*2.3.2. Apparatus*

Kinematic data were also collected at 200Hz using VICON motion capture device (Oxford Metrics, Oxford, UK) to identify the gait cycles by detecting each heel strike (i.e. right heel strike to heel strike). The kinematic markers were located on the hip, knee, ankle, heel, and toe. An electronic trigger was used to synchronize the EMG and kinematic data and to determine the events in which the treadmill speed increased (one trigger per gait speed increase).

## **2.4. Data processing**

The data were processed by using a customized Matlab script (Mathworks, USA R2007a). The detailed specifications of each are provided below.

## *2.4.1. Recurrence Quantification Analysis (RQA)*

The first step was to calculate the % DET by using RQA (RQASP program [29]; also see details in Appendix-RQA formulation). The EMG signals were band-pass filtered from 10-500 Hz [30, 31] however, no other smoothing techniques were used for the remaining signals to maximize the exposure of the raw signals to the nonlinear analysis method [16, 32]. To minimize the potential effect of any noise in the raw EMG signal on the outcome of RQA, the initial param‐ eters (i.e. time delay and embedding dimension) were selected by following the recommended settings (i.e. embedding dimension, time lag, and radius) [29].

For each walking speed and each muscle, the EMG signal was clustered into five data bins that were defined as the epochs of recorded data between each right foot heel strike (i.e. each gait cycle). For each subject, the percentage of recurrence (% REC) and % DET of the clustered EMG signals was calculated for all muscles within each speed condition (% REC is required for the control during the selection of radius, see Appendix-RQA formulation for more details). As the RQA processes the time-delayed reconstructed space phase of the EMG signal, several parameters were defined prior to performing the analysis. The data were analyzed using an embedding dimension of m=6 based on the False Nearest Neighbor technique [33] and time delay of 5 (τ = 0.005 second) based on the Mutual Information (MI) technique [34]. In the MI technique, the first local minimum of the average mutual information is used to detect the time delay. The proximity radius (see Appendix-RQA formulation) was selected as 2 to 10 units of the rescaled "Maximum" unit of the Distance Matrix to keep the percentage of the recurring points in the recurrence plot (RP) of the signal less than 2% , as has been recommended [18].

### *2.4.2. Shuffled surrogates tests*

**2.3. Material and data collection**

134 Electrodiagnosis in New Frontiers of Clinical Research

data collection was completed.

*2.3.2. Apparatus*

increase).

**2.4. Data processing**

detailed specifications of each are provided below.

settings (i.e. embedding dimension, time lag, and radius) [29].

*2.4.1. Recurrence Quantification Analysis (RQA)*

EMG signals were collected using six preamplifier bipolar active electrodes (EMG preampli‐ fier, Type No: SX230, Biometrics Ltd., Gwent, UK) with a fixed electrode distance of 20 mm from rectus femoris (RF), tibialis anterior (TA), lateral gastrocnemius (GA), soleus (SO), vastus medialis (VM), and biceps femoris (BF) of the right lower limb using double sided tape. The electrodes were connected to a DataLINK base-unit DLK900 of the EMG acquisition system which was connected to a PC using USB cable. To achieve acceptable impedance level the skin over the location of each electrode was shaved and cleaned with alcohol swabs. EMG data were collected at 1000 Hz and passed through an amplifier with the gain set at 1000. The amplification bandwidth was 20–460 Hz (input impedance =100 MV, common mode rejection ratio >96 dB (~110dB) at 60 Hz). A zeroing reference electrode was placed above the right lateral malleolus bone and was secured by elastic wrap and tapes. There was no excessive filtration of the EMG data during collection but a digital filter was applied during data processing (see below). During the collection session, the electrodes were not removed from the subjects until

Kinematic data were also collected at 200Hz using VICON motion capture device (Oxford Metrics, Oxford, UK) to identify the gait cycles by detecting each heel strike (i.e. right heel strike to heel strike). The kinematic markers were located on the hip, knee, ankle, heel, and toe. An electronic trigger was used to synchronize the EMG and kinematic data and to determine the events in which the treadmill speed increased (one trigger per gait speed

The data were processed by using a customized Matlab script (Mathworks, USA R2007a). The

The first step was to calculate the % DET by using RQA (RQASP program [29]; also see details in Appendix-RQA formulation). The EMG signals were band-pass filtered from 10-500 Hz [30, 31] however, no other smoothing techniques were used for the remaining signals to maximize the exposure of the raw signals to the nonlinear analysis method [16, 32]. To minimize the potential effect of any noise in the raw EMG signal on the outcome of RQA, the initial param‐ eters (i.e. time delay and embedding dimension) were selected by following the recommended

For each walking speed and each muscle, the EMG signal was clustered into five data bins that were defined as the epochs of recorded data between each right foot heel strike (i.e. each gait cycle). For each subject, the percentage of recurrence (% REC) and % DET of the clustered EMG

*2.3.1. EMG activity*

While many studies have indicated a nonlinear dynamical pattern for EMG signals [10, 14, 15, 17, 18, 35] the nonlinearity of such signals was tested to justify the application of RQA in SYNERGOS [15, 17, 35-38]. A common practice to test the assumption of nonli‐ nearity in a signal (i.e. EMG) is using surrogate data testing [15, 35-37, 39]. During this test the original EMG data are randomly shuffled using different algorithms namely time shuffling to generate random signals. It is expected that the randomization of the signal has significant effects on the nonlinear characteristics of the signal while keeping the line‐ ar characteristics of the signal unchanged which verifies the nonlinear behavior of the signal (i.e. EMG). In this study, 20 series of surrogate data using three algorithms were generated for each set of muscles per gait cycle [15, 35-38]. The approximate entropy (ApEn) and % DET of the original data were used to monitor the changes in the underly‐ ing dynamics of the EMG data after shuffling [40-42]. It was hypothesized that the value of % DET would significantly decrease while the value of ApEn would significantly in‐ crease for the shuffled data (see Appendix-Shuffled Surrogate Tests of EMG). By rejecting the null hypotheses of this testing procedure the existence of underlying nonlinear dy‐ namics of the EMG signal could be assumed and therefore the application of RQA was justified.

#### *2.4.3. SYNERGOS*

We developed the SYNERGOS method to assess the level of MMA based on the activation of each muscle with all possible sets of the other muscles. SYNERGOS employs a two-step method for quantifying MMA. The first step is using RQA to analyze the EMG signals of each recorded muscle separately. The calculated % DET of the EMG signal obtained from each muscle serves as an input variable for the second step of SYNERGOS in which the inputs are combined by using a novel method that quantifies the level of MMA. SYNERGOS accounts for the concomitant activation of all measured muscles rather than only pairs of muscles. This measure results in a single scalar value indicating the overall activity among the set of multiple muscles representing the overall activation of these muscles during the course of the move‐ ment. Fig. 1 shows the schematic of the algorithm.

Where *DETi* represents the % DET for each muscle (i, j, k, etc.) from the EMG signal during

*i j*

1 0

d

*ij i j*

*ijkl ij jk kl* À= ¼ <sup>¼</sup> dd d

Therefore for any combination including a pair or multiple similar muscles the ℵ*ijkl*… is zero. δ and ℵ are used to ignore the coactivation of each muscle with itself so the result of Equation (1) represents only the coactivity of sets of two or more separate muscles. Following the

*DETi*)

1

*i*=1

This calculation represents the interaction of each muscle's activity with the other muscles' activity throughout a dynamic task since these muscles are all active at various times during the task. Each term in Equation 2 calculates the possible coactivation of each muscle with the other muscles in the limb. SYNERGOS basically summarizes the multidimensional correlation tensors of muscle activity into a scalar value while explicitly removing the unidimensional activity of single muscles from such tensors. Consequently, the SYNERGOS method calculates the interaction of all of the muscles, in all possible combinations. The magnitude of SYNERGOS can vary between 0 to 100 indicating the lowest and the highest level of MMA. A SYNERGOS of zero indicates that none of the muscles being measured during a task are simultaneously active regardless of the magnitude of activity in each muscle. A SYNERGOS of 100 indicates that all muscles are simoultanously active and each muscle is activated to its potentially maximum contraction level during each movement cycle (e.g., gait cycle). While theoretically possible, the index could only reach 100 if electrical stimulation was used to achieve tetanus in all monitored muscles. Values between 0 and 100 represent the average simultaneous activation scaled by the magnitudes of activity and temporal sequencing of the respective muscles. During movements a certain coactivity level among several agonist and antagonist muscles exists therefore, a SYNERGOS value between 0 and 100 will be obtained by analyzing

For instance, in the current study the SYNERGOS algorithm for measuring the level of multiple coactivation for pairs of muscles (i.e., the first component in Equation 2) uses the upper triangular matrix of % DET indicated in equation (5) (where D represents % DET of each EMG

*n*

is the Kronocker delta defined in equation 3:

<sup>ì</sup> <sup>=</sup> <sup>=</sup> <sup>í</sup> <sup>¹</sup> <sup>î</sup> (3)

, *SY Nquad* , …) the ℵ is defined as follows:

(4)

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137

*<sup>n</sup>* and represents the geometric mean of

each gait cycle and delta *δij*

While for higher order of SYN (i.e. *SY Ntri*

strategy of the equation (2), *SY Nn*−*muscle* =(∏

the % DET of the recorded muscles.

the measured muscles.

signal).

**Figure 1.** The schematic view of the SYNERGOS algorithm. EMG signals are analyzed using the RQA and the output, % DET for each muscle is imported into the SYNERGOS algorithm which eventually provides a single scalar index repre‐ senting the state of MMA.

In this method, the average of several components is calculated. Each component is an average of the mth roots of the products (m= 2, 3, …, n while n= number of recorded muscles) of % DET of EMG signals for sets of m different muscles (i.e., pairs, triplets, quartets, etc.), where the final component is the nth root of the products of % DET of all n muscles being analyzed (i.e. the geometric mean). The SYNERGOS index was calculated based on the equation (1) by using the % DET derived for each muscle.

$$\text{SYNERSOS} = \frac{1}{n-1} \left[ \text{SYN}\_{\text{bj}} + \text{SYN}\_{\text{frj}} + \text{SYN}\_{\text{quad}} + ... + \text{SYN}\_{n-\text{muscle}} \right] \tag{1}$$

*SY Nbi* represents the paired-muscle coactivities with ( *n* 2 ) possible elements (see equation 2). While *SY Ntri* depicts the contribution of simultaneous coactivity among three-muscle sets to SYNERGOS index with ( *n* 3 ) possible combinations. The same strategy is used to calculate the higher order muscular coactivity among other multiple-muscle sets. SYNERGOS index is elaborated in equation (2) as:

( ) ( ) ( ) <sup>1</sup> <sup>1</sup> 1 2 1 1 <sup>3</sup> <sup>1</sup> <sup>1</sup> <sup>1</sup> 3 <sup>1</sup> <sup>4</sup> 1 . 1 4 *n n ij i j DET DET <sup>n</sup> i ji nnn SYNERGOS ijk i j k DET DET DET <sup>n</sup> <sup>n</sup> i j ik j nnn n ijkl i j k l DET DET DET DET <sup>n</sup> i j ik jl k* d é ù ê ú å å - + æ ö = = ç ÷ è ø <sup>=</sup> ååå -À <sup>+</sup> - æ ö === ç ÷ è ø ååå å -À +¼ æ ö = = == ç ÷ ë û è ø (2)

Where *DETi* represents the % DET for each muscle (i, j, k, etc.) from the EMG signal during each gait cycle and delta *δij* is the Kronocker delta defined in equation 3:

$$
\delta\_{\stackrel{\circ}{ij}} = \begin{cases} 1 & i = j \\ 0 & i \neq j \end{cases} \tag{3}
$$

While for higher order of SYN (i.e. *SY Ntri* , *SY Nquad* , …) the ℵ is defined as follows:

$$
\mathcal{N}\_{ijkl\dots} = \delta\_{ij}\delta\_{jk}\delta\_{kl}\dots \tag{4}
$$

Therefore for any combination including a pair or multiple similar muscles the ℵ*ijkl*… is zero. δ and ℵ are used to ignore the coactivation of each muscle with itself so the result of Equation (1) represents only the coactivity of sets of two or more separate muscles. Following the strategy of the equation (2), *SY Nn*−*muscle* =(∏*i*=1 *n DETi*) 1 *<sup>n</sup>* and represents the geometric mean of

the % DET of the recorded muscles.

**Figure 1.** The schematic view of the SYNERGOS algorithm. EMG signals are analyzed using the RQA and the output, % DET for each muscle is imported into the SYNERGOS algorithm which eventually provides a single scalar index repre‐

In this method, the average of several components is calculated. Each component is an average of the mth roots of the products (m= 2, 3, …, n while n= number of recorded muscles) of % DET of EMG signals for sets of m different muscles (i.e., pairs, triplets, quartets, etc.), where the final component is the nth root of the products of % DET of all n muscles being analyzed (i.e. the geometric mean). The SYNERGOS index was calculated based on the equation (1) by using

While *SY Ntri* depicts the contribution of simultaneous coactivity among three-muscle sets

the higher order muscular coactivity among other multiple-muscle sets. SYNERGOS index

é ù ê ú

( )

d

*ij i j DET DET <sup>n</sup> i ji*

å å - + æ ö = = ç ÷

<sup>1</sup> <sup>1</sup> 1 2

*n n*

1 1 <sup>3</sup> <sup>1</sup> <sup>1</sup> <sup>1</sup> 3

è ø

è ø

*nnn SYNERGOS ijk i j k DET DET DET <sup>n</sup> <sup>n</sup> i j ik j*

*nnn n*

1 4

( )

<sup>=</sup> ååå -À <sup>+</sup> - æ ö === ç ÷

( )

*ijkl i j k l DET DET DET DET <sup>n</sup> i j ik jl k*

ååå å -À +¼ æ ö = = == ç ÷ ë û è ø

<sup>1</sup> <sup>4</sup> 1 .

*SYNERGOS SYN SYN SYN SYN bi tri quad n muscle <sup>n</sup>* <sup>=</sup> é ù + + +¼+ - - ë û (1)

*n* 2

) possible combinations. The same strategy is used to calculate

) possible elements (see equation 2).

(2)

senting the state of MMA.

the % DET derived for each muscle.

136 Electrodiagnosis in New Frontiers of Clinical Research

to SYNERGOS index with (

is elaborated in equation (2) as:

1 1

*SY Nbi* represents the paired-muscle coactivities with (

*n* 3 This calculation represents the interaction of each muscle's activity with the other muscles' activity throughout a dynamic task since these muscles are all active at various times during the task. Each term in Equation 2 calculates the possible coactivation of each muscle with the other muscles in the limb. SYNERGOS basically summarizes the multidimensional correlation tensors of muscle activity into a scalar value while explicitly removing the unidimensional activity of single muscles from such tensors. Consequently, the SYNERGOS method calculates the interaction of all of the muscles, in all possible combinations. The magnitude of SYNERGOS can vary between 0 to 100 indicating the lowest and the highest level of MMA. A SYNERGOS of zero indicates that none of the muscles being measured during a task are simultaneously active regardless of the magnitude of activity in each muscle. A SYNERGOS of 100 indicates that all muscles are simoultanously active and each muscle is activated to its potentially maximum contraction level during each movement cycle (e.g., gait cycle). While theoretically possible, the index could only reach 100 if electrical stimulation was used to achieve tetanus in all monitored muscles. Values between 0 and 100 represent the average simultaneous activation scaled by the magnitudes of activity and temporal sequencing of the respective muscles. During movements a certain coactivity level among several agonist and antagonist muscles exists therefore, a SYNERGOS value between 0 and 100 will be obtained by analyzing the measured muscles.

For instance, in the current study the SYNERGOS algorithm for measuring the level of multiple coactivation for pairs of muscles (i.e., the first component in Equation 2) uses the upper triangular matrix of % DET indicated in equation (5) (where D represents % DET of each EMG signal).

$$
\begin{bmatrix}
D\_{\text{SOD}\,\text{SO}} & D\_{\text{SOD}\,\text{GA}} & D\_{\text{SOD}\,\text{TA}} & D\_{\text{SOD}\,\text{VA}} & D\_{\text{SOD}\,\text{RF}} & D\_{\text{SOD}\,\text{BF}} \\
& D\_{\text{GA}}D\_{\text{GA}} & D\_{\text{GA}}D\_{\text{TA}} & D\_{\text{GA}}D\_{\text{VA}} & D\_{\text{GA}}D\_{\text{RF}} & D\_{\text{GA}}D\_{\text{BF}} \\
& & D\_{\text{TA}}D\_{\text{TA}} & D\_{\text{TA}}D\_{\text{VA}} & D\_{\text{TA}}D\_{\text{RF}} & D\_{\text{TA}}D\_{\text{BF}} \\
& & & D\_{\text{VA}}D\_{\text{VA}} & D\_{\text{VA}}D\_{\text{RF}} & D\_{\text{VA}}D\_{\text{BF}} \\
& & & & D\_{\text{RF}}D\_{\text{RF}} & D\_{\text{RF}}D\_{\text{BF}} \\
& & & & & D\_{\text{BF}}D\_{\text{BF}}
\end{bmatrix}
\tag{5}
$$

Where *SY NGS* , *<sup>j</sup>*

**2.5. Statistical analysis**

Inc., Chicago, Illinois, USA).

**3. Results**

**3.1. Surrogate testing**

within the jth gait speed condition.

is the SYNERGOS index calculated for the jth gait speed condition and *SY Ni*, *<sup>j</sup>*

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139

is the SYNERGOS index calculated for the data clustered in the ith gait cycle (*i* =1, 2, …, 5)

To analyze the efficiency of the proposed method, a restricted maximum likelihood linear mixed model was employed to identify changes in MMA measured by SYNERGOS associated with gait pattern (i.e. walk or run) and with changing gait speed. The model included three fixed effects, speed, pattern (walk or run), and speed-by-pattern interaction, and two random effects, subjects and measurement error (i.e., random within-subject variation). This analytical approach is similar to repeated measures analysis of variance in that it accounts for depend‐ ency resulting from multiple measures per subject but unlike analysis of variance does not require the same number of measures for each subject. The fixed effects were used to test the study hypotheses. The random effects were used to compute intraclass correlation coefficients (ICC) of type (2,1) (i.e., degree of consistency among measures) [43] and the corresponding standard errors of measurement (SEm) as relative and absolute reliability estimates, respec‐ tively (i.e. indicators of the consistency and precision of the SYNERGOS measure). The significance level was set at p≤ 0.05. The analysis was conducted by using SPSS 16.0.1 (SPSS

The results of the discriminant statistics (see Appendix-Shuffled Surrogate Tests of EMG). for each muscle and algorithm are shown in Table. 1. For all subjects, muscles, and gait cycle, the results of three different surrogate tests rejected the null hypotheses of equal or more deter‐ minism in surrogate data compared to the original data (φ > 2 and p< 5% ). The rejection of this null hypothesis indicated significant change in the nonlinear behavior of the surrogate signals (i.e. reduction of determinism) compared to the collected EMG signals which justified the application of higher order nonlinear data analysis techniques such as RQA to investigate

In Fig.2(a) an example of soleus EMG activity obtained during a single gait cycle (right heel strike to right heel strike) is depicted. Soleus contributes to the ankle planterflexion during body propulsion in stance phase of the gait. Muscle activity dramatically increases during midstance and peaks during the terminal stance phase with a rapid decrease in muscle activity in the pre-swing phase. The muscle remains fairly quiet during the swing phase of gait. Fig. 2(b) displays the recurrence plot (RP) of the soleus activity in which recurrent points are positioned along several parallel diagonal recurrent lines demonstrating the existence of a specific deterministic muscular activity in the soleus during the gait cycle. Fig.2(c) represents the randomized shuffling of the EMG signal using surrogate testing algorithms. The RP of the

the underlying dynamical pattern of the EMG signals specifically in SYNERGOS.

The delta function negates the elements of the matrix located on the diagonal (equation 6) for the EMG from the following muscles: rectus femoris (RF), tibialis anterior (TA), lateral gastrocnemius (GA), soleus (SO), vastus medialis (VM), and biceps femoris (BF).

$$
\begin{bmatrix}
0 & D\_{\text{SO}}D\_{\text{GA}} & D\_{\text{SO}}D\_{\text{TA}} & D\_{\text{SO}}D\_{\text{VA}} & D\_{\text{SO}}D\_{\text{RF}} & D\_{\text{SO}}D\_{\text{BF}} \\
0 & D\_{\text{GA}}D\_{\text{TA}} & D\_{\text{GA}}D\_{\text{VA}} & D\_{\text{GA}}D\_{\text{RF}} & D\_{\text{GA}}D\_{\text{BF}} \\
& 0 & D\_{\text{TA}}D\_{\text{VA}} & D\_{\text{TA}}D\_{\text{RF}} & D\_{\text{TA}}D\_{\text{BF}} \\
& & 0 & D\_{\text{VA}}D\_{\text{RF}} & D\_{\text{VA}}D\_{\text{BF}} \\
& & & 0 & D\_{\text{RF}}D\_{\text{BF}} \\
& & & & 0
\end{bmatrix}
\tag{6}
$$

Finally, the technique calculates the sum of the square roots of the Equation 7 matrix elements. The outcome is averaged over the number of combinations (equation 7).

$$\text{SYN}\_{\text{bj}} = \frac{1}{\binom{6}{2}} \sum\_{\substack{\vec{l} = 1 \ \vec{j} = \vec{l}}}^{6} \sqrt{\binom{1 - \delta\_{\vec{l}\vec{j}}}{}} \\ \text{DET}\_{\vec{l}} \text{DET}\_{\vec{j}} = \dots \\ \tag{7}$$

Other components of the SYNERGOS requires the calculation of combinations of % DET of three muscles (*SY Ntri* ), four muscles (*SY Nquad* ), five muscles (*SY N*5), and six muscles (*SY N*6) while controlling for the number of combinations (( 6 2 ) =15 for two muscles, ( 6 3 ) =20 for three muscles, ( 6 4 ) =15 for four muscles, ( 6 5 )=6 for five muscles, ( 6 6 )=1 for six muscles).

Finally, for each subject, to obtain a single SYNERGOS index for the EMG signals during each gait speed, the root mean square of the five SYNERGOS indices obtained from the clustered EMG signals (five gait cycles per gait speed; see Recurrence Quantification Analysis) were calculated (equation 8). This single value represented the quantified MMA during each gait speed.

$$\text{SYN}\_{\text{GS},j} = \sqrt{\frac{\sum\_{i=1}^{5} \text{SYN}\_{i,j}^{2}}{5}} \quad j = 1 \text{ to number of gait speed conditions} \tag{8}$$

Where *SY NGS* , *<sup>j</sup>* is the SYNERGOS index calculated for the jth gait speed condition and *SY Ni*, *<sup>j</sup>* is the SYNERGOS index calculated for the data clustered in the ith gait cycle (*i* =1, 2, …, 5) within the jth gait speed condition.
