Analyzing gastrocnemius EMG-activity and1

sway data from quiet and perturbed standing2

Frank Borg a,∗, Maria Finell b, Ismo Hakala a and Mika Herrala a3

aUniversity of Jyvaskyla, Chydenius Institute, POB 567, FIN-67101 Karleby,4

Finland.5

bFysiofinex, Storgatan 14, FIN-68600 Jakobstad, Finland6

Abstract7

In an experiment we combined force plate measurements and surface EMG in8

studying quiet and perturbed standing, involving MS (Multiple sclerosis) and con-9

trols. The aim of this paper is to report the results thus obtained on the relation10

between filtered gastrocnemius (GA) EMG and the anterior-posterior center-of-11

pressure (A/P COP) coordinate. The main finding is the good correspondece be-12

tween A/P COP and the filtered GA EMG in the low frequency range. The EMG13

envelope was calculated using a zero-lag filter. Combining this with time shifts14

around 250 – 350 ms produced a high correlation (85.5 ± 8.4%) between the GA15

EMG envelope and the A/P COP. This EMG-COP relation was closest when us-16

ing a low cut-off frequency value around 1 Hz in calculating the EMG envelope.17

Based on this filtering procedure we estimated the average EMG-COP time shift to18

be 283 ± 43 ms between the GA-EMG envelope and A/P COP (which ”lags” be-19

hind EMG envelope). This shift is consistent with the 1 Hz cut-off and phase shift20

produced by a corresponding critically damped second order filter, and is about21

twice the corresponding twitch time. These results suggest that GA is to a large22

extent responsible for the phasic control of the anterior-posterior balance during23

quiet standing. A small difference was found between mean time shift thus obtained24

for controls (n = 4) and MS (n = 6) while sway area showed a major difference (p <25

0.01). The paper also compares three alternative filters for numerical calculation of26

the EMG-envelope. (Published as DOI: 10.1016/j.jelekin.2006.06.00)27

Key words: Center-of-pressure, Quiet standing, EMG-force relation,28

Gastrocnemius, Electromechanical Delay29

PsycINFO: 2540, 233030

∗ Corresponding author. Fax: +358 6 8294 295.Email address: borgbros@netti.fi (Frank Borg).

Preprint submitted to Elsevier Science 14 March 2009

1 Introduction1

Quiet and perturbed standing have been researched by many groups over the2

years using force plates, video-based systems, EMG, and more recently also3

ultrasound. These studies have revealed that quiet standing (QS) involves4

a complex muscular dynamics in order to stabilize the basically unstable hu-5

man inverted pendulum (HIP). As has been argued i.a. by Loram et al [12, 11]6

the compliance of the tendon makes it difficult to maintain posture using a7

simple stiffness control. A constant adaptive muscle control is thus needed.8

Since during QS one is leaning a bit forward, the main stabilizing action9

in the sagittal plane is maintained by the plantar flexors (pulling the body10

backwards against gravity). This showed up in the tests by the low tibialis11

anterior (TA) activity during QS. One of our interests has been to try to12

relate the various sway-parameters used in posturology based on force plate13

data to physiological correlates; that is, to provide some physiological inter-14

pretation making the clinical use of the parameters perhaps more transparent.15

The combined force plate and EMG-measurements reveal that the anterior-16

posterior COP-coordinate and the GA-EMG are closely related (see sec. 3.3).17

This means that the A/P COP-coordinate can in part be interpreted in terms18

of the GA-activity. Naturally the whole triceps surae group is involved in the19

plantar flexor activity, but GA may have a central role for the phasic control20

of balance. The GA and A/P correlation has been observed earlier, at least21

as far back as Mulavara et al [16]. Here we show that properly (zero-phase)22

filtered GA EMG and A/P COP time series are quite similar – they are not23

merely statistically correlated – making it possible to calculate a time shift24

between them. GA-EMG and A/P COP data may therefore shed light on the25

EMG-force relation. We compare alternative methods for filtering and calcu-26

lating the EMG-envelope and how they affect the time shift. We discuss the27

interpretation of the time shift and how it might relate to the EMG-fore rela-28

tion, the visco-elastic properties of the muscle-tendon unit and the so-called29

electromechanical delay (EMD).30

Note that we have used the concept of ”time shift” instead of ”phase shift”.31

This is because the relation between the zero-lag EMG-envelope and the A/P32

COP is indeed of the form of a time shift t → t − τ , and because we have33

chosen to express the shift in terms of time instead of phase. However, using a34

causal filter, such as the critically damped filter, the ”shift” is indeed related35

to a phase shift as described below (see Eq.(9)). For the causal filter described36

below, the ”twitch time” τc is related to the ”time shift τ” by τ = 2τc in the37

low frequency bandwidth (f < fc). The twitch time corresponds to the time38

for the impulse response function to reach maximum, and is sometimes also39

referred to as ”contraction time” [21]. The calculation of shift time may be40

thus considered as a way of obtaining an estimate of the twitch time.41

2

A group of controls and an MS-group were involved in the study in order to1

have groups with clearly different balancing abilities. There seems to be only2

a relatively few published studies on the static balance and posturological pa-3

rameters for MS [see e.g. 4, 5, 6]. One could also use groups of young versus4

elderly, but in the case of MS we may have a better idea of the key physio-5

logical differences involved. MS may for instance affect the balance feedback6

mechanism through increasing the feedback delay. Indeed, the big difference7

found in sway areas between MS and controls indicates some important differ-8

ence in the feedback systems. As we find only a minor difference in the shift9

time this suggests that the time shift largely reflects the EMG-force relation.10

Besides the standard eyes open (EO) and eyes closed (EC) quiet standing11

tests we also performed a perturbation test since it was assumed to amplify12

the difference between MS and the controls.13

Finally, the findings on the EMG-force relation are of importance if one wants14

to develop models of the postural feedback system since the control system15

must be adapted to the fact that the force continues a while after the control16

signal ceases.17

2 Methods18

2.1 Participants19

Participants in the tests were adult volunteers from the local MS-society di-20

agnosed with multiple sclerosis (MS) (n = 6, 1 male/ 5 females), and neu-21

rologically intact people (office workers) (n = 4, 1 female/3 males). All the22

participants have signed their informed consent. Average body mass for the23

participants was 74.8 ± 14.2 kg, length 171.8 ± 8.5 cm, body mass index24

(BMI) 25.2 ± 3.3 (range 19.1–30.8) and age 42.5 ± 2.3 years (range 21–64).25

The average age of the MS participants (47.8 yr) was somewhat higher than26

for the controls (36.7 yr). Use of medication, eye-glasses, and similar factors27

that could affect the performance were noted. The MS participants were at the28

time highly functional although there were in some cases history of diplegia.29

Times of first diagnosis of MS were between 1 to 14 years back. Typical symp-30

toms reported were fatigue and weakness in the limbs and for this reason the31

measurement time was chosen to be 40 s instead of the usual 1 minute dura-32

tion. All except one MS-participant (participant number 6) reported weakness33

or fatigue (left or right lower limb). In terms of Kurtzke’s EDSS scale they34

were all judged to be in the 0–4.5 range. Participants are numbered 1–10 with35

1–4 comprising the controls, and 5–10 comprising the MS-group.36

3

2.2 Procedures1

The test protocol comprised 9 trials: 6 quiet standing measurements with al-2

ternating eyes open (EO) and eyes closed (EC) condition, and 3 trials with3

perturbation (and EO). We used three trials per condition for statistical rea-4

son. The same alternating EO-EC order was used for everyone for equalizing5

the conditions and for convenience. All the trials were of 40 s duration. The6

foot stance was standardized with 30 degree angle (splay) between medial7

sides of the feet and a heel-to-heel distance (clearance) of about 2 cm (the8

toes-out position also probably enhances the medial GA activity). The arms9

were held in a relaxed position on the sides. The participants were instructed10

to keep the gaze on a 7 cm × 7 cm spot (sticker) on the wall 3 m ahead.11

The perturbation test was performed using a 1.4 kg mass suspended by a wire12

over a pulley and attached to the person from the back side to the thorax13

just below the scapulae approximately at the Th9-Th10 level (this will corre-14

spond to a perturbing torque around 1.4 kg × 9.81 m s−2 × 1.1 m ≈ 15 Nm).15

About 5 seconds after commencing the measurement a thin thread connect-16

ing the weight and the wire was cut releasing the weight. The computer test17

log shows that the sessions lasted on the average around 20 minutes, while18

the preparations took typically 30 minutes per person. The participants were19

allowed to rest between the trials if needed (longest recorded rest was 5 min).20

2.3 Data acquisition21

COP-data has been obtained using a conventional force plate (Hur Co, www.22

hur.fi) with 4 × 50 kg unidirectional force transducers. The accuracy of the23

force plate is mostly affected by electronic noise. Measuring with a constant24

(calibration) weight results typically in a (Gaussian) COP-fluctuation with a25

standard deviation of 0.3 mm. Surface EMG-measurements were made with26

Noraxon Myosystem 1400 (www.noraxon.com). The amplified outputs of the27

force plate and the Myosystem (signal from its rear D25-connector whose gain28

is preset to 1000 and high-pass cut-off to 10 Hz) were connected in parallel29

to a National Instrument (www.ni.com) 16 bit AD-card model PCI-6036E in-30

terfacing an ordinary PC. According to information from Noraxon the extra31

delay due to the processing by the Myosystem is maximally around 0.5 ms.32

The measurement software was programmed using the National Instruments33

Labwindows CVI tool. EMG and force data were simultaneously sampled with34

the rate of 1000 samples per second (S/s). Force data was smoothed taking35

consecutive 10-point averages resulting in an effective sampling rate of 100 S/s.36

The force data was finally converted to COP-x (medial-lateral) and COP-y37

(anterior-posterior) coordinates and the total vertical force Fz, which were38

saved along with the raw EMG-data (1000 S/s). In six instances the perfor-39

4

mances in the perturbation tests were filmed from the right side (stationary1

video camera) in order to be able to later check whether the participants2

made some extra movements (this occurred only for two participants with a3

more progressed form of MS who occasionally showed some upper limb bal-4

ance reactions). For the EMG-measurements eight channels were used with5

the electrode locations listed in Table 1. The reference electrode was placed6

on left malleolus medialis. Surface Ag/AgCl electrodes (Ambu ”Blue Sensor7

M”, M-00-S, www.ambu.com) were arranged using the standard bipolar config-8

uration, with placements and skin preparations made in accordance with the9

SENIAM recommendations [8]. The skin-electrode impedance was checked in10

each case with a multimeter and was found to vary with the person and the11

location typically in the range of 4 to 8 kOhm (”worst” case had 80 kOhm).12

In this paper we will mainly analyze the medial gastrocnemius EMG. Tibialis13

EMG was generally quiet except in the beginning of the perturbation trials (in14

some cases) when the perturbation mass was pulling on the participant while15

the dorsal flexors resisted the tug. Multifidus (MF) was included in order to16

check its activity in the perturbation tests, the MF-signal appears however to17

be prone cardiac interference.18

2.4 Data analysis, EMG19

The collected data was analyzed using our custom C-programs (Labwindows20

CVI) and Mathcad programs (www.mathsoft.com). A zero lag filter was de-21

signed by first rectifying the EMG, then applying Fast Fourier Transformation22

(FFT), which was multiplied by a real (zero-phase) low-pass (LP) filter factor,23

and finally inverse FFT was applied in order to obtain the filtered signal s(t).24

Mathematically the filtering emg(t) → s(t) can be described by the following25

steps (a modified ”Butterworth zero-lag” low-pass filter, here denoted BW0),26

x1(t) = |emg(t)| . . . rectification (1)

x2(t) = x1(t) − 〈x1〉 . . . subtracting the mean (2)

x2(f) =∫ ∞

−∞e−i2πftx2(t)dt . . .Fourier transform (3)

x3(f) =1

1 +∣

∣

∣

f

fc

∣

∣

∣

nf· x2(f) . . .filtering (4)

s(t) =∫ ∞

−∞ei2πftx3(f)df . . . inverse Fourier transform. (5)

Here fc denotes the LP cut-off frequency. Note that the rectification step27

Eq.(1) is analogous to the rectification procedure for amplitude modulated28

(AM) radio signals which brings out the superimposed low-frequency sound29

5

signal. Similarly for EMG, the rectification enhances the low frequency content1

of the signal. Best fit (in terms of degree of maximal correlation) between A/P-2

COP and filtered GA-EMG was obtained with fc around 1 Hz and the order3

nf ≥ 2. In the calculations we adopted nf = 4. This is not a very sensitive4

parameter as long as nf ≥ 2. In order to fit filtered GA-EMG s(t) to the A/P5

COP data y(t) we have to introduce a time shift or ”delay” τ such that6

y(t) ≈ C · s(t − τ), (6)

for some ”calibration constant” C. The cross-correlation technique is a stan-7

dard method for determining time/phase shifts between signals, and the result8

for EMG-COP in terms of the time shift τ was between 250–350 ms. While the9

above filter was adopted chiefly for mathematical convenience and good cor-10

relation, there is a well known filter loosely based on a muscle model. This is11

the filter corresponding to a second order critically damped system (hereafter12

abbreviated as CRIT2) to be used in step 5 of the BW0-transformation13

h(t) =1

(

1 + i f

fc

)2 (frequency domain) (7)

h(t) =t

τ 2c

e−ttc (time domain) (8)

where t > 0 and 2πfc =1

τc

.

The form of the Eq.(7) with fc = 2.5 Hz has been suggested by Soechting and14

Roberts [19] and later evoked by Basmajian and Luca [1]. It has recently been15

used by Wrbaskic and Dowling [26] in an EMG-driven model. Soechting and16

Roberts [19] introduced the transfer function in Eq.(7) ”to provide a common17

reference for purpose of comparison”. It was based on data obtained by cyclic18

isometric contraction of biceps brachii using a force-feedback instrumentation19

setup. For frequencies f below fc = 1 Hz this filter predicts an almost constant20

delay21

∆t(f) = − 1

2πfarctan

(

2f/fc

1 − (f/fc)2

)

, (9)

which for small f is around - 1/(πfc) yielding a time shift around 318 ms with22

fc = 1 Hz (the contributions from the components f > fc are suppressed). This23

model seems thus to predict the right size of the observed time shift. A further24

observation regarding Eq.(8) is that the filter in time domain corresponds to25

taking a weighted average of the rectified EMG using a window with a size26

6

of the order of τc = 1/2πfc (≈ 159 ms). (Thus note that the twitch time is1

around half the time shift.) In fact the time-version of the BW0-filter in case2

of nf = 4 is given by3

h(t) =π√2

[

sin(√

2πfct)

sign(t) + cos(√

2πfct)]

e−√

2πfc|t|, (10)

where the sign-function is defined by sign(t) = 1 (-1) if t > 0 (t < 0), and 04

otherwise. It means that the EMG-envelope at time t0 is the weighed average5

of rectified EMG in a time interval of the order of tc = 1/(√

2πfc

)

around t0.6

For fc = 1 Hz this characteristic time becomes tc = 225 ms. This suggests one7

could use the traditional RMS-filter (note that this is centered on the time8

t + T/2),9

RMS(t) =

√

1

T

∫ T+t

temg(u)2du. (11)

Indeed, one obtains a fairly good correlation between filtered GA-EMG and10

A/P COP using RMS with the time window T ≈ 300 ms (not a critically11

sensitive value). T can be estimated theoretically by finding the square filter12

of length T which most closely fits the filter Eq.(8). This leads to T = α/2πfc13

where α ≈ 1.793 is the positive solution of the equation 1+ z + z2 = ez. (This14

equation derives from maximizing the correlation between of a T -square filter15

with the filter Eq.(8) with respect to the width T .) Thus, with fc = 1 Hz we16

obtain T = 285 ms. We have also made cursory uses of the classical EMG17

parameter defined as the EMG-turns [24]. The idea is that the turn rate may18

give a useful measure of neuro-muscular activity and thus correlate with the19

muscular force. In our case we first calculated the standard deviation σ of raw20

EMG, and then calculated the times ti for every consecutive crossings of the21

EMG amplitude above some multiple γσ of σ and below -γσ using γ = 2.5.22

From this array ti we get the turns per time unit by forming its histogram23

whose time-resolution ∆t will consequently depend on the number of bins B24

and the duration T of the measurement (40 s in our case), ∆t = T/B. Thus,25

for T = 40 s and B = 80 we get a time resolution of 500 ms.26

As a final method we have also calculated the (complex) coherence, which for27

two time series x and y is here defined by,28

Coh(x, y)(f) =〈x⋆(f)y(f)〉

√

〈|x(f)|2〉√

〈|y(f)|2〉(12)

at the frequency f with 〈. . . 〉 denoting a statistical averaging. In our case the29

averaging was obtained by dividing the time series into sections of 10 sec-30

7

onds (corresponding to a frequency resolution of 0.1 Hz) with 50% overlap,1

calculating the Fourier-transform and their products for these sections and fi-2

nally averaging over all the sections. If x is related to y by a transfer function3

H , then Coh(x, y)(f) = H(f)/|H(f)| = exp (iφ(f)). A time shift τ can be4

calculated from the phase φ thus defined by 2πτ = dφ(f)/df . This was nu-5

merically evaluated by calculating the slope of the phase φ(f) in the frequency6

interval 0.1–1.0 Hz. Coherence is related to correlation by the fact that the7

inverse Fourier transformation of 〈x⋆(f)y(f)〉 = H(f)〈|x(f)|2〉 (in the linear8

case) produces the correlation function. In practice one has also to consider9

the influence of ”noise”.10

2.5 Data analysis, COP11

In this paper we will mostly be interested in the anterior-posterior (A/P) sway12

since this part can be quite well modeled using the human inverted pendulum13

model, and in this case the plantar flexors, whose activity is comparatively easy14

to measure, are to a large degree responsible for the motion. The COP-data15

consists of pairs of coordinates (xi, yi) with x standing for the medial-lateral16

coordinate (positive toward ”the east”), and y for the A/P COP. If we have17

N points then the ”C90” sway area A is defined by18

A =4.605π

N − 1

√

√

√

√

∑

i

(xi − 〈x〉)2∑

i

(yi − 〈y〉)2 −(

∑

i

(xi − 〈x〉)(yi − 〈y〉))2

. (13)

Here 〈x〉 =∑

i xi/N , etc. This particular definition of sway area is motivated19

by the fact that, if the variables x and y are Gaussian, then about 90% of the20

COP-points will lie inside an ellipse (the 90% confidence region) with an area21

A. The coordinates x and y are expressed in units of mm and the area in units22

of mm2. For the perturbation test data we dropped the first 10 seconds and23

used only the remaining 30 seconds of the ”recovery” phase for computing the24

sway area.25

While sway area is a space/time based parameter there is an S-parameter [22]26

based on the power spectrum of COP in the band 1 - 10 Hz. This is obtained27

by fitting the power spectrum of A/P COP (or M/L COP) to a power in terms28

of the frequency f ,29

|y(t)|2 ∝ 1

fS(f in the interval 1 - 10 Hz), (14)

8

where y denotes the Fourier-transform of A/P COP data y. A large S-parameter1

indicates that the high frequency components are suppressed.2

3 Results3

3.1 Sway area, QS-case4

One of our initial purposes of the force plate measurements was to obtain5

further data in order to test how various sway-parameters could reveal possible6

MS vs ”normal” differences. EMG-measurements were added in the hope that7

they would shed light on the muscular dynamics during quiet and disturbed8

standing. In the case of MS, which afflicts the central nervous system (CNS)9

by local degeneration of the myelin sheath (demyelation), the impoverished10

neural transduction properties (e.g. lower conduction velocities) suggest that11

the balance feedback control may be impaired. This is indicated by Fig.1 giving12

an overview of the test results showing the sway area with six QS-trials per13

participant in an alternating order EO-EC-EO . . . beginning with the sets by14

the four controls (1–4), followed by six MS-participants (5–10). Thus there are15

10 × 6 = 60 trials in all displayed. For the set 1 (a control participant) the16

results makes it look like it could belong to the MS-group while the set 6 (an17

MS-participant) might be classified as ”normal”. One may note that (control)18

participant 1 had the highest BMI-value and also reported poor eyesight, while19

MS-participant 6 had been diagnosed with MS only a year before. One peculiar20

feature that sets off the MS-group is that the EC-area is always larger than the21

EO-area for consecutive trials. This is in particular true for MS-participant 622

but not for control 1. On the group level the average eyes closed (EC) sway23

area for controls and the MS-group are 165 ± 107 mm2 (control, EC) and 63324

± 281 mm2 (MS, EC). The ratio between the average values is thus around25

3.8, a statistically significant difference on the group level. If we compute the26

average sway area for each person and for the QS/EC condition, and apply27

the Wilcoxon’s rank test [17, p.496] for the MS and the control groups, then28

their area distributions are found to be different with p < 0.01.29

3.2 Sway area, perturbed case30

The sway area was calculated for the perturbation tests by dropping the first 1031

seconds of the data; thus, only the ”recovery” phase is included. The perturba-32

tion tests show an even greater difference between the controls and MS-group33

(see Fig. 2). The medians of the sway area are 105 mm2 (control) and 691 mm234

(MS) with a ratio 1:6.6. An interesting feature is that for the MS-participants35

9

5, 7, 8 and 10 the sway area increases with each perturbation. We may note1

that the MS-participant 9 had an exceptional long break (5 min) between the2

first and the second perturbation which may have contributed to a smaller3

sway area in the second trial. The MS-participant 6 who shows a reverse4

trend was also the only MS-participant not reporting any fatigue problems.5

We mention these observations because an increase of sway area during re-6

peated perturbations tests could provide a basis for a potential neuro-muscular7

Fatiguability Index applicable to MS. Such an Index could be of interest in8

early detection or assessment of MS-progression [23, 4]. Besides fatigue one9

has also to reckon with another possible contributing factors; the fact that in10

neurogenic diseases the neuro-muscular system may have problems to adapt11

to, and anticipate, perturbations.12

The QS and perturbation sway area results indicate a significant difference13

in the balancing ability between the controls and the MS-group which raises14

the question whether a corresponding ”intrinsic” difference can be seen in the15

EMG-data. We may also note that counteracting the weight pulling, using16

dorsal flexion, was not the typical strategy. The tibialis was mostly quiet – see17

Fig.3 which shows a section of data before and after the perturbation. Instead18

the participants seemed to lean forward and let gravity do the job.19

3.3 EMG vs COP20

The A/P COP-y is almost proportional to the torque T vis-a-vis the ankle21

joints (in the sagittal plane), and thus the muscular force, since we have ac-22

cording to the human inverted pendulum model [10],23

T = yFz + ζFy ≈ ymg + ζmY ∼ ymg. (15)

Here Fz denotes the total vertical ground reaction force (GRF) (deviates from24

the weight mg of the person by less than 1% in the case of QS), Fy is the25

GRF in the y-direction (which by Newton’s equation is equal to mY where26

Y is the center-of-gravity coordinate of the person along the y-direction), and27

ζ is the distance of the ankle joint from the force plate (around 8 cm). As28

indicated the term ymg usually dominates the sum in Eq.(15). The reason is29

that y (the position of COP measured from the ankle joints in the anterior30

direction) is a positive quantity due to a forward leaning position during QS31

with an average value typically around 5 cm, while the magnitude of the32

acceleration (around the order of 1/100–1/10 m s−2) is much less than the33

gravitational acceleration g ( ≈ 9.81 m s−2). From this we may expect – since34

EMG correlates with muscular force – that the EMG measured from plantar35

flexors should correlate with A/P COP. In fact, in many instances there is36

10

a good resemblance between the A/P COP and the GA-EMG envelope as1

demonstrated by Fig.4. The EMG-envelope is calculated using the BW0-filter2

Eq.(1–5) as described above, with the contributions from both legs summed,3

and the result plotted setting the ”calibration constant” equal to 1 (”1 mm4

per µV”). If we enlarge a section of the figure we can see (Fig.5) that there is a5

systematic time shift between A/P COP and the GA-EMG envelope which in6

this case is somewhere in the range of 250–300 ms. This time shift corresponds7

to the time τ in Eq.(6). In Fig.4 we have included the EMG-turns which is also8

seen to reflect the overall pattern of the A/P COP. However, the EMG-turns9

are somewhat problematic to use for time shift calculations because of the10

low time resolution – if one increases the time resolution one tends to loose in11

terms of correlation with A/P COP.12

3.3.1 Time shifts13

We have calculated the correlations and the time shift for all trials, including14

the perturbation trials, making 10 × 9 = 90 trials in all. The results are15

presented in Figs.6-7. As can been seen the GA-EMG vs A/P COP correlation16

stays, with a few exceptions, within the range 80%–100%, while the time17

shift is in the range 250–350 ms. The ”anomalies” in cases of trials nos. 7618

and 78 (corresponding time shifts go ”through the roof”) seem to be due to19

some limitation of the algorithm rather than a lack of an EMG-COP relation.20

(Indeed, plotting the A/P COP vs the GA-EMG envelope, delayed by 320 ms21

– which was found to maximize the correlation for trial no. 78 – we found22

that the points tend to cluster in two groups instead of a single one. This23

contributes to the overall low correlation value though the curves have quite24

similar shapes.) Calculating the average correlation and time shifts excluding25

the two ”anomalous” cases we get 283 ± 43 ms (shift) and 85.5 ± 8.4%26

(correlation). Calculating the time shift separately for the groups we get 29427

± 43 ms (MS) and 266 ± 36 ms (controls). (If we calculate the average time28

shift for each person and apply the Wilcoxon’s rank test to these values then29

the MS and control distributions are deemed to be significantly different on30

the level p = 0.03.) In the case we use fc = 2.5 Hz in the BW0-filter instead31

of fc = 1 Hz the average time shift and correlation (MS + control) become32

236 ± 36 ms and 77.2 ± 9.4%; that is, a decreased correlation, and the time33

shift value no longer relates well to 1/πfc (= 127 ms).34

We have also made calculations using the CRIT2 filter Eq.(7) with fc = 1 Hz35

resulting in the correlation 78.5 ± 12.2% and time shift 22.6 ± 29.6 ms (we36

have again dropped the trial no. 78). The results are summarized in the Table37

2. The comparatively small residual time shift when using the CRIT2-filter38

Eq.(7) shows that it can account for a significant part of the time shift between39

A/P COP and GA-EMG. Tuning the cut-off frequency 10% downwards to40

0.9 Hz reduces the average shift discrepancy still further as shown by the41

11

table. The table also gives results of calculating (again dropping trial no. 78)1

with the RMS-filter. The window T = 285 ms corresponds to an ”optimal”2

approximation of the CRIT2-filter Eq.(7) with fc = 1 Hz. The time shift values3

obtained here can be contrasted with the value of 155 ± 46 ms reported by4

Masani et al [13] (n = 16, young males) for the time shift between zero phase5

filtered GA EMG and A/P COG calculated in a slightly different way (using6

fc = 4 Hz cut-off; this choice of the cut-off may account for circa 50 ms of the7

difference).8

3.3.2 EMG vs A/P COP in time domain9

Figure 8 gives an example how raw EMG (left medial gastrocnemius) may10

relate to A/P COP. (Right gastrocnemius showed in this case a weaker and11

less phasic signal.) This is from quiet standing (EO, participant 3). One can12

see how EMG ”drives” the A/P COP on the ascending side of the A/P COP13

”hills”. The A/P COP downhill parts reflect the turn-off EMD. A typical14

feature is also the burst like nature of EMG signal. In some cases one can15

find smaller amplitude recurrent burst repeating 7–10 times per second. (Kei16

Masani has made similar observation in his studies. Personal communication.).17

This was in one case even found in the RF-EMG though its EMG otherwise18

did exhibit no phasic activity.19

3.3.3 Coherence20

We have applied coherence calculation for A/P COP and GA EMG to the21

whole data set. In the first case we summed rectified EMG (as usual always22

subtracting the mean value first) from left and right GA producing an average23

coherence with A/P COP of the magnitude 80 ± 8% (range 56–93%) and a24

time shift (from the slope of the phase in the 0.1–1.0 Hz band) of 242 ± 6925

ms (range 94–430 ms). In a second case we summed the EMG envelopes of26

left and right GA based on the BW0 filter (1 Hz) which produced an average27

coherence with A/P COP of the magnitude 85 ± 7% (range 67–95%) and a28

time shift of 233 ± 62 ms (range 115–441 ms). Thus the average coherence29

time shift differs by ca 40–50 ms from the correlation time shift based on30

the BW0-filter. In general the magnitude of the coherence was around 80–31

90% in the frequency band 0.1–1.5 Hz while it for higher frequencies dropped32

markedly. These results demonstrate again that the major dynamic activity33

takes place around 1 Hz or below during quiet standing.34

12

4 Discussion1

4.1 EMG-COP time shift2

We have found the BW0-filter Eq.(1-5) to be an efficient filter for calculating3

an EMG-envelope which correlates fairly well with the torque in the quiet and4

perturbed standing cases using EMG from gastrocnemius. In combination with5

COP-data it can be used for determining the phase shift and the corresponding6

time shift between COP and EMG. What does this time shift τ consists in?7

We note that a filter like BW0 is a non-causal filter which in the time domain8

corresponds to taking a weighed average (see Eq.10); thus, the filtered value9

at time t0 depend on future EMG-values at times t > t0. For this reason10

(causality) a time shift of the form Eq.(6) is necessary. Otherwise A/P COP11

(or force/torque) would depend on future EMG-values. Therefore we expect12

the τ in Eq.(6) to be of the order of the time constant tc =(√

2πfc

)−1

in13

Eq.(10). Thus far we have only talked about a mathematical model. From14

the point of interpretation a more interesting fact is that the causal second15

order filter version Eqs.(7, 8) seems to be able to partially account for time16

shift and the A/P COP; that is, it may approximate an EMG-force model.17

Assuming this then the question arises about the physiological counterparts of18

this filter (a second order linear system). Three factors that come to mind are19

latency, electromechanical delay (EMD) associated with activation dynamics,20

and muscle-tendon properties associated with contraction dynamics [7].21

4.1.1 Electromechanical delay22

The ”electromechanical delay” (EMD) sometimes refers to the turn-on time23

which is defined as the time (latency) from the onset of EMG to the onset of24

the force, which may be about the order of 10 ms as e.g. reported by Mora et al25

[14] (among other things it depends on how one defines ”onset”, see Corcos26

et al [3]). There is also a lag associated with the turn-off defined as the time27

from the cessation of EMG to the cessation of the force, and this have been28

reported to be of the order of 100 ms [25, p. 254] or 160-200 ms [9]. The turn-off29

EMD is likely to be due to the chemical inertia of the Ca++-dynamics in the30

muscle and is related to the so called ”activation dynamics” [see e.g. 2, 18, 27,31

and references therein]. The role of the turn-off EMD tail is probably enhanced32

during quiet standing because of the silence of the antagonists (dorsal flexors).33

This may be one contributing factor to why the low 1 Hz cut-off provides34

good correlation between A/P COP and filtered EMG. The EMD lag is also a35

critical component in balancing the ”human inverted pendulum” (HIP) since36

the control must be adapted to the fact that the force continues after the37

”control signal” has ceased. Note that the characteristic time (period/(2 π))38

13

for the HIP for an adult is around 300 ms. Another important factor, as already1

mentioned, is the compliance of the tendon [15, 12, 11] which implies that the2

triceps surae must control the balance in a pulsative manner since it cannot3

lock the HIP in a fixed, slightly forward leaning position.4

One rough approach, in order to understand the turn-off EMD, is to assume5

that a pulse-like signal at t = 0 induces a force (twitch) which increase with6

a time constant τ1 while at about the same time there starts a process with a7

time constant τ2 which will reduce the force increase; i.e., the twitch is of the8

form9

h(t) =(

1 − e− t

τ1

)

e− t

τ2 . (16)

The function Eq.(16) generally illustrates a process involving a force increase10

with a time constant τ1, which will saturate and then decline as the chem-11

ical components generating the force decay (or are reabsorbed) with a time12

constant τ2. One point is that Eq.(16) in many cases, for all ”practical pur-13

poses”, may be indistinguishable from a CRIT2 transfer function Eq.(8). At14

first it may seem that Eq.(8) is obtained from Eq.(16) as an approximation15

by setting a = 1/τ1 and τc = τ2; however, a best fit (in the least mean square16

sense) leads to a more complicated relation. For instance, if we have τ1 = 5017

ms and τ2 = 100 ms then the best fit of the form Eq.(8) is given by the pa-18

rameters a = 47.1 (ms)−1 and τc = 69.3 ms. Using the approximation Eq.(8)19

of Eq.(16) two different time factors are reduced to one ”twitch” time τc. This20

case illustrates the fact that the sort of parameters and values one gets depend21

on the curve-fitting method. While the fitting using Eq.(8) may suggest why22

CRIT2 transfer functions in some cases may yield good approximations for23

EMG-to-force relations. Note that Winter [25], p. 209 quotes twitch times for24

medial gastrocnemius with values in the range 40–110 ms and with a mean25

value of 79 ms (corresponding to a frequency fc = 1/(2πτc) ≈ 2 Hz).26

4.1.2 Mechanical impedance effect27

Besides the activation dynamics may we expect influence of tendon properties28

on the resulting force measured. It is not always clear whether the tendon29

effects are included in the turn-off EMD and the twitch times. Anyway it is30

of interest to try to factor out the ”visco-elastic” component. Let us consider31

some of the salient features of a simplified model. As a hypothesis, suppose the32

contractile elements generate a force Fce determined by the level of activation33

which is measured by EMG. Assume that this force is transmitted to the bone34

via the tendon generating a tendon force Ftend = Fce + KDξce which is finally35

measured as A/P COP. Here ξce denotes the length of the contractile element36

and KD a ”viscosity” parameter (due to the ”parallel viscous element” of the37

14

force-velocity relation). Assuming further that the tendon force is given by1

KP (ξ − ξ0) (a linear relation for small amplitudes), where KP is the tendon2

stiffness and ξ is the tendon length, we obtain for the lumped inverted pendu-3

lum model and small A/P sway an equation of motion of the form (dropping4

a constant term)5

Ix +(

r2KP − mgL)

x = r2KP ξce. (17)

I denotes the body moment of inertia about to the lateral axis with respect6

to the ankle joint, r is the moment arm determined by r∆θ = ∆x for a small7

change in the sway angle ∆θ and corresponding change ∆x in the muscle-8

tendon unit (MTU) length. Using these relations one obtains for the transfer9

function between Fce and Ftend in the frequency domain (ω = 2πf),10

Ftend

Fce

=KP

KP + iωKDA−1, (18)

where we have used the abbreviations,11

A = 1 +r2KP

I (ω2 + Λ), (19)

and12

Λ =mgL − r2KP

I. (20)

Similarily one obtains the relation between the force Fce and muscle length13

ξce,14

ξce

Fce

= − 1

KP A + iωKD

. (21)

These relations involve a new characteristic time τimp = KD/KP .15

In order to get a manageable approximation we may consider the isometric16

case with x approximately constant. This corresponds to setting I = ∞ (A =17

1) in Eq.(18) which then simplifies in the time domain to the transfer function18

hmt(t) =1

τimp

e− t

τimp (t > 0). (22)

15

If we compose (convolute) this with the simplified EMG-force transfer function1

Eq.(8) we get2

htot(t) =T 2

⋆

τ 2c τimp

{

e− t

τimp + e−t

τc

(

t

T⋆

− 1)}

(t ≥ 0), (23)

where 1/T⋆ = 1/τimp−1/τc. To give an example of the effect of the impedance3

term on the total transfer function, assume that τimp = 50 ms and τc = 100 ms,4

then the transfer function Eq.(8) attains maximum at t = τc while the total5

transfer function htot(t) attains maximum at around t = 160 ms. Thus, the6

”mechanical impedance” contributes to the total transfer function by delaying7

the impulse response peak (in this case by about 60 ms). The total ”twitch8

time” of 160 ms would correspond to time shift of circa 2 × 160 ms = 320 ms in9

the low frequency end (f < fc). For the CRIT2-filter twitch time corresponds10

to the time for the impulse response function to reach the peak. We have not11

made direct measurements of the impulse response function, but Fig.3 may12

give an idea of such a function. It shows the reaction to the release of the13

perturbation weight. Determining the time for the A/P COP to reach the14

peak one obtains ca 160 ms and taking its double we get a value in a rough15

agreement with shift time values of the order of 300 ms. van Zandwijk et al16

[27] report an estimated average rise time (from 10% to 90% maximum force17

level) for triceps surae twitches to 142 ms which is comparable to 160 ms18

twitch time.19

The basic theoretical framework of Eq.(17) above seems to encompass some20

of the essential elements. It is similar to Eqs.(1, 2) in [12] except that we use21

lengths instead of angles. Observe that in [12] there is no explicit use of a ve-22

locity term, but their Eq.(9), giving the stiffness K as function of frequency f ,23

implicitely assumes that the tendon force is given by an expression of the form24

(convolution) Ftend(t) =∫

k(t − u)∆ξ(u)du where ∆ξ(u) is the extension of25

the tendon. Theoretically this covers also velocity dependent terms. Returning26

to Eq.(17) we see that, given Λ > 0 (compliant tendon), it predicts an anti-27

phase relation between contraction ξce and MTU length x as experimentally28

observed [12, 11]. The positivity of Λ implies also, according to these relations,29

that one cannot observe MTU ”resonance” in the QS case in contrast to the30

cyclic ankle bending case studied by Takeshita et al [20]. However, in order to31

explain the observed GA EMG–A/P COP shift values in the range of 250–30032

ms the above models seem to require gastrocnemius twitch times in the upper33

end of the observed ranges (100 ms), but this depends also on the contribution34

from the impedance.35

16

4.2 MS and controls difference1

Using a measure such as sway-area (trace-length would also work) a signifi-2

cant difference is found between MS and controls reflecting a generally poorer3

balance for MS. Since MS affects the CNS in a complex way it is hard to point4

to a single cause behind the impairment of balance. Possible culprits could5

be an impaired vestibular system and comprimised somatosensory feedback6

since MS contributes to delayed visual, auditory and somatosensory evoked7

potentials. One has also to reckon with secondary effects on balance e.g. due8

to increased fatiguability. As suggested this effect on balance might be used9

for measuring fatiguability.10

One general idea is that impaired balance may be related to a lack of rapid11

high frequency responses. Calculating the power spectrum exponents S for our12

data (A/P COP, quiet standing, eyes closed) we got S (control) = 3.34 ± 0.6113

and S (MS) = 3.84 ± 0.58, a not significant difference though. (According14

to the Wilcoxon’s rank test we get p = 0.08 whence the MS and control S-15

distributions are ”significantly” different only on the 8% level.)16

The small difference in the time shift values between the MS (294 ± 43 ms)17

and the control (266 ± 36 ms) lends support to the view that the time shift18

mainly reflects the EMG-force relation and to a lesser extent depends on such19

factors as the feedback loop (that may be compromised in MS).20

4.3 Conclusion21

As a part of analyzing the relation between gastrocnemius EMG and the22

anterior-posterior center of pressure we have described the details of a method23

for determining their time shift. This time shift is thought to reflect the EMG-24

to-force relation and the mechanical impedance of the muscle tendon system.25

The turn-off electromechanical delay probably accounts for most of the time26

shift. It remains though to detail the neuro-muscular chain which effects the27

balance control in order to be better able to factor the time shift into iden-28

tifiable physiological components. In future experimental studies it will be29

of interest to use more diverse and larger groups of participants in order in-30

vestigate to what extent, and in what way, the time shift is a function of31

biomechanical and anthropometric parameters. A further goal is to scrutinize32

the EMG-signal for patterns in the time domain which may shed some light33

on the nature of the balance control. There are also room for improvements34

in the methodology such as to use two force plates in order to separate the35

contributions from left and right leg. Additional kinematic sensors would also36

be useful for tracking limb and trunk movements.37

17

4.4 Acknowledgments1

This work was made possible by a project on Biosignals sponsored in large2

part by the Finnish Funding Agency for Technology and Innovation, TEKES3

(www.tekes.fi). We are indebted to Noraxon Co (www.noraxon.com, AZ,4

USA) and Dr Peter Konrad (Noraxon) EMG-measurement issues. CEO Mats5

Manderbacka (Hur Co, Finland, www.hur.fi) has contributed to the project.6

We also acknowledge support from Medirex Co (Finland). Thanks to Kei7

Masani (University of Toronto, IBBME Institute) for extended discussions8

on quiet standing and feedback control. Special thanks to the participants,9

and to Ms Linnea Luokkala, secretary of the regional (Central Ostrobothnia)10

MS-society.11

References12

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by electromyography., 5th edn. Williams & Wilkins14

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modeling: Estimation of muscle forces and joint momenta and movements16

from measurements of neural command. Journal of Applied Biomechanics17

20:367–39518

[3] Corcos DM, Gottlieb GL, Latash ML, Almeida GL, Agarwal GC (1992)19

Electromechanical delay: An experimental artifact. Journal of Elec-20

tromyography and Kinesiolology 2:59–6821

[4] Corradini ML, Fioretti S, Leo T (1997) Early recognition of postural22

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[11] Loram ID, Maganaris CN, Lakie M (2005) Active, non-spring-like muscle1

movements in human postural sway: how might paradoxical changes in2

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[12] Loram ID, Maganaris CN, Lakie M (2005) Human postural sway results4

from frequent, ballistic bias impulses by soleus and gastrocnemius. Jour-5

nal of Physiology 564.1:295–3116

[13] Masani K, Popovic MR, Nakazawa K, Kouzaki M, Nozaki D (2003) Im-7

portance of body sway velocity information in controlling ankle extensor8

activities during quiet stance. Journal of Neurophysiology 90:3774–37829

[14] Mora I, Quinteiro-Blondin S, Prot C (2003) Electromechanical assessment10

of ankle stability. European Journal of Applied Physiology 89:558–56411

[15] Morasso PG, Schieppati M (1999) Can muscle stiffness alone stabilize12

upright standing? Journal of Neurophysiology 83:1622–162613

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[17] Rade L, Westergren B (1998) Mathematics handbook., 4th edn. Stu-19

dentlitteratur20

[18] Ridderikhoff A, Peper CE, Carson RG, Beek PJ (2004) Effector dynamics21

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5 Full Table and Figure captions5

TAB1 The electrode placements. Reference electrode placed on the left mal-6

loleus medialis.7

TAB2 Listing of the A/P COP - EMG envelope correlations and the corre-8

sponding time shifts calculated using a selection of filters and parameters.9

Fig1 Sway area for quiet standing tests for the 10 participants (1–4 controls,10

5–10 MS). The trials are in the order EO, EC, EO, . . . , with 6 trials per11

participant (EO = eyes open, EC = eyes closed). We can see that that the12

MS-group is characterized be a significantly higher sway area in general.13

Another notable feature is that for the MS-group we have always EC-area14

> EO-area for sequential trials.15

FIG2 Sway area for quiet the perturbation tests for the 10 participants (1–416

controls, 5–10 MS). Three perturbation trials per person. Again the MS-17

group has a significantly higher sway area. We also note that 5, 7, 8 and 1018

in the MS-group the area increases with every perturbation.19

FIG3 Perturbation test. Curves from bottom up: medial gastrocnemius right,20

left, right tibialis anterior, and A/P COP. Around t = 5.2 s the ankle torque21

(A/P COP) starts to react to the release of the backward pulling weight.22

FIG4 Example of recording from a quiet standing trial (participant 3). From23

bottom up: Raw EMG (in units of 10 µV) from left medial gastrocnemius,24

A/P COP, EMG envelope and EMG turns (based on a 2.5σ-threshold and25

an 80-point histogram).26

FIG5 Enlargement of a section of the previous figure showing the shift be-27

tween the GA EMG envelope and the A/P COP.28

FIG6 Correlations between A/P COP and the GA EMG envelope (where29

contributions from left and right leg are summed) for all the 90 trials, in-30

cluding the perturbation tests. There are 9 trials per participant, 6 quiet31

standing trial in alternating order EO-EC-EO . . . plus 3 perturbation tests32

(EO). Trials 1–9 by participant 1, trials 10-18 by participant 2, etc.33

FIG7 Time shifts between GA EMG envelope and A/P COP for all the 9034

trials.35

FIG8 Raw GA-EMG (left) and A/P COP during quiet standing (EO). This36

basically illustrates the correspondence between EMG and force (A/P COP).37

One observes how EMG-activity drives the A/P COP which reverberates38

after EMG goes down.39

20

6 Tables & Figures1

Muscle placement

Tibialis anterior (TA) bilateral

Gastroc. medialis (GA) bilateral

Rectus femoris (RF) bilateral

Biceps femoris (BF) right

Multifidus (MF) right

Table 1The electrode placements. Reference electrode placed on the left malloleus medialis.

Filter Correl. (%) Time shift (ms) fc (Hz)

BW0 85.5 ± 8.4 283 ± 43 1.0

BW0 77.2 ± 9.4 236 ± 36 2.5

BW0 58.2 ± 11.6 220 ± 41 10.0

CRIT2 78.5 ± 12.2 23 ± 30 1.0

CRIT2 78.8 ± 12.3 8 ± 30 0.9

RMS 60.7 ± 10.7 231 ± 40 T = 100 (ms)

RMS 72.0 ± 10.9 283 ± 49 T = 285 (ms)

RMS 73.5 ± 11.3 321 ± 67 T = 400 (ms)

Table 2Listing of the A/P COP - EMG envelope correlations and the corresponding timeshifts calculated using a selection of filters and parameters.

21

12

34

56

78

910

11M

easurem

ent/P

articipan

t

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

C90 Area(mm2)

EO

E

C

Fig. 1. Sway area for quiet standing tests for the 10 participants (1–4 controls, 5–10MS). The trials are in the order EO, EC, EO, . . . with 6 trials per participant.

22

1 2 3 4 5 6 7 8 9 10 11Measurement/Participant

0

500

1000

1500

2000

2500

3000

3500

4000

C90

Are

a(m

m2)

1. perturb.2. perturb.3. perturb.

Fig

.2.

Sw

ayar

eafo

rth

eper

turb

atio

nte

sts

for

the

10par

tici

pan

ts(1

–4co

ntr

ols,

5–10

MS).

Thre

eper

turb

atio

ntr

ials

per

par

tici

pan

t.

23

5.1

5.2

5.3

5.4

5.5

5.6

5.7

Tim

e(s)

-100

-80

-60

-40

-20 0 20 40 60 80EMG GAd, GAs, TAd( 10 V), A/P COP(mm)

Fig. 3. Perturbation test. Curves from bottom up: medial gastrocnemius right, left,right tibialis anterior, and A/P COP. Around t = 5.2 s the ankle torque (A/P COP)starts to react to the release of the backward pulling weight.

24

05

1015

2025

3035

40T

ime

(s)

-20 0 20 40 60 80EMG raw, A/P COP, EMG-env., turns

Fig. 4. Example of recording from a quiet standing trial (EO), participant 3. En-velope of EMG from left medial gastrocnemius GA compared with A/P COP. TheEMG turns based on a 2.5σ-threshold and an 80-point histogram.

25

14.0 14.3 14.6 14.9 15.2 15.5 15.8 16.1 16.4 16.7 17.0Time(s)

-7

-2

3

8

13

18

A/P

CO

P,

EM

G-e

nv.

300 ms

Fig

.5.

Enla

rgem

ent

ofa

sect

ion

ofth

epre

vio

us

figu

resh

owin

gth

esh

ift

bet

wee

nth

eG

AE

MG

enve

lope

and

the

A/P

CO

P.

26

09

1827

3645

5463

7281

90M

easurem

ent no

.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

Correlation

Fig. 6. Correlations bewteen A/P COP and the GA EMG envelope for all the 90trials, including the perturbation tests. There are 9 trials per participant, 6 quietstanding trial in alternating order EO-EC-EO . . . plus 3 perturbation tests (EO).

27

0 9 18 27 36 45 54 63 72 81 90Measurement no.

0

100

200

300

400

500T

ime

sh

ift(m

s)

Fig

.7.

Tim

esh

ifts

bet

wee

nG

AE

MG

enve

lope

and

A/P

CO

Pfo

ral

lth

e90

tria

ls.

28

23.9

24.4

24.9

25.4

25.9

26.4

Tim

e(s)

-4 1 6

Raw EMG( 25 V), A/P COP(mm)

Fig. 8. Raw GA-EMG (left) and A/P COP during quiet standing (EO). This ba-sically illustrates the correspondence between EMG and force (A/P COP). Oneobserves how EMG-activity drives the A/P COP which reverberates after EMGgoes down. 29