facultyofmathematics, biomechanicalmodelofthe primates ... · primates’upperlimb pierrekibleur...
TRANSCRIPT
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
4/29 P. Kibleur NHP 2017
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
5/29 P. Kibleur NHP 2017
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
5/29 P. Kibleur NHP 2017
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)
6/29 P. Kibleur NHP 2017
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)
6/29 P. Kibleur NHP 2017
What are the patterns of afferents’firing rates?
Kinematic recordings are reproduced in OpenSim simulations in order to predict them.
Biomechanical model
8/29 P. Kibleur NHP 2017
3 algorithms to process the recorded kinematics into the afferents’ firing rates:Inverse Dynamics Compute Muscle Controls Prochazka’s modela� fx
Computational model
9/29 P. Kibleur NHP 2017
3 algorithms to process the recorded kinematics into the afferents’ firing rates:Inverse Dynamics Compute Muscle Controls Prochazka’s modela� fx
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
9/29 P. Kibleur NHP 2017
3 algorithms to process the recorded kinematics into the afferents’ firing rates:Inverse Dynamics Compute Muscle Controls Prochazka’s modela� fx
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
9/29 P. Kibleur NHP 2017
3 algorithms to process the recorded kinematics into the afferents’ firing rates:Inverse Dynamics Compute Muscle Controls Prochazka’s modela� fx
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
9/29 P. Kibleur NHP 2017
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
11/29 P. Kibleur NHP 2017
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
12/29 P. Kibleur NHP 2017
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?
14/29 P. Kibleur NHP 2017
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
15/29 P. Kibleur NHP 2017
Inverse Dynamics Compute Muscle Controls Prochazka’s modela�
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
Where to validate the model?
16/29 P. Kibleur NHP 2017
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
17/29 P. Kibleur NHP 2017
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
Frontal centre-out task.
0
10
20
30
tricepsshort[]
0 50 100%
0.6
0.8
1
Time
bicepslong[]
Example (filtered) EMG signals.
Muscular model validation: data
17/29 P. Kibleur NHP 2017
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
Frontal centre-out task.
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.
Muscular model validation: data
17/29 P. Kibleur NHP 2017
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
18/29 P. Kibleur NHP 2017
Inverse Dynamics Compute Muscle Controls Prochazka’s modela�
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∙ Validate the inversibility of computations if possible
Where to validate the model?
19/29 P. Kibleur NHP 2017
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
20/29 P. Kibleur NHP 2017
Inverse Dynamics Compute Muscle Controls Prochazka’s modela� f
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∙ Validate the inversibility of computations if possible∙ Validate the firing rates
Where to validate the model?
21/29 P. Kibleur NHP 2017
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
22/29 P. Kibleur NHP 2017
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
24/29 P. Kibleur NHP 2017
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
25/29 P. Kibleur NHP 2017
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
26/29 P. Kibleur NHP 2017
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
28/29 P. Kibleur NHP 2017
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
28/29 P. Kibleur NHP 2017
THANK YOU!