Intelligent Autonomous Systems 9T. Arai et al. (Eds.)IOS Press, 2006c�2006 The authors. All rights reserved.

1025

From Muscle to Brain: Modelling andControl of Functional Materials and

Living Systems

Mihoko Otake �����,� Division of Project Coordination, The University of Tokyo� PRESTO program, Japan Science and Technology Agency

Abstract. This paper describes modelling and control of typical open systems: oneis electroactive polymer gel and another is spinal nervous system. It is very im-portant to estimate the model based on their mechanisms in order to navigate thesubjects into objective states. Firstly, the wave-shape pattern control method wasproposed based on the gel model. Wave-shaped gels with varying curvature wereobtained by switching the polarity of a spatially uniform electric field. Secondly,time series of images which represent distribution of somatic information insidethe spinal cord were successfully obtained through measurement and computationutilizing somatotopic organization model of the spinal cord. The general problemunderlying these studies is the degrees-of-freedom problem. Making use of the na-ture of functional materials or living systems through modelling their mechanismshelped us to solve the problem.

Keywords. modelling, control, electroactive polymer, spinal nervous system,somatosensory information

1. Introduction

Active materials and living systems are both open systems, which are capable of ex-changing matter and energy with their environment. Their internal states vary over timebecause of their characteristics. Therefore, it is very important to estimate the modelbased on their mechanisms in order to navigate the subjects into objective states. Theyare unstable as well as controllable if we understand their mechanism and making useof them. In this paper, modelling, simulation and control of typical open systems are de-scribed: one is electroactive polymer gel and another is spinal nervous system. Both stud-ies were carried out by the author, which challenge to solve degrees-of-freedom prob-lem of soft materials and neuromusculoskeletal systems. The first study takes syntheticapproach. It proposes how to control shape of the functional material, so-called artificialmuscle having conceptually infinite degrees of freedom. In contrast, the second studytakes analytic approach. It investigates how the nervous system perceives and deals withvast numbers of muscular information in the human body.

1Correspondence to: M. Otake, E-mail: otake@cb.k.u-tokyo.ac.jp

1026 M. Otake / From Muscle to Brain: Modelling and Control of Functional Materials

2. Modelling and Control of Functional Materials

2.1. Wave-Shape Pattern Generation of Electroactive Polymer Gel

Electroactive polymers [1] change their shapes in the electric fields. The fact motivatedus to design the whole-body deformable robots. The purpose of the studies have beento establish methods for deriving a variety of shapes and motions of deformable robotswhose bodies are made of active materials. Shape control of such mechanisms is diffi-cult, which is commonly called the degrees-of-freedom problem [2], namely a problemof controlling many points of continuum with a small number of inputs. Mechanismsconsisting of a typical electroactive polymer gel[3] containing poly 2 -acrylamido -2-methylpropane sulfonic acid (PAMPS), named ’gel robots’, were designed, developed,and controlled experimentally[4,5,6,7,8]. We reported that straight beam of gels exhibitwave-shape pattern in a uniform constant electric field. The experimental results suggestthat complex shapes would be generated by simple electric fields. This characteristicshould be useful for shape control of the gel having large degrees-of-freedom. Then, amethod to reach the variety of wave-shapes was proposed[9].

2.2. Modelling of Electroactive Polymer Gel and its Mechanism of Pattern Formation

The nonlinearity of the electroactive polymers is the key to understand the mechanismof wave-shape pattern formation of the gels. An ionic polymer gel in an electric fielddeforms through penetration of the surfactant solution [10]. The state of the gel is char-acterized by the distribution of adsorbed molecules, which determines its overall shape.Adsorption state transition of the gel is approximated in the following local nonlineardifferential equation[11]:

��

��� ��� � �� ��� (1)

where � is the adsorption rate defined as the molar ratio of bound surfactants to the localsulfonates group of the polymer chains inside the gel; � is the current density vector onthe gel surface; � is the normal vector of the gel surface; � and � are association anddissociation constants. The equation shows that the effect of an electric field to a gel isdetermined by the geometry of the equi-potential surface and the gel surface. Adsorptionreaction causes the mechanical deformation. The deformation determines the subsequentreaction. This interaction of deformation and reaction brings out the wave-shape patternformation.

2.3. Wave-shape pattern control of electroactive polymer gel

Wave-shaped gels with varying curvature were obtained by switching the polarity of aspatially uniform electric field. Originally straight-shaped gel deformed into the shapescontaining one, two and three waves. The period for reversing the polarity was exploredthrough numerical simulation. The polarity of one of the electrodes was either anodic(0)or cathodic(1). A control sequence is described with a time interval and its sequence.A time interval of 10 second was initially selected and its sequence of eight intervalswere enumerated from (00000000) to (11111111). Other intervals were also considered

M. Otake / From Muscle to Brain: Modelling and Control of Functional Materials 1027

every 10 seconds from 20 to 120 seconds. We determined (00001111) with 80 secondstime interval as the best input sequence, which generated three-waved shape with largecurvature.

2.4. Experimental Methods

The gel was prepared by radical copolymerization at 323K for 48 hours. The totalmonomer concentration in N,N’ - dimethylformamide was kept at 3.0M in the presenceof 0.01M N,N’- methylenebisacrylamide (MBAA) as a cross-linking agent and 0.01Ma,a’ - azobis (isobutyronitrile) (AIBN) as an initiator. Monomers were 2 - acrylamido-2- methylpropanesulfonic acid (AMPS), n-stearyl acrylate (SA), and acrylic acid (AA)with the composition (AMPS: SA: AA) = (20: 5: 75). After the polymerizations, the gelwas immersed in a large amount of pure water to remove un-reacted reagents until itreached an equilibrium state. In order to apply the electric field, the gel was immersedin a dilute solution of 0.01M lauryl pyridinium chloride containing 0.03M sodium sul-phate. All experiments were carried out at a room temperature of 25 oC. The experimen-tal setup included a pair of parallel platinum plate electrodes of 25 [mm] wide and 40[mm] long each, which were horizontally placed with 40 [mm] vertical spacing betweenthem. A beam-shaped gel of 4 [mm] wide, 21 [mm] long, and 1[mm] thick was alsohorizontally placed in between with one end fixed for 5 [mm] and the other end free. Thetwo electrodes and the gel were immersed in the solution. A spatially-uniform electricfield was applied by the electrodes. The current density was kept constant by a galvano-stat at 0.1 [mA/mm�]. The polarity of the electric field was reversed from anodic(0) tocathodic(1) when the tangential angle at the tip of the gel reached the same values as thatof the simulation. The deformation of the gel was monitored and recorded by a videomicroscope.

2.5. Experimental Results

The experimental snapshots corresponding simulation show the initial (1), transitional(2-8), and final (9) forms of the gel(Figure 1). Let � be an angle between the tangentialline of the gel at the free end and one of the fixing ends. First, the gel bent toward theanode side (2). A portion of gel near the free end started to bend in the other directionwhen ���� went over /2 (3). The deformation of root portion remained same. Again,when � went under /2, a smaller portion of the gel near the free end started to bend thefirst direction (4). The polarity of the electric field was reversed at (5). Then, the gel benttoward the reverse side (6). A portion of gel near the free end started to bend in the otherdirection(7,8) without changing the polarity of the electric field. Finally, the gel reachedthe desired shape (9).

3. From Muscle to Brain

In the previous section, the author proposed how to control shape of the functional ma-terial, so-called artificial muscle having conceptually infinite degrees of freedom basedon chemical mechanism. How the living systems solve the degrees-of-freedom problem?In the human body, the nervous system perceives and deals with vast numbers of mus-cular information. Therefore, the author modeled the nervous system based on anatomy

1028 M. Otake / From Muscle to Brain: Modelling and Control of Functional Materials

10[mm]

(1) (2) (3)

(4) (5) (6)

(7) (8) (9)

Figure 1. Experimental results of the gel which deforms into three-half-waved shape

in order to figure out how the motion data are observed inside the human body, which isdescribed in the following section.

4. Modelling of Living Systems

4.1. Somatosensory Information in the Spinal Nervous System

For health and partially disabled, the spinal nervous system comprising peripheral nervesand spinal cords connect brain and muscles. Therefore, we should be able to estimate thebrain activities through motion measurement. During rehabilitation process, analysis ofwalking motion is critical for monitoring functional recovery of the nervous system afterstroke [12,13]. Visualization and analysis of somatosensory information in the spinalnervous system would help us understand how the brain perceive and regulate its bodymovement, since they interface the brain and muscles. The motivation is to design motorlearning support system for acquisition of motor skill considering neural mechanism. Weshould be able to obtain neural information through analyzing whole body muscle data,

M. Otake / From Muscle to Brain: Modelling and Control of Functional Materials 1029

musculoskeletal

system

nervous

system

motor

command

sensory

input

Figure 2. The information flow between the musculoskeletal system and the nervous system

because the nervous system controls the musculoskeletal system, while the lengths andforces information gets back to the nervous system (Figure 2). Muscles are controlled bydifferent nerves and are classified by the innervated nerves. The 31 pairs of human spinalnerves consist of 8 pairs of cervical nerves (C), 12 pairs of thoracic spinal nerves (T), 5pairs of lumbar nerves (L), 5 pairs of sacral nerves (S), and a single pair of coccygealnerves (Coc). These nerves pass through and depart from the clearance between spinalbones. In order to track the motor information, we developed the anatomical model ofthe peripheral nerves and the spinal cord. Motor neurons were arranged in each layerof the spinal cord and feedback signals which trigger simple reflex were mapped ontothe plane. Groups of muscular data innervated by the same layer of the spinal cord werecompared for each trial and the way of regulation was studied over time[14].

4.2. Computation of Motor Information through Motion Mesurement

We measured ’kesagiri’, a sword swinging motion. The motion was selected because itis a typical coordinated whole body motion which requires motor learning. The snap-shot of ’kesagiri’ is shown in Figure 3. The ’kesagiri’ motion was measured utilizingthe optical motion capture system. The positions of the markers distributed on the bodywere obtained. The frame rate was 33 [frame / sec]. The number of trials was 26. One ofthe trials was utilized for visualization, and two of the trials were selected for analysis.Human motion can be analyzed through combining motion capture system and muscu-loskeletal model. The body motion is mapped onto the musculoskeletal model so that thelengths and the forces of muscles are calculated[15,16,17]. Inverse kinematics problemwas solved utilizing musculoskeletal human model which contains 53 links and 366 mus-cles, whose degrees of freedom is 153[18]. The forces of the muscles were obtained alsoutilizing musculoskeletal human model via inverse dynamics computation. In this way,motor information, which should be obtained at mechano-receptors were calculated.

1030 M. Otake / From Muscle to Brain: Modelling and Control of Functional Materials

(a) (b) (c)

(d) (e) (f)

Figure 3. Snapshot of sword swinging ‘kesagiri’ motion: Motion capture data are mapped onto the muscu-loskeletal model.

4.3. The Images of Spinal Neural Information and its Application for Analysis

The time series of images of the spinal neural information at C5 among 31 segments ofthe spinal cord were mapped from the motor information utilizing the map by applyingthe rules for somatotopic organization. Figure 4 shows the spinal neural image at C5which represents the length of the muscles innervated by the segment. We extracted mus-cle length data on a muscle controlled by these nerves and normalized it with the musclelength when standing. The value is represented by intensity. We can see how the spinalcord segment C5 perceive the whole body motion. C5 innervates the upper part of thebody especially chest and upper arms. Both parts moves rapidly during ’kesagiri’ mo-tion. The analysis method was proposed which calculates correlation and phase contrastof the neural information. Corresponding periods were obtained by local correlations foreach pattern of the different trials. As a result, phase contrasts were obtained. Results ofthe analysis indicated that intersegmental regulation occurs through repetative trials ofcoordinated movements[14].

5. Discussion

Two approaches were taken to study degrees of freedom problem. The first study sug-gests that hysteretic property of the materials helps to solve the degrees-of-freedomprob-lem of deformable robots containing electroactive polymers. From the model of defor-mation and experimental results, we can consider gel as an integrator of the series ofinput. Molecules are adsorbed on the surface of the gels, which deform the shape of thegels. The deformed surface forms a reaction field in the next step. In this way, seriesof input by a time varying electric field are accumulated. The second study implies thatthe parallel processing of the somatosensory information in the spinal cord reduces thedifficulty of the degrees-of-freedom problem of human body movement. The distributed

M. Otake / From Muscle to Brain: Modelling and Control of Functional Materials 1031

(a) (b) (c)

(d) (e) (f)

Figure 4. Somatosensory image of spinal cord at C5 during ’kesagiri’ motion. Each image corresponds toeach posture in Figure 3.

neural circuits in the spinal cord segments receive and process length and forces infor-mation of the innervating muscles. The anatomical model of the spinal cord extractedtime series of partial images from large numbers of muscular data during whole bodymotion.

6. Conclusion

In this paper, wave-shape pattern formation of electroactive polymer gel and estimationof spinal information through external observation are described in terms of modelling.Effectiveness of the models were demonstrated through the following results.

� The wave-shape pattern control method was proposed based on the model. Wave-shaped gels with varying curvature were obtained by switching the polarity of aspatially uniform electric field.

� Time series of images which represent distribution of somatic information insidethe spinal cord were successfully obtained through measurement and computationutilizing somatotopic organization model of the spinal cord.

The general problem underlying these studies is the degrees-of-freedom problem. Thefirst study took synthetic approach while the second study took analytic approach. Mak-ing use of the nature of functional materials or living systems through modelling theirmechanisms helped us to solve the problem. Future work includes development ofmethod for navigating internal state of the nervous system into objective state like elec-troactive polymer gel for supporting motor learning and learning in general.

Acknowledgement

The author would like to thank Prof. H. Inoue with JSPS and AIST, Prof. T. Takagi,Prof. M. Inaba, Prof. Y. Nakamura with the University of Tokyo, Prof. Y. Kakazu, Prof.Y. Osada with Hokkaido University, who provided us valuable suggestions and dis-cussions. This work is supported by Japan Science and Technology Agency Grant for

1032 M. Otake / From Muscle to Brain: Modelling and Control of Functional Materials

PRESTO program "Development of the Bilateral Multiscale Neural Simulator" (PI: Mi-hoko Otake).

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