Intercriteria Decision-Making Method for Speed and Load Effects Evaluation on Upper Arm Muscles in the Horizontal Plane

Abstract

Speed and load effects on the number and type of pair interactions between six elbow and shoulder muscles or muscle (m.) heads were evaluated by the intercriteria decision-making method (ICrA). The surface electromyography (sEMG) signals of the m. deltoideus pars clavicularis (Dcla), m. deltoideus pars spinata (Dspi), m. biceps brachii (BB), m. triceps brachii caput longum (TB), m. brachialis (BR), and m. anconeus (AN) of ten healthy subjects were recorded. The data was collected during cycling movements (CMs) for continuous flexions and extensions in the elbow joint in the horizontal plane. The CMs were performed with and without an added load at four different speeds. The obtained sEMG data were subjected to the ICrA to identify muscle activity and speed correlations. The ICrA results demonstrate that added load resulted in a higher number of consonance relations between muscle activities. Positive consonance (PosC) appears between the Dcla-Dspi, Dspi-BR, BB-BR, and TB-BR criteria pairs for the loaded flexion phases. When extension is in the focus, Dcla-BB is in a consonance relation for no loaded phases, while for the loaded ones, five muscle pairs, namely Dcla-BB, Dcla-BR, Dspi-BR, BB-BR, and TB-BR, hit PosC. Also, the most correlations are found for the fastest phase (1 s) of flexion and extension, regardless of the load. Additionally, correlation dependencies between the two faster (Sp2-Sp1) and the two slower speeds (Sp10-Sp6) were found.

1. Introduction

The musculoskeletal structure of the upper limb provides exceptional mobility and a wide range of motion, enabling various daily tasks that require reaching. Even the most basic limb movements present inherent difficulties that our motor system has evolved to solve [1]. Physiological evidence suggests that the brain employs simple strategies, known as synergies, to generate a wide range of movements, thereby alleviating the burden on the central nervous system [2]. For any given task, a multitude of possible movement strategies [3] exist. Although there are numerous ways our muscles can generate the necessary forces [4,5], the neuromuscular system faces some neural constraints [6]. In these limitations lies the solution to activating specific muscle (m.) synergies.

There is a dearth of studies that examine the complex interactions and correlations between multiple muscles during movement, particularly when factors such as speed and load are altered. Moreover, motor tasks in statics and dynamics, which include both one-joint and two-joint muscles, are rarely combined.

To understand the muscle regulation mechanisms, many authors rely on the electromyography method (EMG), which helps to identify muscle synergies. Osu and Gomi [7] try to predict joint stiffness under static loading using EMG data, during static force control in the horizontal plane. They found that the elbow joint was regulated by the simultaneous activation of both monoarticular (pectoralis major, posterior deltoid, brachioradialis, lateral head of triceps brachii) and biarticular (biceps brachii, long head of triceps brachii) muscles, whereas monoarticular muscles primarily controlled the shoulder joint. This suggests that biarticular muscles are mainly involved in controlling the elbow joint during static force regulation. While biarticular muscles act on both joints, they showed strong covariation with elbow monoarticular muscles.

Several studies on muscle activity during dynamic movements focus on the relationship between movement muscle co-activation with speed and load. Lacquaniti and Soechting [8] investigate the influence of load perturbations on muscle responses applied to the arm during motions. The study found that biceps and triceps activity is not just about elbow movement; these muscles can activate in unexpected ways depending on where the force is applied. They discover that when the forearm is extended and a force is applied to the upper arm, it leads to stronger biceps activation. These findings challenge the simple idea that muscle activity is solely a reaction to changes in muscle length. According to Bazzuchi et al. [9], the torque produced during both elbow flexion and extension is strongly affected by antagonist activation. The triceps consistently showed more antagonist activation than the biceps during elbow flexion. The authors cannot prove the initial hypothesis that speed influences muscle activation levels. Unlike them, Melhorn [10] found that slower contractions resulted in significantly more muscle activity than faster ones. In short, while fast reps make you fatigued quickly, slow reps appear to recruit more muscle fibers. Another study combining speed and load investigation [11] examined motor unit behavior and muscle function during high-speed, elbow flexor workouts. The calculated muscle triceps root mean square of the EMG values showed interactions between repetition type and load during both elbow flexion and extension. This suggests that the triceps, despite being an antagonist during elbow flexion, might play a crucial role as a joint stabilizer, especially during faster movements and at more extended joint angles. Unlike slower, heavy-load exercises, high-speed training may lead to a more balanced contribution of factors like motor unit recruitment, rate coding, and antagonist co-contraction in determining triceps activity.

The abovementioned studies evaluated muscle activity using the surface electromyography (sEMG) method. Surface EMG is a non-invasive method for studying superficial muscles by placing electrodes on the skin. In biomechanics, sports science, and rehabilitation, sEMG is commonly used to gain a better understanding of muscle coordination and timing of muscle contractions, as well as to evaluate motor control strategies. In this study, we precisely chose the investigated muscles. According to the literature [12], we know that the muscles responsible for elbow flexion are the m. brachialis and m. biceps brachii (the two heads are lying one above the other). Extensor muscles are m. triceps brachii and m. anconeus. The medial head of m. triceps is not located superficially, so surface electrodes cannot capture it. The choice is between the long head and the lateral head of m. triceps. The lateral head is the strongest head of the triceps, but it acts just in the elbow. As we have one one-joint (m.brachialis) and one two-joint (m. biceps brachii) flexor, we prefer to investigate one one-joint (m. anconeus) and one two-joint (m. triceps brachii long head) extensor. Two shoulder parts of a muscle were selected—m. deltoideus pars clavicularis and m. deltoideus pars spinata. Anterior fibers of the deltoideus take part in the humerus flexion (drawn forward), and when the forearm is flexed, the biceps brachii also participates in this movement. These fibers are also responsible for inward rotation. Posterior fibers of the deltoideus extend (drawn backward) the humerus, and, when the forearm is extended, the triceps brachii also participates. So, for each flexion or extension in the shoulder and elbow, we have one one-joint muscle and one two-joint muscle.

Validated in numerous investigations as an effective tool for analyzing biological data, developed by Atanassov et al., the intercriteria decision-making method (ICrA) [13] has been aiding in successful decision-making outcomes in medicine [14,15], kinesiology [16], sports [17], etc. The decision-making process, especially in biomedicine and healthcare, not only requires multiple compromises but is also accompanied by various constraints that make reaching a final solution complex. The ICrA, combining mathematical formalisms of index matrices and intuitionistic fuzzy sets, can also support EMG data evaluations. So far, three studies have applied the ICrA to process EMG data from several muscles. In [18], Angelova et al. used the ICrA to examine muscle activity correlations during cyclic movements in the sagittal plane, while in [19,20], the authors applied the ICrA for optimizing the experimental protocols, reducing time duration without losing valuable data.

The ICrA was elaborated for finding correlation dependencies between a set of criteria used for measuring of set of objects. The calculations involved in the ICrA are carried out by means of “<, >, =” for comparisons between object scores against the criteria instead of comparisons between their numerical values [13,21]. Thus, the approach becomes faster than the well-known correlation analysis (CA) methods. Another advantage of the ICrA is that the approach can be applied not only to clear data but for incomplete ones and, in addition, to fuzzy data. After calculations, the ICrA provides the degree of correspondence, non-correspondence, and unlike CA, the degree of “uncertainty” between the criteria [13]. As opposed to standard statistical methods, the ICrA can find the relations between a limited number of criteria measured for each subject. Also, the approach is appropriate for application to data sets varying in size [15]. Detailed comparisons between the ICrA and CA can be found in [14,17,20].

We hypothesize that altering the speed or adding weight during a motor task will prompt the neuromuscular system to adjust its execution strategies, resulting in the activation of different muscle synergies. That is why the purpose of this investigation is to assess how speed and a 0.5 kg load on the wrist affect the number and type of pair interactions between six monoarticular and biarticular elbow and shoulder muscles during movements in the horizontal plane using the intercriteria decision-making method. Also, the correlations between different speeds were identified.

2. Materials and Methods

2.1. sEMG Method

A selection of fifteen healthy volunteers to participate in the quasi-experimental setup was made. The age limit was between 18 and 65 years. All participants were physically healthy, with no history of neurological or orthopedic diseases, and no injuries or motor disorders of the upper limb. The research method and experimental protocol were explained in detail to each subject. On the day of the study, participants signed an informed consent form to participate, which had been previously approved by the Ethics Committee of the Institute of Biophysics and Biomedical Engineering. The experiments complied with the Declaration of Helsinki (ethical principles for medical research involving human subjects). All subjects completed the experimental protocol in full. There were no dropouts during the study.

Electromyographic signals were recorded from six whole muscles or muscle heads—two parts of the m. deltoideus, pars clavicularis, and pars spinata (Dcla, Dspi); m. biceps brachii (BB); and m. triceps brachii—caput longum (TB), m. brachialis (BR), and m. anconeus (AN). A telemetric system with eight channels, Telemyo 2400G2 of Noraxon, Inc. (Scottsdale, AZ, USA), was used. The circle “Skintact-premier” F-301 Ag/AgCl electrodes (Leonhard Lang GmbH, Innsbruck, Austria) with 2.5 cm interelectrode distance were used for non-invasive body contact and assessing surface EMG signals. The sampling frequency was 1500 Hz, which represents the number of times per second that the analog EMG signal is converted into digital values. To determine the contact points of the electrodes with which the prescriptions of the Seniam protocol were used (http://www.seniam.org/), electrodes were placed only on the right hand, the dominant hand of all the participants.

The experimental protocol was performed from a sitting position and consisted of several identical upper limb exercises, which were, however, performed at different speeds and with or without an additional load of 0.5 kg on the wrist. Each motor task was performed within one minute.

Experimental protocol:

• Position of relaxation. The subject sits on a chair with his gaze directed forward, arms relaxed loosely at his sides, and legs with 90-degree flexion at the hip, knee, and ankle joints, feet placed on the floor with a small distance between them.
• Maximal isometric contractions were elicited for the six investigated muscles. The upper limb is passively brought into several starting positions, from which maximal isometric contractions are performed. For this purpose, the examiner stabilizes the upper extremity with the torse and one hand, while with the other and with the weight of the body, exerts pressure to provoke maximal contraction and counteracts the subject’s attempt to move his limb. In this way, muscle by muscle is selectively activated. These signals serve to normalize the EMG recordings.

The subject extends his right arm straight forward (90 degrees of flexion at the shoulder joint). The forearm is pronated, and the palm is facing the floor. From this position, several consecutive elbow flexions and extensions in the horizontal plane are performed with different movement characteristics. From the described starting position of the hand, four phases of activity begin. The first is flexion in the elbow joint until the fingers touch the opposite shoulder. This is followed by a phase of maintaining the position reached. From here comes the extension phase to the described starting position of the arm stretched forward. Finally, there is the phase of maintaining the position reached. Each of the active phases is performed with a duration of 10, 6, 2, and 1 s. Each maintenance phase is always 5 s. So, for the first cycle, we have a flexion phase of 10 s (fl10)—5 s (pose in flexed arm) followed by extension for 10 s (ex10)—5 s (pose in extended arm), which is repeated until the one-minute recording expires. For the second, third, and fourth cycles, abbreviations were related with speed duration, respectively, for flexion for 6 s (fl6), 2 s (fl2), and 1 s (fl1), and extension for 6 s (ex6), 2 s (ex2), and 1 s (ex1). Due to the different duration of the active part of the cycle, a different number of repetitions is obtained. In the subsequent processing, only one complete cycle is selected—the best performance. Next, a half-kilogram ergometric weight is placed on the wrist, and the same cycles are repeated with the same duration. Periods for flexion and extension were 10 s (fl10W/ex10W), 6 s (fl6W/ex6W), 2 s (fl2W/ex2W), and 1 s (fl1W/ex1W). Finally, we have 10 one-minute recordings—a recording of rest, of maximum isometric contraction for each of the 6 measured muscles of flexion and extension in the elbow joint in the horizontal plane (4 for flexion and 4 for extension with different durations of the active phases). The change in each interval was guided by an online Tabata interval timer. Thus, the subject received visual (on-screen countdown of seconds, as well as red color for posture and green color for active movement) and audio commands (a tap for each second that passed).

Figure 1 illustrates the experimental setup, including the raw EMG signals. These signals were recorded over 6 s active phases in the horizontal plane with a 0.5 kg load. The weight used meets three important criteria: it provokes a stronger muscle response, does not cause premature muscle fatigue, and does not engage additional muscle groups, if a grip is used. The channels correspond to specific muscles: Dcla (blue), Dspi (green), BB (red), TB (yellow), AN (purple), and BR (dark green). Channels seven and eight display 2D goniometer (Scottsdale, AZ, USA) data, aiding in movement start and end orientation. The vertical dotted line indicates the second in which the recording in the photo on the side was displayed. Electrode placement is shown on the right, with kinesiotape used to secure sensors and reduce movement artifacts.

Initially, all EMG recordings were visually observed, and only data from four men and six women were selected for analysis. The remaining five participants were excluded due to various issues such as unfilterable abnormal spikes, inability to maintain the experimental rhythm or arm position, significant cable fluctuations, EMG contamination, or unstable recordings. Despite the limitations imposed by the reduced sample size—such as decreased generalizability and potential underrepresentation of the target population—participants still had to be excluded to bring the sample as close as possible to the pre-determined protocol conditions. So, the question with excluding participants is whether to compromise the quality of the experimental design or the generalizability. In this case, priority is given to the reliability of the data over broader generalization.

The study conducted is real and experimental and therefore faces inevitable limitations. Restricting this research to healthy participants only is a purposeful methodological decision that aims to minimize sources of variation arising from pathological conditions (numerous and so different in their genesis and manifestation). Therefore, the focus of the study is on spontaneous muscle activity under normal physiological conditions and on establishing a clear baseline for future studies that would include clinical populations. This limitation reduces the direct generalizability of the results to patients with movement disorders, but it is a necessary step to achieve high internal validity of the experiment.

In order to be a non-invasive investigation, only superficial muscles were examined. This means that some muscles with a main action in a specific direction in the shoulder or elbow must be omitted because we do not have access to them. Despite this limitation, the use of sEMG was chosen because it is a suitable and accessible method for studying the synchronous activation of large muscle groups during functional movements. Something more, the participants do not feel any discomfort or pain during the testing. The duration of the protocol was chosen to maintain a high level of focus and execution precision on the part of the participants. A long protocol would have increased the risk of muscle fatigue and attentional impairment, which would directly compromise the quality of the EMG signals and the execution of the movement at the set pace.

The EMG data recorded during the position of relaxation underwent initial processing. This involved Butterworth high-pass filtration (4th order, 20 Hz cut-off frequency) and Butterworth low-pass filtration (4th order, 350 Hz cut-off frequency), consistent with established methods [22]. The same filtration was then applied to EMGs from maximal isometric contractions to calculate six normalization coefficients for the movement EMGs.

For each movement task, the same filtration and normalization procedures were performed. Following a thorough visual inspection, only one trial from each flexion and extension movement cycle was chosen. The start and end points of these flexion and extension motions were precisely identified, and a specific time interval was selected. Within these intervals, the EMG data were rectified and smoothed (20 samples). Finally, the area under the rectified and smoothed curves was calculated for the corresponding time interval. These processed values were then used for the ICrA analysis, as detailed in the subsequent section.

2.2. ICrA Decision-Making Method

Attanassov et al., the founders of the ICrA approach [13], elaborated the decision-making method for establishing correlation dependencies between a set of criteria. Thus, the slower or the harder to measure criteria can be replaced by those correlated with faster and easier to measure ones. Also, the mathematical tool can be useful for finding known or unknown correlation dependencies from the literature.

For a more accurate decision-making process, the ICrA relies on index matrices (IMs) for data arranging and intuitionistic fuzzy sets (IFSs) that account for uncertainty in the established dependency (positive or negative consonance) or dissonance for each criteria pair. In the beginning, the ICrA requires data sets of multiple objects measured against different criteria, presented in the form of IM.

	O1	…	Oi	…	Om
C1	eC1,O1	…	eC1,Oi	…	eC1,Om
…	…	…	…	…	…
Ck	eCk,O1	…	eCk,Oi	…	eCk,Om
…	…	…	…	…	…
Cn	eCn,O1	…	eCn,Oi	…	eCn,Om

where C₁ … C_n are criteria; O₁ … O_m are objects; and e_C1,_O1 … e_Cn,_Om are elements.

Let $N_{k,l}^{\mu }$ and $N_{k,l}^{\upsilon }$ represent the number of cases in which R(e_Ck,Oi, e_Ck,Oj) and R(e_Cl,Oi, e_Cl,Oj) and, respectively, R(e_Ck,Oi, e_Ck,Oj) and $\overline{R}$(e_Cl,Oi, e_Cl,Oj) are simultaneously satisfied. It is evident that the total number of pairwise comparisons between the n criteria is n(n − 1)/2. Hence,

$${0\le N}_{k,l}^{\mu }+N_{k,l}^{\upsilon } \le {\displaystyle \frac{n(n-1)}{2}}$$

(1)

Let for each k, l such that 1 ≤ k < l ≤ n and for n ≥ 2 we define two counters:

$${\mu }_{Ck,Cl}=2{\displaystyle \frac{N_{k,l}^{\mu }}{n(n-1)}} , {\upsilon }_{Ck,Cl}=2{\displaystyle \frac{N_{k,l}^{\upsilon }}{n(n-1)}}$$

(2)

The pair ${\mu }_{Ck,Cl}, {\upsilon }_{Ck,Cl}$ is an intuitionistic fuzzy pair (IFP). The IFP is an intuitionistic fuzzy evaluation of the relations between two criteria, C_k and C_l. Thus, the initial IM can be transformed into IM, containing only the relations between the criteria.

	C1	…	Ck	…	Cn
C1	〈1, 0〉	…	$\langle {\mu }_{C_1,C_k},{\nu }_{C_1,C_k}\rangle$	…	$\langle {\mu }_{C_1,C_n},{\nu }_{C_1,C_n}\rangle$
…	…	…	…	…	…
Ck	$\langle {\mu }_{C_k,C_1},{\nu }_{C_k,C_1}\rangle$	…	〈1, 0〉	…	$\langle {\mu }_{C_k,C_n},{\nu }_{C_k,C_n}\rangle$
…	…	…	…	…	…
Cn	$\langle {\mu }_{C_n,C_1},{\nu }_{C_n,C_1}\rangle$	…	$\langle {\mu }_{C_n,C_k},{\nu }_{C_n,C_k}\rangle$	…	〈1, 0〉

The final IM sets the degrees of correspondence, non-correspondence, and the degrees of uncertainty between the criteria C₁, …, C_n. Thus, the ICrA-evaluated correlation dependencies have intuitionistic fuzzy pairs form with values between 0 and 1.

The last step of the algorithm is to determine positive (PosC) or negative (NegC) consonance and dissonance between the criteria, depending on the threshold values for μ and ν.

Let 0 ≤ α ≤ 1 and 0 ≤ β ≤ 1 be numbers such that α + β ≤ 1. The two criteria C_k and C_l are in the following:

• PosC for ${\mathrm{\mu }}_{\mathrm{C}\mathrm{k},\mathrm{C}\mathrm{l}}$ > α and ${\upsilon }_{\mathrm{C}\mathrm{k},\mathrm{C}\mathrm{l}}$ < β;
• NegC for ${\mathrm{\mu }}_{\mathrm{C}\mathrm{k},\mathrm{C}\mathrm{l}}$ < β and ${\upsilon }_{\mathrm{C}\mathrm{k},\mathrm{C}\mathrm{l}}$ > α;
• Dissonance, otherwise.

PosC is found when the µ-value is in the interval (0.75; 1.00], NegC appears when the µ-value is between [0.00; 0.25], and dissonance is realized when the µ-value hits the interval (0.25; 0.75]. More details about the µ-value scale can be found in [23].

3. Results

To study the effects of speed and weight, two initial index matrices, one for flexion without added load and one for flexion with added load, were constructed for each different active phase. The criteria in the eight matrices were the investigated muscles or muscle heads (Dcla, Dspi, BB, TB, AN, and BR), the objects were the ten subjects, and the elements were areas under the rectified, normalized, and smoothed sEMG curves. Thus, the dependencies between muscle pairs at each active phase were obtained.

ICrAData software, version 2.5 [24], with a µ-biased algorithm is used for all ICrA calculations in the study. Freely available ICrAData software can be found at http://intercriteria.net/software/ (accessed on 1 June 2025). The green color in the next six tables shows the consonance relation, while the black color indicates dissonance. Positive consonance relations between the variables mean that if one variable increases, the other is also expected to increase.

Table 1. Muscle pair dependencies for flexion calculated by intercriteria decision-making method.

Flexion	Without Weight				With Weight
	fl10	fl6	fl2	fl1	fl10W	fl6W	fl2W	fl1W
Dcla-Dspi	0.69	0.73	0.76	0.78	0.76	0.76	0.76	0.76
Dcla-BB	0.80	0.78	0.73	0.73	0.84	0.80	0.67	0.78
Dcla-TB	0.58	0.69	0.62	0.67	0.64	0.64	0.76	0.67
Dcla-AN	0.60	0.62	0.71	0.76	0.71	0.76	0.76	0.76
Dcla-BR	0.60	0.60	0.67	0.67	0.82	0.78	0.73	0.73
Dspi-BB	0.67	0.69	0.67	0.64	0.69	0.73	0.73	0.76
Dspi-TB	0.67	0.82	0.69	0.84	0.67	0.67	0.82	0.73
Dspi-AN	0.47	0.53	0.69	0.62	0.56	0.64	0.60	0.64
Dspi-BR	0.60	0.64	0.73	0.62	0.76	0.76	0.76	0.76
BB-TB	0.69	0.82	0.71	0.67	0.67	0.71	0.69	0.62
BB-AN	0.62	0.58	0.62	0.62	0.64	0.64	0.60	0.71
BB-BR	0.76	0.78	0.71	0.80	0.80	0.80	0.76	0.78
TB-AN	0.62	0.58	0.56	0.69	0.58	0.58	0.69	0.82
TB-BR	0.80	0.73	0.64	0.78	0.82	0.82	0.84	0.84
AN-BR	0.73	0.71	0.64	0.73	0.71	0.71	0.80	0.84

Legend: Dcla, Dspi—two parts of the m. deltoideus, pars clavicularis, and pars spinata; BB—m. biceps brachii; TB—m. triceps brachii—caput longum; BR—m. brachialis; and AN—m. anconeus. fl10/fl10W—flexion without and with weight for 10 s, fl6/fl6W—flexion without and with weight for 6 s, fl2/fl2W—flexion without and with weight for 2 s, and fl1/fl1W—flexion without and with weight for 1 s.

presents the results altogether for fifteen muscle pairs during flexion with and without added load after the ICrA calculations.

The eight initial index matrices for extension with and without added load have been constructed in a similar way to those for flexion. The results obtained altogether for fifteen muscle pairs after each IM subjected to ICrA are summarized in

Table 2. Muscle pair dependencies for extension calculated by intercriteria decision-making method.

Extension	Without Weight				With Weight
	ex10	ex6	ex2	ex1	ex10W	ex6W	ex2W	ex1W
Dcla-Dspi	0.73	0.73	0.73	0.71	0.73	0.73	0.71	0.76
Dcla-BB	0.87	0.82	0.84	0.78	0.82	0.80	0.82	0.82
Dcla-TB	0.67	0.69	0.62	0.64	0.73	0.62	0.71	0.76
Dcla-AN	0.64	0.76	0.87	0.76	0.69	0.71	0.76	0.69
Dcla-BR	0.58	0.62	0.60	0.64	0.80	0.76	0.80	0.82
Dspi-BB	0.73	0.69	0.71	0.71	0.73	0.76	0.67	0.76
Dspi-TB	0.76	0.78	0.67	0.71	0.78	0.71	0.78	0.73
Dspi-AN	0.60	0.58	0.73	0.60	0.56	0.62	0.60	0.67
Dspi-BR	0.67	0.71	0.73	0.71	0.80	0.76	0.78	0.84
BB-TB	0.76	0.69	0.69	0.64	0.69	0.73	0.71	0.71
BB-AN	0.69	0.76	0.89	0.80	0.67	0.69	0.80	0.78
BB-BR	0.71	0.71	0.71	0.73	0.80	0.87	0.84	0.91
TB-AN	0.62	0.58	0.67	0.49	0.69	0.69	0.60	0.58
TB-BR	0.64	0.62	0.58	0.69	0.84	0.82	0.82	0.76
AN-BR	0.71	0.69	0.69	0.76	0.76	0.78	0.64	0.78

Legend: Dcla, Dspi—two parts of the m. deltoideus, pars clavicularis, and pars spinata; BB—m. biceps brachii; TB—m. triceps brachii—caput longum; BR—m. brachialis; and AN—m. anconeus. ex10/ex10W—extension without and with weight for 10 s, ex6/ex6W—extension without and with weight for 6 s, ex2/ex2W—extension without and with weight for 2 s, and ex1/ex1W—extension without and with weight for 1 s.

.

The other four index matrices constructed for each participant help to find dependencies between different speeds (Sp10, Sp6, Sp2, and Sp1). Two of them are for flexion and two for extension, respectively, with and without added load. Each IM includes the six muscles, or muscle heads, as objects, the four velocities as criteria, and the areas under the rectified and smoothed sEMG curves as elements. In total, forty matrices were subjected to the ICrA for the ten participants (Sb1 to Sb10).

Table 3. Speed dependencies for flexion, along with the number of consonances and dissonances for each pair.

Flexion	Sb1	Sb2	Sb3	Sb4	Sb5	Sb6	Sb7	Sb8	Sb9	Sb10	NbCo	NbDiss
Sp10-Sp6	0.93	0.47	1	1	1	1	0.93	1	0.87	0.80	9	1
Sp10-Sp2	0.93	0.40	0.73	0.93	0.93	0.93	0.93	0.93	0.47	0.67	6	4
Sp10-Sp1	0.93	0.33	0.67	0.93	1	0.93	0.87	0.93	0.80	0.80	8	2
Sp6-Sp2	1	0.93	0.73	0.93	0.93	0.93	0.87	0.93	0.60	0.87	8	2
Sp6-Sp1	1	0.87	0.67	0.93	1	0.93	0.80	0.93	0.93	0.87	9	1
Sp2-Sp1	1	0.93	0.80	1	0.93	1	0.93	1	0.53	0.87	9	1

Legend: Sb1, …, Sb10—subjects from 1 to 10; NbCo—number of consonances, NbDiss—number of dissonances; Sp1—1 s fast speed, Sp2—2 s fast speed, Sp6—6 s slow speed, and Sp10—10 s slow speed.

and

Table 4. Speed dependencies for flexion with added weight, along with number of consonances and dissonances for each pair.

Flexion with Weight	Sb1	Sb2	Sb3	Sb4	Sb5	Sb6	Sb7	Sb8	Sb9	Sb10	NbCo	NbDiss
Sp10-Sp6	1	0.93	1	0.87	0.93	0.93	0.87	0.93	0.87	0.93	10	0
Sp10-Sp2	1	0.87	1	0.87	0.93	0.87	0.87	0.93	0.60	1	9	1
Sp10-Sp1	0.93	0.73	0.87	0.80	0.93	0.87	1	0.93	0.60	0.87	8	2
Sp6-Sp2	1	0.80	1	0.87	1	0.93	1	1	0.73	0.93	9	1
Sp6-Sp1	0.93	0.67	0.87	0.93	1	0.93	0.87	1	0.60	0.80	8	2
Sp2-Sp1	0.93	0.86	0.87	0.80	1	1	0.87	1	0.87	0.87	10	0

Legend: Sb1, …, Sb10—subjects from 1 to 10; NbCo—number of consonances, NbDiss—number of dissonances; Sp1—1 s fast speed, Sp2—2 s fast speed, Sp6—6 s slow speed, and Sp10—10 s slow speed.

show the results for flexion with and without added load along with the number of detected consonance (NbCo) and dissonance (NbDiss) dependencies, while

Table 5. Speed dependencies for extension, along with the number of consonances and dissonances for each pair.

Extension	Sb1	Sb2	Sb3	Sb4	Sb5	Sb6	Sb7	Sb8	Sb9	Sb10	NbCo	NbDiss
Sp10-Sp6	1	0.87	1	1	0.93	1	0.93	0.93	0.87	1	10	0
Sp10-Sp2	0.93	0.87	0.73	1	1	1	1	0.93	0.60	0.87	8	2
Sp10-Sp1	0.93	0.47	0.73	1	1	1	0.87	0.93	0.80	0.93	8	2
Sp6-Sp2	0.93	0.87	0.73	1	0.93	1	0.93	1	0.60	0.87	8	2
Sp6-Sp1	0.93	0.60	0.73	1	0.93	1	0.93	1	0.80	0.93	8	2
Sp2-Sp1	1	0.60	1	1	1	1	0.87	1	0.67	0.93	8	2

Legend: Sb1, …, Sb10—subjects from 1 to 10; NbCo—number of consonances, NbDiss—number of dissonances; Sp1—1 s fast speed, Sp2—2 s fast speed, Sp6—6 s slow speed, and Sp10—10 s slow speed.

and

Table 6. Speed dependencies for extension with added weight, along with the number of consonances and dissonances for each pair.

Extension with Weight	Sb1	Sb2	Sb3	Sb4	Sb5	Sb6	Sb7	Sb8	Sb9	Sb10	NbCo	NbDiss
Sp10-Sp6	0.80	0.93	1	0.93	0.87	1	1	0.93	0.60	0.93	9	1
Sp10-Sp2	0.80	0.93	1	1	0.87	0.93	0.87	0.87	0.93	0.67	9	1
Sp10-Sp1	0.73	0.87	1	0.87	0.93	1	0.80	0.93	0.93	0.73	8	2
Sp6-Sp2	1	0.87	1	0.93	1	0.93	0.87	0.80	0.67	0.73	8	2
Sp6-Sp1	0.93	0.80	1	0.80	0.93	1	0.80	0.87	0.67	0.67	8	2
Sp2-Sp1	0.93	0.93	1	0.87	0.93	0.93	0.93	0.93	1	0.93	10	0

Legend: Sb1, …, Sb10—subjects from 1 to 10; NbCo—number of consonances, NbDiss—number of dissonances; Sp1—1 s fast speed, Sp2—2 s fast speed, Sp6—6 s slow speed, and Sp10—10 s slow speed.

present those for extension.

For better interpretation of the results when speed dependencies were examined (Table 3, Table 4, Table 5 and Table 6), NbCo and NbDiss have been counted. Based on the counted numbers, the pairs Sp10-Sp6 and Sp2-Sp1 are distinguished for flexion as well as for extension.

A graphical representation of the results from Table 3, Table 4, Table 5 and Table 6 is shown in the following figures. Figure 2 summarizes the outcomes for flexion (Table 3 and Table 4), while Figure 3 shows those for extension (Table 5 and Table 6).

In the next section, the obtained muscle and speed pair relations are thoroughly discussed.

4. Discussion

According to the results in Table 1, for flexion with no added load, the muscle pair Dcla-Dspi is in a consonance relation at the fast active phases (fl2, fl1), while the pairs Dcla-BB and BB-BR are in a consonance relation at slow ones (fl10, fl6). However, the results are different when the load is added. A consonance relation is found again for Dcla-Dspi, but this time for all active phases. The same is valid for the BB-BR muscle pair. Two more muscle pairs, namely Dspi-BR and TB-BR, hit the interval for a positive consonance relation simultaneously for the four different speeds. Also, Dcla-BB and Dcla-BR appear in positive consonance at slow speeds (fl10W, fl6W), while Dcla-AN enters into a consonance relation only at fast speeds (fl2W, fl1W).

Table 7. Main muscle pairs in consonance relations during flexion.

Muscle Pairs in Consonance for Flexion Without Weight	Muscle Pairs in Consonance for Flexion With Weight
-	Dcla-Dspi
-	Dspi-BR
-	BB-BR
-	TB-BR

summarizes the main muscle pairs in a consonance relation during all flexion active phases with and without added weight.

Below, a detailed discussion is provided for the four muscle pairs in consonance dependence, established for all active phases with load. According to the authors who investigate joint rigid and muscle control during static forces in the horizontal plane [7], the shoulder joint is dominantly controlled by monoarticular muscles. In our experimental case, monoarticular muscles that maintain stiffness (can contribute to joint stability) in the shoulder joint are Dcla and Dspi. This is probably the reason why they are in consonance. Both muscles from the pair Dspi-BR are monoarticular, but the first one acts in the shoulder joint, while the second acts in the elbow. Functionally, they do not act in the same way. While BR is directly responsible for flexion at the elbow, Dspi plays a stabilizing role in the shoulder that is not directly related to elbow flexion. It is rather to control the position of the shoulder joint in the horizontal plane, as it controls stability and resists unwanted rotation and displacement in the shoulder joint. From the pair BB-BR, BB is a biarticular muscle, and BR is monoarticular. Both are flexors at the elbow joints. Although BB becomes less active when the forearm is in pronation [25], it is still active during flexion at the elbow. In contrast, BR is active during flexion in all positions of the hand [26]; therefore, it is an agonist at the elbow joint, and a consonance dependence can be found. The TB-BR interaction during elbow flexion shows a classic agonist–antagonist relationship (familiar as co-contraction). While BR is a flexor in all forearm positions and is highly active during flexion, TB is likely active for joint stabilization. Simultaneous activation of agonists and antagonists is a deliberate strategy of the central nervous system to regulate joint stability and control movement, especially when performing tasks requiring high precision or load [27].

As might be expected, muscle relations during extension (Table 2) differ from those during flexion (Table 1). At slow speeds, Dspi-TB is in PosC, while the pairs Dcla-AN and BB-AN are in PosC at fast speeds when extension with no added load is in focus. During extension without a load, only the Dcla-BB muscle pair maintained a PosC for all active phases. With the addition of a load, beyond Dcla-BB, four more pairs—Dcla-BR, Dspi-BR, BB-BR, and TB-BR—also exhibited a PosC at all four speeds. While the BB-AN pair showed a PosC again at fast speeds.

Table 8. Main muscle pairs in consonance relations during extension.

Muscle Pairs in Consonance for Extension Without Weight	Muscle Pairs in Consonance for Extension With Weight
Dcla-BB	Dcla-BB
-	Dcla-BR
-	Dspi-BR
-	BB-BR
-	TB-BR

includes the main muscle pairs in consonance relation during all extension active phases with and without added weight.

Similarly, to the flexion, the muscle pairs in consonance dependence, established for all extension active phases with load, are explained in detail. The interactions Dcla-BB and Dcla-BR are complex and determined by the role of each muscle in both joints. The monoarticular Dcla is a flexor and horizontal adductor in the shoulder joint and accordingly maintains the position of the arm in the shoulder. It is not directly involved in the extension of the elbow joint. As mentioned above, BB and BR are flexors in the elbow, and their activity during extension in the elbow joint can be explained as a co-contraction of the antagonists to the extensors of the joint [27].

In the following three interactions (Dspi-BR, BB-BR, and TB-BR) during weighted extension, the activity of BR may be related to elbow joint stabilization and movement control, as its function is in the flexion direction in all forearm positions. Its relationship with the other three muscles is complex because Dspi has no functional relationship with the elbow joint and is not involved in maintaining the desired 90-degree flexion position in the shoulder joint. It probably maintains stiffness (contributes to joint stability) in the shoulder to isolate unwanted movements. The muscles BR and BB are agonists in flexion and together have an antagonistic function in the movement under consideration, so it can be assumed that their relationship in activity is determined by stabilization and movement control in extension. Although the long head of TB is the least active during extension compared to the other two heads [25], it is still an extensor, i.e., acting in the direction we are considering.

As for flexion as well as for extension, when the load is added, a greater number of pairs in consonance are found. Therefore, the load impacts on the type and number of muscle dependencies. The results in Table 1 and Table 2 show that in both flexion and extension, the largest number of detected muscle pairs in consonance are found for the fastest one-second phase, fl1 (5), fl1W (9), ex1 (4), and ex1W (10).

In general, the ICrA was created for cost reduction based on existing correlations between important criteria. The ICrA helps with the criteria number reduction through pairwise comparisons between them and determining the degree of consonance and dissonance dependencies. As mentioned in [13,23], a sufficiently high consonance degree can be assumed as a possible indicator for the elimination of the slower, more time-consuming, or expensive criteria that are involved in one criteria pair with faster, less time-consuming, or cheaper ones. We use this specificity of the ICrA when analyzing the correlation dependencies between the different speeds.

As can be seen from Figure 2 and Figure 3, the largest number of consonance dependencies (38) is found for the pair Sp10-Sp6. Consonance dependencies with only one number less (37) were found for Sp2-Sp1. For the remaining four pairs of criteria, the discovered consonance dependencies are, respectively, 32 for Sp10-Sp2 and Sp10-Sp1 and 33 for Sp6-Sp2 and Sp6-Sp1. The results might be a prerequisite for rehabilitators or coaches to precisely choose the appropriate speed and intensity for the specific needs of recovery or training programs [28,29,30,31].

Speed is an extremely important element in both the training process and rehabilitation. It can provide precision, personalization, and efficiency. In the training process, for athletes seeking to improve their physical fitness, speed is a key factor in achieving different goals. For example, training with a higher speed and a light load develops power, while training with a lower speed and a heavier load develops strength. Speed-based training allows for adaptation of the load, taking into account daily fluctuations in the athlete’s physical condition (fatigue, recovery). In rehabilitation, especially after injuries and neurological diseases, speed can be a tool for safe and effective recovery. In the early stages of rehabilitation, slower and controlled speeds are used, which help restore muscle function and ensure the safety of tissues that are still healing.

This study takes into account many parameters, unlike other studies that focus on two or three muscles in static and dynamic [9,11]. Our study covers static support in the shoulder joint and dynamic motor tasks in the elbow. In addition, the tasks are performed at different speeds and with added weight, which leads to provoking different execution strategies. The extracted data can complement already known knowledge in biomechanics and anatomy under specific control [8,9,11].

5. Conclusions

The effects of speed and load on the number and type of pair interactions between the Dcla, Dspi, BB, TB, AN, and BR were evaluated by the ICrA. The results show that a greater number of muscle pairs in a consonance relation are found for the fastest phases. Furthermore, when a load is added, the consonance relations between the muscle pairs increase during flexion (Dcla-Dspi, Dspi-BR, BB-BR, and TB-BR) and extension (Dcla-BB, Dcla-BR, Dspi-BR, BB-BR, and TB-BR). Concerning different speeds, the most consonance dependencies are found during the slowest two phases (Sp10-Sp6), as well as the fastest two (Sp2-Sp1). These findings are preliminary, but after validation and verification for a larger group could perhaps be applied in rehabilitation activities after injuries and illnesses, and of course, in sports training and the preparation of athletes for the competition calendar.