Invited review Electrical stimulation of excitable tissue ...Electrical stimulation of excitable...

Journal of Neuroscience Methods 141 (2005) 171–198

Invited review

Electrical stimulation of excitable tissue: design ofefficacious and safe protocols

Daniel R. Merrilla,∗, Marom Biksonb, John G.R. Jefferysc

a Department of Bioengineering, University of Utah, 20 South 2030 East, Biomedical Polymers Research Building,Room 108G, Salt Lake City, UT 84112-9458, USA

b Department of Biomedical Engineering, City College of New York, New York, NY, USAc Division of Neuroscience (Neurophysiology), School of Medicine, The University of Birmingham, Birmingham B15 2TT, UK

Accepted 12 October 2004

Abstract

The physical basis for electrical stimulation of excitable tissue, as used by electrophysiological researchers and clinicians in functionalelectrical stimulation, is presented with emphasis on the fundamental mechanisms of charge injection at the electrode/tissue interface. Faradaica is given. Thep resented.E stimulatione damage tot©

K

0d

nd non-Faradaic charge transfer mechanisms are presented and contrasted. An electrical model of the electrode/tissue interfacehysical basis for the origin of electrode potentials is given. Various methods of controlling charge delivery during pulsing are plectrochemical reversibility is discussed. Commonly used electrode materials and stimulation protocols are reviewed in terms offficacy and safety. Principles of stimulation of excitable tissue are reviewed with emphasis on efficacy and safety. Mechanisms of

issue and the electrode are reviewed.2004 Elsevier B.V. All rights reserved.

eywords:Efficacy; Electrode; Interface; Protocol; Safety; Stimulation

Contents

1. Physical basis of the electrode/electrolyte interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1721.1. Capacitive/non-Faradaic charge transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1721.2. Faradaic charge transfer and the electrical model of the electrode/electrolyte interface. . . . . . . . . . . . . . . . . . . . . . . . . . . 1731.3. Reversible and irreversible Faradaic reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1741.4. The origin of electrode potentials and the three-electrode electrical model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1751.5. Faradaic processes: quantitative description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1771.6. Ideally polarizable electrodes and ideally non-polarizable electrodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

2. Charge injection across the electrode/electrolyte interface during electrical stimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1782.1. Charge injection during pulsing: interaction of capacitive and Faradaic mechanisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1782.2. Methods of controlling charge delivery during pulsing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1792.3. Charge delivery by current control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1792.4. Pulse train response during current control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1802.5. Electrochemical reversal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1822.6. Charge delivery by a voltage source between the working electrode and counter electrode. . . . . . . . . . . . . . . . . . . . . . . . 183

∗ Corresponding author. Tel.: +1 801 585 0791; fax: +1 801 581 5151.E-mail address:[email protected] (D.R. Merrill).

165-0270/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
oi:10.1016/j.jneumeth.2004.10.020

172 D.R. Merrill et al. / Journal of Neuroscience Methods 141 (2005) 171–198

3. Materials used as electrodes for charge injection and reversible charge storage capacity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

4. Principles of extracellular stimulation of excitable tissue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

5. Mechanisms of damage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

6. Design of efficacious and safe electrical stimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

1. Physical basis of the electrode/electrolyte interface

Electrical stimulation and recording of excitable tissue isthe basis of electrophysiological research and clinical func-tional electrical stimulation, including deep brain stimulationand stimulation of muscles, peripheral nerves or sensory sys-tems. When a metal electrode is placed inside a physiologicalmedium such as extracellular fluid (ECF), an interface isformed between the two phases. In the metal electrodephase and in attached electrical circuits, charge is carried byelectrons. In the physiological medium, or in more generalelectrochemical terms the electrolyte, charge is carried byions, including sodium, potassium, and chloride in the ECF.The central process that occurs at the electrode/electrolyteinterface is a transduction of charge carriers from electronsin the metal electrode to ions in the electrolyte. The purposeof this review is to introduce the electrochemical processesoccurring at this interface during electrical stimulation ofexcitable tissue and to analyze the properties of stimulationwaveforms and electrode materials used in neuroscienceresearch and clinical applications. Throughout the review,we will illustrate how the choice of electrode materialand stimulation methodology can profoundly influence theresults of acute and chronic electrophysiological studies, aswell as safety during clinical stimulation.

In the simplest system, two electrodes are placed in anelec

es isrmedfinedh theuit fomaytrodten-

fromtroderowured

evenicaltrical

potential profile is forced away from the equilibriumcondition. In the absence of current, the electrical potential isconstant (no gradient) throughout the electrolyte beyond thenarrow interphase region. During current flow, a potentialgradient exists in the electrolyte, generally many orders ofmagnitude smaller than at the interface.

There are two primary mechanisms of charge transfer atthe electrode/electrolyte interface, illustrated inFig. 1. One isa non-Faradaic reaction, where no electrons are transferredbetween the electrode and electrolyte. Non-Faradaic reac-tions include redistribution of charged chemical species inthe electrolyte. The second mechanism is a Faradaic reac-tion, in which electrons are transferred between the electrodeand electrolyte, resulting in reduction or oxidation of chem-ical species in the electrolyte.

1.1. Capacitive/non-Faradaic charge transfer

If only non-Faradaic redistribution of charge occurs, theelectrode/electrolyte interface may be modeled as a simpleelectrical capacitor called the double layer capacitorCdl. Thiscapacitor is formed due to several physical phenomena (vonHelmholtz, 1853; Guoy, 1910; Chapman, 1913; Stern, 1924;Grahame, 1947). First, when a metal electrode is placed inan electrolyte, charge redistribution occurs as metal ions in

s an thef thee, asa-

suchlec-olar

ationules

aryrgedes

ageelec-ther

electrolyte, and electrical current passes between thetrodes through the electrolyte. One of the two electrodtermed a working electrode (WE), and the second is tea counter electrode (CE). The working electrode is deas the electrode that one is interested in studying, witcounter electrode being necessary to complete the circcharge conduction. An electrophysiology experimentalso contain a third electrode termed the reference elec(RE), which is used to define a reference for electrical potial measurements.

A change in electrical potential occurs upon crossingone conducting phase to another (from the metal electo the electrolyte) at the interface itself, in a very narinterphase region, thus forming an electric field (measin V/m) at the interface. This change in potential existsin the equilibrium condition (no current). Electrochemreactions may occur in this interphase region if the elec

-

r

e

the electrolyte combine with the electrode. This involvetransient (not steady-state) transfer of electrons betweetwo phases, resulting in a plane of charge at the surface ometal electrode, opposed by a plane of opposite charg“counterions”, in the electrolyte. A second reason for formtion of the double layer is that some chemical speciesas halide anions may specifically adsorb to the solid etrode, acting to separate charge. A third reason is that pmolecules such as water may have a preferential orientat the interface, and the net orientation of polar molecseparates charge.

If the net charge on the metal electrode is forced to v(as occurs during stimulation), a redistribution of chaoccurs in the solution. Suppose that two metal electroare immersed in an electrolytic salt solution. Next, a voltsource is applied across the two electrodes so that onetrode is driven to a relatively negative potential and the o

D.R. Merrill et al. / Journal of Neuroscience Methods 141 (2005) 171–198 173

Fig. 1. The electrode/electrolyte interface, illustrating Faradaic charge transfer (top) and capacitive redistribution of charge (bottom) as theelectrode is drivennegative: (a) physical representation; (b) two-element electrical circuit model for mechanisms of charge transfer at the interface. The capacitive processinvolves reversible redistribution of charge. The Faradaic process involves transfer of electrons from the metal electrode, reducing hydrated cations in solution(symbolically O + e− → R, where the cation O is the oxidized form of the redox couple O/R). An example reaction is the reduction of silver ions in solution toform a silver plating on the electrode (reaction(1.8a)). Faradaic charge injection may or may not be reversible.

to a relatively positive potential. At the interface that is drivennegative, the metal electrode has an excess of negative charge(Fig. 1). This will attract positive charge (cations) in solutiontowards the electrode and repel negative charge (anions). Inthe interfacial region, there will be net electroneutrality, be-cause the negative charge excess on the electrode surface willequal the positive charge in solution near the interface. Thebulk solution will also have net electroneutrality. At the sec-ond electrode, the opposite processes occur, i.e. the repulsionof anions by the negative electrode is countered by attractionof anions at the positive electrode. If the total amount ofcharge delivered is sufficiently small, only charge redistribu-tion occurs, there is no transfer of electrons across the inter-face, and the interface is well modeled as a simple capacitor.If the polarity of the applied voltage source is then reversed,the direction of current is reversed, the charge redistributionis reversed, and charge that was injected from the electrodeinto the electrolyte and stored by the capacitor may berecovered.

1.2. Faradaic charge transfer and the electrical modelof the electrode/electrolyte interface

Charge may also be injected from the electrode to theelectrolyte by Faradaic processes of reduction and oxidation,w asesR cursa , re-q thati daicc t be

recovered upon reversing the direction of current if theproducts diffuse away from the electrode.Fig. 1(b) illustratesa simple electrical circuit model of the electrode/electrolyte interface, consisting of two elements(Randles, 1947; Gileadi et al., 1975; Bard and Faulkner,1980). Cdl is the double layer capacitance, representingthe ability of the electrode to cause charge flow in theelectrolyte without electron transfer.ZFaradaicis the Faradaicimpedance, representing the Faradaic processes of reductionand oxidation where electron transfer occurs between theelectrode and electrolyte. One may generally think of thecapacitance as representing charge storage, and the Faradaicimpedance as representing charge dissipation.

The following are illustrative examples of Faradaic elec-trode reactions that may occur. Cathodic processes, definedas those where reduction of species in the electrolyte occur aselectrons are transferred from the electrode to the electrolyte,include such reactions as:

2H2O + 2e− → H2↑ + 2OH− (reduction of water) (1.1)

Fe3+ + e− ↔ Fe2+ (simple electron transfer) (1.2)

Cu2+ + 2e− ↔ Cu (Cu metal deposition) (1.3)

P + −

4)

I

a)

hereby electrons are transferred between the two pheduction, which requires the addition of an electron, oct the electrode that is driven negative, while oxidationuiring the removal of an electron, occurs at the electrode

s driven positive. Unlike the capacitive mechanism, Faraharge injection forms products in solution that canno

.tO + 2H + 2e ↔ Pt + H2O

(oxide formation and reduction) (1.

rO + 2H+ + 2e− ↔ Ir + H2O

(oxide formation and reduction) (1.5


IrO2 + 4H+ + 4e− ↔ Ir + 2H2O

(oxide formation and reduction) (1.5b)

2IrO2 + 2H+ + 2e− ↔ Ir2O3 + H2O

(oxide formation and reduction) (1.5c)

Pt + H+ + e− ↔ Pt H (hydrogen atom plating) (1.6)

M(n+1)+(OH)(n+1) + H+ + e− ↔ Mn+(OH)n + H2O

(valency changes within an oxide) (1.7)

Ag+ + e− ↔ Ag (reduction of silver ions) (1.8a)

AgCl ↔ Ag+ + Cl−

(dissolution of silver chloride) (1.8b)

Anodic processes, defined as those where oxidation of speciesin the electrolyte occur as electrons are transferred to theelectrode, include:

2 )

P )

2 )

F )

2

)

R chi hy-d xylr heres e, arede them s aret re-a so-l arera entr ec-t eno seu-do ox-i ed

proton or hydroxyl ion transfer (Rand and Woods, 1974;Frazer and Woods, 1979; Gottesfeld, 1980; Dautremont-Smith, 1982). Reactions(1.8a) and (1.8b)are the reversiblereactions of a silver chloride electrode driven cathodically.Silver ions in solution are reduced to solid silver on the elec-trode (reaction(1.8a)). To maintain the solubility constantKS ≡ (aAg+ )(aCl− ), wherea is the ionic activity, as silverions in solution are reduced the AgCl salt covering the elec-trode dissolves to form silver and chloride ions in solution(reaction(1.8b)) (these reactions are discussed in more detailat the end of this section). In reaction(1.9), water moleculesare irreversibly oxidized, forming oxygen gas and hydrogenions, and thus lowering the pH. Reaction(1.10) is the cor-rosion of a platinum electrode in a chloride-containing me-dia. In reaction(1.11), chloride ions in solution are oxidized,forming chlorine gas. In reaction(1.12), an iron metal elec-trode is dissolved, forming ferrous ions that go into solution.Reaction(1.13) represents a reversible oxide formation ona silver electrode. As electrons are removed from the silvermetal, Ag+ ions are formed. These Ag+ ions then combinewith hydroxyl (OH−) ions from solution, forming an oxidelayer (Ag2O) on the surface of the silver electrode. Notethe transfer of charge that occurs. As electrons are trans-ferred to the electrode and then the external electrical cir-cuit, the silver electrode is oxidized (Ag→ Ag+). Becauseh ox-i n re-m ativec lec-t o thee ionp

1

te ofa 80;P tei ratei trodea alledt weent e toe derk ce isdt rface( ntlyf asst eredt te isl odes

irre-v fr lec-

H2O → O2↑ + 4H+ + 4e− (oxidation of water) (1.9

t + 4Cl− → [PtCl4]2− + 2e− (corrosion) (1.10

Cl− → Cl2↑ + 2e− (gas evolution) (1.11

e → Fe2+ + 2e− (anodic dissolution) (1.12

Ag + 2OH− ↔ Ag2O + H2O + 2e−

(oxide formation) (1.13

eaction(1.1) is the irreversible reduction of water (whis typically abundant as a solvent at 55.5 M), formingrogen gas and hydroxyl ions. The formation of hydroaises the pH of the solution. Reversible reactions, wpecies remain bound or close to the electrode surfacemonstrated by reactions(1.2)–(1.8). In reaction(1.2), thelectrolyte consists of ferric and ferrous ions. By drivingetal electrode to more negative potentials, electron

ransferred to the ferric ions, forming ferrous ions. Inction(1.3), a copper metal electrode is immersed in a

ution of cuprous ions. The cuprous ions in the solutioneduced, building up the copper electrode. Reactions(1.4)nd (1.5a)–(1.5c)are the reversible formation and subsequeduction of an oxide layer on platinum and iridium, respively. Reaction(1.6) is reversible adsorption of hydrognto a platinum surface, responsible for the so-called pocapacity of platinum. Reaction(1.7) is the general formf reversible valency changes that occur in a multilayer

de film of iridium, ruthenium or rhodium, with associat

ydroxyl ions associate with the silver ions, the silverde is electroneutral. However, since hydroxyl has bee

oved from the solution, there is a net movement of negharge from the electrolyte (loss of hydroxyl) to the erode (electrons transferred to the electrode and then tlectrical circuit). The loss of hydroxyl lowers the solutH.

.3. Reversible and irreversible Faradaic reactions

There are two limiting cases that may define the net raFaradaic reaction (Delahay, 1965; Bard and Faulkner, 19letcher and Walsh, 1990). At one extreme, the reaction ra

s under kinetic control; at the other extreme, the reactions under mass transport control. For a given metal elecnd electrolyte, there is an electrical potential (voltage) c

he equilibrium potential where no net current passes bethe two phases. At electrical potentials sufficiently closquilibrium, the reaction rate is under kinetic control. Uninetic control, the rate of electron transfer at the interfaetermined by the electrode potential, and isnot limited by

he rate at which reactant is delivered to the electrode suthe reaction site). When the electrode potential is sufficiear away from equilibrium, the reaction rate is under mransport control. In this case, all reactant that is delivo the surface reacts immediately, and the reaction raimited by the rate of delivery of reactant to the electrurface.

Faradaic reactions are divided into reversible andersible reactions (Bard and Faulkner, 1980). The degree oeversibility depends on the relative rates of kinetics (e


tron transfer at the interface) and mass transport. A Faradaicreaction with very fast kinetics relative to the rate of masstransport is reversible. With fast kinetics, large currents oc-cur with small potential excursions away from equilibrium.Since the electrochemical product does not move away fromthe surface extremely fast (relative to the kinetic rate), thereis an effective storage of charge near the electrode surface,and if the direction of current is reversed then some productthat has been recently formed may be reversed back into itsinitial (reactant) form.

In a Faradaic reaction with slow kinetics, large potentialexcursions away from equilibrium are required for signifi-cant currents to flow. In such a reaction, the potential must beforced very far from equilibrium before the mass transportrate limits the net reaction rate. In the lengthy time frame im-posed by the slow electron transfer kinetics, chemical reac-tant is able to diffuse to the surface to support the kinetic rate,and product diffuses away quickly relative to the kinetic rate.Because product diffuses away, there is no effective storageof charge near the electrode surface, in contrast to reversiblereactions. If the direction of current is reversed, product willnot be reversed back into its initial (reactant) form, since ithas diffused away within the slow time frame of the reac-tion kinetics. Irreversible products may include species thatare soluble in the electrolyte (e.g. reaction(1.12)), precipi-t( n an tingc trodeT imu-l

1t

edb ion,t esm hirde , ther ntialm andc ther

medc ivingf micalpA inc l ofa olatedp occuri sfer-r thep micale lec-

trons, and a difference in inner potentials�φ exists betweenthe two phases (the inner potentialφ is the electrical potentialinside the bulk of the phase). The difference in inner poten-tials between a metal phase and solution phase in contact,�φmetal–solution, defines the electrode interfacial potential. Itis an experimental limitation that a single interfacial potentialcannot be measured. Whenever a measuring instrument isintroduced, a new interface is created and one is unable to sep-arate the effects of the two interfaces. Evaluation must be of acomplete electrochemical cell, which is generally consideredas two electrodes separated by an electrolyte. Thus, prac-tically, potentials are measured as complete cell potentialsbetween two electrodes, either from the working electrodeto the counter electrode, or from the working electrode to thereference electrode.1 A cell potential is the sum of two inter-facial potentials (electrode 1 to electrolyte plus electrolyteto electrode 2), as well as any potential occurring across theelectrolyte as current flows. In the absence of current, the cellpotential between the working electrode and reference elec-trode is called the open-circuit potential, and is the sum of twoequilibrium interfacial potentials from the working electrodeto the electrolyte and from the electrolyte to the referenceelectrode.

Consider the electron transfer reaction between a metalelectrode and a reduction/oxidation (redox) couple O and Ri

w uceds

ual,t atesa en-t ntialo ste rty,2

wg di

dep dew bulks s ine the

notd the po-t es it isd uracy,w t thisp de, ora

ate in the electrolyte, or evolve as a gas (e.g. reactions(1.1),1.9) and (1.11)). Irreversible Faradaic reactions result iet change in the chemical environment, potentially creahemical species that are damaging to tissue or the elechus, as a general principle, an objective of electrical st

ation design is to avoid irreversible Faradaic reactions.

.4. The origin of electrode potentials and thehree-electrode electrical model

An electrical potential, or voltage, is always definetween two points in space. During electrical stimulat

he potentials ofboth the working and counter electroday vary with respect to some third reference point. A tlectrode whose potential does not change over timeeference electrode, may be employed for making poteeasurements. Potentials of the working electrode

ounter electrode may then be given with respect toeference electrode.

Electrochemical potential, also known as transforhemical potential, is a parameter that defines the drorce for all chemical processes, and is the sum of a cheotential term and an electrical potential term (Silbey andlberty, 2001). For a metal and a solution of its own ionsontact to be in equilibrium, the electrochemical potentian electron must be the same in each phase. When two ishases are brought into contact, electron transfer may

f the electrochemical potentials are unequal. Upon traning electrons, a potential difference develops betweenhases that repels further transfer. When electrochequilibrium is achieved, there is no further transfer of e

.

n solution:

O+ ne− ↔ R (1.14)

here O is the oxidized species of the couple, R is the redpecies, andn is the number of electrons transferred.

If the concentrations of both O and R in solution are eqhen the electrical potential of the redox couple equilibrt EΘ′

, the formal potential. More generally, if the concrations of O and R are unequal, the equilibrium poter Nernst potentialEeq may be calculated by the Nernquation (Bard and Faulkner, 1980; Silbey and Albe001):

Eeq = EΘ′ +(RT

nF

)ln

{[O]

[R]

}(1.15)

here [O] and [R] are concentrations in the bulk solution,R is theas constant∼8.314 J/(mol K),T is the absolute temperature, anF

s Faraday’s constant∼96,485 C/mole of electrons.The Nernst Eq.(1.15) relates the equilibrium electro

otentialEeq(the electrical potential of the working electroith respect to any convenient reference electrode) to theolution concentrations [O] and [R] when the system iquilibrium. As the bulk concentration [O] increases or

1 In the electrochemistry literature, the term “electrode potential” isefined consistently. Some authors define the electrode potential as

ential between an electrode and a reference electrode, and sometimefined as the (immeasurable) interfacial potential. For clarity and acchen the term “electrode potential” is used, it should be specified whaotential is with respect to, e.g. the electrolyte, a reference electronother electrode.


bulk concentration [R] decreases, the equilibrium potentialbecomes more positive.

In a system containing only one redox couple that hasfairly fast kinetics, the measured open-circuit potential equalsthe equilibrium potential of the redox couple. If the kineticsof the redox couple are slow, the open-circuit potential (anempirical parameter) may not quickly attain the equilibriumpotential after a perturbation, and if other contaminating re-dox couples are present that affect the equilibrium state, themeasured open-circuit potential does not readily correlatewith any single redox equilibrium potential.

If one begins with a system that is in equilibrium and thenforces the potential of an electrode away from its equilibriumvalue, for example, by connecting a current source betweenthe working and counter electrodes, the electrode is said tobecome polarized. Polarization is measured by the overpoten-tial η, which is the difference between an electrode’s potentialand its equilibrium potential (both measured with respect tosome reference electrode):

η ≡ E − Eeq (1.16)

The electrode interface model ofFig. 1(b) demonstrates themechanisms of charge injection from an electrode; however,it neglects the equilibrium interfacial potential�φ that existsacross the interface at equilibrium. This is modeled as showni tionr anceR c-t l ofa ode,c to ane isu passc andc nt isp rought

andVCE–solutionwill vary from their equilibrium values, i.e.there are overpotentials associated with both interfaces. Also,as current flows there is a voltage drop across the resistive so-lution equal to the product of current and solution resistance:v = iRS. Thus, if current flows and there is a change in themeasured potentialVWE–CE, this change may be from any ofthree sources: (1) an overpotential at the working electrodeas the interfacial potentialVWE–solution varies; (2) an over-potential at the counter electrode as the interfacial potentialVCE–solutionvaries; and (3) the voltage dropiRS in solution.In the two-electrode system, one may only measureVWE–CE,and the individual components of the two overpotentials andiRS cannot be resolved. A third (reference) electrode maybe used for potential measurements. An ideal reference elec-trode has a Faradaic reaction with very fast kinetics, whichappears in the electrical model as a very low resistance forthe Faradaic impedanceZFaradaic. In this case, no significantoverpotential occurs at the reference electrode during currentflow, and the interfacial potentialVRE–solution is consideredconstant. Examples of common reference electrodes are thereversible hydrogen electrode (RHE), the saturated calomelelectrode (SCE), and the silver/silver chloride electrode (Ivesand Janz, 1961). In the three-electrode system, if current flowsthrough the working and counter electrodes and a change isnoted in the measured potentialVWE–RE, this change may bef ork-ia -e them entiala ocesso olu-t andt solu-t r-r mt ls

F ace; (b d“ a, it m ectrode wiv tialRE–solut

n Fig. 2(a). In addition to the electrode interface, the soluesistanceRS(alternatively referred to as the access resistA or the Ohmic resistanceR�) that exists between two ele

rodes in solution is modeled. An electrical circuit modethree-electrode system, including the working electr

ounter electrode and reference electrode immersed inlectrolyte, is shown inFig. 2(b). The reference electrodesed for potential measurements and is not required tourrent for stimulation; a two-electrode system (workingounter electrodes) is sufficient for stimulation. As curreassed between the working and counter electrodes th

he electrolytic solution, the interfacial potentialsVWE–solution

ig. 2. Electrical circuit models: (a) single electrode/electrolyte interfWE”, “CE” and “RE”. If the counter electrode has a large surface areery low valued Faradaic resistance will maintain the interfacial potenV

rom either of two sources: (1) an overpotential at the wng electrode as the interfacial potentialVWE–solutionvaries;nd (2) the voltage dropiRS in solution. Unlike the twolectrode system, only one overpotential contributes toeasured potential change. Furthermore, the overpott the working electrode can be estimated using the prf correction. This involves estimating the value of the s

ion resistance between the working electrode interfacehe reference electrode interface, called the uncorrectedion resistanceRU, and multiplyingRU by the measured cuent. This productVcorr = iRU,estimatedis then subtracted frohe measuredVWE–RE to yield the two interfacial potentia

) three-electrode system. External access to the system is at three points labeleay be considered as strictly a capacitance as shown. A reference elth

ionconstant.


VWE–solution andVRE–solution. SinceVRE–solution is constant,any change inVWE–RE is attributed to an overpotential at theworking electrode interface.

1.5. Faradaic processes: quantitative description

Eq. (1.17), the current–overpotential equation (Bard andFaulkner, 1980), relates the overpotential to net current den-sity through an electrode going into a Faradaic reaction, anddefines the full characteristics of the Faradaic impedance:

inet = i0

{[O](0,t)[O]∞

exp(−αcnfη)

− [R](0,t)[R]∞

exp((1− αc)nfη)

}(1.17)

whereinet is the net Faradaic current across the electrode/electrolyteinterface,i0 is the exchange current density, [O](0,t) and [R](0,t) areconcentrations at the electrode surface (x= 0) as a function of time,[O]∞ and [R]∞ are bulk concentrations,αc is the cathodic trans-fer coefficient and equals∼0.5,n is the number of moles of elec-trons per mole of reactant oxidized (Eq.(1.14)), f≡F/RT,F is Fara-day’s constant∼96,485 C/mole of electrons,R is the gas constant∼8.314 J/(mol K), andT is the absolute temperature.

This equation relates the net current of a Faradaic reac-t den-s ac-t (3)t . Thee oten-t erei onsa hec ci-t ge isd apac-i , andt as tan-ti termd

d Ra orec o in-c reaseT nd-i f re-a eo ),t achez tt nf , ther , andt n the

electrode surface and the bulk electrolyte determines the rateof delivery of reactant, and thus the current.

The overpotential an electrode must be driven to beforeany given current will be achieved is highly dependent onthe kinetics of the system, characterized by the exchangecurrent densityi0. For a kinetically fast system with a largeexchange current density, such asi0 = 10−3 A/cm2, no sig-nificant overpotential may be achieved before a large currentensues. When the exchange current density is many orders ofmagnitude smaller such asi0 = 10−9 A/cm2, a large overpo-tential must be applied before there is significant current.

As current is passed between a working electrode andcounter electrode through an electrolyte, both the workingand counter electrode’s potentials move away from theirequilibrium values, with one moving positive of its equilib-rium value and the other moving negative of its equilibriumvalue. Total capacitance is proportional to area, with capaci-tanceCdl = (capacitance/area)× area. Capacitance/area is anintrinsic material property. Capacitance is defined as the abil-ity to store charge, and is given by:

Cdl ≡ dq

dV(1.18)

whereq= charge andV= the electrode potential with respect to somereference electrode.

totalc storelD eepst ringc littleF yb oseso t isc andw ase.

1n

dea non-p 5;B dec th ch ane( ani cursa ntialw ca-p tos rface.A encee rbeda le

ion to three factors of interest: (1) the exchange currentity i0, which is a measure of the kinetic rate of the reion; (2) an exponential function of the overpotential; andhe concentration of reactant at the electrode interfacexponential dependence of Faradaic current on overpial indicates that for a sufficiently small overpotential, ths little Faradaic current, i.e. for small potential excursiway from equilibrium, current flows primarily through tapacitive branch ofFig. 1, charging the electrode capaance, not through the Faradaic branch. As more charelivered through an electrode interface, the electrode c

tance continues to charge, the overpotential increaseshe Faradaic current (proportional to exp(η)) begins to beignificant fraction of the total injected current. For subsial cathodic overpotentials the left term of Eq.(1.17)dom-nates; for substantial anodic overpotentials the rightominates.

Near equilibrium, the surface concentrations of O anre approximately equal to the bulk concentrations. As mharge is delivered and the overpotential continues trease, the surface concentration of reactant may deche Faradaic current will then begin to level off, correspo

ng to the current becoming limited by mass transport octant. At the limiting currentsiL,c (cathodic, for negativverpotentials) oriL,a (anodic, for positive overpotentialshe reactant concentration at the electrode surface approero, and the terms [O](0,t)/[O]∞ or [R](0,t)/[R]∞ counterache exponential terms in Eq.(1.17), dominating the solutioor net reaction rate. In a mass transport limited reactioneactant concentration at the surface is considered zerohe slope of the reactant concentration gradient betwee

.

s

Thus, an electrode with a relatively large area andapacity (as is often the case for a counter electrode) canarge amount of charge (dq) with a small overpotential (dV).uring stimulation, the use of a large counter electrode k

he potential of the counter electrode fairly constant duharge injection (near its equilibrium value), and there isaradaic current (Eq.(1.17)). Significant overpotentials mae realized at a small working electrode (small for purpf spatial resolution during recording or stimulation). Iommon to neglect the counter electrode in analysis,hile this is often a fair assumption it is not always the c

.6. Ideally polarizable electrodes and ideallyon-polarizable electrodes

Two limiting cases for the description of an electrore the ideally polarizable electrode, and the ideallyolarizable electrode (Delahay, 1965; Gileadi et al., 197ard and Faulkner, 1980). The ideally polarizable electroorresponds to an electrode for which theZFaradaicelemenas infinite resistance (i.e. this element is absent). Sulectrode is modeled as a pure capacitor, withCdl = dq/dVEq. (1.18)), in series with the solution resistance. Indeally polarizable electrode, no electron transfer occross the electrode/electrolyte interface at any potehen current is passed; rather all current is throughacitive action. No sustained current flow is requiredupport a large voltage change across the electrode inten ideally polarizable electrode is not used as a referlectrode, since the electrode potential is easily pertuway from the equilibrium potential. A highly polarizab


(real) electrode is one that can accommodate a large amountof injected charge on the double layer prior to initiatingFaradaic reactions, corresponding to a relatively smallexchange current density, e.g.i0 = 10−9 A/cm2.

The ideally non-polarizable electrode corresponds to anelectrode for which theZFaradaicelement has zero resistance;thus, only the solution resistance appears in the model. Inthe ideally non-polarizable electrode current flows readilyin Faradaic reactions and injected charge is accommodatedby these reactions. No change in voltage across the inter-face occurs upon the passage of current. This is the desiredsituation for a reference electrode, so that the electrode po-tential remains near equilibrium even upon current flow. Ahighly non-polarizable (real) electrode, for which theZFaradaicelement has very small resistance, has a relatively large ex-change current density, e.g.i0 = 10−3 A/cm2. Most real elec-trode interfaces are modeled by aCdl in parallel with a fi-nite ZFaradaic, together in series with the solution resistance(Fig. 2(a)).

Consider a metal electrode consisting of a silver wireplaced inside the body, with a solution of silver ions betweenthe wire and ECF, supporting the reaction Ag+ + e− ↔ Ag.This is an example of an electrode of the first kind, whichis defined as a metal electrode directly immersed into anelectrolyte of ions of the metal’s salt. As the concentrationof silver ions [Ag+] decreases, the resistance of the interfaceincreases. At very low silver ion concentrations, the FaradaicimpedanceZFaradaicbecomes very large, and the interfacemodel shown inFig. 2(a) reduces to a solution resistanceRS in series with the capacitanceCdl. Such an electrodeis an ideally polarizable electrode. At very high silverconcentrations, the Faradaic impedance approaches zeroand the interface model ofFig. 2(a) reduces to a solutionresistance in series with the Faradaic impedanceZFaradaic,which is approximated by the solution resistance only.Such an electrode is an ideally non-polarizable electrode.The example of a silver electrode placed in direct contactwith the ECF, acting as an electrode of the first kind, isimpractical. Silver is toxic, silver ions are not innate in thebody, and any added silver ions may diffuse away. Thesilver wire electrode is a highly polarizable electrode sincethe innate silver concentration is very low and the Faradaicreaction consumes little charge; thus, this configurationis not usable as a reference electrode. The equilibriumpotential, given by a derivation of the Nernst equationEeq=EΘ + (RT/nF) ln[Ag+] = (59 mV/decade) log[Ag+]at 25◦C, is poorly defined due to the low silver ionconcentration. A solution to these problems is to use anelectrode of the second kind, which is defined as a metalcoated with a sparingly soluble metal salt. The commonsilver/silver chloride (Ag/AgCl) electrode, described byreactions (1.8a) and (1.8b), is such an electrode. Thisconsists of a silver electrode covered with silver chloride,which is then put in contact with the body. The Ag/AgClelectrode acts as a highly non-polarizable electrode.The equilibrium potential Eeq=EΘ + 59 log[Ag+] can

be combined with the definition of the silver chloridesolubility constant,KS≡ [Ag+][Cl−] ∼ 10−10 M2, to yieldEeq=EΘ + 59 log[KS/Cl−] = EΘ + 59 logKS− 59 log[Cl−] =EΘ′−59 log[Cl−]. The equilibrium potential of this electrodeof the second kind is seen to be dependent on the finitechloride concentration rather than any minimal silverconcentration, and is well defined for use as a referenceelectrode.

2. Charge injection across the electrode/electrolyteinterface during electrical stimulation

2.1. Charge injection during pulsing: interaction ofcapacitive and Faradaic mechanisms

As illustrated inFig. 1, there are two primary mechanismsof charge injection from a metal electrode into an electrolyte.The first consists of charging and discharging the doublelayer capacitance, causing a redistribution of charge in theelectrolyte but no electron transfer from the electrode to theelectrolyte.Cdl for a metal in aqueous solution has valueson the order of 10–20�F/cm2 of real area (geometric areamultiplied by the roughness factor). For a small enough to-tal injected charge, all charge injection is by charging anddischarging of the double layer. Above some injected charged adaicr elec-t posi-t ns.F ntingt em ich ism -t Thec dl sseso

etalshw e thep ctantm irec-t urs,i i-t e stor-a d fors ction(e essf

by Eq.( e of2 udel apaci-t

ensity, a second mechanism occurs consisting of Fareactions where electrons are transferred between therode and electrolyte, thus changing the chemical comion in the electrolyte by reduction or oxidation reactioig. 1 illustrates a single Faradaic impedance represe

he electron transfer reaction O +ne− ↔ R. Generally theray be more than one Faradaic reaction possible, whodeled by several branches ofZFaradaic(one for each reac

ion), all in parallel with the double layer capacitance.urrent–overpotential Eq.(1.17), and Fick’s first and seconaws for diffusion, give the complete description of proceccurring for any Faradaic reaction.

In addition to the double layer capacitance, some mave the property of pseudocapacity (Gileadi et al., 1975),here a Faradaic electron transfer occurs, but becausroduct remains bound to the electrode surface, the reaay be recovered (the reaction may be reversed) if the d

ion of current is reversed. Although electron transfer occn terms of the electrical model ofFig. 1 the pseudocapacance is better modeled as a capacitor, since it is a chargge (not dissipative) process. Platinum is commonly usetimulating electrodes, as it has a pseudocapacity (by rea1.6)) of 210�C/cm2 real area (Rand and Woods, 1971), orquivalently 294�C/cm2 geometric area using a roughn

actor of 1.4.2

2 The relationship between capacitance and stored charge is given2.3). A 1 V potential excursion applied to a double layer capacitanc0�F/cm2 yields 20�C/cm2 stored charge, which is an order of magnit

ower than the total charge storage available from platinum pseudocance.


It is a general principle when designing electrical stim-ulation systems that one should avoid onset of irreversibleFaradaic processes which may potentially create damagingchemical species, and keep the injected charge at a lowenough level where it may be accommodated strictly by re-versible charge injection processes. Unfortunately, this is notalways possible, because a larger injected charge may be re-quired to cause the desired effect (e.g. initiating action poten-tials). Reversible processes include charging and dischargingof the double layer capacitance, reversible Faradaic processesinvolving products that remain bound to the surface such asplating of hydrogen atoms on platinum (reaction(1.6)) orthe reversible formation and reduction of a surface oxide(reactions(1.4) and (1.5a)–(1.5c)), and reversible Faradaicprocesses where the solution phase product remains near theelectrode due to mass diffusion limitations.

The net current passed by an electrode, modeled as shownin Fig. 1, is the sum of currents through the two parallelbranches. The total current through the electrode is given by:

itotal = ic + if (2.1)

whereic is the current through the capacitance andi f is the currentthrough the Faradaic element.

The current through the Faradaic element is given by thecurrent–overpotential equation(1.17). The current throught

T ntialc TheF upont tial.T po-t ac-i ium.A ins toc ent.W adaici urrene cesso d thep ing tot

, thec o thev

T ime,n c pro-c over-p daicc n

exponential of the overpotential integrated over time:

qf =∫

if dt ∝∫

exp(η) dt (2.4)

The charge delivered into Faradaic reactions is directlyproportional to the mass of Faradaic reaction productformed, which may be potentially damaging to the tissuebeing stimulated or the electrode.

2.2. Methods of controlling charge delivery duringpulsing

Charge injection from an electrode into an electrolyte (e.g.extracellular fluid) is commonly controlled by one of threemethods. In the current-controlled (also called galvanostatic)method, a current source is attached between the workingand counter electrodes and a user-defined current is passed.In the voltage-controlled (also called potentiostatic) method,current is driven between the working electrode and counterelectrode as required to control the working electrode poten-tial with respect to a third (reference) electrode. This maybe used for electrochemical measurements of certain neu-rotransmitters (reviewed byMichael and Wightman, 1999).This method is most often not used for stimulation, and is notdiscussed further in this review. In the third method,VWE–CEc andc im-p nort thirdr l be-t

2

forf yp-i , ac ly ont n thee elye lse.I irec-t thec uls-i t thed tionp sed tor stim-u thes tivew odicr ), al-t (dis-c yp thei ulse

he capacitance is given by Eq.(2.2):

ic = Cdldv

dt= Cdl

dη

dt(2.2)

he capacitive current depends upon the rate of potehange, but not the absolute value of the potential.aradaic current, however, is exponentially dependent

he overpotential, or departure from the equilibrium potenhus, as an electrode is driven away from its equilibrium

ential, essentially all charge initially flows through the captive branch since the overpotential is small near equilibrs the overpotential increases, the Faradaic branch begonduct a relatively larger fraction of the injected currhen the overpotential becomes great enough, the Far

mpedance becomes small enough that the Faradaic cquals the injected current. At this point, the Faradaic prof reduction or oxidation conducts all injected charge, anotential of the electrode does not change, correspond

he capacitor not charging any further.In terms of charge going into the different processes

harge on the double layer capacitance is proportional toltage across the capacitance:

qc = Cdl �V (2.3)

hus, if the electrode potential does not change in teither does the stored charge. The charge into Faradaiesses, however, does continue to flow for any non-zerootential. The Faradaic charge is the integration of Faraurrent over time, which by Eq.(1.17)is proportional to a

t

ontrol, a voltage source is applied between the workingounter electrodes. While this is the simplest method tolement, neither the potential of the working electrode

he potential of the counter electrode (with respect to aeference electrode) are controlled; only the net potentiaween the working and counter electrodes is controlled.

.3. Charge delivery by current control

The current-controlled method is commonly usedunctional electrical stimulation of excitable tissue. This tcally takes the form of pulsing. In monophasic pulsingonstant current is passed for a period of time (generalhe order of tens to hundreds of microseconds), and thexternal stimulator circuit is open circuited (it is effectivlectrically removed from the electrodes) until the next pu

n biphasic pulsing, a constant current is passed in one dion, then the direction of current is reversed, and thenircuit is open circuited until the next pulse. In biphasic png the first phase, or stimulating phase, is used to eliciesired physiological effect such as initiation of an acotential, and the second phase, or reversal phase, is ueverse electrochemical processes occurring during thelating pulse. It is common to use a cathodic pulse astimulating phase (the working electrode is driven negaith respect to its pre-pulse potential), followed by an an

eversal phase (the working electrode is driven positivehough anodic pulsing may also be used for stimulationussed in Section4). Fig. 3 illustrates definitions of the kearameters in pulsing. The frequency of stimulation is

nverse of the period, or time between pulses. The interp


Fig. 3. Common pulse types and parameters.

interval is the period of time between pulses.Fig. 3(b) illus-trates charge-balanced biphasic pulsing, where the charge inthe stimulation phase equals the charge in the reversal phase.Fig. 3(c) illustrates charge-imbalanced biphasic pulsing (de-tailed in Section4) where there are two phases, but the rever-sal phase has less charge than the stimulating phase.Fig. 3(d)illustrates the use of an interphase delay, where an open circuitis introduced between the stimulating and reversal phases.

Upon application of a cathodic current pulse to an elec-trode that starts at a potential close to the equilibrium poten-tial, the term exp(η) is small and initially little charge goesinto any Faradaic reactions, thus the initial charge deliverygoes into charging the double layer capacitance. As chargegoes onto the double layer, the electrode potential movesaway from equilibrium (an overpotentialη develops), andthe Faradaic reaction O +ne− → R starts to consume charge,with net current density proportional to exp(η). The totalinjected current then goes into both capacitive currentic,causing the electrode to continue to charge negatively, andFaradaic currentif . The Faradaic reaction will consume reac-tant O near the surface, and the concentration [O](0,t) drops.Once the concentration [O](0,t) becomes zero, the Faradaicreaction is mass transport limited, and the current into thisreaction no longer increases as exp(η). A portion of the in-jected charge goes into capacitive current, causing the doublel t suf-fi ith al thant is ther ans-p nt),a non-m rther

injected charge. The water window is a potential range thatis defined by the reduction of water, forming hydrogen gas,in the negative direction, and the oxidation of water, form-ing oxygen, in the positive direction. Because water does notbecome mass transport limited in an aqueous solution, the po-tentials where water is reduced and oxidized form lower andupper limits respectively for electrode potentials that may beattained, and any electrode driven to large enough potentialsin water will evolve either hydrogen gas or oxygen gas. Uponreaching either of these limits, all further charge injection isaccommodated by the reduction or oxidation of water.

2.4. Pulse train response during current control

Based on the simple electrical model ofFig. 1, one maypredict different characteristics in the potential waveforms re-sulting from monophasic pulsing, charge-balanced biphasicpulsing, and charge-imbalanced biphasic pulsing. Considerwhat occurs when an electrode, starting from the open-circuitpotential, is pulsed with a single cathodic pulse and then leftopen circuit (illustrated inFig. 4(a), pulse 1). Upon puls-ing the electrode charges, with injected charge being storedreversibly on the double layer capacitance, causing the elec-trode potential to move negative. As the potential continuesto move negative, charge begins to be delivered into Faradaicc n oft rnalc con-t ausest , anda ases)t entiald , the

ayer to continue to charge to more negative potentials. Aciently negative potentials, another Faradaic reaction wower exchange current density (thus more irreversible)he first may start. In the case where this second reactioneduction of water, the reaction will not become mass trort limited (water at 55.5 M will support substantial currend an electrode potential will be reached where theass transport limited reduction of water accepts all fu

urrents (whose magnitude are an exponential functiohe overpotential). At the end of the pulse when the exteircuit is opened, charge on the double layer capacitanceinues to discharge through Faradaic reactions. This che electrode potential to move positive during discharges the electrode discharges (i.e. the overpotential decre

he Faradaic current decreases, resulting in an exponischarge of the electrode. Given a long enough time


Fig. 4. Electrode potentials in response to monophasic and charge-balanced biphasic pulse trains. (a) Ratcheting of potential during monophasic cathodicpulsing. The pre-pulse potential of successive pulses moves negative until all injected charge goes into irreversible processes. (b) Ratcheting during charge-balanced cathodic first biphasic pulsing. The pre-pulse potential of successive pulses moves positive until the same amount of charge is lost irreversibly duringthe cathodic and anodic phases. Shaded areas represent periods of irreversible reactions.

electrode potential will approach the open-circuit potential.However, if the electrode is pulsed with a train whose periodis short with respect to the time constant for discharge (asmay occur with neural stimulation, with a period of perhaps20 ms), i.e. if a second cathodic pulse arrives before the elec-trode has completely discharged, then the potential at the startof the second pulse (the pre-pulse potential) is more negativethan the pre-pulse potential of the first pulse (which is theopen-circuit potential). Because the potential during the sec-ond pulse begins at a more negative potential than the first,a smaller fraction of the injected charge goes into reversiblecharging of the double layer capacitance. The Faradaic re-actions begin accepting significant charge at an earlier timethan in the first pulse, and there is more charge delivered toirreversible reactions during the second pulse than during thefirst as the overall potential range traversed is more negativeduring the second pulse (Fig. 4(a), pulse 2). Upon going toopen circuit after the second pulse, the electrode dischargesthrough Faradaic reactions. Because the potential at the endof the second current pulse is more negative than the potentialat the end of the first current pulse, the potential range duringdischarge between pulses 2 and 3 is also more negative thanbetween pulses 1 and 2, and likewise the pre-pulse poten-tial of pulse 3 is more negative than the pre-pulse potential ofpulse 2. This “ratcheting” of the electrode potential continuesu

u

)

i eac-t penc rre-v eO dys withe

arge-b odic,f en-c thed may

begin to transfer charge into Faradaic reactions as the poten-tial moves negative. The anodic pulse then causes the elec-trode potential to move back positive (illustrated inFig. 4(b),pulse 1). Unlike the exponential decay during the monopha-sic pulsing, the electrode potential now changes accordingto the anodic current and the double layer capacitance, andthere is reversal of charge from the double layer. Becausenot all of the injected charge during the cathodic pulse wentinto charging of the double layer, only some fraction of the in-jected cathodic charge is required in the anodic phase to bringthe electrode potential back to the pre-pulse value. Since theanodic pulse is balanced with the cathodic pulse, the elec-trode potential at the end of the anodic phase of pulse 1is positive of the pre-pulse potential of pulse 1 (the open-circuit potential). During the anodic phase and during theopen circuit following the anodic phase, if the potential be-comes sufficiently positive, anodic Faradaic reactions such aselectrode corrosion may occur. During the open-circuit pe-riod, the electrode discharges exponentially through anodicFaradaic reactions back towards the open-circuit potential,moving negative with time. By the beginning of pulse 2 thepotential is still positive of the pre-pulse potential for pulse1 (the open-circuit potential). Thus, as long as any charge islost irreversibly during the cathodic phase, the potential at theend of the charge-balanced anodic phase will be positive oft nliket -pulsep cursw

( itherimplyoten-

( the

I rge-b ove

ntil the following condition is met:

nrecoverable charge (Qur) per pulse

= injected charge (Qinj ) per pulse (2.5

.e. all injected charge goes into irreversible Faradaic rions that occur either during the pulse or during the oircuit interpulse interval period. Charge delivered into iersible processes is defined as unrecoverable chargQur.nce condition(2.5) is met, the pulsing is in the stea

tate, and the potential excursions repeat themselvesach pulse cycle.

Next, consider the electrode response when a chalanced stimulation protocol is used; cathodic then an

ollowed by open circuit. The electrode begins from opircuit potential. Upon applying the first cathodic pulse,ouble layer reversibly charges, and then the electrode

he pre-pulse potential, and a ratcheting effect is seen. Uhe monophasic case, the ratcheting of the electrode preotential is now in a positive direction. Steady state ochen one of the two following conditions is met:

1) There are no irreversible Faradaic reactions during ethe cathodic or anodic phases, and the electrode scharges and then discharges the double layer (the ptial waveform appears as a sawtooth):

Qur,cathodic= Qur,anodic= 0 (2.6)

2) The same amount of charge is lost irreversibly duringcathodic phase and the anodic phase:

Qur,cathodic= Qur,anodic �= 0 (2.7)

f irreversible processes do occur, for cathodic first chaalanced biphasic pulsing, the electrode potential will m


positive of the open-circuit potential, and during steady-statecontinuous pulsing there is an equal amount of unrecover-able charge delivered into cathodic and anodic irreversibleprocesses.

Finally, consider the electrode response when a charge-imbalanced stimulation protocol is used (not illustrated). Theelectrode begins from open-circuit potential. The responseto the first cathodic pulse is the same as with the monophasicor charge-balanced biphasic waveforms. The anodic phasethen causes the electrode potential to move back positive, butsince there is less charge in the anodic phase than cathodic,the electrode potential does not move as far positive asit did with the charge-balanced biphasic waveform. Thepotential at the end of the anodic phase will be closerto the open-circuit potential than during charge-balancedpulsing. The maximum positive potential will be less whenusing the charge-imbalanced waveform than when usingthe charge-balanced waveform. This has the advantage thatcharge delivered into anodic Faradaic processes such asmetal corrosion is reduced with respect to charge-balancedstimulation. The pre-pulse potential will move under factorsas explained for the monophasic and charge-balancedbiphasic waveforms until the following condition is met:

The net imbalance in injected charge is equal to the netdifference in cathodic and anodic unrecoverable charge:

(

D ulsep rcuitp

lsingc uringp them dingt hreep asic,c uringm ughtb ase,t theo

2

timu-l ssest ingu re ther g thed la-t argeo thee ublel nt of

charge in the reversal phase equal to the charge delivered inthe stimulation phase (a charge-balanced protocol), the elec-trode potential will return precisely to its pre-pulse potentialby the end of the reversal phase and the potential curve willbe a simple sawtooth as shown inFig. 5(a) (corrected forsolution resistance). If reversible Faradaic reactions occurduring the stimulation phase, then charge in the reversalor secondary phase may go into reversing these reactions.Fig. 5(b) illustrates an example reversible Faradaic process,in this case charging of the pseudocapacitance (reduction ofprotons and plating of monatomic hydrogen onto the metalelectrode surface) as may occur on platinum. During reversalthe plated hydrogen is oxidized back to protons. Because theelectrochemical process occurring during the reversal phaseis the exact opposite of that occurring during the stimulationphase, there is zero net accumulation of electrochemicalspecies. Reversible Faradaic reactions include adsorptionprocesses as inFig. 5(b), as well as processes where thesolution phase product remains near the electrode due tomass diffusion limitations. If irreversible Faradaic reactionsoccur, upon passing current in the reverse direction, reversalof electrochemical product does not occur as the product isno longer available for reversal (it has diffused away). Anexample shown inFig. 5(c) is the formation of hydrogengas after a monolayer of hydrogen atoms has been adsorbedo daicr , thep notl ssescc ntial).W ther f thep actlyt ther thatw se (ac

ncedo ut oft n. Inc np velyn timeF ce ofo andf pli-c ,1 ini eta deda e an-o hasicp n re-a ncedp videa hodic

Qinj,cathodic− Qinj,anodic)

≡ Qimbal = Qur,cathodic− Qur,anodic (2.8)

uring charge-imbalanced stimulation, the shift in pre-potential may be either positive or negative of the open-ciotential depending on the amount of imbalance.

Based on these considerations, monophasic puauses the greatest shift of the electrode potential dulsing away from the equilibrium potential, thus causesost accumulation of unrecoverable charge (correspon

o products of irreversible Faradaic reactions) of the trotocol types (monophasic, charge-balanced biphharge-imbalanced biphasic). Furthermore, since donophasic pulsing the electrode potential is not broack towards the equilibrium potential by an anodic ph

here is accumulation of unrecoverable charge duringpen circuit interpulse interval.

.5. Electrochemical reversal

The purpose of the reversal phase during biphasic sation is to reverse the direction of electrochemical procehat occurred during the stimulating phase, minimiznrecoverable charge. A reversible process is one wheeactants are reformed from the products upon reversinirection of current. Upon delivering current in the stimu

ion phase and then reversing the direction of current, chn the electrode capacitance will discharge, returninglectrode potential towards its pre-pulse value. If only do

ayer charging occurred, then upon passing an amou

nto the platinum surface. In the case where a Faraeaction has occurred during the stimulation phaseotential waveform during the stimulation phase is

inear, but displays a slope inflection as Faradaic proceonsume charge (this is charge that doesnot charge theapacitance, thus does not change the electrode potehen an equal amount of charge is then passed in

eversal phase, the electrode potential goes positive ore-pulse potential. To return the electrode potential ex

o its pre-pulse value would require that the charge ineversal phase be equal to only the amount of chargeent onto the capacitance during the stimulation phaharge-imbalanced waveform).

The use of biphasic stimulation (either charge-balar charge-imbalanced) moves the electrode potential o

he most negative ranges immediately after stimulatioomparison (as shown inFig. 4), the monophasic stimulatiorotocol allows the electrode potential to remain relatiegative during the interpulse interval, and during thisaradaic reduction reactions may continue. In the presenxygen, these reactions may include reduction of oxygen

ormation of reactive oxygen species, which have been imated in tissue damage (reviewed byHalliwell, 1992; Stohs995; Hemnani and Parihar, 1998; Imlay, 2003; Bergaml., 2004). The charge-imbalanced waveform has the addvantage that the electrode potential at the end of thdic pulse is less positive than with charge-balanced bipulsing, thus less charge goes into irreversible oxidatioctions such as corrosion when using the charge-imbalarotocol. Charge-imbalanced biphasic waveforms promethod to reduce unrecoverable charge in the cat


Fig. 5. Electrochemical processes and potential waveforms during charge-balanced stimulation: (a) capacitive charging only; (b) reversible hydrogen plating;(c) irreversible hydrogen evolution.

direction (with respect to monophasic stimulation) and inthe anodic direction (with respect to charge-balanced bipha-sic stimulation), thus are an attractive solution to minimiz-ing damage to either the stimulated tissue or the metalelectrode.

2.6. Charge delivery by a voltage source between theworking electrode and counter electrode

An alternative form of charge injection involves the di-rect connection of a voltage source between the workingand counter electrodes.Fig. 6compares the current, workingelectrode to reference electrode voltage (VWE–RE), and work-ing electrode to counter electrode voltage (VWE–CE) wave-forms during monophasic pulsing under current control ver-susVWE–CE control. TheVWE–RE waveforms represent theworking electrode interfacial potentials and do not imply thata reference electrode is required for either control scheme.

F ol andV ringt nc penc

Upon applying a voltage pulse with amplitudeVappbetweenthe working electrode and counter electrode inVWE–CEcon-trol, the current is at its maximum value at the beginning of thepulse as the double layer capacitances of the two electrodescharge and the current is predominantly capacitive. Given along duration pulse, the current will asymptotically approacha value whereVappmaintains a steady-state Faradaic current,with current density given by Eq.(1.17). Fig. 6 illustratesthe steady-state waveforms when using an exhausting circuit(Donaldson and Donaldson, 1986a, 1986b), where at the endof the monophasic voltage pulse the working and counterelectrodes are shorted together, causing the charge on theworking electrode capacitance to rapidly discharge, and theworking electrode potential to attain the counter electrodepotential. If the counter electrode is sufficiently large, its po-tential will not be notably perturbed away from its equilib-rium potential during pulsing, and upon shorting the workingelectrode to the counter electrode, the working electrode po-tential will be brought back to the counter electrode equilib-rium potential. Donaldson and Donaldson showed that duringcathodic monophasic pulsing of real electrodes with an ex-hausting scheme, the potentials of both the working electrodeand counter electrode moved positive in response to a con-tinuous train, increasing the risk of oxidizing reactions suchas corrosion. The discharge of the working electrode is rela-tively rapid duringVWE–CEcontrol with an exhausting circuit,as the working electrode is directly shorted to the counterelectrode. This is contrasted by the relatively slow dischargeusing monophasic current control as shown inFig. 6, with anopen circuit during the interpulse interval. During the open-circuit period, the working electrode capacitance dischargesthrough Faradaic reactions at the working electrode interface.This leads to a greater accumulation of unrecoverable chargeduring the open circuit interpulse interval (current con-trol) than with the short circuit interpulse interval (VWE–CEcontrol). However, in current control, appropriate biphasicpulsing waveforms (Fig. 3) can promote rapid electrodedischarge.

ig. 6. Steady-state voltage and current waveforms using current contr

WE–CE control. Note the rapid discharge of the working electrode duhe short circuit interpulse interval ofVWE–CE control relative to the opeircuit interpulse interval of current control. S.C. = short circuit; O.C. = oircuit; Iapp= applied current;Vapp= applied voltage.


Advantages of theVWE–CEcontrol scheme over the currentcontrol scheme include: (1) the circuitry is simpler (it maybe a battery and an electronic switch); and (2) unrecoverablecharge accumulation is lower during the interpulse intervalthan it would be with monophasic current control. Disadvan-tages of theVWE–CE control scheme include: (1) maximumstimulation of excitable tissue occurs only at the beginningof the pulse when current is maximum, and stimulation effi-ciency decreases throughout the pulse as current decreases,whereas with current control the current is constant through-out the pulse; (2) an increase in resistance anywhere in theelectrical conduction path will cause an additional voltagedrop, decreasing the current and potentially causing it to beinsufficient for stimulation, whereas with current control thecurrent is constant (assuming the required voltage is withinthe range of the stimulator); and (3) neither the current drivennor the charge injected are under direct control using voltagecontrol (Weinman and Mahler, 1964). Because the level ofneuronal membrane depolarization is related to the appliedcurrent, these factors result in a reduction in reproducibilitybetween experiments, as well as between clinical implants,duringVWE–CE control. Moreover, because tissue propertiescan change over time, stimulation efficacy may change whenusingVWE–CE control.

3a

odes (un-s noti sue,n ) Them tion.I dedt terialm If ad ught andt ustb n bei elicita thece ccura levelo ntlyh (5)D ionss ilureo ndedd relya -yeari erialc ation

of the implant. For a chronic electrode, the device electricalimpedance must be stable. The conducting and insulatingproperties of all materials must remain intact.

Dymond et al. (1970)tested the toxicity of several met-als implanted into the cat cerebral cortex for 2 months. Ma-terials were deemed toxic if the reaction to the implantedmetal was significantly greater than the reaction to a punc-ture made from the same metal that was immediately with-drawn (Table 1). Stensaas and Stensaas (1978)reported onthe biocompatibility of several materials implanted passivelyinto the rabbit cerebral cortex (Table 1). Materials were clas-sified into one of three categories depending upon changesoccurring at the implant/cortex interface. (1)Non-reactive:for these materials, little or no gliosis occurred, and normalCNS tissue with synapses was observed within 5�m of theinterface. (2)Reactive: multinucleate giant cells and a thinlayer (10�m) of connective tissue surrounded the implant.Outside of this was a zone of astrocytosis. Normal CNS tissuewas observed within 50�m of the implant. (3)Toxic: thesematerials are separated from the cortical tissue by a capsuleof cellular connective tissue and a surrounding zone of astro-cytosis.Loeb et al. (1977)studied the histological responseto materials used by the microelectronics industry implantedchronically in the subdural space of cats, and found reactionsto be quite dependent on specific material formulations ands

r usei ricw ati-bs non-t elec-t the ab-s 0;S , 1978;B l-l .,1 .,2

sitec h top or ag s inm e al-l ntoa sili-c beenm ise,1 -v to thee min-i latedt edye

. Materials used as electrodes for charge injectionnd reversible charge storage capacity

The ideal material for use as a stimulating electratisfies the following requirements. (1) The passivetimulated) material must be biocompatible, so it shouldnduce a toxic or necrotic response in the adjacent tisor an excessive foreign body or immune response. (2aterial must be mechanically acceptable for the applica

t must maintain mechanical integrity given the intenissue, surgical procedure and duration of use. The maust not buckle if it is to pass through the meninges.evice is to be used chronically, it must be flexible eno

o withstand any small movement between the deviceissue following implantation. (3) The complete device me efficacious. This requires that sufficient charge ca

njected with the chosen material and electrode area toction potentials. The required charge is quantified byharge–duration curve, discussed in Section4. (4) Duringlectrical stimulation, Faradaic reactions should not ot levels that are toxic to the surrounding tissue. Thef reaction product that is tolerated may be significaigher for acute stimulation than chronic stimulation.uring electrical stimulation, Faradaic corrosion reacthould not occur at levels that will cause premature faf the electrode. This again depends greatly on the inteuration of use. During acute stimulation corrosion is raconcern, whereas a device that is intended for a 30

mplant must have a very low corrosion rate. (6) The matharacteristics must be acceptably stable for the dur

urface preparations.Platinum has been demonstrated as biocompatible fo

n an epiretinal array (Majji et al., 1999) and in cochleamplants (Chouard and Pialoux, 1995). Both titanium anderamic (Chouard and Pialoux, 1995) and platinum–iridiumire (Niparko et al., 1989) have been shown as biocomple in cochlear implants.Babb and Kupfer (1984)have showntainless steel and nickel–chromium (Nichrome) to beoxic. Copper and silver are unacceptable as stimulatingrodes, as these metals cause tissue necrosis even inence of current (Fisher et al., 1961; Dymond et al., 197awyer and Srinivasan, 1974; Stensaas and Stensaasabb and Kupfer, 1984). Nickel–titanium shape memory a

oys have good biocompatibility response (Ryhanen et al998), up to a nickel content of 50% (Bogdanski et al002).

The first intracortical electrodes consisted of singleonductive microelectrodes made of material stiff enougenetrate the meninges, either an insulated metallic wirelass pipette filled with conductive electrolyte. Advanceaterials science and microelectronics technology hav

owed the development of multiple site electrodes built osingle substrate, using planar photolithographic and

on micromachining technologies. Such devices haveade from silicon (Jones et al., 1992; Hoogerwerf and W994), and polyimide (Rousche et al., 2001). In further adancements, bioactive components have been addedlectrode to direct neurite growth toward the electrode,

mizing the distance between the electrode and stimuissue (Kennedy, 1989; Kennedy and Bakay, 1998; Kennt al., 1999).


Table 1Classification of material biocompatibility

Classification byDymond et al.

Classification by Stensaasand Stensaas

Other references

ConductorsAluminum Non-reactiveCobalt ToxicCopper Toxic Toxic (Fisher et al., 1961; Sawyer and Srinivasan,

1974; Babb and Kupfer, 1984)Gold Non-toxic Non-reactiveGold–nickel–chromium Non-toxicGold–palladium–rhodium Non-toxicIron ToxicMolybdenum ReactiveNickel–chromium (Nichrome) Reactive Non-toxic (Babb and Kupfer, 1984)Nickel–chromium–molybdenum Non-toxicNickel–titanium (Nitinol) Biocompatible (Ryhanen et al., 1998; Bogdanski

et al., 2002)Platinum Non-toxic Non-reactive Biocompatible (Chouard and Pialoux, 1995;

Majji et al., 1999)Platinum–iridium Non-toxic Biocompatible (Niparko et al., 1989)Platinum–nickel Non-toxicPlatinum–rhodium Non-toxicPlatinum–tungsten Non-toxicPlatinized platinum (Pt black) Non-toxicRhenium Non-toxicSilver Toxic Toxic Toxic (Fisher et al., 1961; Sawyer and Srinivasan,

1974; Babb and Kupfer, 1984)Stainless steel Non-toxic Non-toxic (Babb and Kupfer, 1984)Tantalum ReactiveTitanium Biocompatible (Chouard and Pialoux, 1995)Tungsten Non-reactive

InsulatorsAlumina ceramic Non-reactive Biocompatible (Chouard and Pialoux, 1995)Araldite (epoxy plastic resin) ReactivePolyethylene Non-reactivePolyimide Biocompatible (Stieglitz and Meyer, 1999)Polypropylene Non-reactiveSilastic RTV ToxicSilicon dioxide (Pyrex) ReactiveTeflon TFE (high purity) Non-reactiveTeflon TFE (shrinkable) ReactiveTitanium dioxide Reactive

SemiconductorsGermanium ToxicSilicon Non-reactive Biocompatible (Schmidt et al., 1993; Hoogerwerf

and Wise, 1994; Kristensen et al., 2001)

AssembliesGold–silicon dioxide passivated microcircuit Reactive

Chronic implantation of any device into the central ner-vous system, even those materials considered biocompati-ble, elicits a common response consisting of encapsulationby macrophages, microglia, astrocytes, fibroblasts, endothe-lia and meningeal cells (Rudge et al., 1989). The early re-sponse to material implantation is inflammation (Stensaasand Stensaas, 1978; Rudge et al., 1989; Turner et al., 1999).The chronic response is characterized by a hypertrophy of thesurrounding astrocytes (Stensaas and Stensaas, 1978) whichdisplay elevated expression of intermediate filament proteinssuch as GFAP and vimentin (Bignami and Dahl, 1976), an in-

filtration of microglia and foreign body giant cells (Stensaasand Stensaas, 1978) and a thickening of the surrounding tis-sue that forms a capsule around the device (Hoogerwerf andWise, 1994; Turner et al., 1999).

The reversible charge storage capacity (CSC) of an elec-trode, also known as the reversible charge injection limit(Robblee and Rose, 1990), is the total amount of chargethat may be stored reversibly, including storage in the dou-ble layer capacitance, pseudocapacitance, or any reversibleFaradaic reaction. In electrical stimulation of excitable tis-sue it is desirable to have a large reversible charge stor-


age capacity so that a relatively large amount of chargemay be injected (thus being efficacious for stimulation)prior to the onset of irreversible Faradaic reactions (whichmay be deleterious to the tissue being stimulated or tothe electrode itself). The reversible charge storage capac-ity depends upon the material used for the electrode, thesize and shape of the electrode, the electrolyte compo-sition, and parameters of the electrical stimulation wave-form.

The slow cyclic voltammogram for a material is a graphicdisplay of the current density into various electrochemicalprocesses as a function of the electrode potential as the po-tential is slowly cycled. At any point in time, the amount ofcurrent going into a particular process is determined by thepotential as well as by the reactant concentration, as givenby Eq.(1.17). The water window is defined as the potentialregion between the oxidation of water to form oxygen andthe reduction of water to form hydrogen. Because water doesnot become mass transport limited in an aqueous solution,once the electrode potential attains either of these two waterwindow boundaries, all further injected charge goes into theirreversible processes of water oxidation (anodically) or wa-ter reduction (cathodically). In many studies, the reversiblecharge storage capacity has been defined as the maximumcharge density that can be applied without the electrode po-t uldb t po-t s asi hatm

id-i om-m eirr ea em ula-t ka t al.,1 ringtt termt l.,1 976

a-t ue.B -p ctionu pro-c g oft d ox-i ef that3 re-v fluid( am mum

conditions, including relatively long pulse widths (>0.6 ms).Rose and Robblee (1990)reported on the charge injectionlimits for a platinum electrode using 200�s charge-balancedbiphasic pulses. The reversible charge injection limit was de-fined as the maximum charge density that could be appliedwithout the electrode potential exceeding the water windowduring pulsing. The authors determined the charge injectionlimit to be 50–100�C/cm2 (geometric) using anodic firstpulses, and 100–150�C/cm2 (geometric) using cathodic firstpulses. These values are considerably lower than the theoret-ical values determined by Brummer and Turner, since theelectrode potential at the beginning of a pulse begins some-where intermediate to oxygen and hydrogen evolution and notall of the three reversible processes accommodate charge dur-ing the stimulating pulse. Dissolution of platinum in salineincreases linearly with the injected charge during biphasicstimulation (McHardy et al., 1980). Anodic first pulses causemore dissolution than cathodic first pulses, as the electrodepotential attains more positive values during the stimulating(first) phase.Robblee et al. (1980)have shown that in thepresence of protein such as serum albumin, the dissolutionrate of platinum decreases by an order of magnitude.

The reversible charge storage capacity is dependent uponthe electrode real surface area and geometry. The geometricarea of an electrode is usually easily calculated, but the reala acity.B toe lec-t e inv a ofa n. An se anw leadts s.

me-c lat-i icals m-i .,1 ithm corti-c f barei er,w rials,t r plat-i ngesb n oft

ndrs stor-a id-i tiva-t m

ential exceeding the water window during pulsing. It shoe noted that in fact irreversible processes might occur a

entials within the water window, including such reactionrreversible oxygen reduction (Merrill, in preparation) t

ay become mass transport limited.The noble metals, including platinum (Pt), gold (Au), ir

um (Ir), palladium (Pd), and rhodium (Rh), have been conly used for electrical stimulation, largely due to th

elative resistance to corrosion (Dymond et al., 1970; Whitnd Gross, 1974; Johnson and Hench, 1977). These nobletals do exhibit some corrosion during electrical stim

ion, as shown by dissolution (Brummer et al., 1977; Blacnd Hannaker, 1979; McHardy et al., 1980; Robblee e980, 1983a) and the presence of metal in the neighbo

issue (Robblee et al., 1983b; Tivol et al., 1987). In additiono corrosion of the electrode, there is evidence of long-oxic effects on the tissue from dissolution (Rosenberg et a965; Rosenberg, 1971; Macquet and Theophanides, 1).

Platinum and platinum–iridium alloys are common merials used for electrical stimulation of excitable tissrummer and Turner (1975, 1977a, 1977b, 1977c)have reorted on the electrochemical processes of charge injesing a platinum electrode. They reported that threeesses could store charge reversibly, including charginhe double layer capacitance, hydrogen atom plating andation (pseudocapacity, reaction(1.6)) and reversible oxidormation and reduction on the electrode surface, and00–350�C/cm2 (real area) could theoretically be storedersibly by these processes in artificial cerebrospinalequivalently 420–490�C/cm2 (geometric area)). This isaximum reversible charge storage capacity under opti

rea is the value that determines the total charge caprummer and Turner (1977b)have reported on a methodxperimentally determine the real area of a platinum erode in vitro, however, this may not be applicable to thivo situation. It should also be noted that the real aren electrode may change during the course of stimulatioon-uniform (non-spherical) electrode geometry will cauon-uniform current density (Bruckenstein and Miller, 1970)ith maximum current at the electrode edges, which may

o localized electrode corrosion (Shepherd et al., 1985) or tis-ue burns (Wiley and Webster, 1982) at the electrode edge

Platinum is a relatively soft material and may not behanically acceptable for all stimulation applications. Pnum is often alloyed with iridium to increase the mechantrength. Alloys of platinum with 10–30% iridium have silar charge storage capacity to pure platinum (Robblee et al983a). Iridium is a much harder metal than platinum, wechanical properties that make it suitable as an intra

al electrode. The reversible charge storage capacities oridium or rhodium are similar to that of platinum. Howevhen a surface oxide is present on either of these mate

hey have greatly increased charge storage capacity ovenum. These electrodes inject charge using valency chaetween two oxide states, without a complete reductio

he oxide layer.Iridium oxide is a popular material for stimulation a

ecording, using reversible conversion between Ir3+ and Ir4+

tates within an oxide to achieve high reversible chargege capacity. Iridium oxide is commonly formed from ir

um metal in aqueous electrolyte by electrochemical acion, which consists of repetitive potential cycling of iridiu


to produce a multilayered oxide (Rand and Woods, 1974;Zerbino et al., 1978; Robblee et al., 1983a; Mozota andConway, 1983; Robblee and Rose, 1990). Such activated irid-ium oxide films have been used for intracortical stimulationand recording using iridium wire (Bak et al., 1990; McCreeryet al., 1992b; Loeb et al., 1995; Liu et al., 1999; Meyer andCogan, 2001) or with micromachined silicon electrodesusing sputtered iridium on the electrode sites (Andersonet al., 1989; Weiland and Anderson, 2000). The maxi-mum charge density that can be applied without the elec-trode potential exceeding the water window was reportedfor activated iridium oxide using 200�s charge-balancedpulses as±2 mC/cm2 (geometric) for anodic first puls-ing and±1 mC/cm2 for cathodic first pulsing (Beebe andRose, 1988; Kelliher and Rose, 1989). By using an anodicbias, cathodic charge densities of 3.5 mC/cm2 (geometric)have been demonstrated both in vitro (Beebe and Rose, 1988;Kelliher and Rose, 1989) and in vivo (Agnew et al., 1986).Iridium oxide films can also be formed by thermal decom-position of an iridium salt onto a metal substrate (Robblee etal., 1986), or by reactive sputtering of iridium onto a metalsubstrate (Klein et al., 1989). Meyer and Cogan (2001)re-ported on a method to electrodeposit iridium oxide films ontosubstrates of gold, platinum, platinum–iridium and 316LVMstainless steel, achieving reversible charge storage capacitieso 2

wella 5Na thatd hichf lesss andc sibleo ssi-b ten-t reak-d dis-s ,1 ross,1 ca-t nifi-c sion(n romc mon-s el (rev odm culare only4 areae

itivea trodef e in-t al.,1

trode has a high charge storage capacity, achieved by us-ing sintered tantalum or electrolytically etched tantalum wireto increase the surface area.Guyton and Hambrecht (1973,1974)have demonstrated a sintered Ta/Ta2O5 electrode witha charge storage capacity of 700�C/cm2 (geometric). TheTa/Ta2O5 electrodes have sufficient charge storage capacityfor electrodes in the range of 0.05 cm2 and charge densitiesup to 200�C/cm2 (geometric); however, they may not be ac-ceptable for microelectrode applications where the requiredcharge densities may exceed 1 mC/cm2 (Rose et al., 1985).Tantalum capacitor electrodes must operate at a relativelypositive potential to prevent electron transfer across the ox-ide. If pulsed cathodically, a positive bias must be used onthe electrode.

Stimulation of muscle, peripheral nerve or cortical surfacerequires relatively high charge per pulse (on the order of0.2–5�C), thus platinum or stainless steel electrodes mustbe of fairly large surface area to stay within the reversiblecharge storage capacity. Intracortical stimulation requiresmuch less total charge per pulse, however, in order toachieve selective stimulation, the electrode size must bevery small, resulting in high charge density requirements.With a geometric surface area of 20× 10−6 cm2, the chargeper pulse may be on the order of 0.008–0.064�C, yieldinga charge density of 400–3200�C/cm2 (Agnew et al., 1986;M bea lses,o

rialsc

4t

iso ichr thea llulars elym tra-c tivep due tob ertiesap isw lS enpm eters“ a,1 nta

erveh 1;M of

f >25 mC/cm.The stainless steels (types 303, 316 and 316LVM) as

s the cobalt–nickel–chromium–molybdenum alloy MP3re protected from corrosion by a thin passivation layerevelops when exposed to atmospheric oxygen and w

orms a barrier to further reaction. In the case of stainteel this layer consists of iron oxides, iron hydroxideshromium oxides. These metals inject charge by reverxidation and reduction of the passivation layers. A pole problem with these metals is that if the electrode po

ial becomes too positive (the transpassive region), bown of the passivation layer and irreversible metalolution may occur at an unacceptable rate (Loucks et al.959; Greatbatch and Chardack, 1968; White and G974), potentially leading to failure of the electrode. A

hodic charge imbalance has been shown to allow sigantly increased charge injection without electrode corroMcHardy et al., 1977; Scheiner and Mortimer, 1990). Tita-ium and cobalt–chromium alloys are also protected forrosion by a surface oxide passivation layer, and detrate better corrosion resistance than does stainless steiewed byGotman, 1997). 316LVM stainless steel has goechanical properties and has been used for intramuslectrodes. The charge storage capacity of 316LVM is0–50�C/cm2 (geometric), necessitating large surfacelectrodes.

Capacitor electrodes inject charge strictly by capacction, as a dielectric material separates the metal elec

rom the electrolyte, preventing Faradaic reactions at therface (Guyton and Hambrecht, 1973, 1974; Rose et985). The tantalum/tantalum pentoxide (Ta/Ta2O5) elec-

-

cCreery et al., 1986). Such high charge densities maychieved using iridium oxide electrodes with anodic pur cathodic pulses with an anodic bias.

Table 2lists several parameters of interest for mateommonly used for stimulation.

. Principles of extracellular stimulation of excitableissue

The goal of electrical stimulation of excitable tissueften the triggering of action potentials in axons, whequires the artificial depolarization of some portion ofxon membrane to threshold. In the process of extracetimulation, the extracellular region is driven to relativore negative potentials, equivalent to driving the in

ellular compartment of a cell to relatively more posiotentials. Charge is transferred across the membraneoth passive (capacitive and resistive) membrane props well as through active ion channels (Hille, 1984). Therocess of physiological action potential generationell reviewed in the literature (e.g.Principles of Neuracienceby Kandel et al., 2000), and models have beroposed (Chiu et al., 1979; Sweeney et al., 1987) forammalian myelinated axons in terms of the paramm” and “h” as defined byHodgkin and Huxley (1952952b, 1952c, 1952d)in their studies of the squid giaxon.

The mechanisms underlying electrical excitation of nave been reviewed elsewhere (McNeal, 1976; Ranck, 198ortimer, 1990; Durand, 1995). In the simplest case


Table 2Reversible charge storage capacity and other parameters in electrode material selection

Reversible charge storagecapacity (�C/cm2)

Reversible charge injec-tion processes

Corrosion characteristics Mechanicalcharacteristics

Platinum 300–350 ra; AF, 200�s:50–100 gb; CF, 200�s:100–150 gb

Double layer charging, hy-drogen atom plating, andoxide formation and re-duction

Relatively resistant;greatly increased resis-tance with protein

Relatively soft

Platinum–iridium alloys Similar CSC to Pt Stronger than PtIridium Similar CSC to Pt Stronger than PtIridium oxide AF: ±2200 gc,d; CF:

±1200 gc,d; AB: ±3500gc,d,e

Oxide valency changes Highly resistante,f

316LVM stainless steel 40–50 g Passive film formation andreduction

Resistant in passive re-gion; rapid breakdown intranspassive region

Strong and flexible

Tantalum/tantalum pentoxide 700 gg; 200 gh Capacitive only Corrosion resistanti,j,k,l

r = real area; g = geometric area; AF = anodic first, charge-balanced; CF = cathodic first, charge-balanced; AB = cathodic first, charge-balanced, with anodicbias.

a Brummer and Turner (1977c).b Rose and Robblee (1990).c Beebe and Rose (1988).d Kelliher and Rose (1989).e Agnew et al. (1986).f Robblee et al. (1983a).g Guyton and Hambrecht (1973, 1974).h Rose et al. (1985).i Bernstein et al. (1977).j Donaldson (1974).k Johnson et al. (1977).l Lagow et al. (1971).

stimulation, a monopolar electrode (a single current carry-ing conductor) is placed in the vicinity of excitable tissue.Current passes from the electrode, through the extracellularfluid surrounding the tissue of interest, and ultimately to adistant counter electrode. For a currentI (in amps) flowingthrough the monopolar electrode located a distance r awayfrom a segment of excitable tissue, and uniform conductivityin the fluid ofσ (S/m), the extracellular potentialVe at thetissue is:

Ve = I

4πσr(4.1)

Bipolar and other electrode configurations have more com-plex voltage and current patterns and will not be discussedhere.Durand (1995)has reviewed solutions for electrical po-tential profiles of various systems.

During current-controlled stimulation, the current isconstant throughout the period of the pulse; thus, theVeat any point in space is constant during the pulse. DuringVWE–CE control, current is not constant throughout theperiod of the pulse (Fig. 6) and theVe at any point decreasesduring the pulse.

The electric field generated by a monopolar electrode willinteract with an axon membrane (these principles may begeneralized to any excitable tissue). During cathodic stimu-l ses ar ega-t der-

neath the cathode (depolarizing the membrane). Associatedwith the depolarization of the membrane under the cathode ismovement of positive charge intracellularly from the distantaxon to the region under the electrode, and hyperpolarizationof the membrane at a distance away from the electrode. Ifthe electrode is instead driven as an anode (to more positivepotentials), hyperpolarization occurs under the anode, and de-polarization occurs at a distance away from the anode. Actionpotentials may be initiated at the regions distant from the elec-trode where depolarization occurs, known as virtual cathodes.The depolarization that occurs with such anodic stimulationis roughly one-seventh to one-third that of the depolarizationwith cathodic stimulation; thus, cathodic stimulation requiresless current to bring an axon to threshold. During cathodicstimulation, anodic surround block may occur at sufficientlyhigh current levels, where the hyperpolarized regions of theaxon distant from the cathode may suppress an action po-tential that has been initiated near the electrode. This effectis observed at higher current levels than the threshold val-ues required for initiation of action potentials with cathodicstimulation.

In a mammalian axon, hyperpolarizing with a pulse thatis long compared with the time constant of the sodium in-activation gate will remove the normal partial inactivation.If the hyperpolarizing current is then abruptly terminated (aswith a rectangular pulse), the sodium activation gate conduc-tance increases back to the rest value relatively quickly, butthe activity of the slower inactivation gate remains high for a

ation, the negative charge of the working electrode cauedistribution of charge on the axon membrane, with nive charge collecting on the outside of the membrane un


period of milliseconds; thus, the net sodium conductance isbriefly higher than normal and an action potential may be ini-tiated. This phenomenon, known as anodic break, may be ob-served with either cathodic or anodic stimulation, since bothcause some region of hyperpolarization in the axon. Anodicbreak may be prevented by using stimulating waveforms withslowly decaying exponential phases instead of abrupt termi-nations (van den Honert and Mortimer, 1979, 1981a, 1981b;Fang and Mortimer, 1991a).

Prolonged subthreshold stimuli can produce the phe-nomenon of accommodation. A cathodic pulse to mammalianaxon that produces subthreshold depolarization will increasesodium inactivation, reducing the number of axons that canbe recruited and so increasing the threshold. This is not aproblem with brief pulses that are shorter than the time con-stant of sodium channel inactivation, but can be with moreprolonged pulses.

It is often desirable to have some degree of selectivity dur-ing electrical excitation of tissue. Selectivity is the ability toactivate one population of neurons without activating a neigh-boring population. Spatial selectivity is the ability to activatea localized group of neurons, such as restricting activation toa certain fascicle or fascicles within a nerve trunk. Changesin the transmembrane potential due to electrical excitationare greatest in fibers closest to the stimulating electrode be-c mpli-ta r po-ta leastc siredp cur-r weent Fiberd n ac odald in thet ,1 msw area ves,a ivat-i r iso mo-td n po-t ers.H berst thats n po-t thec vates eend -t ands

The relationship between the strength (current) of anapplied constant current pulse required to initiate an ac-tion potential and the duration of the pulse, known as thestrength–duration curve, is shown inFig. 7(a). The thresh-old current Ith decreases with increasing pulse width. Atvery long pulse widths, the current is a minimum, called therheobase currentIrh. The following relationship has been de-rived experimentally to quantify the strength–duration curve(Lapicque, 1907):

Ith = Irh

1 − exp(−W/τm)(4.2)

whereIth is the current required to reach threshold,Irh is the rheobasecurrent, W is the pulse width, andτm is the membrane time constant.The qualitative nature of the strength–duration curve shownis representative of typical excitable tissue. The quantitativeaspects, e.g. the rheobase current, depend upon factors suchas the distance between the neuron population of interest andthe electrode, and are determined empirically.Fig. 7(b) illus-trates the charge–duration curve, which plots the thresholdchargeQth = IthWversus pulse width. At longer pulse widths,the required charge to elicit an action potential increases,due to two phenomena. First, over a period of tens to hun-dreds of�s, charge is redistributed through the length of theaxon, and does not all participate in changing the transmem-b ;P s,a . Them hesz reu

ino ringo is of-t redb her-m ationo ns ofm

5

ayc itself.D sioni rodep tiono plat-i lularfl ro-c micalp uters red.Cr odic

ause the induced extracellular potential decreases in aude with distance from the stimulation electrode (Eq.(4.1)),s does the second spatial derivative of the extracellula

ential, which is responsible for excitation (Rall, 1977). Thus,ctivation of neurons closest to the electrode requires theurrent. As the distance between the electrode and deopulation of neurons for activation increases, largerents are required, which generally means neurons bethe electrode and desired population are also activated.iameter selectivity is the ability to activate fibers withiertain range of diameters only. Fibers with greater internistance and larger diameter experience greater changes

ransmembrane potential due to electrical excitation (Rattay989). Using conventional electrical stimulation waveforith relatively narrow pulses, the largest diameter fibersctivated at the lowest stimulus amplitude. In motor nerctivating large diameter fibers first corresponds to act

ng the largest motor units first. This recruitment ordepposite of the physiological case where the smallest

or units are recruited first.Fang and Mortimer (1991a)haveemonstrated a waveform that allows a propagated actio

ential in small diameter fibers but not large diameter fibyperpolarizing pulses have a greater effect on larger fi

han smaller, just as for depolarizing pulses. This meansustained hyperpolarization can be used to block actioential initiation selectively in the large fibers, so thatorresponding depolarizing stimuli can selectively actimall fibers. Electrical stimulation protocols have also beveloped (McIntyre and Grill, 2002) for triggering of ac

ion potentials in specific cell types (e.g. interneurons)tructures (e.g. nerve terminals).

rane potential at the site of injection (Warman et al., 1992lonsey and Barr, 1988). Second, over a period of several mccommodation (increased sodium inactivation) occursinimum chargeQmin occurs as the pulse width approac

ero. In practice, theQth is nearQmin when narrow pulses ased (tens of microseconds).

It is generally best to keep the pulse width narrowrder to minimize any electrochemical reactions occurn the electrode surface. The narrowness of a pulse

en limited by the amount of current that can be delivey a stimulator, especially if it is battery operated. Furtore, some kinds of stimulation, such as selective activf certain axons of a nerve, require pulses longer than teicroseconds.

. Mechanisms of damage

An improperly designed electrical stimulation system mause damage to the tissue or damage to the electrodeamage to an electrode can occur in the form of corro

f the electrode is driven anodically such that the electotential exceeds a value where significant metal oxidaccurs. An example of such a reaction is the corrosion of

num in a chloride-containing medium such as extraceluid (Eq. (1.10)). Corrosion is an irreversible Faradaic pess. It may be due to dissolution where the electrocheroduct goes into solution, or the product may form an oolid layer on a passivation film that cannot be recoveharge-balanced waveforms (Fig. 3(b)) are more likely to

each potentials where corrosion may occur during the an


Fig. 7. Strength–duration and charge–duration curves for initiation of an action potential. Rheobase currentIrh is the current required when using an infinitelylong pulse width. Chronaxie timetc is the pulse width corresponding to two times the rheobase current.

reversal phase and the open circuit interpulse interval thanare monophasic waveforms (Fig. 4). The charge-imbalancedwaveform (Fig. 3(c)) has advantages both in preventing tis-sue damage due to sustained negative potentials during theinterpulse interval, and in preventing corrosion by reducingthe maximum positive potential during the anodic reversalphase (Section2).

The mechanisms for stimulation induced tissue damageare not well understood. Two major classes of mechanismshave been proposed. The first is that tissue damage is causedby intrinsic biological processes as excitable tissue is over-stimulated. This is called the mass action theory, and pro-poses that damage occurs from the induced hyperactivityof many neurons firing, or neurons firing for an extendedperiod of time, thus changing the local environment. Pro-posed mass action mechanisms include depletion of oxygenor glucose, or changes in ionic concentrations both intra-cellularly and extracellularly, e.g. an increase in extracellu-lar potassium. In the CNS, excessive release of excitatoryneurotransmitters such as glutamate may cause excitotoxic-ity. The second proposed mechanism for tissue damage isthe creation of toxic electrochemical reaction products atthe electrode surface during cathodic stimulation at a rategreater than that which can be tolerated by the physiologicalsystem.

alc plat-i daicr odes( on),t tionw t thed imu-l issuen .( on-c ucedn nvi-r ins hors

concluded that neural injury from prolonged electricalstimulation is linked to neuronal activity produced by thestimulation, and furthermore that injury derives at least inpart from entry of calcium into the neurons, consistent withthe mass action hypothesis. The authors state that:

“The most useful hypothesis may be that the activation of ex-citatory amino acid receptors does not ‘cause’ neural injury,but merely lowers its threshold in response to a given stressorby magnifying the destructive effect of the stressor, and thatthe manner and degree to which this occurs depends upon thephysical and pharmacological composition of the particularneural substrate, as well as the stimulus parameters.”

Such an interpretation indicates how the mass action andelectrochemical theories of tissue damage are not exclusive.

McCreery et al. (1990)have shown that both charge perphase and charge density are important factors in determin-ing neuronal damage to cat cerebral cortex. In terms of themass action theory of damage, charge per phase determinesthe total volume within which neurons are excited, and thecharge density determines the proportion of neurons close toan electrode that are excited; thus, both factors determine thetotal change in the extracellular environment. The McCreerydata show that as the charge per phase increases the chargedensity for safe stimulation decreases. When the total chargei arged en at-t inedb y mayi einggc on fort

w yp ld

McCreery et al. (1988)have shown that when identicharge-balanced stimulation protocols were applied tonum stimulating electrodes (known to participate in Faraeactions) and tantalum pentoxide stimulating electrconsidered to be strictly capacitive (reversible) in actihe tissue damage induced in cat brain during stimulaas not statistically different. The authors concluded thaamage induced in the cortex under the conditions of st

ation used was due to passage of current through the tot due to electrochemical reaction products.Agnew et al1990)studied stimulation of cat peroneal nerve, and cluded that the damage to an axon is due to the total indeural activity having some effect on the extraaxonal eonment.Agnew et al. (1993)came to similar conclusionstudies of electrical stimulation of the cat brain. The aut

,

s small (as with a microelectrode) a relatively large chensity may safely be used. Tissue damage that has be

ributed to mass action effects may be alternatively explay electrochemical means, as charge and charge densit

nfluence the quantity of irreversible reaction products benerated at the electrode interface.Shannon (1992)repro-essed the McCreery data and developed an expressihe maximum safe level for stimulation, given by:

log

(Q

A

)= k − log(Q) (5.1)

hereQ is charge per phase (�C per phase),Q/A is charge densiter phase (�C/cm2 per phase), and 2.0 >k> 1.5, fit to the empiricaata.


Fig. 8. Charge (Q) vs. charge density (Q/A) for safe stimulation. A microelectrode with relatively small total charge per pulse might safely stimulate using alarge charge density, whereas a large surface area electrode (with greater total charge per pulse) must use a lower charge density.

Fig. 8 illustrates the charge vs. charge density relation-ship of Eq.(5.1) usingk values of 1.7, 1.85 and 2.0, withhistological data from the 1990 McCreery study using catparietal cortex as well as data fromYuen et al. (1981)on catparietal cortex,Agnew et al. (1989)on cat peroneal nerve,andBhargava (1993)on cat sacral anterior roots. Above thethreshold for damage, experimental data demonstrates tissuedamage, and below the threshold line, experimental data in-dicate no damage.

McCreery et al. (1992a)have reviewed damage from elec-trical stimulation of peripheral nerve. They concluded thatdamage may be from mechanical constriction of the nerve aswell as neuronal hyperactivity and irreversible reactions atthe electrode.

Supporting the concept that damage is due to electrochem-ical reaction products is the work byLilly et al. (1952),which demonstrated that loss of electrical excitability andtissue damage occurs when the cerebral cortex of monkey isstimulated using monophasic current pulses. Later,Lilly etal. (1955)showed that biphasic stimulation caused no lossof excitability or tissue damage after 15 weeks of stimu-lation for 4–5 h per day. Lilly interpreted these results asdue to movement of charged particles such as proteins outof physiological position. The concept that monophasic isa more damaging form of stimulation than charge-balancedbp tim-u henm r than0 e-b /in.(t ere-b ulesa 30 so sori-m timu-l outt 5( age

is due to electrochemical products are observations of catmuscle that suggest some non-zero level of reaction prod-uct can be tolerated (Mortimer et al., 1980; Scheiner andMortimer, 1990). These studies showed that monophasicstimulation causes significantly greater tissue damage thana non-stimulated implant at 1�C/mm2 per pulse but not0.2�C/mm2 per pulse, and that charge-balanced biphasicstimulation does not cause significant tissue damage at lev-els up to 2�C/mm2 per pulse. However, in order to preventelectrode corrosion, the charge-balanced waveform must notexceed 0.4�C/mm2 per pulse, otherwise the electrode po-tential is driven to damaging positive potentials during theanodic (reversal) phase and interpulse interval.Scheiner andMortimer (1990)studied the utility of charge-imbalancedbiphasic stimulation, demonstrating that this waveform al-lows greater cathodic charge densities than monophasic priorto the onset of tissue damage as reactions occurring dur-ing the cathodic phase are reversed by the anodic phase,and also that greater cathodic charge densities can be usedthan with the charge-balanced waveform prior to electrodecorrosion since the anodic phase is no longer constrainedto be equal to the cathodic phase, thus the electrode po-tential reaches less positive values during the anodic phaseand interpulse interval. Scheiner found that cat muscle tis-sue was significantly damaged using monophasic stimu-l 2 ge-i dam-app c-t tionss

pla-n ingt ouldb dur-i

“ n thet plies

iphasic was confirmed byMortimer et al. (1970), who re-orted that breakdown of the blood–brain barrier during slation of the surface of cat cerebral cortex occurs wonophasic pulses were used at power densities greate.003 W/in.2 (0.5 mW/cm2), but does not occur with chargalanced biphasic pulses until a power density of 0.05 W2

8 mW/cm2) is exceeded.Pudenz et al. (1975a, 1975b)fur-her showed that monophasic stimulation of the cat cral cortex causes vasoconstriction, thrombosis in vennd arterioles and blood–brain barrier breakdown withinf stimulation when used at levels required for a senotor response; however, charge-balanced biphasic s

ation could be used for up to 36 h continuously withissue damage if the charge per phase was below 0.4�C4.5�C/cm2). Also supporting the hypothesis that dam

ation at 0.4�C/mm per phase, and that when charmbalanced biphasic stimulation was used, tissue wasged with 1.2�C/mm2 per phase cathodic and 0.2�C/mm2

er phase anodic, and could safely tolerate 1.2�C/mm2 perhase cathodic and 0.5�C/mm2 per phase anodic. No ele

rode corrosion was observed under any of the conditudied.

In 1975, Brummer and Turner gave an alternative exation to Lilly’s for why biphasic pulses were less damag

han monophasic. They proposed that two principles she followed to achieve electrochemically safe conditions

ng tissue stimulation:

(1) Perfect symmetry of the electrochemical processes iwo half-waves of the pulses should be sought. This im


that we do not generate any electrolysis products in solution.One approach to achieve this would appear to involve theuse of perfectly charge-balanced waveforms of controlledmagnitude. (2) The aim should be to inject charge via non-Faradaic or surface-Faradaic processes, to avoid injecting anypossibly toxic materials into the body.”

Their model for safe stimulation interprets the charge-balanced waveform in electrochemical terms. Any processoccurring during the first (stimulating) phase, whether it ischarging of the electrode or a reversible Faradaic process,is reversed during the second (reversal) phase, with nonet charge delivered. The observation that monophasicstimulation causes greater tissue damage than biphasic stim-ulation at the same amplitude, pulse width and frequency isexplained by the fact that during monophasic stimulation,all injected charge results in generation of electrochemicalreaction products.

Reversible processes include charging and discharging ofthe double layer capacitance, as well as surface bound re-versible Faradaic processes such as reactions(1.3)–(1.8) and(1.13). Reversible reactions often involve the production orconsumption of hydrogen or hydroxyl ions as the chargecounterion. This causes a change in the pH of the solution im-mediately adjacent to the electrode surface.Ballestrasse et al.(1985)gave a mathematical description of these pH changes,a ar a1 , butt -c es nor(

, thel fora micap pro-d ta 85;Sd dicald rt andt quid(

oc-c ndert re-a hasei eroxi wna mult1 003;B eym tainp iden-t ary

vasodilator (Furchgott, 1988; Ignarro et al., 1988; Umans andLevi, 1995). Nitric oxide is also known to prevent platelet ag-gregation and adhesion (Azuma et al., 1986; Radomski et al.,1987; Moncada et al., 1991). Beckman et al. (1990)haveshown that the superoxide radical reacts with nitric oxide toform the peroxynitrite radical. Oxygen-derived free radicalsfrom the electrode may reduce the nitric oxide concentrationand diminish its ability as the principal vasodilator and as aninhibitor of platelet aggregation. Superoxide depresses vas-cular smooth muscle relaxation by inactivating nitric oxide,as reviewed byRubanyi (1988).

An electrochemical product may accumulate to detrimen-tal concentrations if the rate of Faradaic reaction, given bythe current–overpotential relationship of Eq.(1.17), exceedsthe rate for which the physiological system can tolerate theproduct. For most reaction products of interest there is somesufficiently low concentration near the electrode that can betolerated over the long term. This level for a tolerable reactionmay be determined by the capacity of an intrinsic bufferingsystem. For example, changes in pH are buffered by severalsystems including the bicarbonate buffer system, the phos-phate buffer system, and intracellular proteins. The superox-ide radical, a product of the reduction of oxygen, is convertedby superoxide dismutase and cytochromec to hydrogen per-oxide and oxygen. The diffusion rate of a toxic product mustb ationso sur-f

6

afe.E thed tiono arya dam-a t notb nto ah mentsf issueo thei

ceeds lsei es asd tions( ciousd pro-m ntlyh lowc ach-i ur ata ches,a n sev-e ing:

nd determined that the pH may range from 4 to 10 ne�m diameter electrode during biphasic current pulses

his change extended for only a few�m. Irreversible proesses include Faradaic reactions where the product doemain near the electrode surface, such as reactions(1.1) and1.9)–(1.12).

Free radicals are known to cause damage to myelinipid cell membrane and DNA of cells. A likely candidatemechanism of neural tissue damage due to electrocheroducts is peroxidation of the myelin by free radicalsuced on the electrode surface. Several researchers (Chan el., 1982; Chia et al., 1983; Konat and Wiggins, 19evanian, 1988; Griot et al., 1990; Buettner, 1993) haveemonstrated the great susceptibility of myelin to free raamage. Damage occurs as fatty acyl chains move apa

he myelin goes from a crystalline (ordered) state to a lidisordered) state.

Morton et al. (1994)have shown that oxygen reductionurs on a gold electrode in phosphate buffered saline uypical neural stimulating conditions. Oxygen reductionctions that may occur during the cathodic stimulating p

nclude reactions that generate free radicals such as supde and hydroxyl, and hydrogen peroxide, collectively knos reactive oxygen species. These species may have

iple deleterious effects on tissue (reviewed byHalliwell,992; Stohs, 1995; Hemnani and Parihar, 1998; Imlay, 2ergamini et al., 2004). As free radicals are produced thay interfere with chemical signaling pathways that mainroper perfusion of nervous tissue. Nitric oxide has been

ified as the endothelium derived relaxing factor, the prim

t

l

-

-

e considered, as it may be the case that high concentrnly exist very near the site of generation (the electrode

ace).

. Design of efficacious and safe electrical stimulation

A stimulating system must be both efficacious and sfficacy of stimulation generally means the ability to elicitesired physiological response, which can include initiar suppression of action potentials. Safety has two primspects. First, the tissue being stimulated must not beged, and second, the stimulating electrode itself muse damaged, as in corrosion. An electrode implanted iuman as a prosthesis may need to meet these require

or decades. In animal experimentation, damage to the tr the electrode can seriously complicate or invalidate

nterpretation of results.Efficacy requires that the charge injected must ex

ome threshold (Fig. 7), however, as the charge per puncreases, the overpotential of the electrode increasoes the fraction of the current going into Faradaic reacwhich may be damaging to tissue or the electrode). Judiesign of stimulation protocols involves acceptable comises between stimulation efficacy, requiring a sufficieigh charge per pulse, and safety, requiring a sufficientlyharge per pulse, thus preventing the electrode from reng potentials where deleterious Faradaic reactions occn intolerable rate. The overpotential an electrode reand thus Faradaic reactions that can occur, depend oral factors in addition to the charge per pulse, includ


(1) waveform type (Fig. 4); (2) stimulation frequency; (3)electrode material (a high charge storage capacity allows rel-atively large charge storage prior to reaching overpotentialswhere irreversible Faradaic reactions occur); (4) electrodegeometric area and roughness (determining real area) andtherefore total capacitance; and (5) train effects (Section2).Increasing either the stimulus phase pulse width or the re-versal phase pulse width of a charge-balanced stimulationprotocol has the effect of increasing unrecoverable chargeinto irreversible reactions. Any factor which either drives theelectrode potential into a range where irreversible reactionsoccur (such as a long stimulus phase pulse width) or fails toquickly reverse the electrode potential out of this range (suchas a long reversal phase pulse width) will allow accumulationof unrecoverable charge.

The overpotential an electrode must be driven to beforeany given current will be achieved is highly dependent on thekinetics of the system, characterized by the exchange cur-rent densityi0. For a system with a large exchange currentdensity (e.g.i0 = 10−3 A/cm2), no significant overpotentialmay be achieved before a large Faradaic current ensues (Eq.(1.17)). Wheni0 is many orders of magnitude smaller (e.g.i0 = 10−9 A/cm2), a large overpotential must be applied be-fore there is substantial Faradaic current. Wheni0 is very low,a large total charge can be injected through the capacitivem ence.T tinge ithere

pro-t hina don icals doo . thatp toxicp gni-t d thee

st iouss lses.I s ap-p esigns bea gherl blet sec-o intsr sev-e ssuea onds.B onec hesei Cer-t tivity

during electrical excitation of tissue (Section4). Grill andMortimer (1995)have reviewed stimulus waveforms usedfor spatial and fiber diameter selective neural stimulation, il-lustrating the response of the neural membrane to differentwaveforms. Selective waveforms often require stimulationor reversal phases with long pulse widths relative to con-ventional stimulus waveforms; thus, waveforms optimizedfor physiological responses may not be efficient for revers-ing electrochemical processes. Judicious design of electricalprotocols has allowed the designers of neural prostheses toselectively inactivate the larger neurons in a nerve trunk (Fangand Mortimer, 1991b), selectively inactivate the superficialfibers in a nerve by pre-conditioning (Grill and Mortimer,1997), and prevent anodic break. Lastly, there are applica-tions where tonic polarization mandates the use of very long(>1 s) monophasic pulses; for example, tonic hyperpolariza-tion of the soma to control epileptic activity (Gluckman et al.,1996; Ghai et al., 2000). The use of these various waveformswith long pulse widths allows greater accumulation of anyelectrochemical product, thus requiring additional diligenceby a neurophysiologist or prosthesis designer to prevent elec-trochemical damage.

In addition to biological constraints on the pulse durations,the required current for a short pulse width may also be alimitation. In order to inject the minimum charge requiredf ta ereds

ula-t 03a ,1 . Asd ec-t tion.A ized encys

tionw llus-t oned er-p osited od-i dics si usf ed inl ided.G opha-s ,t ca-t e ast roughF mayb e pe-r in

echanism before significant Faradaic reactions commhis is the generally desirable paradigm for a stimulalectrode, minimizing Faradaic reactions that lead to electrode damage or tissue damage.

The fundamental design criteria for a safe stimulationocol can be stated:the electrodepotentialmust be keptwitpotential window where irreversible Faradaic reactionsot occur at levels that are intolerable to the physiologystem or the electrode. If irreversible Faradaic reactionsccur, one must ensure that they can be tolerated (e.ghysiological buffering systems can accommodate anyroducts) or that their detrimental effects are low in ma

ude (e.g. that corrosion occurs at a very slow rate, anlectrode will last for longer than its design lifetime).

The charge–duration curve shown inFig. 7demonstratehat to minimize the total charge injected in an efficactimulation protocol, one should use short duration pun practice, pulses on the order of tens of microsecondroach the minimum charge, and are often reasonable dolutions. During this relatively short duration one mayble to avoid Faradaic reactions that would occur at hi

evels of total charge with longer pulses. While it is desirao use short duration pulses on the order of tens of micronds, there are applications for which biological constraequire longer duration pulses. The time constants ofral key ion channels in the membranes of excitable tire measured in hundreds of microseconds to millisecy using stimulating pulses with comparable durationsan selectively manipulate the opening and closing of ton channels to accomplish various specific behaviors.ain waveforms have been developed that allow selec

or effect, a large current is required (Fig. 7). This is nolways possible, as may be the case with a battery powtimulator with limited current output.

Certain applications, such as clinical deep brain stimion (McIntyre and Thakor, 2002; O’Suilleabhain et al., 20)nd experimental long-term potentiation (Bliss and Lomo973) require the use of high frequency (>50 Hz) pulsingiscussed in Section2, this can lead to a ratcheting of the el

rode potential not achieved during single pulse stimulappropriate design of stimulation protocols can minimamage by careful attention to the effects of high frequtimulation on the electrode potential.

Fig. 9 summarizes key features of various stimulaaveform types. The cathodic monophasic waveform i

rated inFig. 9(a) consists of pulses of current passed inirection, with an open circuit condition during the intulse interval. At no time does current pass in the oppirection. Commonly the working electrode is pulsed cath

cally for stimulation of tissue (as shown), although anotimulation may also be used (Section4). Of the waveformllustrated inFig. 9, the monophasic is the most efficacioor stimulation. However, monophasic pulses are not usong-term stimulation where tissue damage is to be avoreater negative overpotentials are reached during monic pulsing than with biphasic pulsing (Fig. 4). Furthermorehe electrode potential during the interpulse interval ofhodic monophasic pulsing remains relatively negativhe charged electrode capacitance slowly discharges tharadaic reactions, allowing reduction reactions whiche deleterious to tissue to proceed throughout the entiriod of stimulation. Biphasic waveforms are illustrated


Fig. 9. Comparison of stimulating waveforms. Six prototypical waveforms are rated for relative merit in efficacy and safety: “+++” = best (most efficacious,least damaging to tissue or the electrode); “−−−” = worst.

Fig. 9(b)–(f). The first (stimulating) phase elicits the desiredphysiological effect such as initiation of an action potential,and the second (reversal) phase is used to reverse the directionof electrochemical processes occurring during the stimulat-ing phase (Section2). If all processes of charge injectionduring the stimulating phase are reversible, then the reversalphase will prevent net changes in the chemical environmentof the electrode, as desired. The charge-balanced biphasicwaveform (Fig. 9(b)) is widely used to prevent tissue dam-age. It should be noted that charge balance does not neces-sarily equate to electrochemical balance. As given by Eqs.(2.6) and (2.7), during certain instances of stimulation, thereare irreversible Faradaic reactions during the cathodic phase(e.g. oxygen reduction), and then different irreversible reac-tions during the anodic phase (e.g. electrode corrosion) thatare not the reverse of the cathodic Faradaic reactions. Suchelectrochemical imbalance leads to a potential waveform asillustrated inFig. 4(b), where the potential at the end of theanodic phase is positive of the pre-pulse potential, allowing ir-reversible reactions such as electrode corrosion to occur. Thecharge-imbalanced waveform, illustrated inFig. 9(c), maybe used to reduce the most positive potentials during the an-odic phase with respect to the charge-balanced waveform, andprevent electrode corrosion (Scheiner and Mortimer, 1990).Ideally, the charge in the reversal phase is equal to the charge

going into reversible processes during the stimulation phase,in which case the electrode potential returns to its pre-pulsevalue at the end of the reversal phase.

In addition to electrode corrosion, a second concern withthe charge-balanced biphasic waveform is that the reversalphase not only reverses electrochemical processes of thestimulation phase, but may also reverse some of the desiredphysiological effect of the stimulation phase, i.e. it may sup-press an action potential that would otherwise be inducedby a monophasic waveform. This effect causes an increasedthreshold for biphasic stimulation relative to monophasic.Gorman and Mortimer (1983)have shown that by introduc-ing an open circuit interphase delay between the stimulatingand reversal phases, the threshold for biphasic stimulation issimilar to that for monophasic. This is illustrated inFig. 9(d).Although the introduction of an interphase delay improvesthreshold, it also allows the electrode potential to remain rel-atively negative during the delay period. A delay of 100�sis typically sufficient to prevent the suppressing effect of thereversal phase, and may be a short enough period that dele-terious Faradaic reaction products do not accumulate to anunacceptable level.

As illustrated inFig. 9(e) and (f), the more rapidly charge isinjected during the anodic reversal phase, the more quicklythe electrode potential is brought out of the most negative


range, and thus the less likely that tissue damage will occur.A high current reversal phase, however, means more of a sup-pressing effect on action potential initiation, and also meansthe electrode potential will move positive during the reversalphase, thus risking electrode corrosion.

When evaluating the electrochemistry of a stimulatingelectrode system, both the working electrode and counterelectrode should be considered. If the area, and thus total ca-pacitance, of a counter electrode is relatively large, there is asmall potential change for a given amount of injected charge.Such an electrode will not be perturbed away from its rest-ing potential as readily as a small electrode, and all chargeinjection across this large counter electrode is assumed to beby capacitive charging, not Faradaic processes. If the work-ing electrode is driven cathodically first in a biphasic wave-form (and thus the counter electrode anodically), then duringthe reversal phase the working electrode is driven anodicallyand the counter electrode cathodically. In such a system theworking electrode is often referred to simply as the cathode.Strictly speaking, the working electrode is the cathode duringthe stimulus phase, and during the reversal phase the roles arereversed so that the working electrode is the anode and thecounter electrode is the cathode.

This review has presented several issues to be consideredin the selection of an electrode material and protocol for stim-u d thee wered in-j tingo ctedc s andF um.S ons

A

portf -s t ofH

R

A al-urol

A ndrve:Eng

A ro-erve.

A ctsuro-

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Bhargava A. Long-term effects of quasi-trapezoidal pulses on the struc-nt ofland,

B res-A) inNeu-

B s in

B n inon of

B P,y in–Ti

B ur-Soc

B tem:des.

B ectri-EEE

B s. I.rans

B . II.mits.

B lec-elec-

B lipidphys

lation that are both efficacious and safe to the tissue anlectrode. Six requirements for the choice of a materialiscussed (Section3). Efficacy was presented in terms of

ecting a sufficient charge, while the sometimes conflicbjective of safety was stated as requiring that the injeharge, and thus the overpotential an electrode reachearadaic reaction product produced, is kept to a minimection6 summarized the relative merits of some commtimulating waveforms in achieving efficacy and safety.

cknowledgements

The authors gratefully acknowledge financial suprom NIH-NINDS under Ruth L. Kirschstein NRSA Fellowhip 5F32NS045454, and Wellcome Trust, Departmenealth and Medical Research Council.

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