**3. Results and discussion**

Computational Intelligence in Electromyography Analysis – 56 A Perspective on Current Applications and Future Challenges

MVC.

Matlab® and OriginLab©.

(F30) and 40% (F40) of CVM

20% (F20), 30%, (F30) and 40% (F40) of CVM.

For analyses time-domain the ramp contractions, sEMG-RMS value, were calculated from a 200 millisecond (ms) window at each the following force levels: 10%, 20%, 30% e 40% of

For signal processing of each isometric ramp contractions was used routine development by

**Figure 1.** Box chart of mean,standard deviation and percentile (25,75) in 10% (F10), 20% (F20), 30%,

**Figure 2.** Relation of RMS-sEMG (µV) value versus CVM (kg). The rectangular box is the 10% (F10),

Isometric exercises have shown a diversity of results regarding the strength gain and with it major changes have occurred regarding its inclusion within methods of strength training. This type of training is applied, mostly in clinics specializing in rehabilitation, physiotherapy and sports training centers aimed at improving muscle and joint injuries [8].

One of the most difficult physical qualities to be worked on is the strength, because a mistake in any application can lead to unpleasant consequences, such as stretching and muscle contractures. So the force is a physical quality that shows a vector quantity, it has magnitude and direction. The vectors are displayed graphically by a line of action, showing the direction and an attachment point of great importance for daily tasks as well as sports performance.

In the isometric there is a consensus response to an increase in sEMG as to alter some characteristic muscle joint as the increase in signal amplitude [13,24,25,26] changes the length and range of motion [27] and temperature [28,29,30].

Classic research shown that there is not always a tendency for this linearity. Research by [31] DeLuca & Lawrence (1983) studied the electromyographic behavior of the biceps brachii, deltoid and 1st dorsal interosseous fadigantes isometric contractions. They concluded that for the interosseous muscle was an almost linear relationship, but further analysis showed a characteristic polynomial 2nd order, the same is true for the biceps and deltoid muscles that showed a remarkable non-linearity of your data.

Studies [32] Clamann & Broecker (1979) who analyzed the triceps brachii, biceps, adductor pollicis and 1st interosseous, and [33] Woods & Bigland-Ritchie (1983) who analyzed the triceps brachii, biceps, adductor pollicis and soleus, showed that the electromyographic signal amplitude as a function of force applied to the interosseous muscle and adductor pollicis was always an almost linear relationship to the muscles and biceps, triceps and soleus this relationship was not linear, unless an exception of biceps brachii this relationship was almost linear [32].

Recent research report the nonlinear characteristic between amplitude of depolarization of motor units related to time and muscle strength [11,34]. This non-linear increase was also observed in this present study (Figure 3) in isometric ramp contraction test during time performance. The data presented in a slow onset, over time it has a rapid and finally back to grow slowly of sEMG amplitude.

According [35] Miyashita et al. (1981) and [11] Marson (2010) acting with incremental the amplitude of the electromyographic signal has an almost linear function of time to begin the individual fatigued. After the onset of muscular fatigue process the signal begins to have an increase predominantly curvilinear.

The electromyographic signal has quite often been used as a mean of assessment of muscle fatigue [17]. The increase in amplitude (Figure 3) of the EMG signal as an empirical measure of localized muscle fatigue or as an indicator of muscle fatigue [15].

Research by [15] Dimitrova & Dimitrov (2002) related that muscle fatigue is recognized as a decline in force, or failure to maintain the required or expected force. It may occur at any

Relationships Between Surface Electromyography and Strength During Isometric Ramp Contractions 59

The *f(x)* represents the data set in the RMS *x*-axis (time), A1 is the initial value of the RMS collected, the final value of *A2* RMS, *x0* is the point of inflection of the sigmoidal fit curve, i.e., the instant that there is a change from convex to concave curve which is found by the coordinate (*x0,y0*), where *y0* and found by equation (2). Since the coordinate *y0* is found the

> 1 2 2 *A A*

0 12 2 log( ) 1 *n*

*A A yA*

The *dn* parameter is the value obtained for each of the coordinate values *x* and *y*. After obtaining all the values of *dn* is done an average, and this is adopted with the value of the

Several studies report that the increase in the electrical function of time, fatiguing contractions, is characterized by the linearity between these data. Methods to assess muscle fatigue by surface electromyography are elaborated upon this predominance [11,34,36].

This nonlinear increase was also observed in this present study in ramp isometric contractions test. The data presented in the early slow growth over the same time is a rapid increase and eventually grow back slowly. With these data in hand a mathematical model

was developed, based on the characteristic sigmoidal or logistic curve (Figure 4-6).

**Figure 4.** Relationship, adjust and parameter nonlinear of RMS-sEMG value. BFCL example.

*n*

(2)

(3)

0

*x x d*

*y*

*n*

value of *x0* on the time axis.

constant parameter *dx*.

The *dn* parameter is found using equation (3)

point from the nervous centers and conducting pathways to the contractile mechanism of muscle fibers.

Study by [16] Moritani & Yoshitake (1998) such changes have been shown to be related to hydrogen ion and metabolite accumulation and to sodium and potassium ion concentration shifts. These changes would in turn affect the muscle excitation traction coupling including the muscle membrane properties and muscle action potential propagation, leading to sEMG manifestations of muscle fatigue distinct from mechanical manifestations.

**Figure 3.** The raw sEMG (Raw sEMG), retificated (Rtf sEMG) and Linear envelope (LnrEnv sEMG) during ramp isometric contraction. Example figure.

The EMG amplitude increased progressively with increasing force in all muscles. The similar behavior was expressed as a percent of the RMS-sEMG value obtained during the brief pre-fatigue MVCs.

The data was fitting non linear by equation (1)

$$f(\mathbf{x}) = \frac{A\_1 - A\_2}{1 + e^{(\mathbf{x}\_n - \mathbf{x}\_0) \int\_{\mathbf{x}}}} + A\_2 \tag{1}$$

The *f(x)* represents the data set in the RMS *x*-axis (time), A1 is the initial value of the RMS collected, the final value of *A2* RMS, *x0* is the point of inflection of the sigmoidal fit curve, i.e., the instant that there is a change from convex to concave curve which is found by the coordinate (*x0,y0*), where *y0* and found by equation (2). Since the coordinate *y0* is found the value of *x0* on the time axis.

$$y\_0 = \frac{A1 + A2}{2} \tag{2}$$

The *dn* parameter is found using equation (3)

Computational Intelligence in Electromyography Analysis – 58 A Perspective on Current Applications and Future Challenges

muscle fibers.

Research by [15] Dimitrova & Dimitrov (2002) related that muscle fatigue is recognized as a decline in force, or failure to maintain the required or expected force. It may occur at any

point from the nervous centers and conducting pathways to the contractile mechanism of

Study by [16] Moritani & Yoshitake (1998) such changes have been shown to be related to hydrogen ion and metabolite accumulation and to sodium and potassium ion concentration shifts. These changes would in turn affect the muscle excitation traction coupling including the muscle membrane properties and muscle action potential propagation, leading to sEMG

**Figure 3.** The raw sEMG (Raw sEMG), retificated (Rtf sEMG) and Linear envelope (LnrEnv sEMG)

The EMG amplitude increased progressively with increasing force in all muscles. The similar behavior was expressed as a percent of the RMS-sEMG value obtained during the

> 0 1 2 ( ) 2 ( ) 1 *n x xx d A A f x A e*

(1)

during ramp isometric contraction. Example figure.

The data was fitting non linear by equation (1)

brief pre-fatigue MVCs.

manifestations of muscle fatigue distinct from mechanical manifestations.

$$d\_n = \frac{\mathbf{x}\_n - \mathbf{x}\_0}{\log(A\_1 - A\_2) - 1/y\_n - A\_2} \tag{3}$$

The *dn* parameter is the value obtained for each of the coordinate values *x* and *y*. After obtaining all the values of *dn* is done an average, and this is adopted with the value of the constant parameter *dx*.

Several studies report that the increase in the electrical function of time, fatiguing contractions, is characterized by the linearity between these data. Methods to assess muscle fatigue by surface electromyography are elaborated upon this predominance [11,34,36].

This nonlinear increase was also observed in this present study in ramp isometric contractions test. The data presented in the early slow growth over the same time is a rapid increase and eventually grow back slowly. With these data in hand a mathematical model was developed, based on the characteristic sigmoidal or logistic curve (Figure 4-6).

**Figure 4.** Relationship, adjust and parameter nonlinear of RMS-sEMG value. BFCL example.

Computational Intelligence in Electromyography Analysis – 60 A Perspective on Current Applications and Future Challenges

Relationships Between Surface Electromyography and Strength During Isometric Ramp Contractions 61

The adjustment was made by equation 1. To verify that this setting was close to actual data (data collected) was analyzed the coefficient of determination (r²) between the actual data

According to [37] Enoka and Stuart (1992), [35] Miyashita et al. (1981) in incremental overhead fatiguing exercise with the amplitude of the electromyographic signal has an almost linear function of time until the individual begins to fatigue. After the onset of

This characteristic presented in this mathematical adjustment points that are side left of the parameter *x0* which is the turning point of the concavity of the sigmoidal curve. This behavior provides a characterization of possible fatigue neuromuscular isometric ramp

Investigations have been concerned in the restricted use of the isometric contraction ramp during a single, non-fatiguing, and linearly increasing contraction force variation at short intervals, it is suggested that where the isometric ramp contractions can provide higher resolution in the entire spectrum force, less time required for data acquisition electromyography, and less susceptible to fatigue than contractions step. It is possible, however, that whereas the ramp and contraction power spectrum characteristic of the control strategies can incorporate various engine and comparing the dynamic and isometric

This present study revealed that the relationship between electromyography, force and time has characteristic sigmoidal. This demonstrates that the initial charges in a relationship are slowly increasing, but at intermediate loads this increase is more rapid and exponential. However, this behavior the load end presents a decrease in the rate of increase and maintenance of a depolarization of motor units at the end of execution of the isometric ramp

This sigmoidal relationship data is well described in the equation proposed for modeling (curve fitting) of hamstring muscle electromyographic signal analyzed, which is presented the start point (*A1*), the constant in equation (*dx*), the turning point the concavity of the curve (*x0*) and peak (*A2*) to be kept in mathematical adjustment of the curve in relation to

In summary, the results of this study indicate that RMS values of the hamstrings muscles tend to increase nonlinear whereas force with the number of isometric ramp contractions

Since these responses are characteristic of neuromuscular fatigue, the test described here may be useful for identifying muscle fatigue in ramp isometric contraction test. With this

muscle fatigue process the signal begins to increase a predominantly curvilinear [38].

and the adjusted data, where the r² values greater than 0.80.

contractions.

contraction.

performed.

actual curve acquired.

**5. Future directions**

**4. Conclusion**

contractions isokinetic step.

**Figure 5.** Relationship, adjust and parameter nonlinear of RMS-sEMG value. ST example.

**Figure 6.** Relationship, adjust and parameter nonlinear of RMS-sEMG value. SM example.

The adjustment was made by equation 1. To verify that this setting was close to actual data (data collected) was analyzed the coefficient of determination (r²) between the actual data and the adjusted data, where the r² values greater than 0.80.

According to [37] Enoka and Stuart (1992), [35] Miyashita et al. (1981) in incremental overhead fatiguing exercise with the amplitude of the electromyographic signal has an almost linear function of time until the individual begins to fatigue. After the onset of muscle fatigue process the signal begins to increase a predominantly curvilinear [38].

This characteristic presented in this mathematical adjustment points that are side left of the parameter *x0* which is the turning point of the concavity of the sigmoidal curve. This behavior provides a characterization of possible fatigue neuromuscular isometric ramp contractions.