A New Approach to Gait Variability Quantiﬁcation using Cyclograms

Slavka Viteckova

, Patrik Kutilek

, Radim Krupicka

, Zoltan Szabo

, Martina Hoskovcova

and

Evzen Ruzicka

Faculty of Biomedical Engineering, Czech Technical University in Prague, Kladno, Czech Republic

Department of Neurology and Centre of Clinical Neuroscience, First Faculty of Medicine and General University Hospital

in Prague, Charles University in Prague, Prague, Czech Republic

Keywords:

Gait Variability, Cyclogram, Cyclic Movement Analysis.

Abstract:

Human gait is cyclic movement and its properties are not constant. Gait variability is widely assessed by

ﬂuctuation in spatio-temporal parameters. Since this method operate on a single parameter of the gait cycle,

the cycle signal in its entirety does not affect the result. The objective of this work is to present new gait

variability assessment method. In order to quantify the variability of entire gait cycle, we have proposed and

tested the method based on synchronized cyclograms. The novel approach showed the ability to assess gait

variability. The method is not restricted to gait variability assessment and would be beneﬁcial in different areas

of cyclic movement variability analysis.

1 INTRODUCTION

The properties of movement are not constant when

one moves repeatedly. There are slight alterations in

each individual cycle of movement. Fluctuation in

gait parameters from one stride to the next is referred

as intra-individual gait variability. Fluctuation can be

seen even when there are no environmental or exter-

nal perturbations (Hausdorff, 2005).

The alternation of gait variability shows gait that

is inﬂuenced by disease (e.g. Parkinson’s disease, de-

mentia, multiple sclerosis) (Blin et al., 1990; Jamour

et al., 2012; Kaipust et al., 2012) or healthy ageing

(Grabiner et al., 2001). Increased gait variability is re-

lated to changes in mobility, higher risk of falls (Brach

et al., 2005; Hoskovcov

a et al., 2015) and subtle alter-

ations in underlying physiology (e.g. cardiovascular

changes, mental health) (Hausdorff et al., 1994; Haus-

dorff et al., 2003). Evidence indicates that gait vari-

ability may serve as a quantiﬁable feature of walking

function.

Usually, standard deviation and coefﬁcient of vari-

ation of kinematic or spatio-temporal parameters of

stride are used to assess gait variability (Blin et al.,

1990; Hausdorff et al., 1994; Hausdorff et al., 2003;

Grabiner et al., 2001; Brach et al., 2005). Nonlin-

ear methods, e.g. detrended ﬂuctuation analysis and

approximate entropy, have also been used to quantify

gait variability (Kaipust et al., 2012). The most com-

monly employed parameters are stride length, stride

width, and cycle timing (e.g. duration of various

phases) (Blin et al., 1990; Grabiner et al., 2001; Haus-

dorff et al., 2003; Brach et al., 2005; Kaipust et al.,

2012; Hoskovcov

a et al., 2015). Since these meth-

ods operate on a single parameter of the gait cycle,

the cycle signal in its entirety does not affect the re-

sult. Next, different methods have different require-

ments on walking distance, e.g. nonlinear methods

work better over long walks. However, these methods

and speciﬁed parameters are more difﬁcult to inter-

pret and use in clinical practice.

While spatio-temporal parameters provide infor-

mation about discrete time events (features) variabil-

ity, e.g. the double support phase duration, they do

not describe the complete curves i.e. development of

a feature. For example, curves may have similar peak

values indicating low variablity but different wave-

forms. Therefore, we present an approach to gait vari-

ability quantiﬁcation that enables the evaluation and

comparison of entire stride signals. This comparison

is carried out by the continuous symmetry method,

namely the method of cyclograms (also called cy-

clokinograms) (Goswami, 2003). The concept of cy-

clograms, although known to the biomechanics com-

munity, has not been mentioned as a tool for evaluat-

ing gait variability. The ﬁrst mention of a cyclogram

(Grieve, 1968) argued that a cyclic process such as

walking is better understood if studied with a cyclic

Viteckova, S., Kutilek, P., Krupicka, R., Szabo, Z., Hoskovcova, M. and Ruzicka, E.

A New Approach to Gait Variability Quantiﬁcation using Cyclograms.

DOI: 10.5220/0006546601270132

In Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2018) - Volume 4: BIOSIGNALS, pages 127-132

ISBN: 978-989-758-279-0

127

plot. The method of cyclograms is usually used, but

not limited, to symmetry (similarity) assessment of

contralateral limbs signals. Our approach is to use

the method of cyclograms to assess gait variability via

inter-cycle similarity. Intra-individual gait variability

is assessed by the comparison of entire consecutive

stride signals to each other. It means the similarity

of entire stride signals (not only one parameter of the

stride) is assessed.

In our case, we will use cyclograms for evaluating

gyroscope data, i.e. angular rate of lower limb move-

ments during gait. Cyclograms in conjunction with

gyroscope data has not been used before for evaluat-

ing gait variability. This new application of gyroscope

data and cyclograms can provide new clinical use in

the diagnosis of patients.

2 METHODS

2.1 Participants

In the study we included 34 Parkinson disease (PD)

patients (24 males, 11 females), mean age 67.2 years

(SD 7.9), with mild to moderate PD. The control

group included 21 volunteers (13 males, 8 females),

mean age 65.5 years (SD 8.4), with no history of neu-

ropsychiatric disorders. All PD patients were eval-

uated in OFF and ON medication states within the

same day. The ﬁrst examination in clinically deﬁned

OFF state was followed by an examination in the ON

state after a dose of levodopa equivalent to 150 % of

their usual morning dose. The study was approved by

the Ethics Committee of the General University Hos-

pital in Prague, Czech Republic, and therefore per-

formed in accordance with the ethical standards es-

tablished in the 1964 Declaration of Helsinki.

2.2 Data Acquisition

Xbus Master (Xsens Technologies B.V.), a

lightweight (330g) portable device using motion

tracking units (MTx) for orientation and acceleration

measurement of body segments, was used for the

measurement of segment movements. The MTx unit

with an embedded accelerometer and gyroscope is

an accurate inertial measurement unit measuring

drift-free 3-D orientation and 3-D acceleration. Kine-

matic data was recorded from 3 gyro-accelerometers

with a data sampling rate of 100 Hz. The gyro-

accelerometer units were symmetrically attached

on the lateral shank of each lower leg, 4 cm above

the ankle joint; and the chest, 2 cm below the

sternal notch. They were calibrated according to

manufacturer instructions.

All subjects accomplished an extended Timed Up

& Go Test (ETUG) (Wall et al., 2000). Each subject

was observed and measured while he/she rose from

a chair during the ETUG, walked 7 meters, turned,

walked back, and sat down again. Two repeated col-

lections of ETUG were recorded for each subject (i.e.

patients and healthy subjects). One of two ETUG

trial’s accomplishments was randomly selected and

processed.

The MTx unit of the chest was utilized in iden-

tiﬁcation subcomponents of ETUG (see subsection

Method of Data Processing). Two MTx units, lower

leg units, were used to process all three angular rate

signals in the particular axes. Besides, we evaluated

the magnitude of the angular rate vector

kωk =

vertical

+ ω

horizontal

+ ω

sagittal

(1)

This was done in order to eliminate incorrect place-

ment of the measurement units.

2.3 Method of Data Processing

Before further processing, the raw angular rate sig-

nal was low-pass ﬁltered with a zero-phase second-

order Butterworth ﬁlter with a 60 Hz corner fre-

quency. The ETUG subcomponents, namely sit-to-

stand, gait, turn, and turn-to-sit, were automatically

identiﬁed, see (Salarian et al., 2010). The gait cy-

cles of the steady gait components were determined

by automatic identiﬁcation (Salarian et al., 2010). All

preprocessing and analysis was carried out ofﬂine us-

ing the MatLab (MatLab R2010b, Mathworks, Inc.,

Natick, MA, USA) programming environment.

The GaitRite instrumented walkway (7.0 m long

and 0.6 m wide) and a video camera were used as the

references for the TUG subcomponents and gait char-

acteristics to verify implementation of implemented

algorithms (not published). Previous studies have ver-

iﬁed that the GaitRite is a valid and reliable method

for measuring mean gait characteristics in older adults

(Menz et al., 2004). During each trial, the video cam-

era recorded at 25 frames per second and was used to

determine total step count over the complete trial.

The signals of both lower limbs were used. Gait

cycles signals were time-normalized to the same

length, see Figure 1. The inter-cycle comparisons via

the cyclogram method were done. It can be assumed

that lower variability in gait cycles is demonstrated by

their high level of similarity (low level of dissimilar-

ity). It is possible to use two options to achieve inter-

cycle comparison. The ﬁrst is to compare each gait

cycle to the consecutive one. In this way we get n − 1

BIOSIGNALS 2018 - 11th International Conference on Bio-inspired Systems and Signal Processing

128

Figure 1: Example of six gait cycles from subject no. 1 (PD

OFF). ω - magnitude of angular rate, t-time.

comparisons from n gait cycles. The second option is

to compare each gait cycle with all other cycles. In

this way we get

2!(n − 2)!

(2)

comparison from n gait cycles. The disadvantage of

the ﬁrst option is that the same amount of change (e.g.

same level of dissimilarity) between all consecutive

cycles does not adequately reﬂect the real variability,

e.g. dissimilarity between ﬁrst and last cycle. Thus,

we employed the second option. Then, the median of

all inter-cycles comparisons was computed. Accord-

ing to the assumption, the higher value of dissimilar-

ity represents the greater variability of gait.

2.4 Method of Cyclograms

The creation of cyclograms is based on plotting two

gait variables vs. each other (Figure 2). In the case

of the traditional use of cycles for gait evaluation, two

time-series (trajectories) should be identical and a cy-

clogram should lie on a symmetry line (Kutilek et al.,

2014). In our case, the two time-series are time-series

of two gait cycles. The symmetry line is a straight

line passing through the origin inclined at an angle of

45 degrees. We can also compute the area within the

cyclogram, and its orientation to evaluate the rate of

asymmetry (Goswami, 2003). We can express math-

ematically the cyclogram deviation from the cyclo-

gram of an ideal symmetric gait to obtain a quantiﬁca-

tion of asymmetry. The triplet of geometric properties

of cyclograms, namely the area within the cyclogram

(S), orientation (α), and moment (J), can be repre-

sented by points in 3D space (Figure 3). The ideal

point for symmetric gait has the coordinates (0, 45,

0), (Goswami, 2003). The point in the 3D space of the

geometric properties of a cyclogram was determined

for each measurement. Then, the asymmetry, A, was

deﬁned as the distance from the measurement point,

Figure 2: Example of the cyclogram of angular rates of two

consecutive gait cycles of subject no. 1. ω

-magnitude of

angular rate of the ﬁrst gait cycle, ω

-magnitude of angular

rate of the second gait cycle.

Figure 3: Example of three geometric properties of the cy-

clogram (subject no. 1). The distance from the point of

geometric properties of ideally similar curves (star symbol,

[0, 45, 0]) to the point of current cyclogram properties (di-

amond symbol, [5, 43, 26]) is the quantiﬁer of the curves

dissimilarity.

M, and ideal point I:

A =

− S

)

+ (α

− α

)

+ (J

− J

)

(3)

In our case, the asymmetry, A, is the measure of

the dissimilarity of two gait cycles. The higher value

of dissimilarity, the higher variability of gait cycles.

The indicator of gait variability based on cyclogram

characteristics was calculated for the measured move-

ment of the lower limbs of all healthy subjects and PD

patients.

2.5 Statistical Analysis

Statistical analysis was performed to examine

whether gait variability via the method of cyclograms

is able to distinguish a healthy subject from a PD pa-

tient. The exclusion criterion was that all gait cycles

A New Approach to Gait Variability Quantiﬁcation using Cyclograms

129

Figure 4: The values of cyclogram-based variability quanti-

ﬁers for angular rate magnitude.

before turn are detected. Shapiro-Wilk test was used

to verify the normality of parameters in each observed

dataset. The assumption of normal data distribution in

the observed datasets has been rejected (signiﬁcance

level p = 0.05). Therefore, nonparametric Wilcoxon

signed rank test was used to compare the statisticaly

signiﬁcant differences in gait variability between PD

patients in the ON and OFF state. Nonparametric

Wilcoxon rank sum test was used to compare PD pa-

tient data to norms data. The signiﬁcance level was

set to p < 0.05. Statistical analyses and data pro-

cessing were performed using MATLAB sw (MatLab

R2010b, Mathworks, Inc., Natick, MA, USA).

3 RESULTS

The gait variability assessment via method of cyclo-

grams revealed a signiﬁcant difference between the

control group and PD ON in the variability of the

angular rate about the sagittal-axis (p < 0.01). The

statistically signiﬁcant difference between the control

group and PD OFF has been proven in the variability

of the angular rate about the sagittal-axis (p < 0.01)

and magnitude (p < 0.01). The variability about the

vertical-axis (p < 0.01) and the magnitude of the an-

gular rate (p < 0.01) delivered a signiﬁcant difference

between PD ON and PD OFF. The variability about

the horizontal-axis did not exhibit a statistically sig-

niﬁcant difference in any of the evaluated cases. For

detailed statistical evaluation see Table 1. The dis-

tribution of values of the new variability quantiﬁer is

shown in Figure 4.

4 DISCUSSION

We tested and veriﬁed a new method of gait variability

assessment that is derived from the geometric prop-

erties of cyclograms. To our knowledge, this is the

ﬁrst report of the use of symmetry quantiﬁcation tech-

niques to evaluate stride-to-stride ﬂuctuations.

The results obtained by this novel approach

showed a discriminative ability between evaluated

subjects groups. Hausdorff et al. (Hausdorff et al.,

1998) revealed increased gait variability in PD. Our

results are not inconsistent with his ﬁndings. In con-

trast to their work dealing with relative changes in gait

parameter variability, our work focused on absolute

change in gait cycle variability. Normalization can

be included in signal preprocessing to achieve rela-

tive change in gait variability. Moreover, they anal-

ysed the gait cycle timing while our work deals with

rotational properties of gait. Our results conﬁrm that

medication has an effect on gait variability in PD as

was also mentioned in a previous study (Bryant et al.,

2016).

The advantage of our approach to gait variability

assessment is the analysis of an entire gait cycle un-

like the calculation of coefﬁcients, which are mainly

used for quantiﬁcation of a gait cycle at a speciﬁc

time. Thus, this method can be employed on any

gait signal regardless of precisely predeﬁned events,

e.g. double support phase. The other advantage of

this method is the uniform approach to gait variabil-

ity in all movement direction and thus, the possiblity

of comparing the impact of a disease or pathology

on movement in different directions can be applied.

The analysis of variability in various movement di-

rections can reveal new knowledge and clinical inter-

pretations.

Another potential of this method is that it is a gen-

eral approach to signal variability analysis that can be

employed in other areas of cyclic movement analysis,

e.g. ﬁnger tapping test, stairs ascending/descending,

stand-to-sit-to-stand tests.

Different methods quantify different aspects of

gait variability and work with various spans of gait

signal length, e.g. number of gait cycles. By intra-

subject signal normalization to the same length when

utilized method of cyclograms the result is unaffected

by gait cycle duration. Next, the selection of an ap-

propriate method for speciﬁed research or clinical aim

is crucial in gait variability assessment (Chau et al.,

2005). Therefore, this new approach to gait variability

assessment is not a replacement of existing methods

but is complimentary.

There are limitations to our study. The most im-

portant one is that the sample of the subjects probably

is not representative of the larger population. How-

ever, to verify the ability of the proposed method to

assess gait variability in this preliminary study, a sam-

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130

Table 1: Statistical evaluation of variability via similarity measures. * differences signiﬁcant at the Holm-Bonferroni-corrected

level of p < 0.05 (for 4 tests performed).

Norms vs PD ON Norms vs PD OFF PD ON vs PD OFF

vertical

0.45 0.26 < 0.01∗

horizontal

0.90 0.33 0.12

sagittal

< 0.01∗ < 0.01∗ 0.05

kωk 0.03 < 0.01∗ < 0.01∗

ple of subjects is sufﬁcient. A second limitation in

this study is the number of measurements made of

each subject. Some patients had stability problems, as

is common in these patients, therefore only a limited

number of instrumented tests could be performed to

ensure that patients remained in a stable motor state.

5 CONCLUSIONS

This paper introduced and tested a new method of

stride-to-stride ﬂuctuation using synchronized cyclo-

grams. The variability indicator is based on similarity

assessment of gait cycles. We can designate that this

method is suitable for the evaluation of gait variabil-

ity in practice. The proposed method is not limited

to gait variability assessment and would be beneﬁ-

cial in different areas of cyclic movement variability

analysis. The quantitative analysis of wave form may

bring new knowledge of the variability with respect to

movement disorders.

ACKNOWLEDGEMENTS

This work was supported by Ministry of Health of the

Czech Republic, AZV Grant no. 16-28119a ”Analy-

sis of movement disorders for the study of extrapyra-

midal diseases mechanism using motion capture cam-

era systems”.

REFERENCES

Blin, O., Ferrandez, A., and Serratrice, G. (1990). Quanti-

tative analysis of gait in parkinson patients: increased

variability of stride length. Journal of the Neurologi-

cal Sciences, 98(1):91 – 97.

Brach, J. S., Berlin, J. E., VanSwearingen, J. M., Newman,

A. B., and Studenski, S. A. (2005). Too much or too

little step width variability is associated with a fall his-

tory in older persons who walk at or near normal gait

speed. Journal of NeuroEngineering and Rehabilita-

tion, 2:21–21.

Bryant, M. S., Rintala, D. H., Hou, J., Collins, R. L., and

Protas, E. J. (2016). Gait variability in parkinson’s

disease: levodopa and walking direction. Acta Neuro-

logica Scandinavica, 134(1):83–86.

Chau, T., Young, S., and Redekop, S. (2005). Manag-

ing variability in the summary and comparison of gait

data. Journal of NeuroEngineering and Rehabilita-

tion, 2:22–22.

Goswami, A. (2003). Kinematics quantiﬁcation of gait

symmetry based on bilateral cyclograms. In P, M., B,

W., and Dunedin, Y. T., editors, Proceedings of XIX

Cong Int Soc Biomech, pages 34–43.

Grabiner, P. C., Biswas, S. T., and Grabiner, M. D. (2001).

Age-related changes in spatial and temporal gait vari-

ables. Archives of Physical Medicine and Rehabilita-

tion, 82(1):31–35.

Grieve, D. (1968). Gait patterns and the speed of walking.

Biomedical Engineering, 3(3):119–122.

Hausdorff, J. M. (2005). Gait variability: methods, model-

ing and meaning. Journal of NeuroEngineering and

Rehabilitation, 2(1):19.

Hausdorff, J. M., Cudkowicz, M. E., Firtion, R., Wei, J. Y.,

and Goldberger, A. L. (1998). Gait variability and

basal ganglia disorders: Stride-to-stride variations of

gait cycle timing in parkinson’s disease and hunting-

ton’s disease. Movement Disorders, 13(3):428–437.

Hausdorff, J. M., Forman, D. E., Ladin, Z., Goldberger,

A. L., Rigney, D. R., and Wei, J. Y. (1994). Increased

walking variability in elderly persons with congestive

heart failure. Journal of the American Geriatrics So-

ciety, 42(10):1056–1061.

Hausdorff, J. M., Herman, T., Baltadjieva, R., Gurevich, T.,

and Giladi, N. (2003). Balance and gait in older adults

with systemic hypertension *. American Journal of

Cardiology, 91(5):643–645.

Hoskovcov

a, M., Du

sek, P., Sieger, T., Bro

zov

a, H.,

arubov

a, K., Bezd

cek, O.,

Sprdl

ık, O., Jech, R.,

Stochl, J., Roth, J., and R

cka, E. (2015). Predicting

falls in parkinson disease: What is the value of instru-

mented testing in off medication state? PLOS ONE,

10(10):1–13.

Jamour, M., Becker, C., Synofzik, M., and Maetzler, W.

(2012). Gait changes as an early indicator of de-

mentia. Zeitschrift f

ur Gerontologie und Geriatrie,

45(1):40–44.

Kaipust, J. P., Huisinga, J. M., Filipi, M., and Stergiou, N.

(2012). Gait variability measures reveal differences

between multiple sclerosis patients and healthy con-

trols. Motor Control, 16(2):229–244.

Kutilek, P., Viteckova, S., Svoboda, Z., Socha, V., and

Smrcka, P. (2014). Kinematic quantiﬁcation of gait

asymmetry based on characteristics of angle-angle di-

agrams. Acta Polytechnica Hungarica, 11(5):25–38.

A New Approach to Gait Variability Quantiﬁcation using Cyclograms

131

Menz, H. B., Latt, M. D., Tiedemann, A., Kwan, M. M. S.,

and Lord, S. R. (2004). Reliability of the gaitrite



walkway system for the quantiﬁcation of temporo-

spatial parameters of gait in young and older people.

Gait & Posture, 20(1):20 – 25.

Salarian, A., Horak, F. B., Zampieri, C., Carlson-Kuhta, P.,

Nutt, J. G., and Aminian, K. (2010). itug, a sensitive

and reliable measure of mobility. IEEE transactions

on neural systems and rehabilitation engineering : a

publication of the IEEE Engineering in Medicine and

Biology Society, 18(3):303–310.

Wall, J. C., Bell, C., Campbell, S., and Davis, J. (2000).

The timed get-up-and-go test revisited: Measurement

of the component tasks. Journal of rehabilitation re-

search and development, 37(1):109 – 114.

BIOSIGNALS 2018 - 11th International Conference on Bio-inspired Systems and Signal Processing

132