U.S. patent application number 16/994974 was filed with the patent office on 2020-12-03 for waveform shapes for treating neurological disorders optimized for energy efficiency.
The applicant listed for this patent is Duke University. Invention is credited to Warren M. Grill, Amorn Wongsarnpigoon.
Application Number | 20200376278 16/994974 |
Document ID | / |
Family ID | 1000005020013 |
Filed Date | 2020-12-03 |
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United States Patent
Application |
20200376278 |
Kind Code |
A1 |
Grill; Warren M. ; et
al. |
December 3, 2020 |
WAVEFORM SHAPES FOR TREATING NEUROLOGICAL DISORDERS OPTIMIZED FOR
ENERGY EFFICIENCY
Abstract
Systems and methods for stimulation of neurological tissue apply
a stimulation waveform that is derived by a developed genetic
algorithm (GA), which may be coupled to a computational model of
extracellular stimulation of a mammalian myelinated axon. The
waveform is optimized for energy efficiency.
Inventors: |
Grill; Warren M.; (Chapel
Hill, NC) ; Wongsarnpigoon; Amorn; (Chapel Hill,
NC) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Duke University |
Durham |
NC |
US |
|
|
Family ID: |
1000005020013 |
Appl. No.: |
16/994974 |
Filed: |
August 17, 2020 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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15651072 |
Jul 17, 2017 |
10744328 |
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16994974 |
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14796216 |
Jul 10, 2015 |
9707397 |
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15651072 |
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13118081 |
May 27, 2011 |
9089708 |
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14796216 |
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61348963 |
May 27, 2010 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
A61N 1/3606 20130101;
A61N 1/36146 20130101; A61N 1/0529 20130101; A61N 1/36175
20130101 |
International
Class: |
A61N 1/36 20060101
A61N001/36 |
Goverment Interests
GOVERNMENT LICENSING RIGHTS
[0002] This invention was made in part With government support
under NIH Grant Nos. R01 NS040894 and R21 NS054048. The government
has certain rights to the invention.
Claims
1. A stimulation waveform for application to targeted neurological
tissue, the waveform being selected from a set of waveforms
consisting essentially of Gaussian curves having varying pulse
widths and derived by a prescribed genetic algorithm (GA) coupled
to a computational model of extracellular stimulation of a
mammalian myelinated axon, wherein the set of stimulus waveforms
are optimized for energy efficiency.
2. The waveform according to claim 1 wherein the waveform is
monophasic.
3. The waveform according to claim 1 wherein the waveform is
biphasic.
4. A system for creating a stimulation waveform optimized for
energy efficiency comprising: a population of parent stimulation
waveforms; a genetic algorithm (GA) for generating a population of
offspring stimulation waveforms by mating the population of parent
stimulation waveforms, a computational model of extracellular
stimulation of a mammalian myelinated axon, being operative for
assessing the fitness of individual offspring stimulation waveforms
generated by the genetic algorithm in terms of energy efficiency
and selecting as a new population of the parent stimulation
waveforms the current offspring stimulation waveforms having the
highest energy efficiency values, the selection terminating when
predetermined termination criteria is met.
5. A system for neurological tissue stimulation comprising: a lead
sized and configured for implantation in a targeted tissue
stimulation region with a brain of a patient, and a pulse generator
coupled to the lead, the pulse generator including a power source
comprising a battery and a microprocessor coupled to the battery
and being operable to apply to the lead a stimulation waveform
derived through use of a global optimization algorithm.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 15/651,072, filed on Jul. 17, 2017, entitled
"SYSTEM FOR GENERATING AND APPLYING WAVEFORM SHAPES FOR TREATING
NEUROLOGICAL DISORDERS OPTIMIZED FOR ENERGY EFFICIENCY," which is a
continuation of U.S. patent application Ser. No. 14/796,216, filed
on Jul. 10, 2015, entitled "Waveform Shapes for Treating
Neurological Disorders Optimized for Energy Efficiency," which is
now U.S. Pat. No. 9,707,397, which is a continuation of Ser. No.
13/118,081, filed May 27, 2011, entitled "Waveform Shapes for
Treating Neurological Disorders Optimized for Energy Efficiency,"
which is now U.S. Pat. No. 9,089,708, which claims the benefit of
U.S. Provisional Patent Application Ser. No. 61/348,963, Filed May
27, 2010, and entitled "Energy-Optimal Biphasic Waveform Shapes for
Neural Stimulation," which are all incorporated herein by
reference.
FIELD OF THE INVENTION
[0003] This invention relates to systems and methods for
stimulating nerves in mammals and, in particular, humans.
BACKGROUND OF THE INVENTION
[0004] Implantable and external electrical stimulators assist
thousands of individuals with neurological disorders. These
stimulators generate electrical Waveforms, Which are delivered by
leads to targeted tissue regions to treat the neurological
disorders. Examples of treating neurological disorders using
electrical stimulation include deep brain stimulation, cortical
stimulation, vagus nerve stimulation, sacral nerve stimulation,
spinal cord stimulation, and cardiac pace makers and
defibrillators.
[0005] Implantable stimulators are powered by either primary cell
or rechargeable batteries. When the energy of a primary cell
battery is depleted, the entire stimulator must be replaced through
an expensive and invasive surgical procedure. The energy capacity
of a rechargeable battery determines the recharge interval, as Well
as the overall volume of the implant.
[0006] There are clinical benefits to reducing the frequency of
battery-replacement surgeries or recharge intervals, as Well as
reducing the physical size (volume) of the stimulator itself. The
problem is how one alters stimulation parameters to achieve this
objective without sacrificing clinical efficacy and generating
unwanted side effects. For example, the energy efficiency of
stimulation (i.e., how much energy is consumed for the generation
of a given stimulation pulse) cannot be viewed in isolation. The
charge efficiency of stimulation is also an important consideration
with implanted devices. The charge delivered during a stimulus
pulse contributes to the risk of tissue damage (Yuen et al. 1981;
McCreery et al. 1990). If energy-efficient stimulation parameters
deliver excessive amounts of charge, then the benefits of high
energy efficiency are diminished.
[0007] As shown in FIGS. 1A and 1B, the energy efficiency of
stimulation parameters is dependent upon the amplitude of the
stimulation pulse (typically expressed, e.g., in a range from 10
.mu.A upwards to 10 mA); the width or duration of the stimulation
pulse (typically expressed, e.g., in a range from 20 .mu.s upwards
to 500 .mu.s); the frequency of the pulses applied over time
(typically expressed, e.g., in a range from 10 Hz upwards to 200
Hz); and the shape or waveform of the pulse (e.g., typically,
depending upon the therapeutic objective, square (rectangular) (see
FIG. 2A), or rising ramp (see FIG. 2B), or sinusoid (see FIG. 2C),
or decreasing exponential (see FIG. 2D), or rising exponential (see
FIG. 2E)).
[0008] Previous studies have used passive membrane models to
analyze the effects of waveform shape on efficiency. All previous
studies using passive membrane models have concluded that the
energy-optimal waveform shape is a rising exponential (Offner 1946;
Fishler 2000; Kajimoto et al. 2004; Jezernik and Moran 2005).
[0009] However, in more realistic models and in vivo experiments,
the inventors have found that the rising exponential waveform
proved to be no more energy-efficient than rectangular, ramp, or
decaying exponential waveforms. In fact, in realistic membrane
models, the inventors have found that energy-optimal Waveform
shapes cannot be determined analytically because of the complexity
and non-linearity of the equations that define the excitable
membrane in the model. Also, a "brute force" method of testing
every possible waveform shape is not feasible since the number of
possible waveform shapes is infinite.
SUMMARY OF THE INVENTION
[0010] One aspect of the invention provides systems and
methodologies that couple an optimization algorithm, such as a
global optimization algorithm (e.g. a genetic algorithm) to a
computational model of extracellular stimulation of a mammalian
myelinated axon, to derive a set of stimulus wave forms that are
optimized for a desired parameter, such as energy efficiency.
[0011] One aspect of the invention provides systems and
methodologies that couple a genetic algorithm (GA) to a
computational model of extracellular stimulation of a mammalian
myelinated axon, to derive a set of stimulus wave forms that are
optimized for energy efficiency. This aspect of the invention makes
it possible in a systematic Way to generate and analytically
validate energy-optimal waveform shapes.
[0012] Another aspect of the invention provides systems and
methodologies that include a set of stimulation waveforms that are
optimized using a specially configured genetic algorithm (GA) to be
more energy-efficient than conventional waveforms used in neural
stimulation, as well as more energy-efficient than the conventional
waveforms for excitation of nerve fibers in vivo. The optimized GA
waveforms are also charge-efficient.
[0013] The optimized energy-efficiency of the stimulation waveforms
derived according to the invention make it possible to prolong
battery life of stimulators, thus reducing the frequency of
recharge intervals, the costs and risks of battery replacement
surgeries, and the volume of implantable stimulators.
[0014] The set of stimulus waveforms optimized according to the
invention for energy efficiency can be readily applied to deep
brain stimulation, to treat a variety of neurological disorders,
such as Parkinson's disease, movement disorders, epilepsy, and
psychiatric disorders such as obsessive-compulsion disorder and
depression, and other indications, such as tinnitus. The set of
stimulus Waveforms optimized according to the invention for energy
efficiency can also be readily applied to other classes of
electrical stimulation of the nervous system including, but not
limited to, cortical stimulation, and spinal cord stimulation, to
provide the attendant benefits described above and to treat
diseases or indications such as but not limited to Parkinson's
Disease, Essential Tremor, Movement Disorders, Dystonia, Epilepsy,
Pain, Tinnitus, psychiatric disorders such as Obsessive Compulsive
Disorder, Depression, and Tourette's Syndrome.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] FIG. 1A is a first diagrammatic view (amplitude vs. time) of
a stimulation waveform indicating stimulation parameters of a
hypothetical neural stimulation train.
[0016] FIG. 1B is a second diagrammatic view (power vs. time) of a
stimulation waveform indicating stimulation parameters of a
hypothetical neural stimulation train.
[0017] FIGS. 2A to 2E are diagrammatic views of typical waveforms
used for neural stimulation.
[0018] FIG. 3 is an anatomic view of a system for stimulating
tissue of the central nervous system that includes a lead implanted
in brain tissue coupled to a pulse generator that is programmed
With stimulation parameters to provide a stimulus waveform that has
been optimized for energy efficiency by coupling a genetic
algorithm (GA) to a computational model of extracellular
stimulation of a mammalian myelinated axon.
[0019] FIGS. 4A to 4C are How charts diagrammatically showing the
operation of the genetic algorithm (GA) coupled to the
computational model of extracellular stimulation of a mammalian
myelinated axon.
[0020] FIGS. 5A and 5B are diagrammatic views of the computational
model of extracellular stimulation of a mammalian myelinated axon,
which is coupled to the genetic algorithm (GA).
[0021] FIGS. 6A and 6B illustrate the progression of the genetic
algorithm (GA) coupled to the computational model of extracellular
stimulation of a mammalian myelinated axon for a single trial
(stimulation pulse Width (PW)=0.5 ms), FIG. 6A being a sequence of
plots showing changes in waveform shapes across generations and the
most energy-efficient waveform at each indicated generation, and
FIG. 6B being a graph showing the minimum and mean energy of
population across 10,000 generations, as convergence toward a
common optimal energy-efficiency value occurs.
[0022] FIG. 7 shows curves of the energy-optimal stimulation
waveforms resulting from the GA coupled to the computational model
of extracellular stimulation of a mammalian myelinated axon, for
different PWs, the curves representing the means of the resulting
waveforms across five independent trials, and the gray regions
defining 95% confidence intervals, the waveforms for PW=1 and 2 ms
being combined, and the leading and trailing tails of low amplitude
were truncated.
[0023] FIG. 8 is a representative input/output (I/O) curve that was
constructed when evaluating the energy-efficiency of the GA
waveforms in a population model of one hundred (100) parallel MRG
axons (11.5-.mu.m diameter) distributed uniformly Within a cylinder
With 3-mm diameter.
[0024] FIGS. 9A to 9C are plots showing the energy efficiency of
the GA waveforms in a model of extracellular stimulation of a
population of myelinated axons, FIG. 9A showing the energy-duration
curves for activation of 500 of the axons (mean+/-SE; n=10
different random populations of 100 axons), FIG. 9B showing the
energy efficiency of the GA waveforms compared to conventional
waveform shapes used in neural stimulation (mean, n=10; SE was
negligible) (positive values of "% difference with GA waveform"
indicate that the GA waveforms were more energy-efficient) and FIG.
9C showing the energy efficiency plotted against charge
efficiency.
[0025] FIGS. 10A, 10B, and 10C are sensitivity plots for the GA
waveforms to model parameters, FIG. 10A showing sensitivity to
fiber diameter (D) (curves represent mean of the GA waveforms
across 5 trials for PW=0.1 ms), and FIGS. 10B and 10C showing
sensitivity to the Hodgkin-Huxley model (skewed Gaussian curves
resulted) (curves represent the means of the resulting waveforms
across 5 independent trials, and the gray regions define 95%
confidence intervals for PW=0.2 ms (b) and PW=0.02 ms (c))
(amplitudes are not to scale). Additionally, the GA waveforms were
shown to be insensitive to the number of Waveforms per generation
population, the number of surviving waveforms per generation, the
average initial amplitude of the waveforms, and the mutation rate.
The GA waveforms were shown to be sensitive to changes in dt
(smaller dt leads to more energy-efficient for short PW, and less
energy-efficient for long PW).
[0026] FIGS. 11A and 11B show the set up for the in vivo evaluation
of the GA waveforms.
[0027] FIGS. 12A, 12B, and 12C show the in vivo measurements of
energy efficiency of neural stimulation with the GA Waveforms, FIG.
12A showing the energy-duration curves for generation of 50% of
maximal EMG (mean+/-SE; n=3), FIG. 12B showing the energy
efficiency of GA waveforms compared to rectangular and decaying
exponential waveforms (mean+/-SE; n=3) (positive values of "%
difference with GA waveform" indicate that GA waveforms were more
energy efficient), and FIG. 12C showing energy efficiency plotted
against charge efficiency.
[0028] FIG. 13 shows the energy-optimal biphasic GA waveforms
resulting from the biphasic GA waveforms for varying duration and
timing of the anodic phase (the curves represent the mean of the
cathodic phases of the waveforms across 5 trials of the GA, and
waveforms were shifted to align the peaks).
[0029] 14A to 14H show the energy efficiency of biphasic GA
waveforms in a model of extracellular stimulation of a population
of myelinated axons, FIGS. 14A and 14B being energy-duration curves
for activation of 50% of the axons (mean+/-SE; n=5 different random
populations of 100 axons), FIGS. 14C to 14H being energy efficiency
of GA waveforms compared to conventional waveform shapes used in
neural stimulation (mean+/-SE, n=5) (positive values of "%
difference with GA waveform" indicate that GA waveforms were more
energy-efficient), the Figures showing that waveforms with cathodic
phase first were more energy-efficient than waveforms with anodic
phase first for PW.sub.cathodic.ltoreq.0.2 ms, 0.05 ms, and 0.05 ms
for PW.sub.anodic/PW.sub.cathodic=1, 5, and 10, respectively
(Fisher's protected least significant difference (FPLSD):
p<0.0001); however, waveforms with anodic phase first were more
efficient for PW.sub.cathodic.gtoreq.0.5 ms and 0.2 for
PW.sub.anodic/PW.sub.cathodic=1 and 5, respectively, and for 0.1
ms.ltoreq.PW.sub.cathodic.ltoreq.0.5 ms for
PW.sub.anodic/PW.sub.cathodic=10 (FPLSD: p<0.0001); and energy
efficiency improved as PW.sub.anodic/PW.sub.cathodic increased
(FPLSD: p<0.0001). FIGS. 14A to 14H show that, compared to the
monophasic GA waveforms, the biphasic GA waveforms were less
energy-efficient, but the difference in energy efficiency decreased
as PW.sub.cathodic increased.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
I. System Overview
[0030] FIG. 3 is a system 10 for stimulating tissue of the central
nervous system. The system includes a lead 12 placed in a desired
position in contact With central nervous system tissue. In the
illustrated embodiment, the lead 12 is implanted in a region of the
brain, such as the thalamus, subthalamus, or globus pallidus for
the purpose of deep brain stimulation. However, it should be
understood, the lead 12 could be implanted in, on, or near the
spinal cord; or in, on, or near a peripheral nerve (sensory or
motor), in any subcutaneous tissue such as muscle tissue (including
cardiac tissue) or adipose tissue for the purpose of selective
stimulation to achieve a therapeutic purpose. In addition, the lead
12 may be utilized for transcutaneous stimulation Where electrodes
are placed, not subcutaneous, but on an outer skin surface.
[0031] The distal end of the lead 12 carries one or more electrodes
14 to apply electrical pulses to the targeted tissue region. The
electrical pulses are supplied by a pulse generator 16 coupled to
the lead 12.
[0032] In the illustrated embodiment, the pulse generator 16 is
implanted in a suitable location remote from the lead 12, e.g., in
the shoulder region. It should be appreciated, however, that the
pulse generator 16 could be placed in other regions of the body or
externally to the body.
[0033] When implanted, at least a portion of the case or housing of
the pulse generator can serve as a reference or return electrode.
Alternatively, the lead 12 can include a reference or return
electrode (comprising a bi-polar arrangement), or a separate
reference or return electrode can be implanted or attached
elsewhere on the body (comprising a mono-polar arrangement).
[0034] The pulse generator 16 includes stimulation generation
circuitry, which preferably includes an on-board, programmable
microprocessor 18, Which has access to and/or carries embedded
code. The code expresses pre-programmed rules or algorithms under
which desired electrical stimulation is generated, having desirable
electrical stimulation parameters that may also be calculated by
the microprocessor 18, and distributed to the electrode(s) 14 on
the lead 12. According to these programmed rules, the pulse
generator 16 directs the stimulation through the lead 12 to the
electrode(s) 14, which serve to selectively stimulate the targeted
tissue region. The code may be programmed, altered or selected by a
clinician to achieve the particular physiologic response desired.
Additionally or alternatively to the microprocessor 18, stimulation
generation circuitry may include discrete electrical components
operative to generate electrical stimulation having desirable
stimulation parameters. As shown in FIG. 2, the stimulation
parameters may include a pulse amplitude (expressed, e.g., in a
range from 10 .mu.A upwards to 10 mA); a pulse Width (PW) or
duration (expressed, e.g., in a range from 20 .mu.s upwards to 500
.mu.s); a frequency of stimulation pulses applied over time
(expressed, e.g., in a range from 10 Hz upwards to 200 Hz); and a
shape or Waveform of the stimulation pulses. One or more of the
parameters may be prescribed or predetermined as associated with a
particular treatment regime or indication.
[0035] In the illustrated embodiment, an on-board battery 20
supplies power to the microprocessor 18 and related circuitry.
Currently, batteries 20 must be replaced every 1 to 9 years,
depending on the stimulation parameters needed to treat a disorder.
When the battery life ends, the replacement of batteries requires
another invasive surgical procedure to gain access to the implanted
pulse generator. As will be described, the system 10 makes
possible, among its several benefits, an increase in battery
life.
[0036] As will be described in greater detail later, the
stimulation parameters, which may be prescribed, used by the pulse
generator differ from conventional stimulation parameters, which
may be prescribed, in that the waveform shape of the pulses has
been optimized by use of an optimization algorithm, such as a
global optimization algorithm. An example of a global optimization
algorithm used to optimize an electrical stimulation waveform is a
genetic algorithm (GA) used to optimize energy efficiency of a
waveform for neural stimulation. Use of the Waveform shapes
optimized for energy-efficiency leads to a decrease in power
consumption, thereby prolonging battery life, reducing battery size
requirements, and/or reducing frequency of battery
replenishment.
[0037] Although the following description is based largely on a
genetic algorithm, other optimization algorithms may be employed in
a computational model of neural stimulation to optimize the
stimulation based on a cost function, which can include a variety
of factors, such as energy efficiency. Other optimization
algorithms that may be used include, for example, simulated
annealing, Monte-Carlo methods, other evolutionary algorithms,
swarm algorithms (e.g. ant colony optimization, bees optimization,
particle swarm), differential evolution, firefly algorithm,
invasive weed optimization, harmony search algorithm, and/or
intelligent water drops.
II. Energy-Optimal Waveforms (Monophasic)
[0038] A. Overview
[0039] The inventors have implemented a genetic algorithm in a
computational model of peripheral nerve stimulation, to determine
the energy-optimal waveform shape for neural stimulation. The
energy efficiencies of the GA waveforms were compared to those of
conventional waveform shapes in a computational model of a
population of axons as well as during in vivo stimulation of
peripheral nerve fibers.
[0040] B. Deriving the Genetic Algorithms
[0041] 1. Generally
[0042] The genetic algorithm seeks an optimal solution through a
process based on the principles of biological evolution. As shown
in FIG. 4A, the first generation of a GA starts with a population
of candidate solutions. In FIG. 4A, there are two candidate
stimulation parameters, each having a different wave form (rising
ramp and square). The candidate solutions are analogous to natural
organisms, and the stimulation parameters that characterize each
candidate are its "genes".
[0043] Next, as further shown in FIG. 4A, the fitness of each
solution is assessed using a cost function specific to the
optimization problem. As will be described in greater detail later,
the fitness is assessed in a computational model of extracellular
stimulation of a single myelinated mammalian peripheral axon. The
fitness of each candidate (n) is expressed in terms of energy
efficiency (Energy.sub.n).
[0044] As shown in FIG. 4B, the candidate solutions "mate" with
each other, resulting in offspring solutions that possess a
combination of the parents' genes (i.e., stimulation parameters),
as well as, in time, the genes of the offspring that have mutated
(a different stimulation parameter value, preferably not found in
the parents). The fitness of both the mating process and mutations
promote a thorough search of the solution space, to improve the
chances of discovering the global optimum rather than a local
optimum. Following each generation, the population is partially or
completely replaced by the offspring. As the GA progresses,
beneficial genes remain in the gene pool of the population While
unfavorable genes are discarded.
[0045] As shown in FIG. 4C, this process--evaluating fitness,
mating, and replacing solutions is repeated either for a
predetermined number of generations (such as 10, 20, 50, 100, 200,
500, 1000, 2000, 5000, 10,000, or more generations) or until the
solutions converge upon, towards, or within a desirable range from
a fitness value. The solution with the overall greatest fitness is
the resulting estimate of the optimal solution.
[0046] 2. The Specific Genetic Algorithm
[0047] A specific generic algorithm (GA) was derived to seek the
energy-optimal waveform shape in a computational model of
extracellular stimulation of a single myelinated mammalian
peripheral axon, which is shown in FIGS. 5A and 5B.
[0048] Simulations were run in NEURON (Hines and Camevale 1997)
using the MRG model (fiber diameter=11.5 .mu.m), Which represented
a myelinated mammalian peripheral axon as a double cable model with
a finite impedance myelin sheath and explicit representation of the
nodes of Ranvier, paranodal sections, and intemodal segments
(McIntyre et al. 2002) (see FIG. 5B). Stimulation was delivered
through a current-regulated point source situated within a
conductive medium (300 .OMEGA.-cm) (McNeal 1976) located 1 mm
directly above the center node of the fiber (see FIG. 5A).
[0049] C. Deriving the GA Waveforms
[0050] FIG. 6A shows an overview of the results of the GA waveform
derivation process.
[0051] For each generation of the GA, the population consisted of
fifty (50) stimulation waveforms with fixed pulse width (PW).
Waveforms were discretized in time using a time step equal to that
of the computational model (dt=0.002 ms), and the genes of each
waveform represented the amplitudes at every time step. The values
of the genes of the waveforms of the first generation were selected
at random from a uniform distribution between zero and two times
the cathodic threshold of stimulation with a rectangular waveform
at the equivalent PW (e.g., 807 .mu.A for PW=10 .mu.s; 190 .mu.A
for PW=100 .mu.s; 79.8 .mu.A for PW=1 ms).
[0052] The cost function (F) used to evaluate the fitness of each
waveform equaled the sum of the energy consumed by the waveform (E)
and a substantial penalty if the waveform failed to elicit an
action potential:
F = E + Penalty Equation ( 1 ) E = .intg. 0 PW P ( t ) dt .varies.
dt * n = 1 N I n 2 Equation ( 2 ) ##EQU00001##
Where P is instantaneous power, t is time, I is the instantaneous
current, and N is the number of discretizations (genes) of a
stimulation waveform. If the waveform elicited an action potential,
then Penalty equaled 0, but if the waveform did not elicit an
action potential, then Penalty equaled 1 nJ/ohm (2 to 3 orders of
magnitude larger than E).
[0053] At the end of each generation, the top ten (10) fittest
waveforms (i.e., smallest F) remained in the population while the
remaining forty (40) waveforms were replaced by offspring. Every
waveform, regardless of its value of F, had an equal probability of
being selected as a parent, and each offspring was generated by
combining the genes of two parents using two crossover points. A
crossover point was a randomly selected gene location, where during
mating the genes prior to the crossover point from one parent were
combined with the genes beyond the crossover point from the other
parent. With two crossover points, the effect was a swap of a
segment of one parent's genes with the corresponding section of the
other parent's genes.
[0054] Each gene of the offspring was mutated by scaling the value
by a random factor chosen from a normal distribution (.mu.=1,
.sigma.2=0.025). Because the initial waveforms were monophasic
cathodic pulses, the genes were restricted to negative values.
[0055] The GA was run using a wide range of PWs (0.02, 0.05, 0.1,
0.2, 0.5, 1, and 2 ms) to determine whether the outcome of the GA
varied with PW. For each PW, the GA was run for 5 independent
trials of 10,000 generations with different initial populations.
For each trial, the following was recorded: the energy consumed by
the most energy-efficient waveform of each generation (generation
energy); the most energy-efficient waveform of the final generation
(GA waveform); and the charge (Q) delivered by the GA waveform,
where:
Q = .intg. 0 PW I ( t ) dt = dt * n = 1 N I n . Equation ( 3 )
##EQU00002##
[0056] For each PW, the means and standard errors of the energy and
charge consumed by the GA waveforms across the 5 independent trials
were recorded.
[0057] In this particular GA, the only considerations for the cost
function (F) were energy efficiency and whether or not an action
potential was elicited in the axon. However, F can use other
measures besides energy efficiency, either as the sole
consideration of F, or in combination with other measures. These
other measures may include charge efficiency, power efficiency
(i.e., peak power of waveform), maximum voltage or current,
therapeutic benefit of stimulation, adverse effects, and
selectivity of stimulation (i.e., activation of one population of
neurons or fibers defined by location, size, or type without
activation of other populations). F may include different weights
associated with each measure, reflecting the relative importance of
each measure. For example, F may consider both energy and charge,
and energy may be three times as important as charge for a given
application of stimulation. Then, F=0.75 E+0.25 Q. Thus, the
methodology according to the present invention may produce waveform
shapes that may be optimized to any particular cost function,
including desired cost parameters.
[0058] D. The Resulting GA Waveforms
[0059] Each trial of the GA began with a different population of
random waveforms, but by the end of each trial, the GA converged
upon consistent and highly energy-efficient waveform shapes (as
FIGS. 6A and 6B show). The generation energy converged to within 1%
of the final generation energy by 5000 generations for
PW.ltoreq.0.5 ms and by 9000 generations for PW=1 and 2 ms. As FIG.
7 shows, for each PW, the GA waveforms were very similar across
trials, and across PWs the shapes of the GA waveforms were quite
similar. As FIG. 6 shows, for PW.ltoreq.0.2 ms, the GA waveforms
resembled truncated Gaussian curves, with the peak near the middle
of the pulse. For PW.gtoreq.0.5 ms, the shapes of the GA waveforms
also resembled Gaussian curves but with leading and/or trailing
tails of negligible amplitude.
[0060] E. Assessing the Energy-Efficiency of GA Waveforms
[0061] 1. The Population Model
[0062] (i) Methodology
[0063] The GA waveforms were evaluated in a population model of one
hundred (100) parallel MRG axons (11.5-.mu.m diameter) distributed
uniformly within a cylinder with a 3-mm diameter. Extracellular
stimulation was delivered through a point current source located at
the center of the cylinder. For each PW (0.02, 0.05, 0.1, 0.2, 0.5,
1, and 2 ms), ten (10) populations of randomly-positioned axons
were selected. For each population, input/output (I/O) curves (see
FIG. 8) were constructed of the number of fibers activated vs. E,
as well as the number of fibers activated vs. Q. To adjust the
stimulation amplitude of a waveform, the entire waveform was
scaled. For each I/O curve, the E and Q needed to activate 50% of
the entire population were computed, and the means and standard
errors of these values across the ten (10) axon populations were
calculated. Using the same axon populations, I/O curves for
conventional waveforms used in neural stimulation were calculated:
rectangular, rising/decreasing ramp, rising/decaying exponential,
and sinusoid waveforms (See Appendix for the equations for the
conventional waveforms).
[0064] (ii) Results
[0065] (a) Overview
[0066] The GA waveforms were more energy-efficient than the
conventional stimulation waveform shapes for all PWs in the
population models. The energy-duration curve of the GA waveforms
was concave up (see FIG. 9A), and the minimum E for the GA
waveforms across PWs was less than the minimum E for the
conventional waveform shapes. Of these other shapes, the shape that
most resembled the GA waveforms--the sinusoid--had the lowest
minimum energy across PWs. For PW.ltoreq.0.2 ms, the GA waveforms
were slightly more energy-efficient (<20%) than the other
waveform shapes (see FIG. 9B). Between PW=0.2 ms and 0.5 ms, the
differences in energy efficiency between GA waveforms and the
conventional shapes increased considerably, and these differences
increased further with PW for all but the exponential waveforms.
Because the positions of the axons were randomized in the
population model, these results demonstrate that the superior
energy efficiency of the GA waveforms was independent of the
location of the electrode with respect to the axon.
[0067] The GA waveforms were also more energy-efficient than most
of the waveform shapes when energy was plotted against charge. For
all waveform shapes, the curves of E vs. Q were concave up and many
of the curves overlapped substantially (see FIG. 9C). However, the
curves for the GA waveforms and sinusoid lay under the other
curves, indicating that for a given amount of charge, the GA and
sinusoid waveforms consumed less energy to reach threshold than the
other waveform shapes.
[0068] (b) GA Waveform Sensitivity Analysis
[0069] As shown in FIG. 10A, the energy-optimal waveform shapes
were largely insensitive to variations in the parameters of the GA.
Doubling or halving the number of waveforms that survived to the
next generation or the number of waveforms in each generation had
no substantial effects on the shape of the GA waveforms or their
energy efficiencies (<0.1% difference). Also, the amplitudes of
the waveforms in the initial generation were scaled between 04-16
times the original amplitudes, and scaling factors>0.8 had
little effect on the shape and energy efficiency (<0.1%
difference) of the GA waveform. Scaling factors below 0.6, however,
resulted in initial waveforms that were all below threshold, and
the GA did not converge to an energy-efficient waveform. In
addition, the variance of the normal distribution used in mutations
was scaled between 0-4 times the original variance. With variance:
0 (no mutations), the GA rapidly converged on an energy-inefficient
waveform. However, for all other values of variance the GA produced
nearly identical GA waveforms with approximately the same energy
efficiencies (<0.4% difference).
[0070] As shown in FIG. 10B, although the shape of the GA waveforms
remained consistent when dt was varied between 0.001-0.01 ms, the
energy efficiency did change. Smaller values of dt produced finer
resolution of the waveform shape, which created more
energy-efficient GA waveforms for PW.ltoreq.0.1 ms
(|.DELTA.E|<110). However, the improved resolution also led to
less energy-efficient GA waveforms for PW.gtoreq.1 ms, as a result
of more noise in the waveform (|.DELTA.E|<10.5%).
[0071] In addition to using a fiber diameter of 11.5 .mu.m, we ran
the GA with fiber diameters of 5.7 .mu.m and 16 .mu.m. The GA
waveforms produced for each fiber diameter remained the most
energy-efficient waveforms in their respective models, and their
overall shapes were consistent across diameters (see FIG. 10A).
Further, the GA waveforms optimized for diameter: 11.5 um (see FIG.
7) were still more energy-efficient than the conventional waveform
shapes for excitation of the other two diameters.
[0072] The shape and efficiency of GA waveforms were dependent on
the model of the neural membrane. We ran the GA in a model of a
myelinated axon that consisted of nodes with Hodgkin-Huxley
membrane parameters connected by electrically insulated myelinated
internodes. This model differed from the MRG model both
geometrically (e.g., no paranodal sections) and physiologically
(e.g., lower temperature, no persistent sodium channels), but the
fiber diameter and electrode-fiber distance were unchanged. In the
Hodgkin-Huxley model, for PW.ltoreq.0.05 ms the GA waveforms
generated in the Hodgkin-Huxley model were still unimodal as in the
MRG model but were asymmetric (see FIG. 10B). However, for PW=0.02
ms the GA waveforms from the two models diverged (see FIG. 10C). In
addition, when tested in the Hodgkin-Huxley model, the original GA
waveforms from the MRG model were not uniformly more
energy-efficient than conventional waveform shapes.
[0073] (c) GA Waveform Fit with Analytical Equation
[0074] To gain a better understanding of the exact shapes of the
energy-optimized waveforms, the GA waveforms were fitted to a
piece-wise generalized normal distribution:
f ( t ) = A * e - ( t - .mu. .alpha. L ) .beta. L for t .ltoreq.
.mu. = A * e - ( t - .mu. .alpha. R ) .beta. R for t > .mu. .
Equation ( 4 ) ##EQU00003##
[0075] Where A is the amplitude at the peak, located at t=.mu.;
.alpha.'s and .beta.'s are scale and shape parameters,
respectively, and must be greater than zero and the .alpha.'s and
.beta.'s are preferably less than infinity; and the subscripts
correspond to the left (L) and to the right (R) of the peak. When
.alpha.L=.alpha.R and .beta.L=.beta.R, the function is symmetric
about .beta., and the values of .beta. dictate the kurtosis (i.e.,
peakedness) of the waveform. When .alpha.L.noteq..alpha.R and/or
.beta.L.noteq..beta.R, varying degrees of kurtosis and skewness can
be produced [see Appendix for the equations]. Thus, Equation (4)
may be used to produce an energy-optimal electrical stimulation
waveform
[0076] The parameters of Equation (4) were optimized to fit the
mean GA waveforms (i.e., as shown FIG. 7) using the lsqcurvefit
function in Matlab (R2007b; The Mathworks, Natick, Mass.). The
least-square optimized waveforms fit well with the energy-optimized
waveforms (R2>0.96). Across PWs, the fitted waveforms were not
very skewed (-0.5<skewness<0.5, where skewness=0 is perfect
symmetry), had sharper peaks (kurtosis>0.55) than the normal
distribution (kurtosis=0), and the kurtosis of the fitted waveforms
increased with PW.
[0077] A modified GA was also run, where the stimulation waveforms
were characterized by Equation (4) instead of by the amplitudes at
each time step. As a result, all waveforms were characterized by
only six parameters--A, .mu., .alpha.L, .alpha.R, .beta.L, and
.beta.R--and initial values of these parameters were selected at
random from uniform distributions (A: between zero and four times
the cathodic threshold of stimulation with a rectangular waveform
at equivalent PW; .mu.: 0-PW; .alpha.'s: 0.01-0.5; .beta.'s:
0.01-3).
[0078] Preferably, a waveform defined at least in part by Equation
(4) is generated or controlled by a microprocessor, which may
accept various values for the indicated parameters. The peak
current amplitude (A) varies with the stimulation application, and
may vary between patients, but as described earlier, typically
ranges from about 10 .mu.A to about 10 mA. Parameter .mu. is
preferably between zero (0) and the stimulation pulse width (PW).
Parameters .alpha.L, .alpha.R, .beta.L, and .beta.R are preferably
greater than 0 and less than infinity. One exemplary set of
preferred alpha and beta values for a monophasic GA waveform is
alpha values in the range of about 0.008 milliseconds to about 0.1
milliseconds and beta values in the range of about 0.8 to about
1.8. However, the alpha and beta values may well fall outside of
this range under different circumstances, and changes in the values
may be directly associated with a given fiber diameter.
[0079] The GA waveforms that resulted from optimization with this
modified GA were not substantially different from the waveforms
generated by the initial GA. The shapes of the waveforms were quite
similar to the initial GA waveforms across all PWs (R2>0.93),
and the energy efficiencies improved very little (<2%) for
PW.ltoreq.0.5 ms. However, the modified GA waveforms were more
energy-efficient than the initial GA waveforms for PW=1 and 2 ms
(5.6% and 10.4%, respectively), as a result of the smoothness of
the modified GA waveforms and their ability to reach amplitudes
near zero at the tails. Consequently, the energy-duration curve
with this GA was not concave up as with the original GA, but
instead, E remained constant as PW increased.
[0080] 2. In Vivo Experiments
[0081] (i) Surgical Preparation
[0082] All animal care and experimental procedures were approved by
the Institutional Animal Care and Use Committees of Duke University
and were followed according to The Guide to the Care and Use of
Laboratory Animals, 1996 Edition, National Research Council.
[0083] Experiments were performed on 3 adult male cats. Sedation
was induced with acepromazine (Vedco Inc., 0.3 mg/kg; S.Q.), and
anesthesia was induced with ketamine HCl (Ketaset 35 mg/kg; I.M.)
and maintained during the experiment with .alpha.-chloralose
(Sigma-Aldrich, Inc., initial 65 mg/kg supplemented at 15 mg/kg;
I.V.). The cat was intubated, and respiration was controlled to
maintain end tidal CO2 at 3-4%. Core temperature was monitored and
maintained at 39.degree. C. Fluid levels were maintained with
saline solution and lactated ringers delivered through the cephalic
vein (15 ml/kg/hr, I.V.). Blood pressure was monitored using a
catheter inserted into the carotid artery.
[0084] The sciatic nerve was accessed via an incision on the medial
surface of the upper hindlimb. As FIG. 11A shows, a monopolar cuff
electrode, composed of a platinum contact embedded in a silicone
substrate, was placed around the nerve and secured with a suture
around the outside of the electrode. The return electrode was a
subcutaneous needle. Two stainless steel wire electrodes were
inserted into the medial gastrocnemius muscle to measure the
electromyogram (EMG) evoked by stimulation of the sciatic nerve
(see FIG. 11B). The EMG signal was amplified, filtered (1-3000 Hz),
recorded at 500 kHz, rectified, and integrated to quantify the
response (EMG integral).
[0085] Stimulation and recording were controlled with Labview (DAQ:
PCI-MI0-16E-1) (National Instruments, Austin, Tex.). A voltage
waveform was delivered at a rate of 500 ksamples/s to a linear
voltage-to-current converter (bp isolator, FHC, Bowdoin, Me.) and
delivered through the cuff electrode. The voltage across (V) and
current through (I) the cuff electrode and return electrode were
amplified (SR560, Stanford Research Systems, Sunnyvale, Calif.) and
recorded (fsample=500 kHz). The energy delivered during stimulation
was determined by integrating the product of V(t) and I(t):
E=.intg..sub.O.sup.PWP(t)dt=.intg..sub.O.sup.PWV(t)I(t)dt Equation
(5)
[0086] The charge delivered during stimulation was determined by
integrating I(t) using Equation (3), above.
[0087] (ii) Recruitment Curves
[0088] Recruitment curves of the integral of the rectified EMG as a
function of E and Q were measured for rectangular, decaying
exponential (time constant [.tau.]=132, 263, and 526 .mu.s), and GA
waveforms at various PWs (0.02, 0.05, 0.1, 0.2, 0.5, and 1 ms) in
random order. At frequent intervals over the course of the
experiment, stimulation with the rectangular waveform at a fixed PW
was provided to monitor shifts in threshold. Threshold shifts
occurred in only one animal, and the values of E and Q were scaled
accordingly. Recruitment curves were generated using a similar
procedure as in the computational models: stimulus amplitude was
incremented, three (3) stimulation pulses were delivered at -1 Hz
at each increment, and the average values of E, Q, and EMG integral
were recorded. From each recruitment curve, the values of E and Q
required to generate 50% of the maximal EMG were calculated, and
the values at PW=0.02 ms for the rectangular waveform were defined
as baseline values. Subsequently, all values of E and Q were
normalized to their respective baseline value, and the means and
standard errors across experiments were calculated.
[0089] After log-transformation of the data, the effects of
waveform shape on energy and charge efficiency were analyzed. A
two-way repeated measures AN OVA was performed for each measure of
efficiency; the dependent variable was E or Q, and the independent
variables were waveform shape, PW (within-subjects factors), and
cat (subject). Where interactions between waveform shape and PW
were found to be significant (p<0.05), the data were subdivided
by PW for one-way repeated measures ANOVA. Again, the dependent
variable was E or Q, and the independent variables were waveform
shape (within-subjects factor) and cat (subject). For tests which
revealed significant differences among waveforms (p<0.05), post
hoc comparisons were conducted using Fisher's protected least
significant difference (FPLSD). Although data were log-transformed
for statistical analysis, data were plotted as average percent
difference with respect to the GA waveforms.
[0090] (iii) Results
[0091] The in vivo measurements comparing the efficiency of GA
waveforms to rectangular and decaying exponential waveforms largely
corroborated the results of the population model. For PW 0.05 ms,
the GA waveforms were significantly more energy-efficient than most
of the rectangular and decaying exponential waveforms (p<0.05,
FPLSD) (see FIGS. 12A and 12B). Although the decaying exponential
with .tau.=132 us appeared to be more energy-efficient than the GA
waveforms for PW.gtoreq.0.5 ms, this result was misleading; for
long PWs, increasing the PW for exponential waveforms simply
extends the low-amplitude tail, which has negligible effects on
excitation. As a result, the energy-duration curve for the
exponential waveforms leveled off at long PWs, while the
energy-duration curve for the GA waveforms increased with PW, as in
the population model. When normalized E was plotted against
normalized Q, the GA waveforms appeared to be more energy-efficient
than the rectangular waveform for normalized Q>2 (see FIG. 12C).
However, the GA waveforms were not substantially more
energy-efficient than the decaying exponential waveforms.
III. Energy-Optimal Waveforms (Biphasic)
[0092] The original GA revealed energy-optimal waveforms for
monophasic stimulation. However, most waveforms used for nerve
stimulation are biphasic. Because the charge recovery pulse can
influence the threshold of the primary pulse (van den Honert and
Mortimer 1979), it was heretofore unclear whether the monophasic GA
waveforms would remain energy-optimal for biphasic stimulation.
First, thresholds were recalculated in the single fiber model for
all waveform shapes with the addition of rectangular
charge-balancing anodic phases. The duration was varied
(PW.sub.anodic/PW.sub.cathodic=1, 5, or 10), as was the timing
(preceding or following the cathodic phase) of the charge-balancing
phase. Amplitudes of the anodic phases were adjusted to produce
zero net charge for the entire waveform, and E was calculated from
both phases of the waveform.
[0093] The biphasic results showed that the GA waveforms optimized
for monophasic stimulation were not the most energy-efficient
waveforms across all PWs. Therefore, the GA was modified to seek
energy-optimal biphasic waveform shapes. For each combination of
duration and timing (i.e., before or after the cathodic phase) of
the rectangular charge-balancing anodic phase, five (5) separate
trials were run of the GA to optimize the shape of the cathodic
pulse for PW=0.02-1 ms, and E was calculated from both the anodic
and cathodic phases of the waveform.
[0094] The shapes of biphasic GA waveforms varied with both the
timing and duration of the anodic phase. Most waveforms still
resembled truncated normal curves, but the peaks of the cathodic
phases were shifted away from the anodic phase (see FIG. 13). As
with the monophasic GA waveforms, as PW.sub.cathodic increased the
waveforms generally became flatter. The duration of the anodic
phase relative to the cathodic phase influenced the peakedness of
the resulting waveforms: the shorter the anodic phase, the sharper
the peak of the cathodic phase. However, for waveforms with anodic
phase first, PW.sub.anodic=1 ms and PW.sub.cathodic=0.2 or 0.1 ms,
the peaks of the resulting waveforms were sharper than expected.
Surprisingly, the peaks of both of these waveforms were located
exactly 0.086 ms after the anodic pulse for every trial. Analysis
of the gating parameters and membrane voltage during stimulation
did not reveal any apparent explanations for this particular
shape.
[0095] The biphasic GA waveforms were applied to five randomly
selected populations from the population model, and energy-duration
curves were calculated as in the monophasic case. Energy
efficiencies of the biphasic GA waveforms as well as conventional
waveforms were dependent on the timing and duration of the anodic
phase (see FIGS. 14A and 14B). Conventional waveform shapes were
paired with rectangular charge-balancing anodic phases with the
same duration and timing as the biphasic GA waveforms, and the
energy efficiencies of these waveforms were calculated in the
population model. The biphasic GA waveforms were always more
energy-efficient than the conventional waveform shapes, and the
differences in energy efficiency varied with the duration of the
anodic phase. In general, as PW.sub.anodic/PW.sub.cathodic
increased the difference in energy efficiency between the biphasic
GA waveforms and the conventional waveform shapes decreased (see
FIGS. 14C to 14H). As well, for PW.sub.anodic/PW.sub.cathodic=1 the
differences between the biphasic GA waveforms and the conventional
waveforms were generally greater than the differences in the
monophasic case (FIGS. 8A to 8C), but for
PW.sub.anodic/PW.sub.cathodic=10 the differences were smaller than
in the monophasic case.
IV. CONCLUSION
[0096] The genetic algorithm (GA) described herein mimics
biological evolution, to provide an optimal energy-efficient
waveform shape for neural stimulation. The GA generates highly
energy-efficient GA waveforms that resembled truncated Gaussian
curves. When tested in computational models, and as confirmed by in
vivo peripheral nerve stimulation, the GA waveforms are more
energy-efficient than many conventional waveform shapes. The
differences in energy-efficiency are more substantial for long PW s
than for short PW s. The GA waveforms will extend the battery life
of implantable stimulators, and thereby reduce the costs and risks
associated with battery replacements, decrease the frequency of
recharging, and reduce the volume of implanted stimulators.
[0097] Along with energy efficiency, the charge efficiency of
stimulation is an important consideration with implanted devices.
The charge delivered during a stimulus pulse contributes to the
risk of tissue damage (Yuen et al. 1981; McCreery et al. 1990).
Charge efficiency can be incorporated into the cost function, F
(Equation (1)), with weights associated with charge and energy
efficiency that reflected the relative importance of each factor.
Charge efficiency was not considered in F in the GA described
herein. Nevertheless, the GA waveforms ended up being
simultaneously energy- and charge-efficient.
[0098] In the computational models, the GA waveforms were the most
energy-efficient waveform shapes. All five independent trials of
the GA converged to nearly the same shape for each PW and achieved
similar levels of energy efficiency. In addition, all GA waveforms
resemble truncated Gaussian curves, and none of the variations in
the parameters of the GA had substantial effects on the
outcome.
[0099] The energy efficiencies of non-GA Gaussian or sinusoids have
been investigated previously. Sahin and Tie (2007) found in a
computational model of a mammalian myelinated axon (Sweeney et al.
1987) that Gaussian and sinusoid waveforms had the lowest threshold
energies out of several conventional waveform shapes. However,
unlike the GA waveforms described herein, the Gaussian and sinusoid
waveforms were not the most energy-efficient waveforms across all
PWs. Qu et al. (2005) conducted in vitro experiments on rabbit
hearts and found that defibrillation was achieved with
significantly less energy for Gurvich (biphasic sinusoid) waveforms
than with biphasic decaying exponential or rectangular waveforms.
Dimitrova and Dimitrov (1992) found in a model of an unmyelinated
Hodgkin-Huxley axon that waveforms that resembled postsynaptic
potentials (skewed Gaussian) were more energy-efficient than
rectangular waveforms. Although these previous studies showed that
the sinusoid, Gaussian, or skewed Gaussian waveforms were more
energy-efficient than other waveform shapes, these non-GA waveforms
were not proven to be energy-optimal.
[0100] The GA with genes representing the parameters of the
piece-wise generalized normal distribution (Equation (4)) did not
produce GA waveforms with noticeably different shapes. However, the
waveforms were much smoother, and for long PWs the tails were much
closer to zero. These differences improved the energy efficiency
over the original GA waveforms, particularly for long PW s. As a
result, the energy-duration curve was no longer concave up, as in
the original GA (see FIG. SA), but instead E never increased as PW
increased. This result is more consistent with expectations; one
would expect that at a given PW the GA could produce any waveform
that was produced at a shorter PW bounded by tails of zero
amplitude. Therefore, as PW increases E should either level off or
decrease.
[0101] The different properties of the MRG axon and the
Hodgkin-Huxley axon led to the dissimilarities in the
genetically-optimized waveforms produced in the two models. Not
only were the differences in ion channel dynamics between the two
models substantial, but also the Hodgkin-Huxley axon lacked
paranodal sections, and both factors likely contributed to the
differences in GA waveforms. However, due to the non-linearity and
complexity of the equations governing membrane voltage, it is
difficult to pinpoint which characteristics of the axonal models
were most responsible for the varying results. Additional trials of
the GA in models where specific geometric and physiological
parameters were varied systematically could determine how
energy-optimal waveforms change with model parameters. Thus, the GA
approach can determine energy-optimal waveform shapes for a given
model or system, but the optimal shape may be different in each
case.
[0102] The biphasic GA waveforms exhibited many similarities to the
monophasic GA waveforms. Both sets of GA waveforms were more
energy-efficient than several conventional waveform shapes and were
unimodal in shape. However, the peakedness and locations of the
peaks of the biphasic GA waveforms were different than the
monophasic GA waveforms. The effects of the anodic phase on the
sodium channels explain many of the differences among the shapes of
the biphasic GA waveforms. The anodic phase hyperpolarizes the
membrane, deactivating m-gates and de-inactivating the h-gates of
the sodium channel. When the cathodic phase was delivered first,
the peak likely shifted away from the anodic phase to activate the
sodium channels earlier than in the monophasic case, thus
offsetting the deactivation generated by the anodic phase. When the
anodic phase was delivered first, the peak shifted away from the
anodic phase to allow the m-gate of the sodium channels to return
to baseline. Differences between the monophasic and biphasic GA
waveforms were greater for short PW.sub.anodic than for long
PW.sub.anodic. As PW.sub.anodic increased, the amplitude of the
anodic phase decreased, reducing the effect of the anodic phase on
membrane voltage and the sodium channels. Consequently, the
biphasic GA waveforms began to resemble the monophasic GA waveforms
in both shape and energy efficiency.
[0103] The foregoing description describes the energy and charge
efficiency for excitation of peripheral nerve fibers. Still, the
technical features of the GA waveforms pertain to stimulation of
other components of the nervous system. During spinal cord
stimulation, the targets of stimulation are thought to be axons
(Coburn 1985; Struijk et al. 1993; Struijk et al. 1993), and the
current findings would likely be applicable. As well, our results
would be valid for muscular stimulation, where the targets of
stimulation are motor nerve axons (Crago et al. 1974). The
technical features for the GA waveforms as described herein can
also be relevant for stimulation of the brain because in both
cortical stimulation (Nowak and Bullier 1998; Manola et al. 2007)
and deep brain stimulation (McIntyre and Grill 1999), the targets
of stimulation are thought to be axons.
[0104] GA waveforms could substantially increase the battery life
of implanted stimulators. For example, the stimulators used for
deep brain stimulation last approximately 36-48 months with
conventional waveforms (Ondo et al. 2007). Over 30 years, the
device would have to be replaced about .kappa.-10 times. Over a
clinically relevant range of PWs (.sup..about.0.05-0.2 ms) the GA
waveforms were upwards to approximately 60% more energy-efficient
than either the rectangular or decaying exponential waveforms,
which are the most frequently used waveforms clinically (Butson and
McIntyre 2007). A 60% improvement in energy efficiency would extend
battery life by over 21 months. As a result, over 30 years the
device would only have to be replaced about 5-6 times.
[0105] The GA described herein did not account for the energy
consumed by the electronic circuitry of an implantable stimulator.
A stimulation waveform that can be generated using a simple analog
circuit may consume less energy than a waveform that requires
several active components. If the energy consumption of the
circuitry were incorporated into the GA, then the algorithm may
produce different waveform shapes.
[0106] Various features of the invention are set forth in the
claims that follow.
Appendix 1. Conventional Waveform Shapes
[0107] Thresholds were measured for conventional waveforms used in
neural stimulation: rectangular, rising/decreasing ramp,
rising/decaying exponential, and sine wave. For all shapes,
stimulation was applied at t=0 and turned off at t=PW. The equation
for the stimulus current with the rectangular waveform was
I.sub.stim(t)=K.sub.s*[u(t)-u(t-PW)] Equation (6)
where K.sub.s is the current amplitude, t is time, and u(t) is the
unit step function. The equations for the rising and decreasing
ramp were
I.sub.stim(t)=K.sub.r*t*[u(t)-u(t-PW)] Equation (7)
I.sub.stim(t)=K.sub.r(PW-t)*[u(t)-u(t-PW)] Equation (8)
respectively, where K.sub.r is the magnitude of the slope of the
ramp. The equations for the rising and decaying exponential
waveforms were
I.sub.stim(t)=K.sub.ee.sup.t/.tau.*[u(t)-u(t-PW)] Equation (9)
I.sub.stim(t)=K.sub.ee.sup.(PW-t)/.tau.*[u(t)-u(t-PW)] Equation
(10)
respectively, where K.sub.e is the amplitude at t=0 for Equation
(9) and at t=PW for Equation (10). In the computational models,
.tau. equaled 263 .mu.s. The equation for the sine wave was
I stim ( t ) = K sin * sin ( t PW .pi. ) * [ u ( t ) - u ( t - PW )
] Equation ( 11 ) ##EQU00004##
where K.sub.sin the amplitude of the sine wave. Note that only one
half of one period of the sine wave is delivered during the
pulse.
2. Skewness and Kurtosis of Piece-Wise Generalized Normal
Distribution
[0108] To quantify the shape of the GA waveforms, the waveforms
were fitted to a piece-wise generalized normal distribution, f(t)
(4), and calculated the skewness and kurtosis. First, the peak was
centered about t=0:
.tau.=t-.mu. Equation (12).
Then, f(.tau.) was normalized so the time integral from -.infin. to
+.infin. equaled 1:
N = .intg. - .infin. .infin. f ( .tau. ) d .tau. = .intg. - .infin.
0 f L ( .tau. ) d .tau. + .intg. 0 .infin. f R ( .tau. ) d .tau. =
.alpha. L .GAMMA. ( 1 + 1 .beta. L ) + .alpha. R .GAMMA. ( 1 + 1
.beta. R ) Equation ( 13 ) F ( .tau. ) = f ( .tau. ) / N Equation (
14 ) ##EQU00005##
Next, the mean and variance of the distribution were
calculated:
.tau. = .intg. - .infin. .infin. .tau. * F ( .tau. ) d .tau. = -
.alpha. L 2 .GAMMA. ( 1 + 2 .beta. L ) + .alpha. R 2 .GAMMA. ( 1 +
2 .beta. R ) 2 N Equation ( 15 ) .sigma. 2 = .intg. - .infin.
.infin. ( .tau. - .tau. _ ) 2 * F ( .tau. ) d .tau. 3 .alpha. L
.tau. _ 2 .GAMMA. ( 1 + 1 .beta. L ) + 3 .alpha. L 2 .tau. _
.GAMMA. ( 1 + 2 .beta. L ) + .alpha. L 3 .GAMMA. ( 1 + 3 .beta. L )
+ 3 .alpha. R .tau. _ 2 .GAMMA. ( 1 + 1 .beta. R ) - = 3 .alpha. R
2 .tau. _ .GAMMA. ( 1 + 2 .beta. R ) + .alpha. R 3 .GAMMA. ( 1 + 3
.beta. R ) 3 N . Equation ( 16 ) ##EQU00006##
Finally, from these equations, skewness and kurtosis were
calculated:
skew = .intg. - .infin. .infin. ( .tau. - .tau. _ ) 3 * F ( .tau. )
d .tau. ( .sigma. 2 ) 2 / 2 Equation ( 17 ) kurt = .intg. - .infin.
.infin. ( .tau. - .tau. _ ) 4 * F ( .tau. ) d .tau. ( .sigma. 2 ) 2
. Equation ( 18 ) ##EQU00007##
* * * * *