Probabilistic Information Structure of Human Walking

Myagmarbayar Nergui & Chieko Murai & Yuka Koike &

Wenwei Yu & Rajendra Acharya U

# Springer Science+Business Media, LLC 2010

Abstract Recently, the area of healthcare has been tremen-dously benefited from the advent of high performancecomputing in improving quality of life. Different process-ing techniques have been developed to understand thehidden complexity of the time series and will helpclinicians in diagnosis and treatment. Analysis of humanwalking helps to study the various pathological conditionsaffecting balance and the elderly. In an elderly subjects,falls and paralysis are major problems, in terms of bothfrequency and consequences. Correct postural balance isimportant to well being and its effects will be felt in everymovement and activity. In this paper, Bayesian Network(BN) was applied to recorded muscle activities and jointmotions during walking, to extract causal informationstructure of normal walking and different impaired walking.The aim of this study is to use different BNs to expressnormal walking and various impaired walking, and identifythe most important causal pairs that characterize specificimpaired walking, through comparing the BNs for differentwalking.

Keywords Walking . Bayesian network . Diagnosis .

Muscle . Causal relations

Introduction

Even only in Japan, there are around 1.65 million peoplesuffering from walking function impairment (Health andWelfare Statistics Association in Japan, 2000). Accuratediagnosis, prediction and evaluation of impairment aresignificantly important for walking function restoration, andimprovement of their QOF (Quality Of Life).

A physical impairment is any disability which restricts orconfines the physical function of limbs, or partial or completemotor ability such as physical, sensory, and cognitive orintellectual functions. In clinical practice, the walking functionimpairments are mostly diagnosed empirically, based on localinformation about impaired functions. However, as a biolog-ical behavior, the impaired walking is the result of interactionamong functional components, such as muscular system,skeletal system, and neural pathway. For example, someresearchers have reported that, the weakness in lower-legmuscle will be compensated by upper-leg muscles [1, 2].Thus the local information based empirical diagnosis couldnot support appropriate therapy and training program.

The ultimate goal of this study is to develop tools forassisting diagnosis, prediction and evaluation of walkingfunction impairment, in turn, to support therapy andrehabilitation for walking function restoration. The basicconsiderations include the following 2 issues:

1) Through extracting information structure of humanwalking, the body mechanism of the motion could bewell understood by disclosing the probabilistic causal-ity of walking-related functional components. Althoughphysical models of walking could also help under-standing of walking, it basically needs detailed expres-sion of those functional components, such as muscles,neural pathway, etc.

M. Nergui (*) :C. Murai :Y. Koike :W. Yu (*)Department of Medical System Engineering,School of Engineering, Chiba University,Chiba, Japane-mail: myagaa@graduate.chiba-u.jpe-mail: yuwill@faculty.chiba-u.jp

R. Acharya UDepartment of ECE, Ngee Ann Polytechnic,Singapore, Singapore

ORIGINAL PAPER

J Med Syst (2011) 35:835–844DOI 10.1007/s10916-010-9511-2

Received: 8 March 2010 /Accepted: 2 April 2010 /Published online: 6 July 2010

2) Information from different types of measurement couldbe synthesized through probabilistic causal inference.

In this study, Bayesian Network (BN) was employed asthe framework for probabilistic causal inference. A BN is agraphical notation that encodes conditional dependencerelationships among a set of events [3]. It is a directedacyclic graph where the nodes are probability variablesrepresenting certain events, and offers a way to symbolizethe uncertainties of application [4].

Because the fact that influences and probabilisticinteractions among variables can be described readily in aBN, some researchers realized that, the BN is suitable forthe analysis of biomedical signals, thus since the beginningof the 1990s researchers have been exploring its possibil-ities for medical applications. Some of the researchexamples could be found in [5–9]. BNs were used as toolsto extract causal relation between symptoms and diseasesfrom medical data base [5–7]. In [8], BNs were constructedfrom incomplete and partially correct statistics for multi-disease diagnosis. In [9], a dynamic BN applied forhandling uncertainty in a decision support system couldadapt to monitor patients treated by hemodialysis.

However, the BNs have been rarely applied to the realcontinuous sequence of motion-related biomedical data. In[10], it was used for the upper limb motion categorization.A BN model was used for categorizing the caringprocedure for wheelchair users with spinal injury [11].

In our study, the BN was applied to recorded muscleactivities and joint motions during walking, to extractcausal information structure of normal walking and differ-ent impaired walking. The aim of this study is to usedifferent BNs to express normal walking and differentimpaired walking, and identify the most important causalpairs that characterize one specific impaired walking,through comparing the BNs for different walking.

In order to verify whether it is possible for BNs to extractcausal information structure for different human walking, aseries of gait measurement experiment were conducted. Theelectromyogram(EMG) and angular trajectory of normalwalking, simulated paralyzed walking, paralyzed walkingwere recorded and analyzed using the BN technology.

Figure 1 shows an outline of the causal informationextraction process.

The paper is organized as follows. In the next section, thegait measurement experiment for collecting data of differenthuman walking is described. In Outline of Bayesian network,general concept of BN, in Preprocessing for further analysis

and search algorithms, experiment data preprocessing for BNanalysis is outlined. In Results, results of the analysis areshown, with discussion in Discussion. Finally, conclusionsare presented in Conclusion.

Gait measurement experiment

Subjects

Four persons, two healthy person and two walking-function-impaired persons, took part in the experiment.They were required to walk on a treadmill (DK-1422,Daiko). Table 1 shows their health condition and walkingcondition. In the simulated hemiplegic walking, the healthysubject was asked to wear an orthosis of right hemiplegiasimulation set (MANABITAI, a product of TokushuiryoCo., Ltd.), which gives constraints to the subject’s right-side ankle and knee joint. The special lower extremityorthosis constraining the ankle joint is shown in Fig. 2, bywhich the right ankle is plantar flexed to 108 degree.

Subjects with walking-function-impairment were askedto choose their own walk speed on the same treadmill, and

Gait Measurement for different walking

Data Preprocessingfor future analysis

Bayesian Networkconstruction by R

Fig. 1 Outline of the causal information extraction

Table 1 Subjects data information

Subject Healthcondition

Walkingcondition

Speed

A,B Healthy Normal walking 4[km/h]

Simulatedhemiplegic

1[km/h]

C Ankle mildly paralyzeddue to damage tolower legs

Unlimited 2 [km/h]

D Under knee paralyzeddue to spinal cordinjury, strongspasticity inGastrocnemius

Unlimited 1 [km/h]

Fig. 2 Lower extremity orthosisused for simulated hemiplegicwalking

836 J Med Syst (2011) 35:835–844

a pre-experiment was done to make sure that they can walksafely on the treadmill. Before the experiment, informedconsent was required from all subjects.

Recording muscle activities by EMG sensors

EMG signals could be used not only as the control signalsources to construct interface for prosthetic application[12], but also as a main diagnostics tool for clinicalneurophysiology, i.e., for distinguishing neuromusculardiseases, evaluating low-back pain, kinesiology, disordersof motor control etc. [13].

8 EMG sensors (TYE−1000 M, Sikikou Engineering)were attached to the sites shown in Figs. 3 and 4 sensors foreach side. The sampling frequency is 1,600 Hz.

Recording joint trajectories by a motion capture system

A motion capture system (captureEx, Library-Inc), contain-ing 3 cameras (Himawari GE60, 60fps, Library-Inc) wasused to record the trajectories of reflective markers attachedat the hip joint (coxa), knee joint and ankle joint of both

legs. Move-tr/3D software (Library-Inc) was used to build alink model and calculate the joint angles from recordedreflective marker trajectories. Figure 4 shows operations tocalculate joint angles from joint trajectories.

Outline of Bayesian network

Bayes’ theorem

A BN is a kind of directed acyclic graph (DAG) where thenodes are probability variables representing certain events.Generally, the BN can be defined as a set of nodes whichare random variables, an assembly of directed arcs betweenthe nodes, and a set of Conditional Probability Tables(CPT) that are associated with each node. A directed arcfrom Y to X, represents the conditional dependencybetween the variables, and this dependency is indicatedwith P(X/Y), which is the conditional probability for Xgiven that Y [14, 15]. The Bayesian Networks are used formedical diagnostics reasoning because it make available away of controlling probabilistic inference about the terms

Fig. 4 Operations to calculate joint angles from joint trajectories

Fig. 3 Locations for muscleactivity measurement and jointmotion [13]

J Med Syst (2011) 35:835–844 837

related with the handling procedure in the case ofuncertainty. And it is also used in the field of body skillmodeling and diagnosing faults in systems, and so on.

Features of Bayesian network

Bayesian networks are graphical structures for representingthe probabilistic relationships among a large number ofvariables and doing probabilistic inference with thosevariables [14].

BN has the following features.

& Each variable of data is handled as a stochastic variable.& Each variable of data is expressed as a node on BN

model.& Arc expresses the probabilistic causal relations between

variables on BN model.& The causal relation is evaluated at the conditional

probability.& A BN is a directed acyclic graph (DAG).

Preprocessing for further analysis and searchalgorithms

Preprocessing EMG data for further analysis

At first, raw EMG signals were full-wave rectified, andmoving averaged, then down-sampled to 60 Hz, which isthe sampling rate of the motion capture system, thenstandardized by the maximum and minimum of all8 EMG channels. The standardized signals were furtherdiscretizated to two values ON, OFF by a threshold valueof 70%. Figure 5 shows the process, which was imple-mented in MATLAB 7.0 (Mathworks).

Preprocessing joint angle data for further analysis

Hip, knee and ankle joint angles were calculated from the jointtrajectory data by the motion capture system. Then, hip jointangle data were separated to 2 phases: Straighten, Flexion;knee joint angle data were separated to 3 phases: Extension,Flexion, Straighten; ankle joint angle data were separated to 3phases: Forsiflexion, Plantarflex, Dorsiflexion-hold. Figure 6gives an illustration of the phase separation and Fig. 7 showsthe joint angle separation details.

BN node and arc assignment

Each phase of a joint angle was assigned a node; each EMGsite was assigned a node too. For each experimentcondition, two BNs were constructed, one for left side,another for right side. The node assignment was summa-rized in Table 2. For all the nodes, two values, ON and OFFcould be taken. Moreover, according to prior knowledge ofhuman walking, some arcs were prohibited for thesimplification of calculation. Table 3 shows the prohibitedarcs.

Search algorithm for BN

The BN structure learning algorithms can be grouped intwo categories:

1. Constraint-based algorithms: these algorithms learn thenetwork structure by analyzing the probabilistic rela-tions entailed by the Markov property with conditionalindependence tests and then constructing a graph whichsatisfies the corresponding d-separation statements. Theresulting models are often interpreted as causal modelseven when learned from observational data [14].

2. Score-based algorithms: these algorithms assign a scoreto each candidate the Bayesian network and try to

Original signal

Full-wave rectificationMoving averageStandarization

Discretization

time [s]

EMG data

Fig. 5 EMG data preprocessing for BN analysis

Flexion

Flexion

Extension (hold straighten)

Straighten

Plantarflex

Straighten

Dorsiflexion-hold

Dorsiflexion

Fig. 6 An illustration of joint angle phase separation

838 J Med Syst (2011) 35:835–844

maximize it with some heuristic search algorithm.Greedy search algorithms are a common choice, butalmost any kind of search procedure can be used.

All the BNs in this paper, employed a score-basedalgorithm as a Greedy search algorithm, and an evaluationfunction of Bayes’ factors [3, 4, 14], implemented by deal-package of R package [15].

Results

BN models

Figures 8, 9, 10 and 11 show the causal probabilisticnetworks extracted from left side data recorded during thenormal walking of subject A and B, the simulated

hemiplegic walking of subject A, paralyzed walking ofsubject C, paralyzed walking subject D, respectively.

These BNs could be compared by their structures. In thecase of normal walking (Fig. 8), both subjects showedcausal relationships between the following muscle and jointnodes: quadriceps femoris node (QF) and hip joint nodes(co-fl,co-st), QF and knee joint nodes (kn-st,kn-ex,kn-fl),semitendinosus node (SE) and hip joint nodes, SE and kneejoint nodes, TA and ankle nodes (an-ho,an-do,an-pl),Gastrocnemius (GA) and knee nodes, GA and ankle nodes.

The results agree with the common anatomical andbiomechanical knowledge that, each skeletal muscle con-tributes directly to one or two joint motions, i.e, Quadricepsfemoris and semitendinosus are related to hip joint motionand knee joint motion. Tibialis anterior is related to anklejoint motion. Gastrocnemius is related to knee joint motionand ankle joint motion (Fig. 3) [13, 14].

Hip straighten On Off On

Hip flexion Off On Off

Knee extension On Off Off

Knee flexion Off On Off

Knee straighten Off Off On

Ankle dorsiflexion On Off Off

Ankle plantarflex Off On Off

Ankle dorsiflexion-hold Off Off On

Dorsiflexion

Flexion

Flexion

Flexion

Flexion

Straighten Straighten

Straighten Extension

Dorsiflexion Dorsiflexion

Plantarflex

Fig. 7 Phase separation detailsfor joint angle data

Table 2 Node assignment

Node name Meaning Node name Meaning

kn-fl Knee-flexion co-st Hip-straighten

kn-ex Knee-extension co-fl Hip-flexion

kn-st Knee-straighten QF Quadricepsfemoris

an-pl Ankle-plantarflex SE Semitendinosus

an-do Ankle-dorsiflexion TA Tibialis anterior

an-ho Ankle-dorsiflexion-hold

GA Gastrocnemius

Node1 Arc Node2

Joint-1 → Joint-2

Joint-1 ← Joint-2

Muscle ← Joint

QF → Ankle joint

SE → Ankle joint

TA → Hip joint

→ Knee joint

GA → Hip joint

Table 3 Prohibited arcs

Joint-1, Joint-2: one arbitraryjoint from 3 joints

J Med Syst (2011) 35:835–844 839

Moreover, due to the special lower extremity orthosisthat gave constraints to subject’s right-side ankle and kneejoint, simulated hemiplegic walking is not bilaterallysymmetric, as reflected by the BN models shown inFig. 9. In BN model of right side, the ankle joint nodedorsiflexion-hold is isolated from the other nodes. On theother hand, BN model of left side has a high similarity withthe BN model of normal walking (Fig. 8).

In the BNs of walking-function-impaired gait (Figs. 10and 11), there are fewer arcs than BNs of normal walking.Especially the number of arcs between muscle nodes issmall compared with that of normal walking. In Fig. 10, theBN model of mildly paralyzed subject, the ankle joint nodedorsiflexion-hold is isolated from the other nodes. Further-more, TA node is not linked to any joint nodes. Figure 11 isthe BN model of under knee paralyzed subject. GA node isisolated from the other nodes, corresponding to subject’sspasticity in GA.

Subject A(Left) Subject B(Left)

Fig. 8 BN model of normalwalking

Fig. 9 BN model of simulatedhemiplegic walking (subject A)

Right Left

Subject C(Left)

Fig. 10 BN model of ankle mildly paralyzed (subject C-Left)

840 J Med Syst (2011) 35:835–844

Conditional probability of joint angle nodes

Figures 12, 13, 14 and 15 show the conditional probabilityof the nodes of the networks extracted from left side datarecorded during the normal walking of subject A and B, theleft and right side data of the simulated hemiplegic walkingof subject A, left side data of paralyzed walking of subjectC, paralyzed walking subject D, respectively.

In case of normal walking and simulated hemiplegicwalking, (Figs. 12 and 13), causal relationships between theankle nodes (ankle-plantarflex, dorsiflexion, dorsiflexion-hold) and muscle nodes (Tibialis Anterior (TA), Gastroc-nemius (GA)) were weak. On the right side of simulatedhemiplegic walking, no ankle dorsiflexion-hold appeared,due to the special lower extremity orthosis.

In the BN of subject C (mildly paralyzed subject,Fig. 14), there is a strong causal link between ankledorsiflexion node and TA.

In the BN of subject D (under knee paralyzed, Fig. 15),no activity was shown in GA nodes, which corresponds to

Fig. 12 Ankle node of condi-tional probability of normalwalking (Left)

Fig. 13 Ankle node of conditional probability of simulated hemiplegic walking (subject A)

Subject D(Left)

Fig. 11 BN model of under knee paralyzed (subject D-Left)

J Med Syst (2011) 35:835–844 841

the subject’s spasticity in GA. The causal relationshipbetween TA and ankle node is not strong.

Rationality of BN

If two gait patterns are similar, the BN structures extractedfrom the data of the two gait patterns should be similar to eachother, consequently, their scores for a same data set should becomparable. The rationality of the model cannot be shownenough by the score. However, as noted above, our result wasshown that the symptom of the trouble was expressible to bequantitative and qualitative by BN. Figure 16 shows thescores when one data set was modeled by different BNs. Alarger value means a network that provides a better model fora data set. As expected, for both normal walking data sets, themodel extracted from another normal walking data set showedthe best match, followed by simulated walking. The paralyzedwalking showed the worst match.

Discussion

Our preliminary results showed that, the BNs could extractcausal probabilistic structures that characterize differentwalking.

Biomedical signals are usually contaminated by differentnoise sources, and subject to the changes of individualcharacteristics and experiment environment. That is why inthe research efforts on classification based on biomedicalsignals, such as, classifying human gait based on leggesture [16], foot pressure lesions classification usingkinematic data [17], and tracking hip joint motion [18],probabilistic approach was employed. Since it could offer a

Fig. 15 Conditional probability of ankle node (subject D-Left)

Fig. 14 Conditional probability of Ankle node (subject C-Left)

Nor Normal: Normal walking, Sim Simulated: Simulated hemiplegic walking, C: Subject C, ankle mildly paralyzed, D: Subject D, under knee paralyzed, L: Left, R:Right

Data: B-Normal-Left

A-Simulated-Left

A-Simulated-Right

C-LeftD-Left

OwnA-Normal-Left

-15000

-14900

-14800

-14700

-14600

BN Model

Sco

re

Data: A-Normal-Left

A-Simulated-Left

A-Simulated-Right

C-Left

D-Left

B-Normal-LeftOwn

-15600

-15500

-15400

-15300

-15200

-15100

BN Model

Sco

re

Fig. 16 Scores of a data set matched to different BN models

842 J Med Syst (2011) 35:835–844

way of guiding probabilistic inference while handlingprocedure with uncertainty, the Bayesian probabilisticapproach was used in this study to analyze the recordingsof different walking.

In this study, the nodes of BNs were assigned to muscleactivities and joint angle trajectories, which cover theimportant aspects of motor control and motion analysis.The BN representation would allow some clear cause-effectpairs, especially the muscle-joint pairs, which makes itpossible to diagnose the muscle-related walking functionimpairments. This makes our study different with thesymptom-disease BNs in [6], and body site-site BNs in[19].

Known impairments (mild paralysis and spasticity), andan artificial impairment (simulated hemiplegic walking)could be identified or reflected by the extracted causalstructures. However, the possibility using the approach forprediction for different cases through information structuredatabase should be also explored.

In this research, we investigated the feasibility of usingBNs for the diagnosis of impaired walking. Normalwalking, simulated hemiplegic walking, two types ofimpaired walking were recorded from 4 subjects. Toincrease subject number, especially impaired walking caseswill be one of the important future tasks. Furthermore, theexperiment will be conducted at various walking conditions(at different walking speed, on slope way, during stairclimbing, etc.).

Another important issue that should be tackled is thelocal minimum of the search algorithms for BNs. Althoughfor the 4 subjects, 3 types of walking (normal, simulatedhemiplegic, paralyzed walking), the search algorithmsfound the reasonable and rational solutions, it does notguarantee the optimal solutions for the causality inferencewithout any a priori knowledge.

Moreover, efforts should be made to investigate andexplore more appropriate representation for the causality forthe human walking function. For example, Hybrid BayesianNetwork (HBN) [20], which can express mutual influenceby a combination of directed arcs and undirected arcs, andDynamic Bayesian Network (DBN) [21], which canexpress time-dependent causality.

Conclusion

In this study, we showed that, it is possible to use the BN toextract the probabilistic causal information from differenttypes of information of human walking: muscle activitiesand joint trajectories. The causal networks extracted fromdifferent types of gait measurement data could reflect thedifference between the normal walking, simulated hemiple-gic walking and paralyzed walking. Thus, the approach

could be useful for diagnostically, therapeutically, andrehabilitative uses.

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