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Faculty of Mathematics,Biomechanical model of theprimates’ upper limb

Pierre Kibleur Prof. Auke Ijspeertlol Marco Caprogrossolol Nathan Greinerlol Shravan Tata RamalingasettyFebruary 12th, 2018

1 Introduction

2 Modelling

3 Validation

4 Experiments

5 Conclusion

Contents

2/29 P. Kibleur NHP 2017

Introduction

Worldwide, 50 000 people a year suffer a Spinal Cord Injury (SCI), with lifetimeconsequences.Half of the patients are under 30 years old.The injury is often localized, leaving hope to one day find a treatment.But after 40 years of research, we cannot restore basic limb functionality.

Motivation


Prof. Courtine

Instead, Grégoire Courtine’s pragmatical approach focuseson electrically stimulating the proprioceptive feedback into the spinalcord below the SCI, in order to recruit the reflex loop. It has beenshown to restore walking capabilities in humans with partial SCI.

Adapt the methodology to stereotypical motion of the upper limb.Start with Non Human Primates (NHP).

Motivation


An epidural electrode stimulates groups ofactuators’ sensory neurons’ afferent fibres’ firingrates, to recruit the sensorimotor limb control.

Brain

Produces motion if synchronous withdescending modulation from the brain.

Electrical Epidural Stimulation (EES)


What are the patterns of afferents’firing rates?

Kinematic recordings are reproduced in OpenSim simulations in order to predict them.

Biomechanical model


3 algorithms to process the recorded kinematics into the afferents’ firing rates:Inverse Dynamics Compute Muscle Controls Prochazka’s modela� fx

Computational model



Joint angles that minimize the error in marker position are used to calculate joint torques.

q =argminq

∑

i!i‖

‖

‖

xexpi − xi(q)‖

‖

‖

2,

� =M(q)q̈ + C(q, q̇) +G(q).

Computational model



Muscle activations able to render the torques minimize muscle fatigue (Anderson, 2001).min ∑

ma2m +

∑

i!i(q̈∗i − q̈i)

2,

s. t. �j =∑

mFm(t) ⋅ rj,m(q).

Computational model



Afferent firings are estimated from stimuli different fibres respond to (Prochazka, 1999).

⎛

⎜

⎜

⎝

fIafIbfII

⎞

⎟

⎟

⎠

=⎛

⎜

⎜

⎝

�l �v �a 0 cIa0 0 0 �F 0 l 0 a 0 cII

⎞

⎟

⎟

⎠

⎛

⎜

⎜

⎜

⎜

⎜

⎝

ΔlvpaF1

⎞

⎟

⎟

⎟

⎟

⎟

⎠

= A�m(t).

Computational model


Modelling

Imported SIMM arm model (Chan, 2006):∙ Macacca Mulatta∙ Right arm∙ 7 bones (6 monkey + human hand)∙ 3 of them fixed∙ 7 degrees of freedom∙ 39 musculo-tendon units∙ 18 of them unparametrized

�aS

�rS

�fS

�fE

�p

�aW �fW

xy

zy

Geometry, leeway of the modelled arm.

Base model


Fix the model in OpenSimin order to use it for thecomputations, at differentlevels of the musculoskele-tal modelling.

Segments -> Joints -> Actuators:a)

- length

- mass

- CoM

- Inertia

b)

- operating range

- joint coupling

- damper

- ligament

c)

- optimal fibre length

- tendon slack length

- pennation angle

- maximal isometric force

Model adaptations


Validation

Inverse Dynamics Compute Muscle Controls Prochazka’s modela�

Forward Dynamicsq

x

here

∙ Validate the torques, before even trying to compute muscle activities

Where to validate the model?


Published results of the study of humans’ planar elbow flexion are used (Gribble, 1999).

Compare torques manually computed with OpenSim’s:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

−0.2

−0.1

0

0.1

0.2

Time [s]

Joint

torque

s[Nm]

��fS, simulation

��fE, simulation

��fS, manual

��fE, manual

Task:

z

x

y

Morphometrical validation: dynamics



Forward Dynamicsq

x

here

∙ Validate the torques, before even trying to compute muscle activities∙ Validate individual actuators’ properties (Hicks, 2015)

Recently enforced by implementation (Millard, 2013)∙ Validate the muscle activities



69 EMG-kinematic simultaneous recordings of NHP frontal centre-out tasks are sharedwith us (Miller, Chowdhury, 2017). 22 muscles are monitored.

xy

Frontal centre-out task.

Muscular model validation: data


69 EMG-kinematic simultaneous recordings of NHP frontal centre-out tasks are sharedwith us (Miller, Chowdhury, 2017). 22 muscles are monitored. Find the important ones.

xy


0

10

20

30

tricepsshort[]

0 50 100%

0.6

0.8

1

Time

bicepslong[]

Example (filtered) EMG signals.



69 EMG-kinematic simultaneous recordings of NHP frontal centre-out tasks are sharedwith us (Miller, Chowdhury, 2017). 22 muscles are monitored. Find the important ones.

xy


0 0.2 0.4 0.6 0.8 1

teres major

deltoid medial head

triceps short head

Standard correlation in normalized time.

Mean and variance of the correlation between all EMGrecordings.



Compare EMGs of important muscles to computedcontrols.

0

0.5

1

tricepshort

EMG Computed muscle activity

0

0.5

1

deltoidmedial

0 50 100%

0

0.5

1

Time

teresmajor

0 50 100%

Time

Static PushingStatic Pushing

Profiles of muscle activity, recorded and computed.

Allow the computed activity to beearlier than the EMG: Δt ≤ .1s(Miller, 1993).

maxΔt ∫

tf

t0EMG(t) ⋅ a(t + Δt)dt,

0 0.2 0.4 0.6 0.8 1

T. M.

T. S.

D. M.

Preak cross-correlation

Muscular model validation: muscle controls



Forward Dynamicsq

x

here


Recently enforced by implementation (Millard, 2013)∙ Validate the muscle activities∙ Validate the inversibility of computations if possible



0

10

20

30

θf S[deg]

Average recorded kinematics Muscle-induced joint angles output

0 50 100%

50

60

70

80

Time

θf E[deg]

Static Pushing

Principal joint angle evolutions, frontal-centre out task.

a

�

q

Inverting the previouscomputations enables usto feed the model muscleactivities, and observethe resulting kinematics.

Model validation: feed-forward kinematics


Inverse Dynamics Compute Muscle Controls Prochazka’s modela� f

Forward Dynamicsq

x

here


Recently enforced by implementation (Millard, 2013)∙ Validate the muscle activities∙ Validate the inversibility of computations if possible∙ Validate the firing rates



C5

C6

Bic

eps

bra

chii

C7

C8

T1

Ia Ib II

C5

C6

Tri

cep

sb

rach

ii

C7

C8

T1

0 Time 100 % 0 Time 100 % 0 Time 100 %

Activity

Min Max

Elbow flexion (.5s):

Elbow extension (.5s):

Afferent fibres activities with parameters tuned to the cat’s normal locomotion (Prochazka, 1999),based on motor pools distributions in the Non Human Primate (Jenny, 1983).

Validation: firing rates predictions


Experiments

Recorded kinematics

Forward control

−200204060

�f S[de

g]

Recorded kinematics Muscle-induced joint angles output

9 9.5 10 10.5 11 11.5 12 12.5 13 13.5406080100120140

Time [s]

�f E[de

g]

Reaching Grasping ReturningPreparation

Principal joint angle evolutions, reaching & grasping task.

Experiment: reaching & grasping task


C5

C6Bicepsbrachii

C7

C8

T1

Ia Ib II

C5

C6

Tricepsbrachii

C7

C8

T1

9 Time [s] 13.5 9 Time [s] 13.5 9 Time [s] 13.5

Activity

Min MaxPreparation Reaching

Grasping Returning

Biceps and Triceps afferent activities


C5

C6

C7

C8

T1

Ia Ib II

9 Time [s] 13.5 9 Time [s] 13.5 9 Time [s] 13.5

Activity

Min MaxPreparation Reaching

Grasping Returning

Afferent fibres activities with parameters tuned to the cat’s normal locomotion, based on motorpools distributions in the NHP.

Averaged afferent activities


Conclusion

Current State:∙ Macacca fascicularis right arm∙ Fully parametrized∙ Integrated in computations chain∙ Estimates sensorineural activity

Future developments:1 Add functionality2 Improve physiological correctness3 Replace cost function4 Use spinal maps to tune the EES

Summary


THANK YOU!

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