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1
Practical Applications of Muscle Stimulation
William DurfeeDepartment of Mechanical Engineering
University of MinnesotaMinneapolis, USA
www.dmdconf.org
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NON-INVASIVE ASSESSMENT OF MUSCLE FUNCTION
External mechanical properties provide window into muscle excitation & contraction mechanismsElectrical stimulation provides controlled inputSystem identification methods reveal muscle parametersRequires mathematical model of muscleNon-invasive
MUSCULOSKELETAL SYSTEMSTIM
u(t)
FORCE/MOTION
y(t)
3
Most common non-invasive muscle force assessment method
Durfee & Iaizzo, Encyclopedia of Medical Devices and Instrumentation, 2006
Encyclopedia of Medical Devices and Instrumentation, 2nd ed . J.G. Webster, ed., Vol6, pp 62-71, Hoboken, John Wiley & Sons, 2006.
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MATHEMATICAL MODELS OF
WHOLE MUSCLE MECHANICS
5
Hill models are still the gold
standard
Proceedings of the Royal Society of London, B. 126(843):136-195, 1938.
SE
PE
CE
Contractile element force depends on several variables
Force = f (neural input, length, velocity)
F
Activation
F
Velocity
F
Length
CE
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Multiplicative model for CE force
CE Force-Velocity
Fscale
IRC
CE Force-Length
Activation Dynamicsu
V
X X
Model for isolated muscle
X
�
�
PE Force-Velocity
CE Force-Velocity
Fscale
IRC
CE Force-Length
Activation Dynamics (2nd order)
PE Force-Length
u
V
X
V
X
Force
Passive Element
Active Element
∑
∑
Fu
x,v
7
Model OK for isolated muscle
0
5
10
15
20
25
30
35
0 4 8 12 16
Forc
e (N
)
Time (s)
Durfee & Palmer, IEEE Trans. Biomed. Eng., 41(3):205, 1994
Experiment
Model
Identification of intact muscle properties more challenging
1. Skeletal geometry2. Muscle in series with a springy tendon
www.ebookwholesale.co.uk/fatloss.htm?hop=0www.rad.washington.edu/atlas/bicepsbrachii.html
What you want
What you have
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MUSCULOSKELETALSYSTEMSTIM
u(t)
FORCE/MOTION
y(t)
MT GEOM
GEOM-1
u(t)
LDθ(t)τ(t)f(t)
x(t)
Skeletal geometry
Some muscles have significant springs
Tibialis Anterior
http://www.rad.washington.edu/atlas2/tibialisanterior.html
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Tendon spring leads to inaccuracies in estimating muscle force-length curve
Zajac, Crit. Rev. Biomed. Eng., 1989, Figure 13
a(t)LM(t)
VM(t)
CE
SE
PE
muscle
tendon
FM(t)=FT(t)=f(t)
passive
Muscle-tendon model
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WHAT'S WRONG WITH THE MUSCLE MODEL
Invariant F-A, F-L, F-V (no change with activation)Invariant twitch dynamics (uniform fiber types)Time-invariant (no fatigue)
KSE
KPE(θ)
CE Mm
BPE(θ)
MJ(θ)
Full model has muscle-tendon acting against limb load
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KSE
KPE(θ)
CE Mm
BPE(θ)
MJ(θ)
KSE
KPE(θ)
CE Mm
BPE(θ)
MJ(θ)
states excitation, 65
4
3
2
1
=====
qqqq
VqLq
CE
CE
ωθ
)(2
),()(
1)()(
1)()(
1
)(1),,(1
52
66
65
343
33
133
4
43
135212
21
tkuqaaqq
qqfqM
qfqM
qqfqM
q
qqfM
qqqfM
q
PDJ
PEJ
TJ
Tm
CEm
+−−=
=
−−−−=
=
−+=
=
&
&
&
&
&
&
Simulation equations
CE Force-Length
Gordon, J. Physiol., 1966
( )
parameters shape,,
11exp)(
=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎥⎦
⎤⎢⎣
⎡ −+−=
ωρβ
ω
ρβLLFFL
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CE Force-Velocity
FORCE
VELOCITYSHORTENINGLENGTHENING
LINEAR FIT
( )
( ) *)(
*)(
2
22
1
11
bVVabVF
bVVabVF
FV
FV
+−
=
+−
= shortening
lengthening
Modeling twitch dynamics
Staticnonlinearity
Lineardynamic system
Hammerstein model
stim force
Identify LDS with impulse responseDurfee & Palmer, IEEE TBME, 1994
Identify SL by deconvolutionDurfee & MacLean, IEEE TBME, 1989
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Twitch force varies with stim strength
Recruitment Plot
0
100
200
300
400
500
600
700
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Pulse Width Percentage
020406080
100120140
0 100 200 300 400
Time (mS)
Torq
ue
2)( ask+
FORCE TWITCH
BEST FIT
2nd-order, critically damped linear system fits well enough
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Using nonlinear force twitch
response as a metric
15
0
50
100
150
200
250
300
350
400
450
500
0 50 100 150 200 250 300 350 400
Time (ms)
Torq
ue
Single pulse twitch
0
50
100
150
200
250
300
350
400
450
500
0 50 100 150 200 250 300 350 400
Time (ms)
Torq
ue
Double pulse twitch, if ideal linear system
y 2y
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0
50
100
150
200
250
300
350
400
450
500
0 50 100 150 200 250 300 350 400
Time (ms)
Torq
ue
Double pulse twitch, real
3.2 y
Doublet pulse spacing affects twitch force
0
0.5
1
1.5
2
2.5
3
3.5
1 26 51 76 101 126 151 176 201 226 251 276
Time (ms)
Forc
e
Doublets at 1,2,3,4,5,6,7,8,9,10,20,30,40,50 ms
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Nonlinear summation for TANormalized Peak Torque
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 30000 40000 50000
Normalized TTI
0
1
2
3
4
5
6
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 30000 40000 50000
Nonlinear summation depends on which muscle
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
0 1 2 3 4 5 6 7 8 9 10
IPI (ms)
BicepsQuadricepsTibialis AnteriorMean
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Normalized twitch parameters same for all recruitment levels
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
L1 L2 L3 L4 L5 L6 L7
2.300.640.68X2.180.005.80HDT
2.300.271.29X2.180.006.25HPW
2.300.740.542.180.072.00CT
2.300.101.902.180.062.12ST
2.300.920.282.180.241.34TTI
2.300.590.752.180.700.64PT
Sig.FcritPFSig.FcritPF
L2-L7L1-L7
Metric
WHAT'S NEXT
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Identification strategy
1. Passive length-tension: slowly move2. Twitch dynamics: isometric3. Active length-tension: slowly move
when active4. Force-velocity: apply rich velocity
perturbations about steady-state
Current isometric apparatus
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Improved apparatus
Force, EMG, temp, laptop/USB
Force vs. Acceleration
-15-10-505
1015
-2 -1 0 1 2
Acceleration (g)
Forc
e (lb
-f)
A simple clinical tool to measure limb inertia
KSE
KPE(θ)
CE Mm
BPE(θ)
MJ(θ)
KSE
KPE(θ)
CE Mm
BPE(θ)
MJ(θ)
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Build database of properties for several muscles in non-diseased subjects
F-L, F-V, contraction dynamics, doublet properties
Nash Avery Search for Hope Fund and the Paul and Sheila Wellstone Muscular Dystrophy Center, University of Minnesota.
FES-AIDED GAIT: A NEW APPROACH
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Brain
Spinal Cord
Limb
Stimulator
FEXTERNAL
CONTROL STIMULATORInputs
Measurements
FEXTERNAL
Improve health through weight bearingBrief standing: social and functionalLimited ambulation in vicinity of wheelchairNo balance, no change in neuro function
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Liberson foot-drop system, 1961
Heel switch triggered peroneal n. stimulationCorrection of foot-drop following strokeStarted field of FESSeveral commercial and research embodiments
Medtronic implanted foot-drop system
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STIMULATION PLUS SMART ORTHOTICS
Muscle stimulation
provides power
Brakes for locking and
control
Orthosis provides guidance
and support
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CBO Increases speed and distance
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Without CBO With CBO
Gait Speed
0.09
0.12
Spee
d (m
/s)
0
10
20
30
40
50
60
Without CBO With CBO
Gait Distance
25
50
Dis
tanc
e (m
)
IEEE Trans Rehab Eng, 4(1):13, 1996, IEEE Trans Rehab Neural Eng, 2003
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CBO has better step-to-step repeatability
0
20
40
60
80
100
120
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
20
40
60
80
100
120
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time (sec)
With CBO
Time (sec)
Without CBO
Kne
e an
gle
(deg
)
Kne
e an
gle
(deg
)
IEEE Trans Rehab Eng, 4(1):13, 1996, IEEE Trans Rehab Neural Eng, 2003
ENERGY STORING BRACE
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Energy Budget~30 nM over 60 deg of motion31.4 J per extensionExtract 14 J per cycle
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J. Biomechanical Engineering, 127(6):1014-1019, 2005.
ADAMS dynamic model
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Gas springs
Cylinders
Accumulator
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Hip belt
Placeholders for brakes
Knee brace
Prismatic joint
Ab/adductionhinge
Medial hinge
POWEREDHUMAN-ASSIST
TOOLS
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Engineering Research Center for Compact & Efficient Fluid Power
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Compact power sourcesNatural interface and controlPortable and/or wearable
And a few other projects
Replacing muscle
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Muscle metricsShort-stroke, linear actuator
5-20% shortening strokePull force: 30 lbs/sq. in.90 W/lb
180 lb athlete w/ 72 lb of muscle puts out 370 W sustained 5 W/lb for human muscle for continuous use
25% efficientCompliant, back-drivableFatiguesCleanQuiet !
Vogel (2001), "Prime Mover"
Power (W/lb)
0
50
100
150
200
250
Muscle--peak Muscle--sustained
Electric motor Automobileengine
Vogel (2001), "Prime Mover"(Aircraft engine, piston: 700; Aircraft engine, turbine: 2500)
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Miniature free-piston air-compressor
FUTURE MICRO FPAC + 1KPSI TANK
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