Advanced biofeedback from surface electromyography signals using fuzzy system

Abstract

The aims of this study were to develop a fuzzy inference-based biofeedback system and investigate its effects when inducing active (shoulder elevation) and passive (relax) pauses on the trapezius muscle electromyographic (EMG) activity during computer work. Surface EMG signals were recorded from clavicular, descending (bilateral) and ascending parts of the trapezius muscles during computer work. The fuzzy system readjusted itself based on the history of previous inputs. The effect of feedback was assessed in terms of muscle activation regularity and amplitude. Active pause resulted in non-uniform muscle activity changes in the trapezius muscle depicted by increase and decrease of permuted sample entropy in ascending and clavicular parts of trapezius, respectively (P < 0.05) compared with no pause. Concomitantly, the normalized root mean square of EMG increased approximately 5% in descending part of trapezius bilaterally (P < 0.01). These findings confirm that advanced feedback can change the pattern of muscle activation.

Appendix I

Permuted sample entropy (PeSaEn) is calculated through the steps listed below:

Step 1. Form a time series of data u(1), …u(N), given N raw data values from measurements equally spaced in time. Normalize the time series to its standard deviation.

Step 2. Fix the embedding dimension m, an integer, and the tolerance distance r, a positive real number. The value of m represents the length of compared runs (a window), and r effectively represents a filter.

Step 3. Form a sequence of vectors X(1), … X(N - m + 1) in ℜ^m, real m-dimensional space, as X(i) = [u(i), ···, u(i + m − 1)]

Step 4. Use the sequence X(1), … X(N − m + 1) to construct, for each i, C ^m _i (r) = {number of X(j)such that d[X(i), X(j)] ≤ r}/(N − m).

d[X(i), X(j)] for vectors X(i) and X(j) is defined as d[X(i), X(j)] = max |u(i + k − 1) − u(j + k − 1)| for k = 1, … m and i ≠ j

Step 5. Next, define $\Upphi^{m} \left( r \right) = {\frac{{\sum\limits_{i = 1}^{N - m} {C_{i}^{m} \left( r \right)} }}{N - m}}$

Step 6. SaEn = $- \ln \left( {{\frac{{\Upphi^{m + 1} \left( r \right)}}{{\Upphi^{m} \left( r \right)}}}} \right)$.

The lowest non-zero ratio ${\frac{{\Upphi^{m + 1} \left( r \right)}}{{\Upphi^{m} \left( r \right)}}}$ in step 6 where there is only one matched vector (distance is below a limit) equals to ${\frac{2}{{\left( {N - m - 1} \right)\left( {N - m} \right)}}}$ so the maximum achievable value for SaEn will be ln (N − m) + ln (N − m − 1) − ln (2).

We did a minor modification to this algorithm to fulfill the time requirement of our online application. In Step 5, Φ^m(r) is computed using only a limited number (q) of indices which are randomly permuted over whole time series indices. The same indices are then used to compute Φ^m+1(r).

The variability term which is introduced due to randomized indices involved in the estimation of PeSaEn has been compared to the total variability due to variable inputs from a family of pseudorandom time series called MIX(P) with controllable regularity defined by p. This family of time series has been used to assess the statistical properties of approximate entropy [25, 26]. For 0 ≤ P ≤ 1 and $X_{j} = \sqrt 2 \sin \left( {{\frac{2\pi j}{12}}} \right)$ where Y _j independent identically distributed (i.i.d) random variable uniformly distributed on $\left[ { - \sqrt 3 ,\sqrt 3 } \right]$, MIX(P) is defined as MIX(P) _j  = (1 − Z _j )X _j  + Z _j Y _j where Z _j also i.i.d and equals to one with probability P or equals to zero with probability (1 − P). Obviously, the higher the P the more irregular the time series. This time series has the mean equal to zero and standard deviation to one for all P but the irregularity is increasing along with P. This is one typical example where statistical descriptors fail to distinct the time series classes.

Using Monte-Carlo simulation testing the PeSaEn method for a wide range of P values between 0 and 1 in such a way that for every single P, independent time series were fed to the algorithm and PeSaEn was estimated while the permutation of indices was kept constant for entropy estimation This process was repeated for the same time series but with different permuted indices.

For every single P and q, the calculated PeSaEn values, a random effect model were fitted S _ij  = μ + τ _j  + ε _ij with S the estimated PeSaEn, μ the intercept, τ _i the variability term due to methodological uncertainty and ε _ij the variability due to the error term. Assuming that τ _j  ∼ N(0, σ ² _τ ), the confidence interval of ratio of the methodological variability to total variance can be estimated [21]. When the upper limit of confidence interval for this ratio is below 0.1 (as popular confidence level in one-sided tests) the methodological variability considered negligible. It was found for a time series with 500 samples and q > 300 the methodological variance was negligible.

In this study the embedding dimension and tolerance were set to m = 2 and r = 0.2 × SD of input time series.