Control of human spine in repetitive sagittal plane flexion and extension motion using a CPG based ANN approach

ABSTRACT
The complexity associated with musculoskeletal modeling, simulation, and neural control of the human spine is a challenging problem in the field of biomechanics. This paper presents a novel method for simulation of a 3D trunk model under control of 48 muscle actuators. Central pattern generators (CPG) and artificial neural network (ANN) are used simultaneously to generate muscles activation patterns. The parameters of the ANN are updated based on a novel learning method used to address the kinetic redundancy due to presence of 48 muscles driving the trunk. We demonstrated the feasibility of the proposed method with numerical simulation of experiments involving rhythmic motion between upright standing and 55 degrees of flexion. The tracking performance of the model is accurate to within 2° while reciprocal muscle activation patterns were similar to the observed experimental coordination patterns in normal subjects. The suggested method can be used to map high-level control strategies to low-level control signals in complex biomechanical and biorobotic systems. This will also provide insight about underlying neural control mechanisms.

Full-text

Available from: N. Sadati, Jan 27, 2016
Abstract— The complexity associated with musculoskeletal
modeling, simulation, and neural control of the human spine is
a challenging problem in the field of biomechanics. This paper
presents a novel method for simulation of a 3D trunk model
under control of 48 muscle actuators. Central pattern
generators (CPG) and artificial neural network (ANN) are used
simultaneously to generate muscles activation patterns. The
parameters of the ANN are updated based on a novel learning
method used to address the kinetic redundancy due to presence
of 48 muscles driving the trunk. We demonstrated the
feasibility of the proposed method with numerical simulation of
experiments involving rhythmic motion between upright
standing and 55 degrees of flexion. The tracking performance
of the model is accurate to within 2° while reciprocal muscle
activation patterns were similar to the observed experimental
coordination patterns in normal subjects. The suggested
method can be used to map high-level control strategies to low-
level control signals in complex biomechanical and biorobotic
systems. This will also provide insight about underlying neural
control mechanisms.
I. INTRODUCTION
ow back pain is a widespread disorder in industrialized
countries. Based on epidemiological reports, 80% of the
population faces this activity limitation at least once in their
lifetime [1] which places tremendous human and economic
costs to individuals and societies. Handling heavy loads,
with fast trunk motions (i.e. movements with extreme trunk
angular position, velocity and acceleration), repetitive
movements, and awkward postures are some of the risk
factors related to low back injuries. Hence, better
understanding of the neuro-musculo-skeletal system
performance would help us to recognize various
abnormalities in spine behavior and assist us in a way to
A. Sedighi is a M.Sc. student of Mechanical Engineering at Sharif
University of Technology, Tehran, Iran (e-mail: sedighi@mech.sharif.edu).
N. Sadati is a professor of School of Electrical Engineering at Sharif
University of Technology, Tehran, Iran (e-mail: sadati@sharif.edu).
B. Nasserolesmali received his M.Sc. in Mechanical Engineering from
Sharif University of Technology, Tehran, Iran and is now a Ph.D. candidate
in Bioengineering at University of Strathclyde, Glasgow, Scotland, UK (e-
mail:bahman.nasseroleslami@strath.ac.uk)
M. Khorsand Vakilzadeh received his M.Sc. in Mechanical Engineering
from Sharif University of Technology, Tehran, Iran (e-mail:
Khorsand@mech.Sharif. edu).
R. Narimani is a lecturer of School of Mechanical Engineering at Sharif
University of Technology, Tehran, Iran (e-mail: narimani@sharif.edu).
M. Parnianpour is an adjunct professor of School of Mechanical
Engineering at Sharif University of Technology, Tehran, Iran and a
professor in Department of Information and Management Engineering,
Hanyang University, Ansan, Gyeonggi-do, Rep. of Korea
(parnianpour@sharif.ir).
design the workplace to reduce the risk of injuries. For this
purpose, we can use biomechanical models to investigate the
consequences of various movement strategies for estimation
of muscle forces and joint reaction forces affecting the spine
[2].
The complexity of spinal models is partly due to
kinematic and kinetic redundancies in the multi-link spinal
system driven by multiple-muscles. In the literature, various
optimization methods are often used to solve the kinematic
and kinetic redundancies [3-5]. However, the difficulty with
optimal control methods is the selection of an appropriate
cost function used for solving the optimization problem.
Different cost functions will produce significantly different
results [6]. Recently, Nasseroleslami et al. [7] used a neuro-
fuzzy network, and a special reward function which depends
on the muscle moment arm to update its weights. In this
approach, they could solve the kinetic redundancy problem
while the error between actual and desired trajectories drives
the neuro-fuzzy system. A yet unanswered question is the
relative role of the feedback system and the optimization
process which determines the muscle recruitment and human
movement planning. Full-state feedback is not only
unrealistic from neurophysiological viewpoint, but may also
cause instability in presence of short and long delays.
Therefore, a combination of feed-forward and feedback
control using an internal model of the system may be closer
to reality [4].
To answer these questions, we remark that there are
evidences that the central pattern generators (CPGs) in
spinal cord can produce rhythmic motion in vertebrate
animals. In robotics literatures, the CPG is sometimes used
to produce the desired trajectories for motion planning [2],
[8-11]. In other applications, the CPG has been used to
generate the control commands in functional electrical
stimulation (FES) systems. In particular, Stites and Abbas
[12] employed pattern generators and pattern shapers to
drive a swinging leg. However, they did not use position or
velocity feedback errors in the pattern generator system.
Zhang [6] also used CPGs and neural networks in an FES
application. In simulated experiments, he achieved normal
walking patterns, but he did not deal with muscle
redundancy.
The primary aim in this paper is to simulate the spine as a
3D pendulum driven by 48 muscle actuators during flexion
and extension tasks in the sagittal plane. For this aim, we use
CPG as it used in FES studies to activate muscles.
Furthermore, based on reference [6], we will use artificial
neural network (ANN) between muscle’s model and CPG.
Control of Human Spine in Repetitive Sagittal Plane Flexion and
Extension Motion Using a CPG based ANN Approach
A. Sedighi, N. Sadati, B. Nasseroleslami, M. Khorsand Vakilzadeh, R. Narimani, M. Parnianpour
L
978-1-4244-4122-8/11/$26.00 ©2011 IEEE 8146
33rd Annual International Conference of the IEEE EMBS
Boston, Massachusetts USA, August 30 - September 3, 2011
Page 1
This ANN plays the role of spinal interneurons. We also use
a novel learning method to train the ANN for solving the
kinetic redundancy problem. In next sections we will
describe the details of the model, present the simulation
results of oscillatory maneuvers and briefly discuss the
results.
II. M
ETHODS
A. Trunk model
A 3D inverted pendulum is considered to model the trunk.
The model is constrained at L5-S1 with a ball and socket
joint and controlled with 48 muscles actuators [13]. The
dynamic equation of the trunk is as follows:
)(
11
θ
GNWWWJWJ
input
+=
(1)
where
1
J
,
WW
,
W
,
input
N
,
θ
and
)(
θ
G
are inertia matrix,
skew symmetric matrix corresponding to
W
, angular
velocity in the body coordinate system, net muscular torque
around L5-S1, angular position vector and the moment
vector from gravity, respectively [13].
B. Muscle model
We use the popular Hill-type muscle model, as described
by:
))()().(.(
max
lflflfaff
pvl
+=
(2)
where
a
is the muscle activation,
l
is muscle length,
l
is
contraction velocity,
l
f
is force-length relationship,
v
f
is
force-velocity relationship,
p
f
is muscle passive force
function, and
max
f
is the maximum muscle force which can
be calculated by multiplying Physiological Cross Section
Area (PCSA) with maximum muscle stress.
C. CPG model
Experimental observations have shown that there are
neural circuits in the spinal cord known as central pattern
generators (CPGs) [8]. CPGs can generate motor primitives
from high level commands that lead to a high dimensional
muscle recruitment pattern. When a CPG is utilized as part
of an FES control, it provides phase, frequency, and
amplitude which are necessary for generating a desired
motion [6].
In the literature, we can find various mathematical models
of the CPG [14-16]. Among them, Matsouka’s model [16] is
widely used [6], [17], [18]. For our purpose Matsouka’s
model is adopted due to its simple structure to facilitate
implementation. The model consists of two neurons: one
drives the flexor and the other drives the extensor; these
neurons have a self and mutual inhibitory interaction.
Mathematically, the model can be written as follows:
2222
12221
112
21111
yvv
Lechyvxx
yvv
Lechyvxx
i
+=
+=
+=
++=
τ
βτ
τ
β
τ
(3)
where
21
22
11
)0,max(
)0,max(
yyy
xy
xy
out
=
=
=
In the above equations,
1
x ,
1
v ,
2
x , and
2
v are the internal
states of the oscillators and
out
y
is the CPG output.
1
τ
and
2
τ
are the time constants,
c
is tonic input,
L
is feedback
gain,
e
is sensory feedback, and finally
h
and
β
represent
the mutual and self inhibitory parameters, respectively. To
have a rhythmic oscillation, the ratio between
1
τ
and
2
τ
must be in the range of 0.1-0.5 [19]. If we choose
L
large
enough, it will guarantee that the oscillator frequency will
entrain with sensory feedback [6]. We should pre-set the
CPG frequency according to the motion frequency.
Moreover, its frequency can be calculated using the
following equation [20]:
21
2
1
)1)(1(1
2
1
ττ
τ
τβ
π
++
=
h
f
(4)
Based on reference [10], one oscillator is used per degree
of freedom. In our work, since the desired motion is in the
sagittal plane, we designed an oscillator for the flexion
angle. For the other two DOFs, we set zeros as the CPG
output.
D. Artificial neural networks
There are complicated circuitries and interneurononal
connections between the CPG and motoneurons [6] that can
be simulated by ANN’s [6]. A radial basis function (RBF)
neural network is proposed for this purpose [6], with a
different learning method inspired form Nasseroleslami’s
formulation [7] to deal with redundancy problem.
To accomplish our aim, for each muscle we consider an
RBF neural network. As a result, we have 48 sub networks
in total. CPG output is fed to each sub network, and we
calculate the outputs according to the following equation:
=
=
m
j
ijiji
w
1
φα
(5)
where
)
2
)(
exp(
2
2
ij
ij
ij
cyout
σ
φ
=
i
represents the muscle activation,
ij
φ
is the membership
function of the hidden neurons,
ij
w
is the weight of
membership functions,
y
ou
t
is the CPG output,
ij
c
is the
center of the Gaussian functions,
ij
σ
represent the
variances,
i
is the muscle index, and
j
represents the
number of hidden neurons in the second layer.
Now ANN must be trained to achieve a satisfactory
control. So we consider the following cost function:
8147
Page 2
22
21
22
)(
2
1
)(
2
1
)(
2
1
)(
2
1
α
α
ααα
kehehkE
rkrkEEE
e
eee
++=
+=+=
(6)
where
e
is the error between desired and actual trajectory,
e
is the rate of error,
α
is the muscle activation, and finally
e
k
, and
α
k
are selected to normalize the values.
Selection of the center values is the vital first step in RBF
neural networks. The Gaussian function’s center and
variance, as well as their weights will be updated. Updating
the parameters are done as follows:
i
ii
i
ii
i
ii
u
E
kuku
E
kk
W
E
kWkW
=+
=+
=+
η
σ
ησσ
η
)()1(
)()1(
)()1(
(7)
On the other hand, because
J
is a function of muscles
moment arm, it can be used to resolve the redundancy in
musculoskeletal system, based on muscles configuration.
J
can be calculated as follows [9]:
iiK
i
active
i
active
i
K
K
K
i
K
iK
PCSAd
f
f
M
M
J ...
=
=
α
θ
α
θ
(8)
where
ik
d
is the moment arm of the
th
i
muscle around the
th
k
direction, and
i
PCSA
is the muscle physiological cross
sectional area.
E. Computational algorithm
Muscle length can be calculated based on its insertion and
origin, while its insertion changes instantaneously according
to angular position. Muscle velocity is computed by
derivative of the muscle length with respect to time.
Consequently, muscle moment arm can be described by the
following equation:
T
T
lllllll
=
=
Θ
321
θθθθϕψ
(9)
Control algorithm, as depicted in Fig. 1, consists of two
parts: feed-forward and feed-back paths.
Feed-forward path: CPG produces basic information like
amplitude, phase, and motion frequency. Its output feeds
ANN. Then, muscle dynamics is driven with ANN’s output.
Finally, muscles output act as actuators to control the trunk
motion.
Feed-back path: in this stage, error between desired and
actual trajectories is fed to CPG to adjust its frequency based
on the error frequency. In fact, CPG entrains with error
which is the main CPG’s characteristic. In addition,
combination of the error feedback and muscle’s activation
are used in the cost function. In this strategy, we can obtain
the updating rule for Gaussian function parameters.
III. R
ESULTS AND DISCUSSION
We have simulated an oscillatory movement between 0 to
55° with a frequency of 2 Hz. The activations of flexor and
extensor muscles are shown in Fig. 2c. As we can see in this
figure, the amplitude of extensor muscle activations is much
larger than the flexor muscle activations because we have
modeled gravity in our simulation. Furthermore, the flexor
and extensor activations are in phase while they are anti
phase with each other; indeed, when the flexor muscles are
active, the extensor muscle must be inactive, and vice versa.
Fig. 2a illustrates a very good tracking performance of the
system. The maximum error between the simulated and
desired angular position is 0.035 rad (see Fig. 2b).
Therefore, our system has accomplished a satisfactory
performance which can be further optimized by adjusting the
free parameters.
Fig. 1. Schematic diagram of the control algorithm.
Fig. 2. (a) Desired and actual position and velocity profiles, (b) muscles
activation profile: R-RA and R-LT are abbreviations for right Rectus
Abdominus and right Longissimus Thoracis, respectively, (c) moment
profile around joint, (d) and profile for flexion and extension motion in
sagittal plane.
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Page 3
The oscillator limit cycle has been depicted in Fig. 3. It
shows that the CPG has a stable limit cycle. Furthermore, it
means motor primitives and the stability of the patterns
contribute to tracking performance of the controller while
kinetic redundancy has been resolved as well.
Previous methods, which consider CPG in their models
[6], [12], [17] must separate the flexor and extensor muscles
from each other. The CPG model sends the signal to each of
them separately. However, in our model, the CPG sends a
signal for all muscles. Furthermore, we do not need to
separate the flexors and extensors from each others because
our learning method can predict the relative activities of the
muscles. In addition, the system keeps the flexor muscles in
phase with each other and out of phase with the extensor
muscles. It is possible to include the stability constraints to
promote co-activation to satisfy the required joint impedance
in light of possible perturbation in the system. Since learning
methods are dependent on muscle moment arms and their
cross sectional area, muscles activation levels were different
among agonist muscle groups and it is confirmed with the
observed normal behavior of the muscles [3].
Although we have provided the preliminary results of a
mathematical model that entails setting of a large number of
parameters, we see promising similarity in comparison to
experimental findings in the literatures [21-22]. We have
designed additional experiments that tests the muscle
recruitment patterns and movement profiles for point to
point and repetitive trunk planar and complex movements
with different cycle time, range of motion and directions.
The similarity of predictions under similar boundary
conditions gives additional confidence about feasibility of
the complex mathematical model.
Some of the limitations of our model emerge from the
simplifications. We have ignored some DOFs of the trunk
model and further assumed that the whole system acts as an
inverted pendulum. Passive tissues were not considered in
the model and the joint was considered as ball and socket
while in real systems, the translational degrees of freedom
should be considered as well. These limitations shall be
eliminated in future to yield a more realistic model.
R
EFERENCES
[1] C. T. Leondes, Computer and Computational Methods in Biomechanics.
vol. I, CRC Press, 2000.
[2] M. Abedi, G.R. Vossoughi, M. Parninpour,"Control of lumbar spine
flexion-extension movement by PD controller and feedback and
feedback linearization method," in Proc. IEEE Int. Conf. on Control,
Automation and Systems, pp. 2024-2029, 2010.
[3] S. Zeinali-Davarani, H. Hemami, K. Barin, A. Shirazi-Adl, M.
Parninapour, "Dynamics stability of spine using stability-based
optimization and muscle spindle reflex," IEEE Transactions on Neural
System and Rehabilitation, vol. 16, no. 1, pp.106-118, Feb. 2008.
[4] M. Khorsand-Vakilzadeh, H. Salarieh, M. Asghari, M. Parninapour, "A
computation tool to simulate trunck motion and predict muscle
activation by assigning different weights to physical criteria," in Proc.
IEEE Int. Conf. on
Biomedical Engineering, 2011.
[5] D. G. Thelen, F. C. Anderson, and S.L. Delp, "Generating dynamic
simulation of movement using computed muscle control," J. Biomech.,
vol. 36, no. 3, pp. 321-328, Mar. 2003.
[6] D. Zhang, K. Zhu, "Modeling biological motor control for human
locomotion with functional stimulation," Biolo. Cybern., vol. 96, pp.
79-97, 2007.
[7] B. Nasseroleslami, M. Parnianpour, M. Boroushaki, G.R. Vossoughi,
"Predication of torso muscle recruitment using emotional learning
based neuro-fuzzy controller", ISME, 2006.
[8] N. Sadati, Guy A. Dumont, and Kaveh A. Hamed, “Design of a neural
controller for walking of a 5-link planar biped robot via optimization,
Book’s Chapter, Human-Robot Interaction. Daisuke Chugo (ed.),
March 2010.
[9] J.K. Ryu, N. Young Chong, B. Jae You, "Locomotion of snake-like
robots using adaptive neural oscillators," Intel. Serv. Robotics, vol. 3,
no. 1, pp. 1-10, 2010.
[10] J.K. Ryu, N. Young Chong, B. Jae You, H. Christense, "Adaptive
CPG based coordinated control of healthy and robotic lower limb
movements," The 18
th
IEEE Int. Sym. on Robot and Human Interactive
communication, pp. 122-127, 2009.
[11] G. Lei Liu, M.K. Habib, K. Wantanabe, K. Izumi, "Central pattern
generators based on matsuoka oscillators for the locomotion of biped
robots," Artif. Life Robotics, vol. 12, pp. 122-127, 2009.
[12] E.C. Stites, J.J. Abbas, "Sensitivity and versatility of an adaptive
system for controlling cyclic movments using functional neuromuscular
stimulation," IEEE Transactions on Biomedical Engineering, vol. 47,
no. 9, pp.1287-1292, Sep. 2000.
[13] J. Cholewicki, J.M. McGill, "Mechanical stability of the in vivo
lumbear spine: Implication for injury and chronic low back pain," Clin.
Biomech., vol. 11, no. 1, pp.1-15, Jan. 1996.
[14] L. Righetti, J Buchli, A.J. Ijspeert, "Dynamics Hebbian learning in
adaptive frequency oscillators," Physica D: Nonlinear Phenomena, vol.
216, pp. 269-281, 2006.
[15] R. Ghigliazza, P. Holmes, "A minimal model of central pattern
generators and motoneurons for insect locomotion," SIMA J. Appl.
Dyn. Syst., vol. 3, pp. 671-700, 2004.
[16] K. Matsouka, "Mechanisms of frequency and pattern control in the
neural rhythm generators,"Biolog. Cybern. vol. 56, pp. 345-353, 1987.
[17] N. Ogihara, N. Yamazaki "Generation of human bipedal locomotion
by a bio-mimetic neuro-muscleo-skeletal model,"Biolog. Cybern. vol.
84, pp. 1-11, 2001.
[18] G. Taga, "A model for the musculoskeletal system for human
locomotion II," Biolog. Cybern. vol. 84, pp. 113-121, 1995.
[19] M. Williamson, "Robot arm control exploiting natural dynamics," PhD
thesis, Massachusetts of Technology, Cambrige, MA, 1999.
[20] D. Zhang, K. Zhu, "Theoretical analysis on neural oscillators toward
biomimic robot control," Int. J. of Humaniod Robotics, vol. 4, no. 4,
pp. 697-715, 2007.
[21] L. Oddson, A. Thorstensson, "Fast voluntary trunk flexion
momvements in standing: motor pattern," Acta Physiol Scand, vol. 129,
no. 1, pp. 93-106, 1987.
[22] E. Ross, M. Parnianpour, D. Martin, "The effect of resistance level on
muscle coordination patterns and profile during trunk extension,"
Spine, vol. 18, no. 13, pp. 1829-1838, 1993.
Fig. 3. Limit cycle of oscillator in phase space.
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
x1
x2
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