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					Neuromechatronics: Frog lab
     - neither neural nor mechatronic


Goal: use muscles to control movement

1)   implant intramuscular electrodes
2)   stimulate implanted muscle pairs
3)   measure the movement
4)   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   motor pool A

                                                   tendon
                                             aponeurosis



                             muscle B
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
                                                     Empirical fit:
                                                       vM = b(FMO – FM) / (FM + a)


                                shortening
                       force



                                             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
                                      no interactions between activation,
                                      length, and velocity effects, linear
                                      in activation (all inaccurate)
         velocity
                             length
Activation dynamics
   - from neural input to ‘active state’ of muscle




 from neural input              to muscle activation             to muscle force




      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
 Tendons
      tendon confuses relation between anatomy and muscle length



                                                musculotendon system
                       LT1

       LMT                        LMT                            LT
                 LM                                -                     tendon
                                                                         compliance
                                                       LM
                                  a(t)    muscle contraction          FM = FT
                                          dynamics

       LT2
                                                       vM
                                  vMT              -                     tendon
                                                                         compliance
                                                            vT

LT = LT1 + LT2



    => we need to model tendon compliance (DFT/DLT)
 Interaction dynamics between muscle and tendon
                      LT1

       LMT                                  musculotendon system
                 LM

                               LMT                            LT
                                                -                       tendon
                                                    LM                  compliance


                               a(t)                                FM = F T
                                      muscle contraction
       LT2                            dynamics

                                                    vM
                               vMT                                      tendon
                                                -                       compliance
                                                         vT


LT = LT1 + LT2


                                                                                         LMT
                        a(t)                                  FT
                               musculotendon                                  skeleton
                               system

                                                                                         vMT
Muscle action from its anatomy
  - muscle causes movement by acting through its attachments




                                                          LMT
             a(t)                       FT
                        musculotendon          skeleton
                        system

                                                          vMT


                hip
                                                          semitendinosus

                      predicted ST
                      path
  knee

                            1cm                             1cm   0.2N


                    ankle
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            predicted FL curves
 on stim rate (f) and muscle length




 everything else is a free parameter
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
                                             predicted FV curves
 - modelling the nonlinear dependence

FV dependence on length




FV dependence on delayed
 activation and length
 - introduce ‘effective length’ as delayed
   memory of length
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    vastus externus   biceps femoris   semimembranosus
rectus anticus

action:            action:           action:          action:
knee extensor,     knee extensor     knee flexor,     hip extensor,
hip flexor                           hip flexor       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?

				
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posted:12/3/2011
language:English
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