That is, given the changes in the pattern of activity in the neurons

directly affected by stimulation, what changes occur either downstream from the point

of stimulation or even further distant within interconnected networks of neurons.”

It is increasingly recognized that functional outcomes of electrical stimulation on

the nervous system can oftenonly be understood in the context of network

architec-ture (e.g., the connectivity of the brain) and ongoing activity (e.g., the state of the

brain;Kwon et al., 2011) This is manifest on several scales On the global scale,

electrical neuromodulation will travel along the brains existing connections For

these reasons, even presumably focal stimulation will produce brain-wide changes

Modern analysis of interventions such as TMS (Bestmann, 2008) and DBS (Kahan

et al., 2014; Kent et al., 2015; Min et al., 2012) leverages characterization of these

connections On a local network scale, the ongoing activity of a network will

funda-mentally influence what actions electrical stimulation has; with highly organized

processes such as oscillations, the effects of stimulation are almost entirely explained

by how these processes are altered (Frohlich and McCormick, 2010; Kang and

Lowery, 2013; Reato et al., 2010, 2013b) At the cellular level, the background

ac-tivity of neurons may influence their responsiveness to stimulation, more simply that

an active neurons will be closer to threshold (Radman et al., 2009b) but also through

amplifying synaptic activity onto neurons (Bikson et al., 2004; Rahman et al., 2013)and other processes (Rosenbaum et al., 2014).

For network changes in the third step, we mean quantifiable metrics/features ofthe network activity such as oscillation power, frequency, or coherence (Frohlich andMcCormick, 2010; Lee et al., 2011; Parra and Bikson, 2004; Reato et al., 2010) Pre-cisely because many network behaviors are emergent properties of a coupled andactive system, so to are the effects of stimulation a result of network dynamics(Berzhanskaya et al., 2013; Francis et al., 2003; Reato et al., 2013b) The networkresponse to stimulation may therefore not be obvious from action at the level of iso-lated cell, even if stimulation acts by polarizing cells (Step 2) Similarly for infor-mation processing in the third step the tools are computational models withprecise aggregate metrics, finally in the fourth step are these neuroscience quantitiesrelated to more abstract representations of cognitive function Though evidently,with predicting behavioral changes the net outcome of computational neurostimula-tion, the selection of system in Step 3 is entirely based on making the bridge to higherfunction as well as hypothesis for cellular targets based on Step 2

The third step of analysis of network function (and its bridging to behavior in thefourth step) is fundamental to understanding the specificity of stimulation The pur-pose of any neuromodulation intervention is to generate a desired behavioral or clin-ical outcome (i.e., improvement in symptoms) without stimulation-generated sideeffects Specificity can be enhanced by guiding current to specific brain regions(Step 1) but since no brain region is involved in one brain function and most brainfunctions involve multiple regions, anatomical targeting of current flow can enhancebut does not in itself explain specificity Similarly, the dose, and especially the wave-form, of stimulation can shape which neuronal elements are activated (Step 2) but theability to capture neurons specific to just one task is unrealistic Therefore, we sug-gest only through nuance in understanding network and information processingchanges, can we rationally consider the origins, and limits, of neuromodulationspecificity

Notions of activity dependence of stimulation support the concept of “functionaltargeting.” We propose functional targeting, in contrast to anatomical targeting.Functional targeting supposes that an endogenously active brain process (e.g., a brainprocess activated by concurrent training) is preferentially sensitive to electricalstimulation—various forms of selectivity then can arise (Bikson et al., 2013b)

In some applications, especially for peripheral stimulation, simple changes inneuronal firing can be linked to the operative behavioral (functional) changes, forexample, when the intended outcome of stimulation is a motor response But in caseswhere actions are central, and where there is a higher order cognitive or behavioraltarget, a final step is needed to bridge from cellular and network changes

As discussed in Step 2, electric field produced during electrical stimulation iscoupled to the network via cellular polarization—meaning the cell that make upthe computational model of Step 3 is polarized based on principles set in Step 2.Though the quasi-uniform assumption is applied in Step 2, it has important implica-tions for the feasibility of Step 3 The quasi-uniform assumptions assumed a network

10 CHAPTER 1 Modeling sequence and quasi-uniform assumption

is exposed to one electric field or that discrete nodes in a network are each exposed to

one electric field This single electric field thus represents the input from electrical

stimulation to that network If one makes general assumptions about a homogeneous

cellular structure in the network, one can apply the quasi-uniform assumption

with-out needing to solve for the polarization of every element in a network For example,

one can assume stimulation primarily couples through soma polarization of the

pri-mary output excitatory neuron in a brain region, such as the CA1 pyramidal neuron

soma, and then based on a single or distributed average coupling constant provide a

polarization input to all excitatory neurons somas in the network One can consider

other neuronal elements such as various excitatory cell types, interneurons, or axon

terminals, and apply a cell- or process-specific average polarization The principle

remains that under the quasi-uniform assumption, a regional electric field is applied

to one or more “characteristic” neuronal elements that are replicated across the

net-work In this way, modeling stimulation of a network is tractable albeit with

assump-tions about average and net effects

There are some situations where the effects on network activity are directly

linked to desired behavioral outcomes For example, for approaches such as ECT

where therapy is based on the hypothesis that behavioral benefits derive from the

generating seizures, modeling predictions may attempt to converge on regional

sei-zure thresholds (Bai et al., 2010) These are often collapsed to functions of regional

electric field, following the quasi-uniform assumption, where an (waveform

spe-cific) electric field seizure threshold is set any given brain region Even so, refined

approach for brain targeting, hypothesis that efficacy may be mediated by electrical

stimulation independent of seizures, and approaches to reduce side effects (Sackeim

et al., 2008), may adopt more sophisticated computational neurostimulation

ap-proaches (Bai et al., 2012)

Conversely, in the case of seizure control, reduction on network epileptiform

ac-tivity is considered a direct aim of treatment or at least directly correlated with

de-sired clinical outcomes There is significant data on success in controlling

epileptiform activity in animal models where often the goal is simply to stop or

re-duce neuronal firing (Ghai et al., 2000), but mixed success in the clinic (Sugiyama

et al., 2015) The lack of correlation of epileptiform activity with behavior may

there-fore be a crutch holding back advancement, including recognizing that brain regions

perform multiple complex functions (Sunderam et al., 2010)

An ambitious step in computational neurostimulation is relating network changes

produced by electrical stimulation to behavior This process is challenging for issues

generic to neuroscience, the link between cellular function and cognition is complex

and unknown Indeed, one of the attractions of experimental design informed by

computational neurostimulation is to use interventional brain stimulation and

obser-vation on behavior to bridge this divide

A key consideration in developing models that bridge to behavior is if to limitconsideration to a brain “node” (a limited anatomical region) of interest or to explic-itly model distributed brain processing (spanning multiple distant but connectedbrain regions) Evidently any higher brain function (behavior, cognition, therapeuticaction) reflects distributed brain processes, but for the purposes of computationalneurostimulation, this relevant question is what scale (node or distributed network)

of models provides meaningful predictions of behavior changes produced by modulation Some stimulation modalities, like the conventional tDCS approach, in-evitably influence regions across the brain—and interpretation of behavioral changesbased on any single node is an assumption (Seibt et al., 2015) Alternatively, directaction on multiple nodes in a network can be embraced as inherent to the net actions

neuro-of stimulation (Brunoni et al., 2014; Dasilva et al., 2012; Douglas et al., 2015; Senco

et al., 2015) where connectivity parameters can be informed by functional imaging ortractography (Sweet et al., 2014) This analysis has been particularly advance forDBS (McIntyre and Hahn, 2010) Perhaps, the most obvious criticism of the singlenode notion is that when suprathreshold stimulation is applied, inevitably not only isthe target activated but all antidromic orthodromic, and axons of passage—thus at themost basic level stimulation effects a network This does not mean that one cannotlink local (node specific) changes to behavior, but some sophistication in consideringthe function of the node is required

One type of bridge to behavior is based on the modulation of network oscillations,either acutely or leading to lasting changes (Reato et al., 2015) For example, Schiffand colleagues demonstrated an empirical link between electrical stimulation fre-quency, oscillations, and behaviors in rat (La Corte et al., 2014) Reato and col-leagues used computational neurostimulation constrained by human EEGrecording to link entrainment of slow-wave oscillations by transcranial electricalstimulation which changes in plasticity that could in turn explain learning changesobserved experimentally (Reato et al., 2013a) Merlet and colleagues proposedmethods to link tACS with EEG changes (Merlet et al., 2013) Similarly, Ali andcolleagues (Ali et al., 2013) developed a model for tACS based on large-scale cor-tical oscillations There is a reasonable well-established experimental and theoreticalpathways linking stimulation with changes in network oscillations (Park et al., 2005;Reato et al., 2013b) Network oscillations have in turn been linked to specific cog-nitive states and behavior (Cheron et al., 2015; Colgin, 2015)

A simplistic bridge from cellular/network activity to behavior is to adopt either a

“sliding scale” concept of brain function (notably for tDCS and post-rTMS), digms of “virtual lesions” (including in acute TMS, DBS), or theories based on

para-“pacing/over-riding” (for example in SCS) These concepts are node based in thatthey explain the actions of neuromodulation by local effects, though they are not ex-clusive of considering the stimulated node as part of distributed network For exam-ple, DBS is hypothesized to create a virtual lesion of a node, thereby removing itsinfluence on the broader network, or to pace the node, thereby increasing drive inupstream/downstream regions (McIntyre et al., 2004) Or, for example, tDCS may

be hypothesized to shift the excitability of one node involved in task In SCS, the

12 CHAPTER 1 Modeling sequence and quasi-uniform assumption

gating theory suggests driving (pacing) a set of neurons generates downstream

ef-fects related to gain control These approaches are attractive (and ubiquitous)

be-cause they typically do not require any numerical simulation, but rather a block

diagram approach to understanding brain function and disease They do not require

sophistication in understanding information processing with a node or the possibility

that some functions may be enhanced while other disrupted in the same network And

these approaches lend themselves to simple integration with Step 2; for example,

tDCS that depolarizes the soma slides excitability and so brain function “up.”

Neu-roscientists, biomedical engineers, and clinicians naturally gravitate to trivial

expla-nations, when faced with unknowns and complexity But these approaches rarely

withstand rigorous conceptual consideration or experimental validation

Computa-tional neurostimulation is the alternative

Changes in synaptic plasticity can be linked conceptually to any lasting changes

and learning Understanding how stimulation affects synaptic plasticity is therefore a

generic substrate to link cellular/network and behavioral phenomena—in the sense

that any evidence for some synaptic plasticity is used as a mechanistic substrate for

some learning But to avoid reverting to a “sliding scale” explanation (e.g., “more”

synaptic plasticity is “more learning” and “more therapy”), it is necessary to develop

computational neurostimulation models that are capable of different forms and

path-way of synaptic plasticity In this path-way, one can link a specific change in plasticity

with a targeted change in learning or behavior

APPROACHES

Cameron McIntyre summarized (ISBN: 978-0-12-381409-8): “Defining

relation-ships between the anatomical placements of the electrode [Step 1], the stimulation

parameter settings, the relative proportion of neurons directly stimulated [Step 2], the

stimulation-induced network activity [Step 3], and the resulting behavioral outcomes

[Step 4], represent the state-of-the-art process for deciphering the therapeutic

mech-anisms of neurostimulation therapies However, integration of such systems is so

complex that it typically requires computational models and numerous simplifying

assumptions to analyze appropriately In turn, numerous scientific questions remain

unanswered on the stimulation-induced network activity generated by therapies like

DBS Nonetheless, as new experimental data become available, and modeling

tech-nology evolves, it will be possible to integrate synergistically the results of systems

neurophysiology with large-scale neural network models to create a realistic

repre-sentation of the brain circuits being modulated by neurostimulation Such advances

will enable the development of novel stimulation technology (electrodes, pulsing

paradigms, pulse generators, etc.) that can be optimized to achieve specific clinical

goals; thereby improving patient outcomes.”

Computational neurostimulation is the framework by which to rationally

orga-nize empirical data, formulate quantitative hypothesis, and test new interventions

Developing computational neurostimulation models requires the right balance of tailed multiscale model with appropriate reductionism (Douglas et al., 2015;Frohlich et al., 2015; Holt and Netoff, 2014; Karamintziou et al., 2014; Mina

de-et al., 2013; Modolo de-et al., 2011; Shukla de-et al., 2014) This review attempts to presentthe modeling process as tractable, even when dealing with unknowns, including se-rializing modeling steps and applying the quasi-uniform assumption where relevant.The research and optimization process should be considered as iterative and so com-putational neurostimulation is a tool to continuously refine approaches The alterna-tive is a qualitative andad hoc testing of protocols, where both isolated positive andnegative clinical findings may do little to advance the science of treatment becausethey are not placed within a rational interventional framework

A central motivation for computational neurostimulation is that the interventionalparameter space (dose, timing, task, inclusion citation, etc.) is too wide, given thecost and risk of human trials, for “blind” empirical optimization Computational neu-rostimulation is thus necessary for rational optimization of neuromodulation proto-cols (Beriault et al., 2012; de Aguiar et al., 2015) At early stages, such effort must behighly experimental data constrained (Douglas et al., 2015; Merlet et al., 2013;Shamir et al., 2015) and typically constrained to a limited range of dose settings.Computational neurostimulation is also the bridge by which data from animal studiescan be rationally incorporated into models for interventions

Approaches using closed-loop stimulation are inherently state dependent and quire computational neurostimulation (Cheng and Anderson, 2015; Gluckman et al.,2001; Gorzelic et al., 2013; Grahn et al., 2014; Liu et al., 2013; Priori et al., 2013;Shamir et al., 2015) As relevant and practical for any given approach, feedback can

re-be based on output at any of the four stages: (1) recording of current flow patterns for

a given dose (Datta et al., 2013b), (2) monitoring of cellular responses such as unitfiring rat, (3) changes in network activity such as local field potentials (Bergey et al.,2015; Gluckman et al., 2001; Merlet et al., 2013), and (4) behavior (Shamir et al.,

2015) Even if based on assumptions (which can be tested) and simplifications(which may not necessarily reduce value in clinical optimization), a computationalneurostimulation approach that spans across these stages is a rational substrate forclosed-loop dose optimization

In many instances, even if computational neurostimulation can be applied usingconceptually sequential steps, a more holistic approach may be required For exam-ple, ongoing neuronal activity (Step 3) may influence both polarization sensitivity(e.g., baseline oscillation level modulates polarization length; Reato et al., 2010)and resulting effects of stimulation on firing patterns (e.g., baseline firing pattern de-termines effects of stimulation) Thus network- and activity-dependent consider-ations can influence Step 2 The state of neuronal networks can be controlledthrough behavioral interventions (Step 4), such that engaging in a task will influencenetwork activity (Step 3) and hence susceptibility to electrical stimulation

It may be that only by integrating predictions at multiple scales can a valuable andcoherent prediction arise (Ali et al., 2013; Douglas et al., 2015) For example, in acomputational neurostimulation models of electrical modulation of sleep

14 CHAPTER 1 Modeling sequence and quasi-uniform assumption

homeostasis, it was necessary to consider both polarization polarity inversions across

cortical folds (which at cellular level may seem to cancel a polarity-specific effects)

with neuronal network binding across brain region products by slow-wave

oscillations—whereby a net effect of stimulation was produced through rectification

and modulation of oscillations and then plasticity (Reato et al., 2013a) This effort

was both experimentally constrained by electrographic recordings from human, as

well as animal data on polarization sensitivity (Reato et al., 2010), and used to predict

behavioral (learning) changes Such efforts, which use computational

neurostimula-tion to bridge dose to behavior, however rudimentary, demonstrate the feasibility

and application of computational neurostimulation, and so are encouraging for

ongoing work

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1 Corresponding author: Tel.: +212-650-6791; Fax: +212-650-6727,

e-mail address: bikson@ccny.cuny.edu

Abstract

Since 2000, there has been rapid acceleration in the use of tDCS in both clinical and cognitive

neuroscience research, encouraged by the simplicity of the technique (two electrodes and a

bat-tery powered stimulator) and the perception that tDCS protocols can be simply designed by

plac-ing the anode over the cortex to “excite,” and the cathode over cortex to “inhibit.” A specific and

predictive understanding of tDCS needs experimental data to be placed into a quantitative

frame-work Biologically constrained computational models provide a useful framework within which

to interpret results from empirical studies and generate novel, testable hypotheses Although not

without caveats, computational models provide a tool for exploring cognitive and brain

pro-cesses, are amenable to quantitative analysis, and can inspire novel empirical work that might

be difficult to intuit simply by examining experimental results We approach modeling the

ef-fects of tDCS on neurons from multiple levels: modeling the electric field distribution, modeling

single-compartment effects, and finally with multicompartment neuron models

Keywords

Transcranial direct current stimulation, Computational neuroscience, Transcranial magnetic

stimulation, Hodgkin–Huxley models, Numerical simulation

This chapter addresses the contribution of computational neuron models and basic

animal research to our understanding of the neural mechanisms of transcranial direct

current stimulation (tDCS) Though we attempt to put in perspective key

computa-tional studies to model experimental data in animals, our goal is not an exhaustive

Progress in Brain Research, Volume 222, ISSN 0079-6123, http://dx.doi.org/10.1016/bs.pbr.2015.09.003

cataloging of relevant computational or animal studies, but rather to put them in thecontext of ongoing effort to improve our understanding of tDCS Similarly, though

we point out essential features of meaningful studies, we refer readers to originalwork for methodological details

Modern noninvasive brain stimulation techniques have their origin in old theoretical and experimental applications of electrical stimulation on centraland peripheral nervous tissue Beginning with the demonstration of the electricalexcitability of the cerebral cortex by Gustav Fritsch and Eduard Hitzig in 1870(Carlson and Devinsky, 2009; Fritsch and Hitzig, 1870), the study of the nervoussystem has been intimately connected with the application of electricity to influence

decades-or evoke neural activity While the electrical stimulation of nervous tissue has maderemarkable contributions to neuroscience, the motivation behind tDCS is to modu-late cellular activity to support cognitive, sensory, and motor functions (i.e., neuro-modulation) The cellular basis of neuromodulation with direct current stimulation(DCS) remains an active area of research with evidence from bothin vitro and in vivoanimal models of tDCS The motivation for both animal research and computationalmodeling of tDCS is evident: to allow rapid and risk-free screening of stimulationprotocols and to address the mechanisms of tDCS with the ultimate goal of informingclinical tDCS efficacy and safety This chapter highlights some of the known mech-anisms of tDCS with an emphasis on developing a predictive understanding of DCSthrough multilevel computational neuron models We present the known cellularmechanisms of tDCS derived from experimental and theoretical analysis beginningwith the basic question: which neural elements are excited by DCS?

CURRENT STIMULATION?

A battery-driven constant current generator delivering weak currents (
1 mA) tween a pair of saline-soaked sponge electrodes induces a voltage gradient (change

be-in voltage/change be-in distance) be-in the brabe-in (Fig 1;Miranda et al., 2007a; Rahman

et al., 2013; Ranck, 1975) The direct effect of the induced electric field is a passivechange in membrane potential (Vm) (Chan and Nicholson, 1986; Radman et al.,2009b; Tranchina and Nicholson, 1986) The timing and magnitude of a change

inVmis determined by the resistive and capacitive properties of the cellular brane A neuron in a resistive extracellular media can be modeled as a series of equiv-alent electrical circuits (compartments) coupled together with an internal resistance(Ri) (Gerstner et al., 1997; Holt and Koch, 1999) The extracellular voltage (Ve) com-partment specifically polarizes the cell (Arlotti et al., 2012; Chan et al., 1988;Rahman et al., 2013) That is, current entering cellular compartments near the pos-itive electrode hyperpolarizes the membrane (membrane potential becomes morenegative), while current flowing out of compartments proximal to the negative elec-trode is depolarized (membrane potential becomes more positive) (Chan andNicholson, 1986; Chan et al., 1988; Durand and Bikson, 2001; Radman et al.,2009b) For typical cortical pyramidal cells in layer 5, a positive electrode on the

mem-cortical surface (referred to as the anode) hyperpolarizes apical dendrites while

si-multaneously depolarizing the soma and basal dendrites (Fig 1)

The passive change in membrane potential alters current flow through

voltage-gated ion channels (Ali et al., 2013; Bikson et al., 1999; Stagg and Nitsche, 2011)

The magnitude and timing of these currents depend on channel gating kinetics

So-dium and potassium channels in the soma, responsible for action potential

genera-tion, are especially susceptible to changes in voltage when the somatic membrane

potential is depolarized or hyperpolarized by DCS (Bikson et al., 2004) The site

of action potential initiation, the axon initial segment, may be especially susceptible

to somatic membrane potential changes because of the high density of sodium

chan-nels Recently, other important voltage-dependent channels have been identified that

play a critical role in activating neurons, including the HCN channel (Ali

et al., 2013)

All neural elements, including dendrites, somas, and axons, are susceptible to

po-larization in the induced electric field to different magnitudes depending on passive

and active membrane properties and the orientation of the neuron relative to the

di-rection of current flow In the simplest case of a cylindrical axon of semi-infinite

length in a homogenous extracellular media exposed to a uniform electric field,

cur-rent flows from the positive electrode to the negative electrode resulting in

polari-zation along the longitudinal axis (Fig 2;Ranck, 1975; Rattay, 1989)

Modeling electrical stimulation of neural elements can be performed as a

combina-tion of two steps The first step involves calculacombina-tion of the spatial distribucombina-tions of the

induced electric fields produced by tDCS (Datta et al., 2009; Miranda et al., 2006)

FIGURE 1

Cortical pyramidal cells are biphasically polarized in the voltage gradient induced by tDCS

Compartments proximal to the anode are hyperpolarized, while distal compartments are

simultaneously depolarized A simple two-compartment model is simulated to show the

relative biphasic polarization in the soma/axon compartment and dendritic compartments

27

2 Modeling electrical stimulation

This is achieved by using finite element models of current flow (Fig 3A) SincetDCS generates static electric fields at 0 Hz (direct current), it is unnecessary to per-form calculations of the temporal distributions of the induced field (calculations are

at steady state) The second step is to model the polarization neuronal structuresusing compartmental analysis

On the macroscopic scale, tissue resistivity and cerebrospinal fluid influencecurrent flow, electric field direction, and magnitude (Miranda et al., 2007a,b;Salvador et al., 2010) White matter, which is anisotropic (electrical conductivity

of brain tissue is inhomogeneous), results in a gyri-specific spatial distribution

of the electric field (Miranda et al., 2007a,b; Salvador et al., 2010), which hassome important functional consequences for neural excitability Simply stated,the change in membrane potential along axons is highly influenced by tissue het-erogeneity between gray and white matter Modeling work shows that changes intissue conductivity can give rise to action potentials in a myelinated axon (Miranda

et al., 2007a) Many models of cellular polarization in an electric field, however,implicitly utilize the “quasi-uniform” assumption, which allows one to consider auniform electric field along a cell without considering tissue conductivity (Bikson

to subcortical regions (Salvador et al., 2010, 2011) Polarization was maximal at the

site of axonal bends, consistent with previous modeling studies in strong (like TMS)

and weak (like tDCS) electric fields (BeMent and Ranck, 1969; Plonsey and Barr,

2000; Ranck, 1975; Rubinstein, 1993)

There is a lack of polarization along the somatodendritic axis when a tangential

field is directed perpendicular to a pyramidal neuron (Fig 2;Bikson et al., 2004;

Rahman et al., 2013) However, a straight axon, branching off the main axon,

ori-ented parallel to the electric field polarized maximally at the terminal and an action

potential was generated near the terminal, which propagates antidromically toward

the main axon (Arlotti et al., 2012; Hause, 1975; Rahman et al., 2013) This is

con-sistent with previously reported findings that the electric field direction may

prefer-entially polarize alternate neural processes to the soma (like axon terminals and fiber

bending points) to induce APs independent of somatic polarization (Hause, 1975;

Plonsey and Barr, 2000; Ranck, 1975; Rubinstein, 1993) It should be noted that

the field strength in the Salvador model was simulated for TMS, which is

signifi-cantly higher than tDCS-induced fields, but qualitatively it demonstrates the concept

of axon terminal polarization by tangential fields in gyral crowns Recent analysis of

the distribution of tangential and radial electric field components in the gyral crown

and wall shows that tangential direct electric fields do dominate in gyral crowns

(Rahman et al., 2013) Processes along the direction of the electric field in regions

where tangential electric fields dominate are therefore subject to greater polarization

than processes oriented orthogonal to the electric field

FIGURE 3

tDCS produces current flow along cortical gyri (A) Finite element models of current flow

illustrate the directionality of the net electric field (B) The net electric field can be

decomposed into a tangential (Ey) and radial (Ex) vector components The relative magnitude

of these vectors determines the direction of net current flow (C) The relative electric field

magnitude at the gyral wall is typically>1, suggesting tangential current flow dominates in the

gyral crown Models suggest pyramidal cells in the gyral crown that are oriented orthogonal to

the tangential electric field may not be polarized Processes that are oriented along the

tangential field in the gyral crown, like axons, are polarized In the gyral wall, the dominant

electric field direction is inward (radial) Current flows along neurons in the gyral wall and

polarizes the cell along its somatodendritic axis

29

2 Modeling electrical stimulation

Since cortical convolutions influence electric field direction, recent studies havelooked closely at the direction of the induced electric field in gyral crowns and walls.The direction of the extracellular voltage gradient in the gyrus is qualitatively differentfrom the gyral walls (Fig 3A, false color represents the calculated voltage gradient in afinite element model of current flow in a gyri-precise head model of tDCS) The in-duced electric field is decomposed into two field components (Fig 3B) The radialcomponent is directed perpendicular to the cortical surface (parallel to the somatoden-dritic axis of cortical pyramidal neurons) The tangential field is parallel to the corticalsurface (perpendicular to the somatodendritic axis of pyramidal neurons) The direc-tion of the induced electric field relative to the neuron has important functional signif-icance (discussed in the next sections) By analyzing the electric field directionsregionally under electrodes, and in gyral crowns and walls,Rahman et al (2013)foundtangential fields are 7–12 times more prevalent than radial fields in the gyral crown and0.3–2 times more prevalent in gyral walls The importance of this finding is that elec-tric fields are dominantly oriented along corticocortical afferent axons and not alongthe somatodendritic axis in the gyral crown.

The relative magnitude of the two components of the induced electric field(Ex¼normal and Ey¼tangential) is considered and quantified on multiple scales(Fig 3B), including global field distributions in the brain, regionally under/betweenelectrodes, and in subregions on gyral crowns/walls The ratio of tangential to normal(Ey/Ex) field magnitudes describes the relative magnitudes in each region, such that

Ey=Ex> 1 corresponds to greater tangential fields on average and Ey=Ex< 1 sponds to greater radial fields on average (Fig 3C) The metric is represented inFig 3C with a schematic representation of the voltage distribution overlaid on eachregion of interest along a cortical gyrus

corre-Implicit to the current flow modeling described above and then to the neuronalpolarization model described next is the quasi-uniform assumption The quasi-uniform assumption suggests that for tDCS, the resulting electric fields produce

a regional polarization that is well approximating by considering the uniformelectric field in each region Or put differently, during tDCS the small change inelectric field over the scale of the neuronal axis can be modeled as uniform(Bikson et al., 2012)

In the 1980s, Chan and colleagues (Chan and Nicholson, 1986; Chan et al., 1988)used electrophysiological recordings from turtle cerebellum and analytical modeling

to quantify polarization under low-frequency sinusoid electric fields—these seminalstudies identified morphological determinants of neuron sensitivity to applied elec-tric fields.Bikson et al (2004)extended this work to rat hippocampal CA1 neuronsand then to cortical neurons (Radman et al., 2009a,b) with the approach of quanti-fying cell-specific polarization by weak DC fields using a single number—the

“coupling constant” (also called the “coupling strength” or “polarization length”)