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VIII INTERNATIONAL SYMPOSIUM ON COMPUTER SIMULATIONS IN BIOMECHANICS
Motor Units Based
Hierarchical Genetic Algorithm
for Prediction of Muscle Force
Activation Patterns
Hristo Aladjov
Rositsa Raikova
July 2001
Centre of Biomedical Engineering,
Bulgarian Academy of Sciences
e-mail: [email protected], [email protected]
The Problem
How does the nervous system control muscles
in order to perform movements.
Muscles can only contract.
More than one muscle is needed to control the
position for single degree of freedom.
Muscles consist of muscle fibers with various
physiological properties.
Motor Unit (MU) twitch is highly nonlinear
function of time. Muscle force is a sum of all
MUs twitches and depends on large amount of
parameters: MUs firing rate, muscle length,
contraction speed, fatigue, etc.
The problem
Page 1
Mathematical Model
For one degree of freedom model there exists
only one (joint moment) equation:
One equation
d1   F1  d 2   F2  ...  d n   Fn  M external  
and set of constrains:
i
0  Fi  Fmax
, i  1..n.
Constrains
Many
unknowns
for determining unknown muscle forces.
Mathematical Model
Page 2
Optimization Methods
Why to use Optimization is suitable way for solving
optimization indeterminate equations.
The philosophy of optimization approaches is
close to the natural process of adaptation and
learning.
What do we
need
For the purposes of the optimization multiple
formal criteria must be defined. It is preferable
if they have clear physiological interpretation.
Precise model of muscle is needed in order to
determine muscle force in a similar to the
natural way.
Optimization Methods
Page 3
Muscle models
Single force
Muscle is presented as a single force.
Phenomenological
Phenomenological models - emphasizes on
mechanical properties of the muscles, by
considering them as a system of passive and
contractive elements.
Motor Unit
Based
Motor units based muscle model is presented in
the current paper
Changing Fmax, Tc,
Thr, Ttw we model
different types motor
units.
Muscle Models
Page 4
Genetic Algorithms
Purpose
Advantages
In the present work genetic algorithms are used
as an multiobjective optimization tool for
motor control investigation.
Genetic algorithms does not restrict the
internal representation of the model. They just
control the process of decision searching.
Each solution can be achieved by means of
genetic operations with clear physiological
interpretation.
Like in human nervous system it is possible to
define independent control mechanisms on
different hierarchical levels reflecting one and
the same controlled property.
Multiple different solutions are investigated
simultaneously.
Advantages
Page 5
Genetic Algorithms
Drawbacks
Genetic algorithms are not deterministic.
They produce different solutions after consecutive
executions.
Generally they are slower then classical
numerical approaches.
In the sense of classical definition genetic
algorithms are not able to solve time dependent
problems, but here is presented approach that is
able to overcome this disadvantage.
Drawbacks
Page 6
Genetic Algorithm
Problem encoding
MU1,1
MU2,1
MU3,1
MUp,1
MU1,2
MU2,2
MU3,2
MUp,2
MU1,n
MU2,m
MU3,k
MUp,l
Implementation
Muscle1
Muscle2
Muscle3
Motor Center1
t1
t2
t3
t1
Motor Unit 1
t2
t3
t1
tn
Motor Unit 2
Musclep
Motor Center2
t2
Motor Unit K
Motor Center3
Muscle 1
Genetic operations
Parents
3.5
33
89
140 210
15
46
120 180
Offspring
Crossover
3.5
33
120 180
15
46
89
140 210
3.5
33
Parent
140 210
Offspring
Mutation
3.5
33
89
Crossover moment
Implementation
210
89
Page 7
Genetic Algorithm
GA for motor Choose the initial solution, by setting up the
moments of neural stimulation of all MUs.
control
Use individual MUs twitches to calculate
muscle forces, joint moments, reactions.
Estimate solutions with respect to fitness
function. Fitness function is weighted or pareto
optimal combination of different criteria.
Choose ( better ) solutions and modify them
by means of genetic operations.
Repeat the last three steps until given error
threshold is reached.
GA for motor control
Page 8
Genetic Algorithm
Idea
Flowchart
START
Select MU or muscles for
genetic operations
Initialize MUs activation
1
Yes
Continue
evolution ?
3
Apply genetic operations
over selected objects
2
4
No
STOP
Estimate population and
select surviving individuals
5
Idea
Page 9
Genetic Algorithm
Performance Caching calculated muscle forces.
boosting
Techniques for reducing the number of
estimation points
Variable precision.
Estimation point oscillations.
Estimation with moving time frame.
Synchronous mutation operation.
Performance boosting
Page 10
Results
Elbow
flexion
y
TRI
BIC
BRA
BRD
ANC
O
x
l

G
Fitness
Performance improvement
2
1.5
Method
HGA w ithout Cache
Pure HGA w ith Cache
1
HGA w ith Moving Frame
0.5
Time [h:m:s]
0
2:24:00
2:09:36
1:55:12
1:40:48
1:26:24
1:12:00
0:57:36
0:43:12
0:28:48
0:14:24
0:00:00
Results
HGA
Cache
Variable precision
Moving frames
Oscillate estimation points
Synchronous mutation
Comp. time
02:07:13
01:19:11
00:25:37
00:23:27
00:24:20
00:39:02
Page 11
Fitness
0.07156
0.07156
0.06875
0.06155
0.06875
0.03636
Results
Elbow
flexion
y
TRI
BIC
BRA
BRD
ANC
O
x
l

G
Fitness
Performance improvement
2
1.5
Method
HGA w ithout Cache
Pure HGA w ith Cache
1
HGA w ith Moving Frame
0.5
Time [h:m:s]
0
2:24:00
2:09:36
1:55:12
1:40:48
1:26:24
1:12:00
0:57:36
0:43:12
0:28:48
0:14:24
0:00:00
Results
HGA
Cache
Variable precision
Moving frames
Oscillate estimation points
Synchronous mutation
Comp. time
02:07:13
01:19:11
00:25:37
00:23:27
00:24:20
00:39:02
Page 12
Fitness
0.07156
0.07156
0.06875
0.06155
0.06875
0.03636
Results
Elbow
flexion
y
TRI
BIC
BRA
BRD
ANC
O
x
l

G
Fitness
Performance improvement
2
1.5
Method
HGA w ithout Cache
Pure HGA w ith Cache
1
HGA w ith Moving Frame
0.5
Time [h:m:s]
0
2:24:00
2:09:36
1:55:12
1:40:48
1:26:24
1:12:00
0:57:36
0:43:12
0:28:48
0:14:24
0:00:00
Results
HGA
Cache
Variable precision
Moving frames
Oscillate estimation points
Synchronous mutation
Comp. time
02:07:13
01:19:11
00:25:37
00:23:27
00:24:20
00:39:02
Page 13
Fitness
0.07156
0.07156
0.06875
0.06155
0.06875
0.03636
Conclusions
Current HGA realization is able to produce
principally similar results during different
runs, despite its non deterministic nature.
Numerical experiments with 1 DOF elbow
model showed that experimental observations
as triphasic-behavior and antagonist cocontraction can be predicted.
Introduced acceleration techniques show
good improvement in speed without loss of
precision.
HGA can be used for detailed investigation of
motor control mechanisms. Observed trends
about the significance and role of separate
criterion can be easily implemented in real time
control algorithms
Conclusions
Page 14
Future plans
Use HGA for modeling muscle activation
patterns for more than one degree of freedom.
Use HGA for investigating point to point
movements.
Obtain the initial solution as a result of
experience and modify it on the basis of
abstract goals.
Investigate EMG-force relationship.
Future plans
Page 15