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

motor pool A motor pool B  motor neuron muscle B muscle A tendon aponeurosis Muscle properties - alpha motor neuron and all the muscle fibers it innervates

Mechanisms of force production - force length properties  force produced by the muscle is highly state dependent - non-linear function of muscle length LMOLMO 1.5 L M O 0.5 L M O FMOFMO

Mechanisms of force production - force velocity properties force velocity shortening lengthening power => muscle force nonlinear function of velocity Empirical fit: v M = b(F M O – F M ) / (F M + a)

Mechanisms of force production - modelling muscle properties Hill-type models: ‘active state’ F = A(t)*F(l)*F(v) no interactions between activation, length, and velocity effects, linear in activation (all inaccurate) force velocity length

Activation dynamics - from neural input to ‘active state’ of muscle e.g. first order activation dynamics dA(t)/dt + [1/  act (  + (1 –  )u(t)] a(t) = u(t)/  act from neural inputto muscle activationto muscle force depends on calcium dynamics

Tendons tendon confuses relation between anatomy and muscle length L MT LMLM L T1 L T2 muscle contraction dynamics tendon compliance tendon compliance - - L MT v MT a(t) LTLT vTvT F M = F T LMLM vMvM musculotendon system L T = L T1 + L T2 => we need to model tendon compliance (  F T /  L T )

Interaction dynamics between muscle and tendon L MT LMLM L T1 L T2 muscle contraction dynamics tendon compliance tendon compliance - - L MT v MT a(t) LTLT vTvT F M = F T LMLM vMvM musculotendon system L T = L T1 + L T2 musculotendon system skeleton FTFT L MT v MT a(  )

Muscle action from its anatomy - muscle causes movement by acting through its attachments semitendinosus musculotendon system skeleton FTFT L MT v MT a(  )

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

force length curve is altered at different strengths Non-linear effect of activation strength

Model activation dependence on stim rate (f) and muscle length predicted FL curves everything else is a free parameter Non-linear effect of activation strength - modelling the nonlinear dependence

FV curve at different stim rates FV curve at different lengths Non-linear effect of activation strength - effects on force-velocity function

FV dependence on length FV dependence on delayed activation and length - introduce ‘effective length’ as delayed memory of length predicted FV curves Non-linear effect of activation strength - modelling the nonlinear dependence

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 + RAVEBFSM vastus internus rectus anticus action: knee extensor, hip flexor vastus externus action: knee extensor biceps femoris action: knee flexor, hip flexor semimembranosus action: hip extensor, Knee flexor

IP iliopsoas action: hip flexor deep muscle, in between VE and BF Frog anatomy - muscles of the dorsal thigh

Frog anatomy - actions of muscles - evoked isometric forces BF IP

VE VI Frog anatomy - actions of muscles - evoked isometric forces

SMRA Frog anatomy - actions of muscles - evoked isometric forces

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?