**4. Restoration of walking by artificial peripheral nerve system — Simulation study with neuro‐musuculo‐skeletal model of rat**

### **4.1. Purpose**

One application of PNIs is to replace the part of neural networks for a particular movement by artificial electrical networks or artificial digital networks. In this section, we propose a method of PNIs for partially impaired neural networks. When we look at injured persons, it is common that some muscles do not work because the corresponding motor neurons are damaged but the muscles do not receive any damage themselves. In such cases, the muscles can work if the motor commands are provided.

In this section, we make the following assumptions as conditions for our simulation of injured ratʹs walking. First, motor commands to muscles for walking are generated by specified neural networks. The networks is called central pattern generator (CPG), which has been identified in spinal cords of mammalian. The upper central nervous system is assumed to give only the trigger of walking. Second, some sensory systems, which may be muscle spindles or another somatosensory organs, are damaged but we are able to obtain the necessary signals for constructing the motor commands by using some artificial sensors instead of the damaged sensory systems. Third, we are able to provide the constructed motor commands for the target muscles through reinnervation type electrodes, which are described in Section 2. Based on these assumptions, we give a walking simulation of rat to show the possibility of practical usages of PNIs. Simulations of human bipedal walking have been successfully proposed [21, 22]; therefore, we may restore the walking motion for patients with spiral cord injury if our proposed method works well for rat walking.

An example of the experimental setup corresponding to the simulation is given in Figure 5. The camera system including image processing is to obtain the necessary signals such as joint angles, joint angular velocities, and other signals for the positions and orientations of body

**Figure 5.** Proposed experimental setup for reconstructing walking motion.

segments. It is possible to extend this type of neuroprosthetic system with portable sensors and other electrical devices to more practical one for disabled persons.

The purpose of this section is to conduct walking simulation which will play an importantrole of our succedent neuroprosthetic system. The basic concept of the neuroprosthetic system is shown in Figure 5. The role is to check whether the designed artificial CPG controller works adequately or not, and whether the sensing system is able to provide necessary information forthe controllerʹs adapting to the environmental changes. Thus, the walking simulation given in this section means the preliminary study of motion planning and control for our succedent neuroprosthetic system.

#### **4.2. Neuro‐musuculo‐skeletal model**

**4. Restoration of walking by artificial peripheral nerve system — Simulation study with neuro‐musuculo‐skeletal model of rat**

One application of PNIs is to replace the part of neural networks for a particular movement by artificial electrical networks or artificial digital networks. In this section, we propose a method of PNIs for partially impaired neural networks. When we look at injured persons, it is common that some muscles do not work because the corresponding motor neurons are damaged but the muscles do not receive any damage themselves. In such cases, the muscles

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

In this section, we make the following assumptions as conditions for our simulation of injured ratʹs walking. First, motor commands to muscles for walking are generated by specified neural networks. The networks is called central pattern generator (CPG), which has been identified in spinal cords of mammalian. The upper central nervous system is assumed to give only the trigger of walking. Second, some sensory systems, which may be muscle spindles or another somatosensory organs, are damaged but we are able to obtain the necessary signals for constructing the motor commands by using some artificial sensors instead of the damaged sensory systems. Third, we are able to provide the constructed motor commands for the target muscles through reinnervation type electrodes, which are described in Section 2. Based on these assumptions, we give a walking simulation of rat to show the possibility of practical usages of PNIs. Simulations of human bipedal walking have been successfully proposed [21, 22]; therefore, we may restore the walking motion for patients with spiral cord injury if our

An example of the experimental setup corresponding to the simulation is given in Figure 5. The camera system including image processing is to obtain the necessary signals such as joint angles, joint angular velocities, and other signals for the positions and orientations of body

> Electric Stimulator

CPG Controller Stimulator for movement

**4.1. Purpose**

Biomedical Engineering

22

can work if the motor commands are provided.

proposed method works well for rat walking.

Injured limb

**Figure 5.** Proposed experimental setup for reconstructing walking motion.

: Marker for measuring positions of body

: Reinnervation type electrodes

The neuro‐musculo‐skeletal model of rat is composed of a rigid link system, joint torque generators, neural controllers of CPGs with the upper level triggers. The inertial properties of the entire body are represented by a three dimensional 17‐rigid‐link system with 16 joints. All the joints are one degree‐of‐freedom, and the axes of the joints are perpendicular to sagittal plane. The schematic views in sagittal and horizontal planes are given in Figure 6. The dappled circles indicate the center of mass of each segment.

A viscoelastic passive moment induced by soft tissues and a passive moment of nonlinear elasticity induced by tendons and bones assumed to act on each joint. The characteristic is given by

$$\text{passive}\_{i}\left(\boldsymbol{\theta}\_{i},\dot{\boldsymbol{\theta}}\_{i}\right) = k\_{i1}^{I}\exp\left[k\_{i2}^{I}\left\{k\_{i3}^{I} - \left(\boldsymbol{\theta}\_{i} - \overline{\boldsymbol{\theta}}\_{i}\right)\right\}\right] + k\_{i4}^{I}\exp\left[k\_{i5}^{I}\left\{\left(\boldsymbol{\theta}\_{i} - \overline{\boldsymbol{\theta}}\_{i}\right) - k\_{i6}^{I}\right\}\right] + c\_{i}^{I}\dot{\boldsymbol{\theta}}\_{i} \tag{1}$$

where *θ<sup>i</sup>* is the *i*‐th joint angle variable, *θ* . *<sup>i</sup>* is the *i*‐th joint angular velocity variable, and another parameters are constants representing the joint characteristics. These parameters were determined from the estimations for human joints [23]. The inertia properties of each body segment, such as the mass and the moment of inertia, were estimated from the size of anato‐ mized each body segment with the average density of rat body [24].

**Figure 6.** Assumed skeletal system of rat.

The functions of the neural control system are divided into two types. The first function is a rhythm pattern generator corresponding to the spinal cord level. This subsystem composes CPGs which work as command generators for the joints. The command generation of each CPG starts by receiving a stimulus from the higher center. Each unit of CPG is a second‐order nonlinear dynamical system with the inputs from the higher center and the sensory systems. During movement of the link system, somatic sensory signals are fed back to the CPGs so that the musculo‐skeletal system is able to interact with the environment. This is the second function of the neural control system.

The neural control system of CPG is a nonlinear feedback controller :

$$\frac{1}{T\_r}\dot{\mathbf{x}}\_i + \boldsymbol{\infty}\_i = -\sum\_{j=1}^n a\_{ij}\mathbf{y}\_j - b\boldsymbol{z}\_i + \boldsymbol{u}\_i + \mathbf{s}\_i \tag{2}$$

$$\frac{1}{T\_a}\dot{z}\_i + z\_i = y\_i \tag{3}$$

The joint torque is determined as follow:

istics defined by (1).

and foot clearance.

**4.4. Discussion**

**4.3. Simulation results**

*τ* = *pF yF* ‐ *pE yE* (5)

Neural Interfaces: Bilateral Communication Between Peripheral Nerves and Electrical Control Devices 25

where *yF* and *yE* are the outputs of one pair of CPGs in which one CPG generates flexion torque and the other CPG generates extension torque at each active joint. For another joints except these active joints, the rotational motions will be induced according to the passive character‐

The interaction between the foot and the ground was modelled as a combination of springs and dampers. The ground reaction forces produced by the springs and dampers were assumed

In this simulation, we did not take the muscle model into considerations. However, the generated muscle forces corresponding to the generated torques by this neural controller can

We searched for suitable parameters of the CPG‐based controller such as *Tr*, *Td*, *aij*, *b*, etc. in each joint to achieve a realistic walking pattern, using a performance index that is a weighted linear combination of energy consumption per unit walking distance, muscle fatigue index

Figure 8 shows the walking simulation results in sagittal plane which are calculated by 0.1 second. Mammalians with four limbs are usually able to move in some patterns, such as walk, trot, and gallop. Each pattern is appeared around the corresponding optimal velocity. In mammaliansʹ moving, ʺoptimalʺ means energy efficient way in gate patterns for getting unit moving distance. From Figure 8, the pattern of ʺwalkʺ is observed and the moving velocity is matched approximately to the optimal velocity ofrat walking. Figure 9 shows that the outputs of CPGs successfully generated rhythmic patterns as functions of time and indicated appro‐ priate phase shifts each other for coordinated motions in four limbs. The corresponding generated torques are given in Figure 10. The similar patterns as the CPG outputs are observed. We can define the period of walking from Figure 10, and it is 0.2 second. The phase shift is ‐180 degree from the left fore‐limb to the right fore‐limb, and also ‐180 degree from the left fore‐limb to the left hind‐limb. On the other hand, the phase shift between the left fore‐limb and hind‐limb is ‐97 degree and in the right side it is the same. These phase shifts match to the pattern of ʺwalkʺ [26]. Figure 10 shows the active joints angles controlled by the CPG control‐ lers. It seems that the difference between left and right angels both in fore‐limbs and hind‐ limbs comes from the effect of initial conditions on the joint angels and joint angular velocities.

We observed a large rolling motion of the trunk in the walking simulation. This can be explained by the fact that no joint of rolling motion is introduced in the skeletal model. At this stage, we do not have any knowledge about rolling joints of rat. The placements, passive

to act on four points of each foot: two in the heel and two in the toe.

be estimated with an appropriate procedure by the method in [23].

$$y\_i = \max\left(0, \ x\_i\right) \tag{4}$$

Here, *i* and *j* are the oscillator numbers that are coupled in the antagonistic relation, *xi* is the membrane potential of the neuron, *Tr*, *Td* and *b* are the coefficients corresponding to aging variation, *yi* is the firing rate of the neuron, *aij* is the weight coefficient, *zi* is a variable corre‐ sponding to the adaptation level,*si* is the stimulation inputfrom the brain, and *ui* is the feedback signal from the somatic sensation. The oscillator neurons represented by equations (2), (3) and (4) are coupled to one another in a depressive manner, and the entire walking behavior undergoes an adaptation process by causing an oscillation in each joint movement [25]. Movement of a joint is coupled with that of other joints. In this simulation, only the four joints at shoulders and hips were assumed to generate actively the torques. One pair of the oscillator unit is attached at one of the four joints. The extra‐connections between CPGs of left and right shoulders, and also between CPGs of left and right hips are assumed for coordinating the motions of left and right limbs. These extra‐connections cause mutually inhibitions between left and right CPGs and then generate alternate motions between the left and right limbs. The structure of CPGs is given in Figure 7.

**Figure 7.** Structure of CPGs.

The joint torque is determined as follow:

The functions of the neural control system are divided into two types. The first function is a rhythm pattern generator corresponding to the spinal cord level. This subsystem composes CPGs which work as command generators for the joints. The command generation of each CPG starts by receiving a stimulus from the higher center. Each unit of CPG is a second‐order nonlinear dynamical system with the inputs from the higher center and the sensory systems. During movement of the link system, somatic sensory signals are fed back to the CPGs so that the musculo‐skeletal system is able to interact with the environment. This is the second

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

*aij y <sup>j</sup>* ‐ *bzi* + *ui* + *si* (2)

+ *zi* = *yi* (3)

) (4)

function of the neural control system.

Biomedical Engineering

24

structure of CPGs is given in Figure 7.

**Figure 7.** Structure of CPGs.

The neural control system of CPG is a nonlinear feedback controller :

 + *xi* = ‐ ∑ j=1 n

> 1 *Ta zi*

LF

u0 u0

*w21 w43*

RF

RH

LH

*yi* =max (0, *xi*

Here, *i* and *j* are the oscillator numbers that are coupled in the antagonistic relation, *xi* is the membrane potential of the neuron, *Tr*, *Td* and *b* are the coefficients corresponding to aging variation, *yi* is the firing rate of the neuron, *aij* is the weight coefficient, *zi* is a variable corre‐ sponding to the adaptation level,*si* is the stimulation inputfrom the brain, and *ui* is the feedback signal from the somatic sensation. The oscillator neurons represented by equations (2), (3) and (4) are coupled to one another in a depressive manner, and the entire walking behavior undergoes an adaptation process by causing an oscillation in each joint movement [25]. Movement of a joint is coupled with that of other joints. In this simulation, only the four joints at shoulders and hips were assumed to generate actively the torques. One pair of the oscillator unit is attached at one of the four joints. The extra‐connections between CPGs of left and right shoulders, and also between CPGs of left and right hips are assumed for coordinating the motions of left and right limbs. These extra‐connections cause mutually inhibitions between left and right CPGs and then generate alternate motions between the left and right limbs. The

1 *Tr xi*

$$
\pi = p\_F y\_F - p\_E y\_E \tag{5}
$$

where *yF* and *yE* are the outputs of one pair of CPGs in which one CPG generates flexion torque and the other CPG generates extension torque at each active joint. For another joints except these active joints, the rotational motions will be induced according to the passive character‐ istics defined by (1).

The interaction between the foot and the ground was modelled as a combination of springs and dampers. The ground reaction forces produced by the springs and dampers were assumed to act on four points of each foot: two in the heel and two in the toe.

In this simulation, we did not take the muscle model into considerations. However, the generated muscle forces corresponding to the generated torques by this neural controller can be estimated with an appropriate procedure by the method in [23].

We searched for suitable parameters of the CPG‐based controller such as *Tr*, *Td*, *aij*, *b*, etc. in each joint to achieve a realistic walking pattern, using a performance index that is a weighted linear combination of energy consumption per unit walking distance, muscle fatigue index and foot clearance.

### **4.3. Simulation results**

Figure 8 shows the walking simulation results in sagittal plane which are calculated by 0.1 second. Mammalians with four limbs are usually able to move in some patterns, such as walk, trot, and gallop. Each pattern is appeared around the corresponding optimal velocity. In mammaliansʹ moving, ʺoptimalʺ means energy efficient way in gate patterns for getting unit moving distance. From Figure 8, the pattern of ʺwalkʺ is observed and the moving velocity is matched approximately to the optimal velocity ofrat walking. Figure 9 shows that the outputs of CPGs successfully generated rhythmic patterns as functions of time and indicated appro‐ priate phase shifts each other for coordinated motions in four limbs. The corresponding generated torques are given in Figure 10. The similar patterns as the CPG outputs are observed. We can define the period of walking from Figure 10, and it is 0.2 second. The phase shift is ‐180 degree from the left fore‐limb to the right fore‐limb, and also ‐180 degree from the left fore‐limb to the left hind‐limb. On the other hand, the phase shift between the left fore‐limb and hind‐limb is ‐97 degree and in the right side it is the same. These phase shifts match to the pattern of ʺwalkʺ [26]. Figure 10 shows the active joints angles controlled by the CPG control‐ lers. It seems that the difference between left and right angels both in fore‐limbs and hind‐ limbs comes from the effect of initial conditions on the joint angels and joint angular velocities.

### **4.4. Discussion**

We observed a large rolling motion of the trunk in the walking simulation. This can be explained by the fact that no joint of rolling motion is introduced in the skeletal model. At this stage, we do not have any knowledge about rolling joints of rat. The placements, passive

characteristics such as range of joint angle and viscoelastic property should be clarified before the rolling joints are introduced in the skeletal model. The proper introduction such rolling joints reduces the magnitude of trunk rolling motion and may improve the simulation quality in comparison with the actual walking motion of rat.

 Forefoot Left Hindfoot Left Forefoot Right Hindfoot Right

Neural Interfaces: Bilateral Communication Between Peripheral Nerves and Electrical Control Devices 27

 Forefoot Left Hindfoot Left Forefoot Right Hindfoot Right

Time [msec]

Time [msec]

We extended the model to the case of more active joints controlled by the neural controllers. Other four active joints were introduced at elbows in fore‐limbs and at knees in hind‐limbs. The simulation results showed that the generated motion was a pattern of ʺgallopʺ. From this simulation, it will be required that we consider the method for distinguish patterns of moving

Although there exist several problems to be solved, the simulation results presented here indicate the possibility of functional restoration for the cases of partially impaired neural networks. We will be able to use this simulation technology for checking whetherthe designed artificial CPG controller works adequately or not, and for providing necessary information to the controllers adapting to the environmental changes. The usage of this kind of online

0 100 200 300 400 500

0 100 200 300 400 500

Joint T

Joint A

**Figure 11.** Joint angles at shoulders and hips.

simulator is also illustrated in Figure 5.


when we search the parameters in the neural controllers.

n

gle

[degree]

**Figure 10.** Generated joint torques.


orq

0

1

ue [N

m]

cycle

**Figure 8.** Walking simulation results.

**Figure 9.** CPGs' outputs as commands for joint torques in steady state.

**Figure 10.** Generated joint torques.

characteristics such as range of joint angle and viscoelastic property should be clarified before the rolling joints are introduced in the skeletal model. The proper introduction such rolling joints reduces the magnitude of trunk rolling motion and may improve the simulation quality

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

in comparison with the actual walking motion of rat.

Biomedical Engineering

26

0 10 20 30 40 [mm]

**Figure 8.** Walking simulation results.

C


**Figure 9.** CPGs' outputs as commands for joint torques in steady state.


0

1

2

P

G

o

utp

ut

0 10 20 30 40 [mm]

0 10 20 30 40 [mm]

0 10 20 30 40 [mm]

0 10 20 30 40 [mm]

t=0.4[sec]

cycle

Time [msec]

0 100 200 300 400 500

0 10 20 30 40 [mm]

 Forefoot Left Hindfoot Left Forefoot Right Hindfoot Right

0 10 20 30 40 [mm]

0 10 20 30 40 [mm]

0 10 20 30 40 [mm]

t=0.8[sec]

t=0.7[sec]

t=0.5[sec]

t=0.6[sec]

t=0.2[sec]

t=0.3[sec]

t=0.0[sec]

t=0.1[sec]

**Figure 11.** Joint angles at shoulders and hips.

We extended the model to the case of more active joints controlled by the neural controllers. Other four active joints were introduced at elbows in fore‐limbs and at knees in hind‐limbs. The simulation results showed that the generated motion was a pattern of ʺgallopʺ. From this simulation, it will be required that we consider the method for distinguish patterns of moving when we search the parameters in the neural controllers.

Although there exist several problems to be solved, the simulation results presented here indicate the possibility of functional restoration for the cases of partially impaired neural networks. We will be able to use this simulation technology for checking whetherthe designed artificial CPG controller works adequately or not, and for providing necessary information to the controllers adapting to the environmental changes. The usage of this kind of online simulator is also illustrated in Figure 5.

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