Article

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

Sharif University of Technology, Tehran, Iran.

Conference proceedings: ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference 08/2011; 2011:8146-9. DOI: 10.1109/IEMBS.2011.6092009 Source: PubMed

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Available from: N. Sadati, Jan 27, 2016Abstract— 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

α

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

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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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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

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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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- References (23)
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**ABSTRACT:**The role of motor control in development of low back pain is subject of many researches both in theoretical and experimental fields. In this work flexion-extension movement of lumbar spine have been controlled by three different methods, including feedback linearization (FBL), PD control and their combinations. The model involves 7 links: 1 link for pelvis, 5 links for lumbar vertebrae and 1 link for trunk. Torque actuators have been used on each joint to make them follow desired trajectory. In linear control method, equations of motion have been linearized with respect to upright position and then control signals have been applied in the direction of eigenvectors. Robustness of each method against noises, sensory delay and parameters uncertainty have been investigated. Desired trajectory of each joint has been produced by Central Pattern Generators (CPGs), which was the subject of our previous work. The results show that PD controller in comparison with feedback linearization method is more robust in presence of noise and parameters uncertainty, but FBL controller is better when we have sensory delay. Combination of these methods leads to better control in all three simulations. - [Show abstract] [Hide abstract]
**ABSTRACT:**This paper proposes a CPG-based control architecture using a frequency-adaptive oscillator for undulatory locomotion of snake-like robots. The control architecture consists of a network of neural oscillators that generates desired oscillatory output signals with specific phase lags. A key feature of the proposed architecture is a self-adaptation process that modulates the parameters of the CPG to adapt the motion of the robot to varying coefficients of body-ground friction. This process is based on the frequency-adaptation rule of the oscillator that is designed to learn the periodicity of sensory feedback signals. It has an important meaning of establishing a closed-loop CPG much more robust against environmental and/or system parameter changes. We verify the validity of the proposed locomotion control system employing a simulated snake-like robot moving over terrains with different friction coefficients with a constant velocity. - [Show abstract] [Hide abstract]
**ABSTRACT:**We adapt the generic three-dimensional bursting neuron model derived in the companion paper (SIAM J. Appl. Dyn. Syst., 3 (2004), pp. 636-670) to model central pattern generator interneu- rons and slow and fast motoneurons in insect locomotory systems. Focusing on cockroach data, we construct a coupled network that retains sufficient detail to allow investigation and prediction of biophysical parameter changes. We show that the model can encompass stepping frequency, duty cycle, and motoneuron output variations observed in cockroaches, and we reduce it to an analyti- cally tractable symmetric network of coupled phase oscillators from which general principles can be extracted. The model's modular form allows dynamical analyses of individual components and the addition of other components, so we expect it to be more generally useful. - [Show abstract] [Hide abstract]
**ABSTRACT:**This paper develops a novel control system for functional electrical stimulation (FES) locomotion, which aims to generate normal locomotion for paraplegics via FES. It explores the possibility of applying ideas from biology to engineering. The neural control mechanism of the biological motor system, the central pattern generator, has been adopted in the control system design. Some artificial control techniques such as neural network control, fuzzy logic, control and impedance control are incorporated to refine the control performance. Several types of sensory feedback are integrated to endow this control system with an adaptive ability. A musculoskeletal model with 7 segments and 18 muscles is constructed for the simulation study. Satisfactory simulation results are achieved under this FES control system, which indicates a promising technique for the potential application of FES locomotion in future. - [Show abstract] [Hide abstract]
**ABSTRACT:**Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999. Includes bibliographical references (p. 143-150). This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. by Matthew M. Williamson. Ph.D. - [Show abstract] [Hide abstract]
**ABSTRACT:**One important mechanical function of the lumbar spine is to support the upper body by transmitting compressive and shearing forces to the lower body during the performance of everyday activities. To enable the successful transmission of these forces, mechanical stability of the spinal system must be assured. The purpose of this study was to develop a method and to quantify the mechanical stability of the lumbar spine in vivo during various three-dimensional dynamic tasks. A lumbar spine model, one that is sensitive to the various ways that individuals utilize their muscles and ligaments, was used to estimate the lumbar spine stability index three times per second throughout the duration of each trial. Anatomically, this model included a rigid pelvis, ribcage, five vertebrae, 90 muscle fascicles and lumped parameter discs, ligaments and facets. The method consisted of three sub-models: a cross-bridge bond distribution-moment muscle model for estimating muscle force and stiffness from the electromyogram, a rigid link segment body model for estimating external forces and moments acting on the lumbar vertebrae, and an 18 degrees of freedom lumbar spine model for estimating moments produced by 90 muscle fascicles and lumped passive tissues. Individual muscle forces and their associated stiffness estimated from the EMG-assisted optimization algorithm, along with external forces were used for calculating the relative stability index of the lumbar spine for three subjects. It appears that there is an ample stability safety margin during tasks that demand a high muscular effort. However, lighter tasks present a potential hazard of spine buckling, especially if some reduction in passive joint stiffness is present. Several hypotheses on the mechanism of injury associated with low loads and aetiology of chronic back pain are presented in the context of lumbar spine stability. - [Show abstract] [Hide abstract]
**ABSTRACT:**Nonlinear oscillators are widely used in biology, physics and engineering for modeling and control. They are interesting because of their synchronization properties when coupled to other dynamical systems. In this paper, we propose a learning rule for oscillators which adapts their frequency to the frequency of any periodic or pseudo-periodic input signal. Learning is done in a dynamic way: it is part of the dynamical system and not an offline process. An interesting property of our model is that it is easily generalizable to a large class of oscillators, from phase oscillators to relaxation oscillators and strange attractors with a generic learning rule. One major feature of our learning rule is that the oscillators constructed can adapt their frequency without any signal processing or the need to specify a time window or similar free parameters. All the processing is embedded in the dynamics of the adaptive oscillator. The convergence of the learning is proved for the Hopf oscillator, then numerical experiments are carried out to explore the learning capabilities of the system. Finally, we generalize the learning rule to non-harmonic oscillators like relaxation oscillators and strange attractors.