Neuromechatronics: Frog lab
- neither neural nor mechatronic
Goal: use muscles to control movement
1)
2)
3)
4)
implant intramuscular electrodes
stimulate implanted muscle pairs
measure the movement
alter stimulation to control the direction of movement
 FES: functional electrical stimulation
- to restore function after paralysis
- in conjunction with a neural prosthesis
- use neural signal to control a paralyzed limb
Frog lab
-
muscle properties
- state dependent torque motor
- non-linear activation function
-
frog hindlimb anatomy
-
experimental set up and A/D
-
animal handling and dissection
Muscle properties
- alpha motor neuron and all the muscle fibers it innervates
a motor neuron
muscle A
motor pool B
tendon
aponeurosis
muscle B
motor pool A
Mechanisms of force production
- force length properties
FMO
0.5 LMO
LMO
1.5 LMO
force produced by the muscle is highly state dependent
- non-linear function of muscle length
Mechanisms of force production
- force velocity properties
lengthening
force
Empirical fit:
vM = b(FMO – FM) / (FM + a)
shortening
power
power
velocity
=> muscle force nonlinear function of velocity
Mechanisms of force production
- modelling muscle properties
Hill-type models: ‘active state’
F = A(t)*F(l)*F(v)
force
velocity
no interactions between activation,
length, and velocity effects, linear
in activation (all inaccurate)
length
Activation dynamics
- from neural input to ‘active state’ of muscle
from neural input
to muscle activation
depends on calcium dynamics
e.g. first order activation dynamics
dA(t)/dt + [1/tact (b + (1 – b)u(t)] a(t) = u(t)/tact
to muscle force
Tendons
tendon confuses relation between anatomy and muscle length
musculotendon system
LT1
LMT
LM
LMT
LT
LM
a(t)
muscle contraction
dynamics
LT2
vMT
vM
vT
LT = LT1 + LT2
=> we need to model tendon compliance (DFT/DLT)
tendon
compliance
FM = F T
tendon
compliance
Interaction dynamics between muscle and tendon
LT1
LMT
musculotendon system
LM
LMT
a(t)
LT2
LT
-
LM
muscle contraction
dynamics
tendon
compliance
FM = F T
vM
vMT
tendon
compliance
vT
LT = LT1 + LT2
a(t)
LMT
musculotendon
system
FT
skeleton
vMT
Muscle action from its anatomy
- muscle causes movement by acting through its attachments
LMT
a(t)
musculotendon
system
FT
skeleton
vMT
hip
semitendinosus
knee
predicted ST
path
1cm
ankle
1cm
0.2N
Muscle properties
- strong state dependence of force on length and velocity of movement
- activation dynamics, between neural input and ‘active’ muscle contraction
- tendon dynamics mediate interaction between muscle and limb
- limb movement from muscle contraction via muscle anatomy
Non-linear effect of activation strength
- activation strength as reflected in stimulation frequency
… varying stim rate at a constant length
… varying length at a constant rate
=> nonlinear scaling of FL curve with activation strength
Non-linear effect of activation strength
force length curve is altered at different strengths
Non-linear effect of activation strength
- modelling the nonlinear dependence
Model activation dependence
on stim rate (f) and muscle length
everything else is a free parameter
predicted FL curves
Non-linear effect of activation strength
- effects on force-velocity function
FV curve at different stim rates
FV curve at different lengths
Non-linear effect of activation strength
- modelling the nonlinear dependence
FV dependence on length
FV dependence on delayed
activation and length
- introduce ‘effective length’ as delayed
memory of length
predicted FV curves
Virtual muscle (Cheng Brown and Loeb)
- empirically based model, but looking more carefully at interactions
- but too complicated for the simple control here
Muscle properties
- strong state dependence of force on length and velocity of movement
- activation dynamics, between neural input and ‘active’ muscle contraction
- tendon dynamics mediate interaction between muscle and limb
- limb movement from muscle contraction via muscle anatomy
- non-linear effects of activation strength on evoked force
=> not a trivial motor to control (especially in motion)
Frog anatomy
- muscles of the dorsal thigh
VI + RA
VE
BF
SM
vastus internus
rectus anticus
vastus externus
biceps femoris
semimembranosus
action:
knee extensor,
hip flexor
action:
knee extensor
action:
knee flexor,
hip flexor
action:
hip extensor,
Knee flexor
Frog anatomy
- muscles of the dorsal thigh
IP
deep muscle, in between
VE and BF
iliopsoas
action:
hip flexor
Frog anatomy
- actions of muscles
- evoked isometric forces
BF
IP
Frog anatomy
- actions of muscles
- evoked isometric forces
VE
VI
Frog anatomy
- actions of muscles
- evoked isometric forces
RA
SM
Frog hindlimb muscles
- muscles with complex variations in actions across the workspace
=> choose muscle combinations which allow a range of motion
Experimental setup and A/D
1) Implant intramuscular electrodes
- bipolar stimulating electrodes
- generally nerve stimulation is better, but harder
electrode configuration
electrodes placed orthogonal to the
orientation of the muscle fibers
- create a voltage across a set
of fibers (actually probably nerve)
exposed region of electrode
Experimental setup and A/D
2) stimulate implanted muscle pairs
stimulation isolation unit
- to protect the animal from outside power sources
- output is proportional to the input
biphasic stimulation to balance applied charge and reduce damage
biphasic current pulse
positive and negative phases
same amplitude so there’s no
net charge accumulation and no
damage
Use train of stimulation: frequency, amplitude, pulse width, number of pulses
to specify response strength (specified in AO out)
Experimental setup and A/D
caveat:
- we really don’t need anything greater than 1ms pulses to stimulate muscle
- DDA AO card digitizes (under Matlab) at 500Hz => 2ms pulses mininum
- long pulse durations, even with charge balancing, can cause damage
 if responses fade with repeated stimulation, might be possible to switch to the
sound card instead
Experimental setup and A/D
3) measure movement
Two ways:
video tracking (today)
- use webcam to track movements of the leg following stimulation
- calculate direction of movement from video
- this is relatively straightforward technically and is most functional
- but it’s the most difficult
- limb dynamics come into play
- state dependence of muscle actions
isometric force (next class)
- attach leg to force transducer
- measure evoked isometric forces
- calculate direction of force
- more straightforward since limb dynamics and state dependence
are irrelevant
- (but transducers came in yesterday)
Experimental setup and A/D
4) alter stimulation to control movement
After measuring movement direction, update stimulation parameters to
produced desired direction.
offline:
- apply stim train with one set of parameters
- based on evoked direction of movement, change parameters
- repeat until desired direction
online
- continuously monitor movement
- alter stimulation online to affect movement
Control parameters are up to you:
- amplitude, pulse width (though not with 2ms min), frequency,
number of pulses
Experimental setup and A/D
Today’s goals
1) make electrodes
2) dissect frog and implant muscles
3) set up A/D for stimulation
4) record video of leg movement to stimulation
- for single muscles
- for a pair of muscles, varying strength
5) choose 2 control parameters and compare effects
- for a single muscle
Lab report
4) record video of leg movement to stimulation
- for single muscles
- for a pair of muscles, varying strength
5) choose 2 control parameters and compare effects
- for a single muscle
- Quantify the above data
- plots of stimulating two muscles, varying relative strengths
- plots of effects of two different stimulation parameters
- which is the best parameter for control?