EMG Based Muscle Force Estimation using Motor Unit Twitch Model

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					       EMG Based Muscle Force Estimation using Motor Unit Twitch Model and
                       Convolution Kernel Compensation
                                  R. Istenic1, A. Holobar1,2 , R. Merletti2 and D. Zazula1
                      Faculty of Electrical Engineering and Computer Science, University of Maribor, Maribor, Slovenia
                                     LISiN, Department of Electronics, Politecnico di Torino, Torino, Italy

     Abstract— In this paper we introduce a new method for             This means that we hardly measure the force of just one
muscle force estimation from multi-channel surface electro-            muscle. Usually, several muscles contribute to the force
myograms. The method combines a motor unit twitch model                level which we detect.
with motor unit innervation pulse trains, which are estimated              Knowing all these facts, we are trying to verify and vali-
from multi-channel surface electromyograms. The motor unit
twitches are then aligned to the innervation pulse trains and
                                                                       date two approaches that predict the muscle forces from the
summed up to obtain the total muscle force. The method was             SEMG observations. We decided to use isometric ramp
tested on real surface EMG signals acquired during force               contractions, because this kind of exercise gives higher
ramp contractions of abductor pollicis brevis muscle in 8 male         probability that we really observe the force level produced
subjects. With 22 ± 5 (mean ± std. dev.) motor units identified        just by one selected muscle. By constant force contractions,
per subject, the force estimation error of our method was 16 ±         it can happen that the tested subject produces force by acti-
4 % RMS. These results were compared to the method which               vating also other muscles, which are not under the recording
uses the EMG amplitude processing to estimate muscle force.            electrodes.
The results of our new concept proved to be completely com-                In the sequel, we reveal our new force estimation ap-
parable to those of EMG amplitude processing.
                                                                       proach which sums up the MU twitches aligned by the de-
    Keywords— muscle force estimation, EMG force relation,             composed innervation pulse trains. We briefly summarize
twitch, convolution kernel compensation.                               the muscle force generation model introduced by [2] and
                                                                       two methods for muscle force estimation: the SEMG ampli-
                                                                       tude processing and the convolution kernel compensation
                        I. INTRODUCTION                                (CKC) decomposition. Section III explains the experiments
                                                                       and compares the model-based forces obtained on real
   Force production in a muscle is regulated by two main               SEMGs with the real measured forces. Sections IV and V
mechanisms: the recruitment of motor units and the modula-             discuss the results and conclude the paper.
tion of their discharge rates. The greater the number of
motor units recruited and their discharge frequency, the
greater the force will be. The same two mechanisms deter-                                                II. METHODS
mine also the electric activity in a muscle. Thus a direct
relationship between the electromyogram (EMG) and ex-                  A. Muscle force model
erted muscle force might be expected [1].
   In order to estimate muscle force from surface electro-                We adopted the muscle force model proposed in [2]. The
myograms (SEMG), we have to know the relationship be-                  complete pool consisted of 120 motor units. The distribu-
tween the electrical and mechanical behavior of muscles.               tion of twitch forces for the motor units was represented as
When the electric response of muscles is measured by                   an exponential function [2]. A large number of motor units
SEMG, only part of the muscle and active motor units (MU)              produced small forces, while relatively few units generated
is detected. Another problem that arises is that superficial           large forces.
MUs contribute more to the observed SEMG than deep                        Twitch force was modeled as the impulse response of a
MUs. As we know that the force produced by a muscle                    critically damped, second order system. Fuglevand [2] used
means a resultant of all MU forces, we also have to take               Eq. 1 to represent a motor unit twitch:
into account that the MUs trigger with different frequencies,
                                                                                   P ⋅ t 1−( t / T ) ,
they may be recruited at different time intervals, and the              f (t ) =        ⋅e                                       (1)
amount of force they exert at every excitation (the force                           T
twitch) depends on the MU type [2].                                    where T is contraction time to peak force of the twitch and
    Reference muscle forces are measured externally via the            P is its peak amplitude. Twitch amplitudes were assigned
moments they cause in the observed joint or extremities.
according to rank in the recruitment order, and twitch con-      we deal with a limited MU pool. In our experiment, the
traction times were inversely related to twitch amplitudes       method recognized 22 ± 5 MUs per subject (mean ± std.
[2]. The range of twitch forces used in the model was 100-       dev.). This number is substantially smaller than the one
fold. One unit of force was equivalent to the twitch force of    proposed in [2] (120 MUs), hence, the twitch force and
the first unit recruited, and the last unit recruited had a      twitch contraction time ranges from [2] had to be modified.
twitch force of 100 units. The range of twitch contraction       Firstly, with recorded contractions ranging from 0 to 10 %
times was 3-fold, with the twitch for the first recruited unit   maximum voluntary contraction (MVC), we assumed only
having the time to peak duration of 90 ms, and for the last      low-threshold units are recruited. To correlate MUs with
recruited unit of 30 ms.                                         twitch forces correctly, the recognized MU innervation
   All MUs followed the widely reported sigmoidal rela-          pulse trains were sorted according to the recruitment order.
tionship between MU force and firing rate. The total force       The first recruited MU was assigned twitch force of 1 unit
of the muscle was determined as a linear summation of all        with contraction time of 90 ms, while the last recruited MU
the individual MU forces.                                        had a twitch force of 1.6 units with contraction time of 80
                                                                 ms. Such values would be assigned to the first twenty units
B. Muscle force estimation using SEMG amplitude                  of all 120 MUs in model [2] (see Fig. 1).
                                                                                                                          Motor unit twitch forces
                                                                                                         → MU22
   The majority of today’s methods use SEMG amplitude to
estimate force. They rely on conventional SEMG amplitude                                           1.4
processing, such as rectification followed by low pass filter-
ing, to preprocess the SEMG before relating it to torque.                                          1.2

                                                                       Twitch force (arb. units)
Clancy et al. [3] found that advanced SEMG processing that
                                                                                                    1             → MU1
incorporates signal whitening and multiple-channel combi-
nation significantly improve force estimation. Both whiten-
ing and multiple-channel combination reduced EMG-torque
errors and their combination provided an additive benefit.                                         0.6
   Potvin et. al [4] found that high pass filtering of SEMG
signals improves SEMG based muscle force estimates. An                                             0.4
iterative approach was used to process the EMG from the
biceps brachii, using progressively greater high pass cutoff                                       0.2
frequencies (20-440 Hz in steps of 30 Hz) with first and
sixth order filters, to determine the effects on the accuracy                                            100      200     300   400 500       600    700   800   900
of force estimates. The results indicate that removing up to                                                                    Time (ms)
99% of the raw SEMG signal power resulted in significant
and substantial improvements in force estimates. For the         Fig. 1 MU twitch forces assigned to recognized MUs for contraction up to
                                                                 10 % MVC. Only low threshold motor units were assumed to be recruited
purpose of force prediction, it appears that a small high        with twitch forces from 1 to 1.6 units and contraction times from 90 ms to
band of SEMG frequencies may be associated with force                                              80 ms.
while the remainder of the spectrum has little relevance.
                                                                     Model [2] allows also gain in MU twitch force to vary as
C. Our method                                                    a function of the firing rate. The maximum gain is obtained
                                                                 when contraction time of the twitch equals the interstimulus
   For a muscle force modeling, described in Subsection          interval (interval between two firings). This gain factor was
II.A, innervation pulse trains of individual MUs are needed.     used to amplify the MU twitch force for each discharge.
They were obtained from recorded SEMG signals with the              The force produced by a single MU is equivalent to the
Convolution Kernel Compensation (CKC) method de-                 sum of individual amplified twitches. The mechanical ac-
scribed in [5] and [6]. The method extracts MU discharge         tions of MUs were assumed to be independent of one an-
patterns in low-level (0-10% MVC) force-varying isometric        other, thus the total force in the muscle was determined as
contractions, is not sensitive to superimpositions of action     the sum of the individual MU forces.
potentials and detects on average a larger number of MUs            Both measured and estimated forces were filtered with
that it is usually possible with single-channel intramuscular    first order Butterworth low pass filter with cutoff of 1Hz.
EMG [5]. However, it is able to recognize only superficial
MUs, which have the greatest impact on SEMG. As a result,
               III. EXPERIMENTAL RESULTS                       equal to 180 Hz, the low pass cutoff frequency to 1 Hz
                                                               while the non-linear normalization constant was 23 [4].
                                                               With 60 SEMG channels available, only the channel with
A. Data acquisition
                                                               the smallest RMS error was taken into consideration. The
    SEMG recording took part at LISiN, Department of Elec-     measured and predicted muscle forces for subject A (7 con-
tronics, Politecnico di Torino. Eight healthy male subjects    secutive ramp contractions) are depicted in Fig 2. Our
(age 27.0 ± 2.3 years, height 181.1 ± 6.7 cm and weight of     method yields 9.9% error (Eq. 2) and correlation coefficient
75.5 ± 9.0 kg) participated to the experiment. SEMG signals    of 0.98, while Potvin's method 12.2% error and correlation
were acquired by a matrix of 61 electrodes arranged in 5       coefficient of 0.96. Fig. 3 depicts the results for the 6th
columns and 13 lines (with four corner electrodes missing).    force ramp only.
Inter-electrode distance was 3.5 mm.
    The electrode matrix was located with the columns in the                                                                    Comparison of Measured and Predicted Force
direction of the muscle fibres and covered the entire distal                                 10

semifibre length (from the innervation zone to the distal                                         9
tendon) and part of the proximal semifibre of abductor pol-
licis brevis muscle. Before electrode placement, the skin

                                                                   Force Amplitude (% MVC)
was abraded with abrasive paste. The matrix was fixed on                                          7

the skin by adhesive tape and a reference electrode was                                           6
placed at the wrist.
    A custom designed brace was used to measure abduction
force. The subject’s wrist was fixed in a padded wood sup-                                        4
port with the head of the thumb phalanx in touch with a load                                      3
cell. The force signal was amplified, provided as feedback
to the subject on an oscilloscope, and recorded in parallel
with the SEMG signals. The subjects performed three                                               1
maximal voluntary contractions separated by 2-min rest,                                           0
after which the electrode grid was located over the abductor                                       0                       10    20      30      40     50       60      70   80   90
                                                                                                                                                  Time (s)
pollicis brevis. The subject was then asked to linearly in-
crease force from 0% to 10% MVC in 6 s and then decrease        Fig. 2 Comparison of measured force (thick solid line), force estimated
from 10% to 0% MVC in other 6 s, using the visual feed-         with our method (dashed line) and force estimated with Potvin's method
back on force. All together, 7 consecutive force ramps were      (thin solid line). The forces were estimated from real SEMG signals
recorded from each subject. The SEMG signals were ampli-                                       (subject A)
fied, band-pass filtered (3 dB bandwidth, 10-500 Hz) and
                                                                                                                                 Comparison of Measured and Predicted Force
sampled at 1650 Hz by a 12 bit A/D converter.

B. Results                                                                                                             8
                                                                                             Force Amplitude (% MVC)

   To compare estimated and measured force and to calcu-                                                               7

late estimation error, both forces must be normalized first.                                                           6
In our case, linear normalization w.r.t. the maximum force                                                             5
amplitude was used. Estimation error was computed as root
mean square (RMS) percent error (Eq. 2). In addition, the
correlation coefficient between signals was also computed.                                                             3

               RMS ( f estimated − f measured )                                                                        2                   Measured Force

ErrorRMS % =                                    ⋅ 100    (2)                                                           1
                                                                                                                                           Predicted Force - twitch
                                                                                                                                           Predicted Force - amplitude
                  RMS ( f measured )
                                                                                                                           62    64      66      68      70      72      74   76
                                                                                                                                                  Time (s)

   Results of our method were compared to the Potvin’s          Fig. 3 Comparison of measured force (thick solid line), force estimated
method described in [4]. The method builds on a single          with our method (dashed line) and force estimated with Potvin's method
SEMG channel and uses high-pass filtering to enhance the         (thin solid line). The forces were estimated from real SEMG signals
force estimation. The high pass cutoff frequency was set           (subject A, 6th force ramp) and normalized w.r.t. their peak value.
   Both methods were tested on signals from all 8 subjects.                               V. CONCLUSION
Errors and correlation coefficients were calculated for each
subject. Average error was 15.8% ± 4.2% for our method             Several simulation studies of the MU force model were
and 16.1% ± 3.5% for Potvin's method [4]. Average correla-      proposed in the past [2, 7]. Our study went a step further as
tion coefficient was 0.96 ± 0.02 for our method and 0.93 ±      we investigated how this model is performing on real
0.03 for the compared one.                                      SEMG signals. Despite some open issues discussed in Sec-
   As found by Potvin [4], high pass filtering of SEMG sig-     tion IV, our method yields comparable results to the Pot-
nals improved the force estimation also by our signals. High    vin’s method [4] which is based on SEMG amplitude proc-
pass cutoff frequencies were changed from 20 Hz to 420 Hz       essing.
in steps of 80 Hz. The optimal sixth order high pass cutoff
frequency for our signals was found to be 180 Hz. At that
frequency the minimal error was obtained (Table 1).                                    ACKNOWLEDGEMENT

                               Table 1                            This work was supported by the Slovenian Ministry of
                                                                Higher Education, Science and Technology (Contract No.
  High pass cutoff frequency (Hz)        RMS error              1000-05-310083 and Programme Funding P2-0041) and
                20                        16.8 %                European Commission within the Sixth Framework (Project
               100                        16.3 %                Cybermans) and Marie Curie Intra-European Fellowships
               180                        16.1 %                Action (DE MUSE, Contract No. 023537).
               260                        17.3 %
               340                        16.7 %
               420                        18.4 %                                             REFERENCES
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                                                                     neering and noninvasive applications. John Willey & Sons, New Jer-
                        IV. DISCUSSION                               sey.
                                                                2.   Fuglevand A J, Winter D A, Patla A E. (1993) Models of recruitment
   Our method performed well in comparison to the Pot-               and rate coding organization in motor-unit pools. Journal of Neuro-
vin’s method. However, there are some open issues to be              physiology 70:2470-2488
                                                                3.   Clancy E A, Bida O, Rancourt D (2007) Influence of advanced elec-
discussed when interpreting the results of our method.               tromyogram (EMG) amplitude processors on EMG-to-torque estima-
   The first one is the number of MUs that can be detected           tion during constant-posture, force varying contractions. Journal of
by the pick-up electrodes and recognized by the decomposi-           Biomechanics 39(14): 2690–2698
tion algorithm. With surface electrodes only part of all ac-    4.   Potvin J R, Brown S H M (2004) Less is more: high pass filtering, to
                                                                     remove up to 99% of the surface EMG signal power, improves EMG-
tive MUs is detected. Moreover, not all the detected MUs             based biceps brachii muscle force estimates. JEK 14:389-399
are recognized by the CKC decomposition technique. This         5.   Holobar A, Zazula D, Gazzoni M, Merletti R, Farina D (2006) Non-
implies that our method operates on a limited set of MUs.            invasive analysis of motor unit discharge patterns in isometric force-
Question arises whether this set is representative enough for        varying contractions. ISEK Proc., XVI congress of ISEK, Torino, It-
                                                                     aly, 2006, pp 12
the purpose of force estimation. Typically, the number of       6.   Holobar A, Zazula D (2004) Correlation-based decomposition of
MUs contributing to the muscle force is much larger than             surface EMG signals at low contraction forces. Med. Biol. Eng. Com-
the number of recognized MUs. Nevertheless, the results of           put 42:487-495
this study demonstrate that, at least in the case of abductor   7.   Zhou P, Rymer W Z (2004) Factors governing the form of the relation
                                                                     between muscle force and the EMG: A simulation study. Journal of
pollicis brevis muscle, recognized motor units form a good           Neurophysiology 92:2878-2886
base for force estimation.
   Finally, co-activation of antagonist and agonist muscles
must be taken into account. As we stated in introduction,            Address of the corresponding author:
force at a joint is normally produced by several concurrently        Author: Rok Istenic
active muscles. For the best possible force estimations all          Institute: Faculty of Electrical Engineering and Computer Science,
muscles that contribute to the joint force must be included                          University of Maribor, Maribor
in SEMG recordings and in the force estimation process.              Street: Smetanova 17
                                                                     City:      2000 Maribor
                                                                     Country: Slovenija
                                                                     Email: rok.istenic@uni-mb.si