**6. Use of correlation analysis to assess the level of asymmetry in muscles**

Electromyography is the only objective and informative method of studying the leading diseases of the nervous system, the functional state of the peripheral nervous system. Electromyography allows not only to determine the nature of the disease and its topical diagnosis, but also to objectively monitor the effectiveness of treatment and predict the time and stages of the recovery process [38].

Although symmetry is considered ideal in the body, this is not the case. In other words, the muscle mass of a healthy person's limbs has a slightly different mass and strength compared to the opposite side. One method of determining asymmetry is the analysis of EMG signals received by surface electrodes [25, 39].

The application of various methods to the processing of EMG signals, including mathematical, statistical, and complex, can be found in numerous literature sources [16, 29, 40–42]. It should be noted that despite the widespread use of complex mathematical processing methods in recent decades to increase the accuracy of calculations and reliability of diagnostic results, the development of processing devices based on the application of such methods is weak in terms of processing algorithms and constructive implementation. In this regard, the application of classical processing methods does not lose its relevance.

Correlation functions characterize the stable statistical characteristics of EMG. Some of these features have a functional or phenomenological value in the interpretation of EMG, but some of them open up new interesting ways in the neurophysiological analysis of the neuromotor apparatus.

In [43], the authors used a correlation analysis method to recognize the movement of the limbs. The obtained measurement results are compared with the EMG placed in the database and the signals are classified. The method of mutual correlation was used in [44] to analyze the process of renewal of the unit of movement of the nervous-muscular system. [45] examined the correlation between the age of patients with Packerson's disease and the frequency of tremor.

*Methods and Tools for Assessing Muscle Asymmetry in the Analysis of Electromyographic… DOI: http://dx.doi.org/10.5772/intechopen.103061*

The maximum value of the correlation function (correlation coefficient) characterizes the relationship of processes over time, their degree of class.

Interference EMF is the result of a large number of potentials located in the separation area. However, then it is impossible to separate the action potentials of individual units of action. The dispersion of loads over time passing through motoneurons is not so great. Therefore, the statistical determination of the phase relationship of the two interfering EMGs allows to reveal the relationship of the action potentials of the two groups of units of motion over time (if these two EMGs reflect the loads of different HV). Based on this, cross-correlation analysis has opened up great opportunities in the study of synchronization of motoneuron charges.

#### **6.1 Problem solving methods and approbation**

In the mutually correlated analysis of EMG, the integral of the derivatives of two different functions is found. If they are not completely dependent and the phase ratios are random, the mutual correlation function will be equal to o for any τ. If the processes are related and the phases of any of the two curves at τ often overlap, then the mutual correlation function τ will be positive at the considered value.

In order for the value of the correlation function not to depend on the change in EMG or amplification of the electromyograph, it is normalized, ie it is expressed as part of the average power of both processes [46]:

$$R\_{norm}(\tau) = \frac{\frac{1}{T} \int\_0^T f\_1(t) f\_2(t + \tau) dt}{\sqrt{\frac{1}{T} \int\_0^T f\_1^2(t) dt} \sqrt{\frac{1}{T} \int\_0^T f\_2^2(t) dt}} \tag{16}$$

As a result of normalization, the correlation value is relative (it indicates the share of class electrical events in total electrical activity).

It is not advisable to use the correlation analysis method to measure the duration of the waves, as this quantity can be obtained by a simple instrument or by visual means.

The maximum of the mutual correlation function is accompanied not only by the value of τ = 0, but also by a slip.

This shift indicates that there is a connection between the two EMFs. But one of them is late compared to the other. The average value of this delay is characterized by the value of the landslide, ie it is possible to speculate on which EMG delay is based on its direction. A small displacement may be due to a difference in the path of excitation from one electrode to another. Therefore, significant landslides greater than 3–4 ms are considered.

If we imagine the human body divided into two parts from the center, it is not difficult to see that most organs are symmetrical and consist of right and left parts: limbs (hands, feet), cerebral hemispheres, lungs, kidneys, and so on. Even the only visible organs in the general system consist of two symmetrically divided parts, such as the heart (right and left atrium, right and left ventricle), and so on.

Some pathological changes, working conditions, habits, and some sports form asymmetries that can cause serious complications in the body. This leads to the pathology of the part that consumes more energy after a certain period.

Various methods and tools are used in clinics and hospitals to identify such deficiencies. **Figure 14** shows the measurement results recorded using the ME6000-EMQ - 12-channel electromyograph.

In this example, 12 measurements are made without separation, and the results reflect the muscle strength in the form of a graph or figure. In this device, muscle

#### **Figure 14.**

*Measurement result recorded using ME6000-EMQ device.*

strength is recorded on a scale equal to 480 μV. The measurement time is 30 seconds. Here, the value is taken as the result of an indicator equal to the maximum amplitude. That is, for example, **Figure 1** shows the maximum value of muscle strength in the quadriceps femoris muscle - vastus lateralis, and this muscle is considered to have undergone asymmetry. However, it is not possible to see the level of asymmetry in other muscles here.

The muscles being measured are the main muscles that control the movement of the lower extremities. Muscles used in experiment are the same, and are given in **Table 1**.

The measurement results are collected in the form of a file with.dbf, .xls, .m, or any other possible extensions for further processing. An example is **Figure 15**. Here L and R show the left and right parts as the corresponding muscle.

The appropriate sequence of operations is then performed to calculate the correlation function or correlation coefficient of the corresponding pair of signals.

Computer modeling of calculations was performed in the Excel software package. The results of the calculated correlation coefficient are shown in **Table 8**, and the histogram of the results for muscles is shown in **Figure 3**.

As can be seen from the table, the results obtained (correlation coefficients) are the value of the correlation dependence of the muscle pair on each other (right or left) and not on the environment. This result does not show the difference between a muscle in one area and another, but the relationship between a pair of muscles over time. On the other hand, this approach allows us to determine how weak or strong the degree of class failure in the muscles is, and thus which muscle mass is more prone to asymmetry. These can be seen more clearly visually in **Figure 16**.
