Abstract
The stimulation waveform describes the applied current, i(t), or voltage, v(t), as a function of time. The characteristics of the stimulation waveform contribute to the effectiveness, efficiency, and risks of electrical stimulation, and thus consideration of waveform characteristics is of paramount importance in the design and application of neuromodulation therapies. This chapter reviews the fundamental considerations of waveform effects as well as designs intended to improve performance in the three performance domains of efficiency, selectivity, and risk.
Keywords
Charge, Efficiency, Selectivity, Threshold
Outline
Introduction 95
Performance Requirements for Stimulation Waveforms 95
Excitation Properties With Conventional Rectangular Pulses 96
Alternative Waveform Shapes to Enhance Performance 99
Effect of Waveform on Energy Required for Stimulation 100
Waveforms to Enhance Stimulation Selectivity 100
Unbalanced Waveforms to Reduce Risk of Corrosion 101
Acknowledgments 101
References 101
Acknowledgments
Preparation of this chapter was supported in part by Grants R37 NS040894 and R01 NS050514 from the US National Institutes of Health.
Introduction
The primary requirement for a stimulation waveform is the ability to excite or activate neurons or nerve fibers. Although necessary, this fundamental requirement is rarely sufficient, and the criteria of risk of potential tissue damage, stimulation selectivity, and energy efficiency of stimulation are also important considerations.
In this chapter I consider waveforms directed at the generation of action potentials (excitation or activation) rather than waveforms that are intended to generate a block of conduction, which are reviewed elsewhere ( ). These latter include, for example, high-frequency sinusoidal waveforms that can generate a complete, graded, and reversible block of action potential conduction in both peripheral nerve fibers ( ) and central nerve fibers ( ), although responses can be substantially more complex than simply excitation or block, depending on the waveform frequency and amplitude ( ). Moreover, while both pulse repetition rate (frequency) ( ) and the temporal pattern of stimulation ( ) can have profound impacts on the effects of stimulation, these features are not considered further here.
Performance Requirements for Stimulation Waveforms
Nondamaging
While generating the degree and pattern of activation required for therapeutic efficacy or functional restoration, the applied stimuli must not damage either the tissue where they reside or that they stimulate or the electrodes that are used to deliver stimulation. The mechanisms underlying stimulation-induced injury of neural tissue remain unclear, and empirical studies are required to document risks of new stimulation paradigms.
The most successful attempt to harmonize a range of empirical data is the Shannon model of stimulation-induced tissue injury ( ). The model defines a line separating stimulation regimes in which tissue damage was observed from regimes in which tissue damage was not observed, and the equation of this line is given by
Log(QA)=k−log(Q)
Log(QA)=k−log(Q)
Log ( Q A ) = k − log ( Q )
Although useful to provide guidance for selection of nondamaging stimulation parameters, the Shannon model is a fit to empirical data, and thus is valid only for the conditions under which those data were collected. In addition to charge density (Q/A) and charge per phase (Q), the interactions between the stimulation waveform and the potential risk for tissue damage are affected by other factors including stimulation pulse repetition rate (frequency), stimulation duty cycle, current density (equal to the current amplitude divided by the geometric surface area of the stimulation electrode), electrode size, electrode material(s), and the region of the nervous system that is stimulated ( ). For example, although the Shannon model was used to establish a suggested limit on the parameters of nondamaging deep brain stimulation (DBS), the data used to inform the form and parameterization of the model are quite different from both the stimulation parameters of DBS and the brain locations where DBS is typically delivered ( ). In this chapter I primarily focus on the efficacy of stimulation waveforms and while I do consider, for example, the importance of biphasic waveforms to reduce the risk of potential damage to the electrode or tissue, the reader is referred to other sources for a more comprehensive review of stimulation-induced damage ( ).
Selectivity
Selectivity refers to the ability to activate the neurons, neural elements (e.g., presynaptic terminals), or nerve fibers that are targeted for stimulation and intended to produce the desired therapeutic effect while not activating nontargeted neurons, which might, for example, produce unwanted side effects. When considering peripheral nerve stimulation, this selectivity could include both nerve fiber diameter selectivity, that is, the ability to stimulate selectively nerve fibers with a specific range of diameters (e.g., ), as well as nerve fiber position selectivity, that is, the ability to stimulate selectively nerve fibers lying in a particular position within a compound nerve (e.g., ). When considering spinal cord stimulation, selectivity can refer to the ability to activate dorsal column fibers without activation of dorsal root fibers (e.g., ), or the ability to activate dorsal column fibers with the targeted dermatome(s) where pain is experienced ( ). Finally, for brain stimulation, this could include stimulation location, including the subthalamus for tremor control ( ), discrete targets within the pallidum ( ) or subthalamic nucleus ( ), or a specific region of cortex ( ). Alternatively, selective brain stimulation could refer to the ability to activate selectively particular neural elements ( ), for example, antidromic activation of projection axons or activation of local cells without concomitant activation of neighboring or even intermingled axons of passage ( ). In all cases, such selectivity is influenced by the electrode geometry, as well as the stimulation waveform.
Efficiency
The energy required for a particular waveform to generate neural activation is an important consideration, as this will contribute to the battery life of an implanted pulse generator. An additional important consideration related to efficiency is the energy required by the hardware to generate the stimulation waveform. While there may be modest savings in threshold energy associated with stimulation waveform shapes ( ), these savings may be offset by the power consumed by the electronics to generate such waveforms. Thus, the design of the stimulation hardware is an integral component of the efficiency of any particular stimulation waveform ( ).
Excitation Properties With Conventional Rectangular Pulses
Threshold
The generation of an action potential (excitation or activation) is a nonlinear response to a stimulus of sufficient intensity. A stimulus insufficient to generate excitation is termed subthreshold, the minimum intensity required to generate excitation is termed threshold, and a stimulus with superfluous intensity to generate excitation is referred to as suprathreshold. As described later, the intensity of the stimulus can be adjusted or controlled by alteration of the stimulation pulse amplitude, the stimulation pulse duration, and, in some instances, the pulse repetition rate or stimulation frequency ( ). Further, the stimulation threshold, that is, the minimum intensity stimulus required for excitation, is dependent on the shape of the stimulation waveform, the electrode geometry, and the properties of the surrounding tissue, as well as the geometry and electrical properties of the neural elements being activated.
Strength–Duration Relationship
The strength–duration relationship describes the threshold stimulus amplitude, I th or V th , as a function of the duration or pulse width, PW , of a monophasic rectangular stimulus pulse and is shown in Fig. 8.1A . The strength–duration curve can be described by the Lapicque equation,
Ith(PW)=Irh1−e−(PWln(2)∗Tch).
Ith(PW)=Irh1−e−(PWln(2)∗Tch).
I th ( P W ) = I rh 1 − e − ( P W ln ( 2 ) ∗ T ch ) .
However, empirical data of threshold as a function of the pulse duration appear to be better fit by the Weiss equation,
Ith(PW)=Irh[1+(TchPW)].
Ith(PW)=Irh[1+(TchPW)].
I th ( P W ) = I rh [ 1 + ( T ch P W ) ] .
Charge–Duration Relationship
First, the charge–duration relationship, describing the threshold charge, Q th , as a function of the duration or pulse width, PW , can be obtained by integrating the threshold current over time, and for a rectangular pulse is simply the product of the threshold current amplitude and the pulse duration, yielding
Qth(PW)=Irh(PW+Tch).
Qth(PW)=Irh(PW+Tch).
Q t h ( P W ) = I rh ( P W + T ch ) .
Reducing the charge required for excitation reduces the risk of tissue damage (recall that both charge per phase and charge density appear in the Shannon model and are cofactors in whether stimulation produces neural damage). As well, shorter pulse widths may reduce the propensity of stimulation to cause electrode corrosion. Corrosion is an electrochemical reaction that depends on the voltage across the electrode–tissue (electrolyte) interface, V e ( ). Because the interface behaves similar to a capacitor, this voltage is determined by the charge per phase in the stimulation pulse, V e = Q/C dl , where C dl is the double-layer capacitance of the electrode (proportional to electrode area). Reducing the threshold charge reduces V e , and thereby reduces the probability of generating electrode corrosion.
In addition to reducing the threshold charge, shorter pulse durations increase the threshold difference between different-diameter nerve fibers, that is, short PWs increase fiber diameter selectivity, which decreases the gain between the stimulus magnitude and the number of nerve fibers activated ( ). Similarly, shorter pulse durations increase the spatial selectivity of stimulation by increasing the threshold difference between nerve fibers lying at different distances from the electrode ( ).
The shortest practical pulse duration is typically determined by the power supply (compliance) voltage of the stimulation circuitry, V ss . The voltage across the electrical load encountered by the stimulation circuit (Z load , i.e., the impedance of the electrodes and tissue) is given by the product of the stimulation current and the load impedance (V = I ∗ Z load ), and cannot exceed V ss . Because the threshold current amplitude increases steeply at short pulse durations ( Fig. 8.1A ), the power supply voltage limits the minimum pulse duration.
Power–Duration Relationship
Similarly, the power–duration relationship can be obtained as the product of the stimulation current and the stimulation voltage, P = I ∗ V. By Ohm’s law (V = I ∗ R load or Z load ), we can replace the stimulation voltage with the product of the stimulation current and the electrical load, yielding
Power(PW)=Ith2(PW)∗Zload=Irh2[1+(TchPW)]2∗Zload.
Power(PW)=I2th(PW)∗Zload=I2rh[1+(TchPW)]2∗Zload.
Power ( P W ) = I th 2 ( P W ) ∗ Z load = I rh 2 [ 1 + ( T ch P W ) ] 2 ∗ Z load .
Energy–Duration Relationship
As well, the energy–duration relationship can be obtained as the product of the stimulation power and the pulse duration,
Energy(PW)=Power(PW)∗PW=Ith2(PW)∗Zload∗PW.
Energy(PW)=Power(PW)∗PW=I2th(PW)∗Zload∗PW.
Energy ( P W ) = Power ( P W ) ∗ P W = I th 2 ( P W ) ∗ Z load ∗ P W .
Energy(PW)=Irh2[1+(TchPW)]2∗Zload∗PW.
Energy(PW)=I2rh[1+(TchPW)]2∗Zload∗PW.
Energy ( P W ) = I rh 2 [ 1 + ( T ch P W ) ] 2 ∗ Z load ∗ P W .
ⅆEnergy(PW)ⅆPW=Irh2∗Zload∗[PW∗2(1+TchPW)(−TchPW2)+(1+TchPW)2]=0.
ⅆEnergy(PW)ⅆPW=I2rh∗Zload∗[PW∗2(1+TchPW)(−TchPW2)+(1+TchPW)2]=0.
ⅆ Energy ( P W ) ⅆ P W = I rh 2 ∗ Z load ∗ [ P W ∗ 2 ( 1 + T ch P W ) ( − T ch P W 2 ) + ( 1 + T ch P W ) 2 ] = 0.
Stimulation Pulse Polarity
Monophasic Stimuli: Cathodic Versus Anodic Pulses
The polarity or sign of the stimulation pulse can influence the threshold for activation as well as the complement of nerve fibers or neural elements that are activated by the stimulus pulse. In the simplest instance of a long homogeneous nerve fiber activated by a single extracellular point-source electrode ( Fig. 8.2 ), cathodic (negative) stimuli applied extracellularly depolarize the nerve fiber beneath the electrode and, if the depolarization is sufficient, an action potential is generated. The cathode can be envisioned as a sink of positive current. Conversely, anodic (positive) stimuli applied extracellularly hyperpolarize the nerve fiber beneath the electrode, and the anode can be envisioned as a source of positive current.
There are two mechanisms by which anodic stimuli, which hyperpolarize the membrane beneath the electrode, can generate action potentials: virtual cathodes and anode break excitation. Monophasic anodic pulses applied extracellularly generate a triphasic pattern of membrane polarization ( Fig. 8.2 ) as a result of current entering the nerve fiber beneath the anode (producing central hyperpolarization) and current leaving the nerve fibers in adjacent regions of the nerve fiber (producing surrounding depolarization). These regions of surrounding depolarization are referred to as “virtual cathodes,” because depolarization is generated there, and if the stimulus current amplitude is large enough, then action potential initiation will occur at the virtual cathodes.
Monophasic anodic stimulus pulses can also generate action potentials at the termination of a long duration pulse via anode break excitation. Protracted hyperpolarization of the membrane results in deinactivation of the voltage-gated sodium channels ( ) and renders the membrane hyperexcitable. The inflow of sodium that occurs upon repolarization can therefore lead to an action potential. As the time constant for inactivation is comparatively long, anode break excitation typically requires long-duration (≥500 μs) pulses.
The effects of stimulation pulse polarity are somewhat more complex when stimulating in the central nervous system (CNS), where neural elements include, in addition to comparatively long passing axons, terminating (i.e., presynaptic) axons ( ) and local cell bodies ( ). For example, monophasic anodic stimuli can excite terminating axons ( ) or activate local cells ( ) at lower amplitudes than monophasic cathodic stimuli, and thus pulse polarity can be exploited to produce element-selective stimulation.
Monophasic Versus Biphasic Stimuli
Under most conditions biphasic stimulus pulses are required to prevent damage to the stimulating electrodes or the underlying tissue. The primary phase of the stimulus delivers charge, Q, onto the double-layer capacitance of the electrode–electrolyte (tissue) interface, C dl , producing a voltage across that interface, V e = Q/C dl ( ). The secondary phase of a biphasic stimulus removes the charge put onto the double-layer capacitance by the first phase of the pulse, shifts the electrode potential, V e , in a direction opposite to that of the primary phase, and, in the absence of any irreversible reactions, returns V e to its equilibrium potential. As the electrochemical reactions that occur at the electrode–tissue interface are dependent upon the voltage across the interface, preventing shifts in V e precludes such reactions from occurring ( ). Therefore, most applications of chronic neural stimulation employ biphasic stimulation pulses.
The secondary (charge recovery) phase of the stimulation waveform, however, can have effects on excitation. First, the second phase can arrest an action potential generated by the first pulse and will thus increase the threshold for excitation ( ). This effect will occur in neurons that are just above threshold and thus will have an impact on only a small number of neurons. Further, this effect is dependent on the duration and amplitude of the primary as well as the secondary phase of the stimulus, and the increase in threshold as a result of the secondary phase increases as the pulse duration is made shorter ( ). The effect of the secondary phase on the reversal of excitation or increase in the threshold can be minimized by introducing an interphase delay between the primary and the secondary phases of the stimulus ( ).
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