# Characteristics of Postural Muscle Activity in Response to A Motor-Motor Task in Elderly
## 2 Materials and Methods
### Data Processing  
All data were processed offline using MATLAB software (MathWorks, Natick, MA, USA). The signals from the first and second accelerometers were used to determine the timing that the pendulum (T\(0\)) and the sliding board (bT\(0\)) started moving away. The onsets of the accelerometer signals were detected using the Teager-Kaiser onset time detection method [27; 28]. The sensors on these segments also used the Teager-Kaiser method to identify the onset timing of segment movements.  
Figure 1: Schematic representation of the experimental setup. Additional mass: an additional 5% body weight or 30% body weight placed on the cart. Accelerometer 1: accelerometer attached to the cart, and Accelerometer 2: accelerometer attached to the sliding board. Red boxes represent the placements of electrodes. RA: rectus abdominis, ES: erector spinae, RF: rectus femoris, BF: biceps femoris, TA: tibialis anterior, and MG: medial gastrocnemius.  
All EMG data were high-pass filtered at 20 Hz, full-wave rectified, and low-pass filtered using linear envelope at 2 Hz (2 nd order Butterworth) [26; 29]. Subsequently, the Teager-Kaiser method was used to identify the onset of muscle activity for individual muscle (EMG\({}_{\text{onset}}\)). The integrals of EMG activity of all studied muscles (\(\int\)EMG\({}_{\text{s}}\)) were calculated during the six epochs: (1) from \(-750\) ms to \(-550\) ms, (2) from \(-550\) ms to \(-350\) ms, (3) from \(-350\) ms to \(-150\) ms, (4) from \(-150\) ms to \(+50\) ms, (5) from \(+50\) ms to \(+250\) ms, and 6) from \(+250\) ms to \(+450\) ms in relation to T0. The 1-4 epochs were used to calculate components of feedforward postural adjustments and the 5-6 epochs for feedback postural adjustments [30; 31]. Moreover, \(\int\)EMG\({}_{\text{s}}\) of the baseline activity were obtained during a 200 ms time window at the beginning of the trial. Subtraction of \(\int\)_baseline_ was used to eliminate the effects of each muscle baseline activity. Values larger than zero (\(\int\)_EMG-\(\int\)baseline_ \(>0\)) were referred as activation of muscles and values smaller than zero (\(\int\)_EMG-\(\int\)baseline_ \(<0\)) as inhibition of muscles. Thus, the \(\int\)_EMG\({}_{\text{Epochs 1-6}}\)_ were normalized by \(\int\)_EMG\({}_{\text{max}}\)_[26], which was the maximum value throughout all experimental trials for each muscle in each epoch and shown the example of \(\int\)_EMG\({}_{\text{Epoch 1}}\)_ as:  
\[\int\text{baseline}=\int\limits_{0}^{200}\text{EMG} \tag{1}\]  
\[\int\text{EMG}_{\text{Epoch1}}=\frac{\int_{T0-750}^{T0-550}\text{EMG}-\int \text{baseline}}{\int\text{EMG}_{\text{max}}} \tag{2}\]  
Subsequently, the sums and differences between normalized \(\int\)EMG values (Equation (2)) of RA and ES muscles for the trunk segment, RF and BF muscles for the thigh segment, and TA and MG muscles for the shank segment were calculated in Epochs 1-6, separately.  
\[C=\int\text{EMG}\text{central}+\int\text{EMG}\text{orsal} \tag{3}\]  
\[R=\int\text{EMG}\text{central}-\int\text{EMG}\text{orsal} \tag{4}\]  
\(C\) indexes were calculated as the sum of \(\int\)_EMG_ of the antagonist-agonist muscle pairs to represent co-contraction and R indexes as the difference between \(\int\)_EMG_ in the muscle pairs to represent reciprocal activation [32]. Using the shank segment as an example, the \(C\) and \(R\) values in the Epoch 1 were calculated as:  
\[C_{\text{shank Epoch1}}=\int TA_{\text{Epoch1}}+\int\text{MG}_{\text{Epoch1}} \tag{5}\]  
\[R_{\text{shank Epoch1}}=\int TA_{\text{Epoch1}}-\int\text{MG}_{\text{Epoch1}} \tag{6}\]  
The same \(C\) and \(R\) values were calculated for the thigh and trunk segments in the Epochs 2-6. All variables were calculated for each trial then averaged over five trials and presented with means and standard errors.