Assessing the Effects of TMS Intensities and Muscle Conditions on the Evoked Responses of the First Dorsal Interosseous Muscle Using Statistical Methods and InterCriteria Analysis

Abstract

This study aims to apply standard statistics and InterCriteria analysis (ICrA) for assessing the effects of different transcranial magnetic stimulation (TMS) intensities and three muscle conditions on the evoked responses of the first dorsal interosseous muscle (FDIM). Surface electromyograms from the right FDIM of ten right-handed healthy volunteers were recorded, and amplitudes of motor evoked potentials (MEPs), latencies of MEPs, and silent periods were obtained. ICrA was used for the first time as a supplementary tool along with the applied statistical methods. Three case studies were processed by the ICrA approach for a wide examination of neuromuscular excitability in humans. As a result, the relations between increasing TMS intensities, MEP amplitudes, MEP latencies, and silent periods were established at relaxed muscle condition, isometric index finger abduction condition, and co-contraction of antagonist muscles condition. Also, the dependencies between MEP amplitudes, MEP latencies, and silent periods themselves, and for different TMS intensities, were outlined. The results confirmed relations known from the literature and showed new ones.

1. Introduction

Transcranial magnetic stimulation (TMS) method gives new research opportunities and medical applications for neuroscience and clinical neurology purposes [1,2]. TMS is a non-invasive technique for brain stimulation and is an appropriate way to study human neurophysiology pathways. A single-pulse TMS delivered to the primary motor cortex evokes a response in a target muscle, named motor evoked potential (MEP). The amplitude of MEP is a measure of corticospinal excitability. The latency of MEP is the period between TMS and the first appearance of MEP amplitude and is a measure of the time taken for intracortical processing, conduction, spinal processing, and neuromuscular transmission. The corticospinal silent period is a measure of the time of corticospinal inhibition that is observed only in active muscle but never in relaxed muscle condition. The excitability and evoked responses vary between individuals [3,4,5,6]. A usual method for the limitation of individual differences in TMS studies is the usage of motor threshold at relaxed muscle condition (RMT) for a baseline of TMS intensities used in the experiments [6]. RMT is the lowest TMS intensity that elicits MEP in relaxed muscle. The most commonly used technique for recording MEPs is surface electromyography. Electromyographic (EMG) signals have increasingly wide applications, including in both clinical and research studies, and support or rehabilitation devices, etc. [7]. EMG recordings from the first dorsal interosseous muscle (FDIM) are the most used combination in TMS studies [3,5,8].

TMS allows for examination of neurological pathways from the primary motor cortex to the muscles during different muscle activity conditions, e.g., relaxed muscle condition, isometric abduction, co-contraction of antagonist muscles, etc. Furthermore, different TMS intensities allow for comparison of changes in nervous-muscle excitability and inhibition in repeated all other conditions. Researchers investigating these problems use statistical methods to process the results. The authors examine several main characteristics of MEP amplitudes and different correlation dependencies that can be sought via standard statistical tests such as ANOVA and post hoc tests [5,9,10].

Standard data processing may require additional procedures, such as rectification of EMG recordings and data normalization [9,11]. Statistical software cannot deal with small, limited data samples for a few variables and cases. The results are based on a specific group or population rather than individual observations. Also, statistics is only one of the methods that can be used for studying a problem (https://www.tutorhelpdesk.com/, accessed on 15 March 2025). The newly developed InterCriteria analysis (ICrA), proposed by Atanassov et al. [12] in 2014, overcomes these limitations. ICrA successfully works with raw data obtained in different International System units and can find the relations between the limited number of criteria measured for each subject. This approach is appropriate for application to data sets varying in size [13]. Moreover, ICrA can evaluate the degree of correspondence and non-correspondence between the criteria, and in addition, the degree of uncertainty [12]. Hence, the approach can be performed along with the common statistics to supplement the results.

ICrA has numerous applications in different fields and was confirmed as a suitable tool, especially for biomedical research [13,14,15,16]. From its creation, this approach has attracted more and more attention. It is not surprising that several papers recently prove the relevance of the tool in new branches of biomedical investigations [17,18,19], among them EMG data processing. Till now, three manuscripts [20,21,22] have applied ICrA over appropriately processed EMG signals received during voluntary muscle contractions. In [20], the authors investigated two phases of a cyclic movement—flexion and extension, and after that explained correlations in muscle activity during different conditions (velocity and loading). They find different muscle interactions for flexion and extension movements performed in the sagittal plane. In [21], ICrA was applied to assess the correlations between flexion and extension phases again in the sagittal plane, which differ in loading and time duration. After objective analysis, based on ICrA results and subjective analysis based on research needs, the authors excluded some movement tasks from the full experimental protocol and proposed a new one, saving 30% of the initial runtime duration. In [22], the authors compare the results obtained by ICrA, Pearson’s, and Spearman’s correlation analyses (CA) for movements performed in the horizontal plane and concluded that ICrA and Spearman’s CA produced matching outcomes, but the three methods are reliable for that kind of data investigation. A successful ICrA application over EMG data recorded during voluntary muscle contractions raises the idea of testing the approach over muscle responses evoked by TMS.

The purpose of this research is to evaluate the effects of different TMS intensities and three muscle conditions on the evoked responses of FDIM, applying standard statistics and InterCriteria analysis. Here, we present a new viewpoint to the conventional processing of the TMS data, implementing for the first time the promising ICrA approach for elucidation of human nervous-muscle excitability.

2. Materials and Methods

2.1. Experimental Protocol

The procedures are described with sufficient detail to allow other authors to replicate the protocols, while well-established methods are briefly presented and appropriately cited.

Subjects. Ten right-handed healthy subjects, with a mean age of 34 (standard deviation (SD) 10 years, age range 27–52 years), participated. The hand dominance was determined by the Edinburgh Handedness Inventory [23], and the absence of neurological or psychological symptoms was determined by the TMS Adult Safety-Screening Questionnaire [24]. The inclusion criteria cover age, handedness, and health status. In the beginning, twenty volunteers gave their written informed consent to participate in this study. Four of them stopped the experimental procedure immediately after the first stimulus. The data of another six subjects were excluded during the offline processing of the experimental data. Exclusion criteria were: (1) the EMG activity did not correspond to the respective muscle condition task, and (2) the evoked responses were unclear to identify.

Due to the above exclusion criteria, the group sample size became smaller than expected. Although the small sample size complicates summarizing the findings, may not properly represent the target group, and limits the generalizability for a larger set of subjects, the data processing followed all statistical and representation rules.

Transcranial magnetic stimulation. The research complies with all ethical and regulatory issues related to TMS and all recommendations of the “Safety of TMS Consensus Group” [25]. The experimental procedure was approved by the ethics committee of the Institute of Biophysics and Biomedical Engineering at the Bulgarian Academy of Sciences (№ 487/17.05.2018). TMS was provided by a single-pulse monophasic MagStim200 stimulator (MagStim Co., Whitland, UK) connected to a BiStim module (MagStim Co., Whitland, UK) with a figure-of-eight coil (mean diameter 7 cm). The coil was oriented to produce an approximately posterior–anterior current flow perpendicular to the central sulcus. All TMS intensities were determined as a percentage of maximum stimulator output (peak magnetic field = 2 T). The stimulation coil was adjusted over the optimal area of the left motor cortex to produce motor-evoked potentials in the right first dorsal interosseous muscle. The motor hotspot was localized following the procedures recommended for motor threshold evaluation [3]. The motor threshold at relaxed muscle condition was detected by applying a threshold hunting paradigm [26], according to which the experimental procedure starts with higher TMS intensities and goes to lower intensities. All individual RMTs were determined as a minimum TMS intensity that produced 5 MEPs out of 10 consecutive stimuli. Responses with an amplitude of 0.05 mV (peak-to-peak) or greater were defined as MEPs [27]. TMS intensities selected for the current experimental protocol were 100%, 110%, 120%, 130%, and 140% of the individual measured RMT.

Muscle condition tasks. TMS intensities were sequentially applied during three muscle condition tasks: relaxed muscles, isometric index finger abduction, and co-contraction of antagonist muscles. Each muscle task had 3 repeats with each stimulus intensity.

EMG recordings. We used modular BIOPAC hardware items (BIOPAC Systems Inc., Goleta, CA, USA) connected to an unconventional computerized system for data acquisition, amplifying, recording, storing, and processing of the EMG signals. Surface electromyograms were recorded from the right FDIM by a pair of surface Ag/AgCl disc electrodes (8 mm diameter). The active pole of the electrode was fixed on the muscle belly, and the reference pole—on the distal tendon at the index finger base. EMG activity and force signal were continuously monitored for visual feedback on the correct execution of muscle condition tasks. After amplification (gain increase of the input signal ×1000) and filtering (band passes 10 Hz–1 kHz), EMG signals were digitized (sampling rate 2 kHz) and stored on a disk for offline analysis. A land electrode was used to reduce unwanted outdoor signals.

Experimental procedure. Subjects were seated comfortably in a chair, with the right arm gently fixed in slight shoulder abduction from the trunk (20°) and flexion in the elbow (110°). The hand and forearm were pronated and relaxed on horizontal support. The right index finger was positioned in a non-movable manipulandum connected to a force transducer sensitive in all directions. The other right fingers were immobilized with Velcro straps (Figure 1).

All experiments started with the determination of the individual maximum voluntary contraction (MVC) level without TMS. Each subject’s force was measured as a maximal index finger contraction in the direction of abduction. Then, each subject released 20% of the individual MVC level in the direction of abduction. In all experiments, at the monitor of the experimental session, the indicator line (IL) was fixed according to the individually measured 20% MVC level. The IL was used to provide real-time visual feedback about the current MVC level, but it does not show the EMG activity and force level in detail observed in offline data processing. Both the researcher and the subject verified that any deviations would be handled immediately. Then, we determined individual RMTs as previously described. After these, TMS was applied during the three muscle condition tasks: (1) relaxed muscles: without voluntary muscle activity and zero force production; (2) isometric index finger abduction: voluntary activity of index finger in the direction of abduction as close as possible to 20% of individual MVC level in direction of abduction; (3) co-contraction of antagonist muscles: voluntary simultaneously activated antagonist muscles, matching level equal to 20% MVC in direction of abduction by increasing the angle stiffness and without producing of external force. TMS intensities during each muscle condition task were 100%, 110%, 120%, 130%, and 140% of individual RMT. If the individual measured RMT was high, the following TMS intensities were applied as far as the stimulator reached its maximal output, and it was impossible to produce a higher stimulus intensity. Three sample repeats were made to the subject for each TMS intensity at each muscle condition task.

Data processing. Epochs of 2 s duration (400 ms prior and 1600 ms after the stimulus) were stored on a disk for offline analysis. The measured parameters in relaxed muscle condition (R), isometric index finger abduction condition (A), and co-contraction of antagonist muscles condtion (C) were: (1) peak-to-peak amplitude of MEPs, further noted as R_Ampl, A_Ampl, and C_Ampl, respectively, measured in mV; (2) duration of latency of MEPs, named for convenience R_Lat, A_Lat, and C_Lat, respectively, measured in ms; and (3) duration of silent periods in the two active muscle conditions, abbreviated as A_SP and C_SP, measured in ms. Statistical analyses were made using the STATISTICA data analysis software system, installed version 8.1 (StatSoft Inc., Tulsa, OK, USA) [28]. The effect of different types of muscle conditions and the effect of different TMS intensities were evaluated by two-way repeated measures ANOVA with factors “muscle condition task” (relaxed muscles, index finger abduction, co-contraction of antagonist muscles) and “TMS intensity” (100%, 110%, 120%, 130%, 140% RMT). A test of sphericity was used to check the variances of the differences between sessions. The variances of the differences were considered to be equal if the test reported a significance level of p ≥ 0.05, and sphericity was assumed. If the test reported significance levels of p ≤ 0.05, sphericity was then not assumed, and Greenhouse–Geisser correction was applied. When the effects were significant (p ≤ 0.05), post hoc comparisons were performed using the Bonferroni test. Statistical analyses were made for the group data.

2.2. Theory Behind the InterCriteria Analysis

InterCriteria analysis [12] is a contemporary alternative to classical correlation analyses that provides a level of uncertainty (π), except degrees of agreement (µ) and disagreement (v) for pairwise comparison of the considered criteria. Mathematical apparatuses of index matrices (IM) and intuitionistic fuzzy sets are embedded in ICrA, respectively, for structuring the input data and accounting for the uncertainty.

If the set of m evaluated objects O is denoted by O = {O₁, O₂, …, O_m}, and the set of values assigned to the objects by n criteria C, C$=${C₁, C₂, …, C_n}, is denoted by O(C) = {O₁(C₁), O₁(C₂), …, O_m(C_n)}, than the ICrA initial index matrix (IIM) can be presented in the following form:

		C1	C2	…	Cn
	O1	O1(C1)	O1(C2)	…	O1(Cn)
IIM =	O2	O2(C1)	O2(C2)	…	O2(Cn)
	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
	Om	Om(C1)	Om(C2)	…	Om(Cn)

ICrA proceeds to form a pairwise comparison between every two different criteria in IIM. For that purpose, the counter of agreement $N_{k,l}^{\mu }$ and one of disagreement $N_{k,l}^{\upsilon }$ are generated. The value of the first counter is incremented when both relations between two data pairs coincide (<, < or >, >), while the value of the second counter is incremented when dual relations (<, > or >, <) are detected. The score of uncertainty is incremented in the other cases.

The following rule is met for the sum of the two counters:

$$0 \le N_{k, l}^{\mu }+N_{k,l}^{\upsilon } \le m(m-1)/2$$

(1)

where m is the number of objects and m(m − 1)/2 denotes the total number of pairwise comparisons between the evaluations of m objects.

For every k, l such that 1 ≤ k ≤ l ≤ m and m ≥ 2, two normalised values, the named degrees of agreement and disagreement can be obtained:

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

(2)

The constructed intuitionistic fuzzy pair ${\mu }_{Ck,Cl}, {\upsilon }_{Ck,Cl}$ evaluates the relation between the criteria C_k and C_l, and 0 ≤ ${\mu }_{Ck,Cl}+{\upsilon }_{Ck,Cl}$ ≤ 1. If there is a difference, it is considered as a degree of uncertainty: ${\pi }_{Ck,Cl}$= 1 − ${\mu }_{Ck,Cl}-{\upsilon }_{Ck,Cl}$.

Starting from m × n IIM, ICrA obtains m × m final index matrix (FIM), in the presented form:

		C1	…	Ck	…	Cn
	C1	〈1, 0〉	…	${\mu }_{C1,C\mathrm{k}},{\upsilon }_{C1,C\mathrm{k}}$	…	${\mu }_{C1,Cn},{\upsilon }_{C1,Cn}$
	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
FIM =	Ck	${\mu }_{C\mathrm{k},C1},{\upsilon }_{C\mathrm{k},C1}$	…	〈1, 0〉	…	${\mu }_{C\mathrm{k},Cn},{\upsilon }_{C\mathrm{k},Cn}$
	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
	Cn	${\mu }_{Cn,C1},{\upsilon }_{Cn,C1}$	…	${\mu }_{Cn,C\mathrm{k}},{\upsilon }_{Cn,C\mathrm{k}}$	…	〈1, 0〉

FIM sets the degrees of agreement and disagreement between every two criteria. Correlation dependencies in ICrA are in the intuitionistic fuzzy pair form with values varying in the interval [0; 1].

The threshold values α = 0.75 and β = 0.25 for ${\mu }_{Ck,Cl} \mathrm{a}\mathrm{n}\mathrm{d} {\upsilon }_{Ck,Cl}$ are automatically set in the used here ICrAData software, version 2.5 (https://intercriteria.net/software/, accessed on 25 February 2025). The two criteria C_k and C_l are in positive consonance when ${\mu }_{Ck,Cl}$ > α and ${\upsilon }_{Ck,Cl}$ < β. Negative consonance appears when ${\mu }_{Ck,Cl}$ < β and ${\upsilon }_{Ck,Cl}$ > α. Dissonance is detected otherwise. The µ-scale for consonance and dissonance, according to [29] is given in

Table 1. ICrA µ-scale for consonance and dissonance.

Meaning	µ-Values
consonance
strong positive	(0.95, 1.00]
positive	(0.85, 0.95]
weak positive	(0.75, 0.85]
strong negative	[0.00, 0.05]
negative	(0.05, 0.15]
weak negative	(0.15, 0.25]
dissonance
strong dissonance	(0.43–0.57]
dissonance	(0.33–0.43] ∪ (0.57–0.67]
weak dissonance	(0.25–0.33] ∪ (0.67–0.75]

for completeness.

3. Results

A thorough investigation of the effects of TMS intensities and muscle conditions on the evoked responses of the first dorsal interosseous muscle using standard statistical methods, along with the InterCriteria analysis, is presented here.

3.1. Standard Data Processing Results

The mean RMT was 65% (64.50 ± 8.64, mean ± SD) of the stimulator output. The presented electromyogram in Figure 2 demonstrates from left to right: pre-TMS EMG activity, TMS artefact, MEP latency, MEP amplitude, silent period, and post-SP EMG activity.

Data processing with two-way repeated measures ANOVA showed a significant effect of both factors, “TMS intensity” and “motor condition task”. We presented the results for the subject group in Figure 3. MEP amplitudes at relaxed muscles were the lowest at all TMS intensities compared to both abduction and co-contraction active motor tasks, and amplitudes of MEPs at abduction were the highest. At relaxed condition, recruitment curve was very close to linear and analysis with Bonferroni post hoc test found that MEP amplitudes were significantly lower (p ≤ 0.05) in comparison to those at abduction in all investigated TMS intensities (100%, 110%, 120%, 130%, 140% RMT) (Figure 3a). The results from comparison of MEP amplitudes at relaxed muscles and co-contraction showed that MEP amplitudes at relaxed condition task were not significantly lower (p ≤ 0.05) only in 100% RMT (Figure 3a). The test did not find considerable differences between MEP amplitudes in abduction and co-contraction (Figure 3a). There were no considerable differences between silent periods in abduction and co-contraction (Figure 3b), and between MEP latencies in all muscle condition tasks and all investigated TMS intensities (Figure 3c). Also, tests did not find any considerable differences between the pairs 100–110%, 110–120%, 120–130%, and 130–140% RMT of MEPs amplitudes, and MEPs latencies in relaxed condition, abduction, and co-contraction, respectively and between the same pairs of silent periods in abduction and co-contraction, respectively. However, there is a stable trend for the growth of MEP amplitude sizes and silent period durations with the increase in TMS intensity (Figure 3a,b). MEP latencies did not show any considerable trend (Figure 3c).

3.2. ICrA Data Processing Results

For the completeness of the current investigation and a deeper understanding of human nervous-muscle excitability, three case studies processed by the ICrA approach will be considered further. The three case studies differ in the objects and criteria. All ICrA calculations were performed using averaged raw data from all three repeats for each stimulus intensity at each muscle condition task.

Case study 1. Assessing relations between the TMS intensities, amplitude of MEPs, latency of MEPs, and duration of silent periods during the three muscle condition tasks.

For each subject (S), three IIMs were constructed, first for relaxed muscles, second for isometric index finger abduction, and third for co-contraction of antagonist muscles. Each IIM contains the respective number of stimulus intensities from the individual recruitment curve and measured parameters for the relevant motor task.

The criteria in IIMs are stimulus intensities, amplitude of MEPs, latency of MEPs, and silent periods. As was mentioned before, because of the high individual RMT, measurements stopped at 130% RMT in two subjects’ cases, and at 120% RMT in one subject’s case. Thus, the number of IIM objects for some subjects decreases from five to four or three, respectively.

Altogether, thirty IIMs were obtained for the ten subjects. Each IIM was processed by ICrAData software, version 2.5 (https://intercriteria.net/software/, accessed on 25 February 2025), and the results have been summarized in the next three tables.

Table 2. ICrA obtained relations between TMS, R_Ampl and R_Lat during relaxed muscle task.

Relaxed Condition	µS1	µS2	µS3	µS4	µS5	µS6	µS7	µS8	µS9	µS10
TMS-R_Ampl	1	1	0.8	0.7	1	1	1	1	1	1
TMS-R_Lat	0.4	0.7	0.8	0.1	0.17	0.5	0.7	0.8	0.9	0.8
R_Ampl-R_Lat	0.4	0.7	0.6	0.4	0.17	0.5	0.7	0.8	0.9	0.8

includes the results for the ten subjects during the relaxed condition task.

Table 3. ICrA obtained relations between TMS, A_Ampl, A_Lat, and A_SP during the abduction muscle task.

Abduction	µS1	µS2	µS3	µS4	µS5	µS6	µS7	µS8	µS9	µS10
TMS-A_Ampl	0.6	0.67	0.83	1	0.83	0.8	1	1	1	0.9
TMS-A_Lat	0.2	0.33	0.67	0.6	0.67	0.3	0.5	0.3	0.7	0.4
TMS-A_SP	1	1	1	1	0.83	1	1	1	1	1
A_Ampl-A_Lat	0.6	0.67	0.83	0.6	0.83	0.4	0.5	0.3	0.7	0.5
A_Ampl-A_SP	0.6	0.67	0.83	1	0.67	0.8	1	1	1	0.9
A_Lat-A_SP	0.2	0.33	0.67	0.6	0.5	0.3	0.5	0.3	0.7	0.4

and

Table 4. ICrA obtained relations between TMS, C_Ampl, C_Lat, and C_SP during the co-contraction muscle task.

Co-Contraction	µS1	µS2	µS3	µS4	µS5	µS6	µS7	µS8	µS9	µS10
TMS-C_Ampl	0.6	0.67	0.83	1	0.83	0.9	1	1	1	1
TMS-C_Lat	0.3	0	0.67	0.5	0.5	0.7	0.1	0.3	0.7	0.7
TMS-C_SP	1	1	0.83	0.9	1	1	1	1	1	1
C_Ampl-C_Lat	0.4	0.33	0.5	0.5	0.67	0.6	0.1	0.3	0.7	0.7
C_Ampl-C_SP	0.6	0.67	1	0.9	0.83	0.9	1	1	1	1
C_Lat-C_SP	0.3	0	0.5	0.4	0.5	0.7	0.1	0.3	0.7	0.7

present ICrA outcomes when the abduction and co-contraction are considered.

The results obtained after the ICrA application differ for each subject (Table 2, Table 3 and Table 4). The differences can be explained by the individual neuronal subjects’ characteristics and the task performance strategy.

Case study 2. Finding the relations between the amplitude of MEPs, the latency of MEPs, and the durations of the silent periods themselves.

ICrA is applied to thirty IIMs, but in this case, for finding the relations between MEP amplitudes, MEP latencies, and silent period durations themselves during the three muscle condition tasks. Each IIM contains data for stimulus intensities and the three MEP amplitudes (R_Ampl, A_Ampl, and C_Ampl), three MEP latencies (R_Lat, A_Lat, C_Lat), and two silent periods (A_SP, C_SP) as criteria. The objects again are different experimental cases in which the end of the TMS recruitment curves varies depending on the individual RMT.

Table 5. ICrA obtained relations between the amplitude of MEPs themselves at the three muscle conditions.

Amplitude of MEPs	µS1	µS2	µS3	µS4	µS5	µS6	µS7	µS8	µS9	µS10
R_Ampl-A_Ampl	0.6	0.67	0.5	0.7	0.83	0.8	1	1	1	0.9
R_Ampl-C_Ampl	0.6	0.67	0.5	0.7	0.83	0.9	1	1	1	1
A_Ampl-C_Ampl	0.8	0.33	1	1	1	0.7	1	1	1	0.9

,

Table 6. ICrA obtained relations between the latency of MEPs themselves at the three muscle conditions.

Latency of MEPs	µS1	µS2	µS3	µS4	µS5	µS6	µS7	µS8	µS9	µS10
R_Lat-A_Lat	0.7	0	0.67	0.3	0.33	0.4	0.2	0.5	0.8	0.4
R_Lat-C_Lat	0.7	0.33	0.67	0.5	0.67	0.3	0.2	0.2	0.6	0.6
A_Lat-C_Lat	0.5	0.33	0.33	0.5	0.67	0.3	0.4	0.6	0.4	0.3

and

Table 7. ICrA obtained relations between the silent periods themselves at abduction and co-contraction muscle conditions.

Silent Periods	µS1	µS2	µS3	µS4	µS5	µS6	µS7	µS8	µS9	µS10
A_SP-C_SP	1	1	0.83	0.9	0.83	1	1	1	1	1

show only the results for each subject concerning the relations between the amplitude of MEPs, the latency of MEPs, and the durations of silent periods themselves. Since the correlations between TMS intensity and the three quantities have already been obtained in the previous case study, they are not presented here.

The results for each subject differ from the others, as can be seen from Table 5, Table 6 and Table 7. The possible reasons could be attributed again to the individual’s excitability characteristics.

Case study 3. Determining the relations between the amplitude of MEPs, the latency of MEPs, and the durations of silent periods for different TMS intensities.

IIM for case study 3 was constructed as follows: the criteria are amplitude of MEPs, latency of MEPs, and durations of silent periods at relaxed condition, abduction, and co-contraction at the five different stimulus intensities, and the objects are the respective number of investigated subjects. In the results presentation, the considered pairs of parameters are consistent with the possible physiological combinations. For the same muscle task (relaxed muscles, isometric index finger abduction, and co-contraction of antagonist muscles), the pairs are respectively MEP amplitude–MEP latency (R_Ampl-R_Lat, A_Ampl-A_Lat, C_Ampl-C_Lat), MEP amplitude–silent period (A_Ampl-A_SP, C_Ampl-C_SP), and latency–silent period (A_Lat-A_SP, C_Lat-C_SP). For different muscle tasks, the pairs are with the same parameter: MEP amplitude (R_Ampl-A_Ampl, R_Ampl-C_Ampl, A_Ampl-C_Ampl), MEP latency (R_Lat-A_Lat, R_Lat-C_Lat, A_Lat-C_Lat), and silent period (A_SP-C_SP).

Table 8. ICrA obtained consonance relations at different TMS intensities.

100% RMT	µSall	110% RMT	µSall	120% RMT	µSall	130% RMT	µSall-2	140% RMT	µSall-3
A_100Ampl-C_100Ampl	0.87	A_110Ampl-C_110Ampl	0.80	-	-	A_130Ampl-C_130Ampl	0.83	A_140Ampl-C_140Ampl	0.86
A_100SP-C_100SP	0.87	A_110SP-C_110SP	0.82	A_120SP-C_120SP	0.84	-	-	-	-
A_100Lat-C_100Lat	0.78	A_110Lat-C_110Lat	0.76	-	-	-	-	-	-
-	-	-	-	R_120Lat-A_120Lat	0.82	-	-	R_140Lat-A_140Lat	0.76
-	-	R_110Lat-C_110Lat	0.80	-	-	-	-	-	-
-	-	-	-	-	-	-	-	C_140Ampl-C_140SP	0.19
-	-	-	-	-	-	-	-	C_140Lat-C_140SP	0.24

summarizes these pairs in a consonance relation.

4. Discussion

According to the purpose of the paper, an evaluation of the effects of five TMS intensities and three muscle conditions on the evoked responses of FDIM using standard statistical data processing and InterCriteria Analysis for the first time for such an experimental study was fulfilled.

In previous TMS studies, some relations between motor tasks, TMS intensity, MEP amplitude, and SP, as well as a lack of any trend in MEP latency, were observed [3,4,5,6,10,27,30,31,32,33,34]. Also, the results showed that MEP amplitudes increase with the increase in TMS intensity, as well as SP durations increase when TMS intensity and MEP amplitude sizes increase. The dependencies mentioned above raise the a priori hypotheses that will be confirmed or revised in this study.

ICrA finds pairs of criteria as in positive (PsCo) or negative consonance (NgCo), as in dissonance for the ten investigated subjects, according to the results obtained in case study 1. Figure 4 summarizes the number of consonance relations for each pair of criteria at the three muscle conditions.

The outcomes presented in Table 2, Table 3 and Table 4 and Figure 4 show dependence in PsCo for TMS intensity and amplitude of MEPs pairs as at relaxed condition (TMS-R_Ampl), as well as at abduction (TMS-A_Ampl) and co-contraction (TMS-C_Ampl). There is only one exception for the TMS-R_Ampl pair, in dissonance, namely, for S4. While for the TMS-A_Ampl and TMS-C_Ampl pairs, the results of two subjects (S1 and S2) differ from the others, falling into dissonance. Standard used statistic data processing [5,32] did not give considerable changes between pairs of measured MEP amplitudes (100–110%, 110–120%, 120–130%, 130–140% RMT) at all three muscle conditions. Though there were stable trends for the growth of MEP amplitudes with the increase in TMS intensity (Figure 3). It is known that MEP amplitudes are directly affected by the excitability of the motor cortex [25,26,27,33,34,35,36,37].

Results of ICrA demonstrate the general dependence of MEP amplitude size on the increase in TMS intensity known from other studies [2,3,4,5,10,25,27]. It is worth noting that ICrA marked the results of three subjects with specific recruitment curves that were not pointed out by conventional data processing.

The recruitment curve of S4 at the relaxed condition had a plateau with a peak at 120% RMT, which was different from the other subjects, who had linear curves. MEP amplitudes of S4 increased from 100% to 120% RMT stimulus intensity, but after 120% RMT in contrast to other subjects, MEP amplitudes decreased (Figure 5a). Results of S1 also demonstrate non-linear curves. Recruitment curves of S1 have a plateau in 130% RMT at abduction and in 120% RMT at co-contraction (Figure 5b). Individual motor threshold at relaxed condition of S2 was very high (80% of maximum stimulator output). The curve had three stimulus intensities instead of five because we reached the maximal stimulator output before 130% of the individual RMT. The curve at abduction was not linear or with a plateau, and the curve at co-contraction had a plateau in 110% RMT (Figure 5c), although the subject performed the tasks correctly. We assume that the dissonance exceptions in ICrA results for S1, S2, and S4 pointed to individual subject characteristics of EMG activity and responses to TMS, which were not marked by the conventional statistics. However, it should be mentioned that TMS intensity is directly related to the MEP amplitude but does not directly reflect the absence of muscular activity despite voluntary contraction.

Going deeper into details, the results summarized in Table 3 and Table 4, and partially interpreted in Figure 4, show additional consonance relations during the abduction and co-contraction. The dependences are found for the pairs formed from the silent periods and TMS intensity (TMS-A_SP and TMS-C_SP), as well as the silent periods and amplitude of MEPs (A_Ampl-A_SP and C_Ampl-C_SP). The TMS-A_SP and TMS-C_SP pairs fall into PsCo for all subjects, while the pairs A_Ampl-A_SP and C_Ampl-C_SP are simultaneously in dissonance for S1 and S2. Results of ICrA are in line with the general dependence that silent period duration is influenced by the stimulus intensity, and also high MEP amplitudes resulting in longer SP [33,34,35,36,37]. Also, as known from the literature [3], the duration of the cortical silent period evoked by a single suprathreshold stimulus intensity may be used as a measure of GABA_B-ergic inhibition. The results for S1 and S2 are connected with those mentioned before about individual subject characteristics of EMG activity and responses to TMS, which were not pointed out by the conventional statistics. However, we should note that SP duration is directly related to the voluntary contraction [32,33,34,35,36]. It is thought that behavioral and cognitive factors can influence SP duration, as well as motor and non-motor neurological disorders [2,3,37].

The pair TMS-R_Lat found at the relaxed condition is an interesting exception. For this pair, ICrA outlines altogether six consonance relations as presented in Figure 4. Four results are in PsCo (for subjects S3, S8, S9, S10), two in NgCo (S4, S5), and four in dissonance (for subjects S1, S2, S6, S7). In general, it can be concluded that there is a consonance relation for the TMS-R_Lat, but the results should be interpreted carefully until further investigations confirm this finding.

For the remaining pairs of criteria (TMS-A_Lat; TMS-C_Lat; R_Ampl-R_Lat; A_Ampl-A_Lat; C_Ampl-C_Lat; A_Lat-A_SP; C_Lat-C_SP), no clearly defined relations were observed. It is obvious that MEP latencies are involved in all mentioned pairs. Also, it should be noted that only for the pairs that included MEP latency was there the uncertainty π calculated for some of the subjects (the results are not shown here, but for completeness are discussed). As proposed in [38], the reason could be some equal values of MEP latency at different TMS intensities for these subjects. Some authors found that individual MEP latencies vary considerably from trial to trial, and this variation is continuous and is accompanied by a systematic covariation in MEP amplitude, as larger MEP amplitudes are associated with shorter latencies [39] and higher stimulus intensities [5]. The amplitude and latency of MEP provide a direct measure of corticospinal excitability. A larger MEP amplitude may signify greater cortical excitability, while a longer MEP latency may be associated with decreased cortical excitability [2,4,40], but intraindividual and interindividual differences in excitability must be noted. The biological relevance of interindividual differences in TMS-evoked measurements shows that variations in cortical myelination are connected to differences in corticomotor hotspot location and motor control precision [4,35]. Nevertheless, in standard data processing, we did not find a considerable connection between the pairs, stimulus intensity–MEP latency, MEP amplitude–MEP latency, and MEP latency–SP duration, verified also after ICrA application, with only one exception for the TMS-R_Lat pair at the relaxed muscle condition.

For better interpretation of the ICrA results from case study 2, Figure 6 presents a summarized number of consonance relations for each pair of criteria at the three muscle conditions.

As shown in Figure 6, the results obtained from case study 2 reveal that the pairs R_Ampl-A_Ampl and R_Ampl-C_Ampl are in PsCo for six out of ten subjects, while the pair A_Ampl-C_Ampl is in PsCo for eight out of ten subjects (Table 5). There was a clear consonance relation in PsCo for the amplitude of MEPs themselves. As can be expected, most of the results for the pairs R_Lat-A_Lat, R_Lat-C_Lat, and A_Lat-C_Lat are in dissonance (Table 6). Moreover, only for the pair A_Lat-C_Lat, there is no one consonance relation. It can be concluded that no dependencies were found between the latency of MEPs themselves at the three investigated muscle condition tasks. It is worth noting again that only for the pairs between the latency of MEPs themselves, the degrees of uncertainty are detected. The last pair from case study 2, A_SP-C_SP, is in PsCo for all ten subjects (Table 7); hence, it can be summarized that there is evident consonance dependence between the durations of the silent periods themselves. We may presume, according to the combination of standard data processing and ICrA results, that our findings could be evidence that there is a lower level of excitability during the co-contraction of antagonist muscles than in reciprocal activity of the agonist muscle [33,41,42], and that in the cortical excitability are involved different nerve cell populations during different muscle condition tasks [43,44].

As can be seen from Table 8, which summarizes the results for case study 3, the most consonance relations (four) are found for TMS intensities 110% and 140% RMT. Three, two, and one consonance relations were found for TMS intensities, respectively, at 100%, 120%, and 130% RMT. Most of the criteria pairs are in PsCo, but there are also two pairs, namely, C_140Ampl-C_140SP and C_140Lat-C_140SP, detected in NgCo. It is interesting to note that the negative consonance results were only in pairs during the co-contraction condition at the highest TMS intensity.

ICrA found a consonance relation in PsCo between the amplitude of MEPs during abduction and co-contraction conditions for four of altogether five studied cases, namely for TMS intensities 100%, 110%, 130%, and 140% RMT (Figure 7a). This result is interesting because the recruitment curves were linear with a stable trend of increasing (Figure 3a), but from the literature, it is known that at 120–130% RMT are involved the maximal corticospinal structures. The individual 120% or 130% RMT stimulus intensity activates the maximal number of pyramidal tract structures and strong corticospinal projections to the motoneurons innervating the targeted muscle. This leads to the largest response to TMS and parameters of the evoked muscle responses (MEPs) reflect the sum of neural activity of corticospinal neurons [2,3,45,46]. We suspect that positive consonance marked the differences between the pairs of MEP amplitudes, which reflect excitability structures involved in the different motor condition tasks. The standard data processing did not find any considerable differences, but there was a stable trend of increasing MEP amplitudes, and ICrA noticed it.

The pair between the silent periods during abduction and co-contraction condition appeared in PsCo for TMS intensities 100%, 110%, and 120% RMT (Figure 7b). As mentioned before, 120% RMT stimulus intensity activates the maximal number of pyramidal tract structures. Due to SP, which is a result of the involvement of both excitable and inhibitory mechanisms, this could be a possible reason for the end of the trend in 120% RMT. We may assume that these PsCo results point to the differences between SP durations, which reflect inhibition structures involved in the different motor condition tasks. The standard data processing did not find any considerable differences, but there was a stable trend of increasing SP durations with the increase in TMS intensity and connected MEP amplitudes. One possible reason that at 130% and 140% RMT the ICrA results were not in consonance is the mixed individual results of the subjects. The mean values of group data formed linear curves (see Figure 3b) in which the conventional statistics did not find considerable changes. We assume that ICrA detects the specific changes in the data set that standard statistics cannot find.

Another coincidence was found for the criteria pairs, namely, A_100Lat-C_100Lat and A_110Lat-C_110Lat (Figure 7c), and also R_120Lat-A_120Lat and R_140Lat-A_140Lat (Figure 7d). All detected coincidences are presented for clarity in Figure 7.

For the remaining three criteria pairs in consonance (R_110Lat-C_110Lat, C_140Ampl-C_140SP, and C_140Lat-C_140SP), the relation appears only once; hence, there were no coincidences detected for different TMS intensities. The rest of the criteria pairs are in dissonance or are excluded from the discussion due to the already explained reasons. As can be expected, the uncertainty appears mainly for the pairs of criteria involving the latency of MEPs. But here, due to the specific manner of data arrangement in IIM and equal values for SP durations for S5 and S6, the uncertainty is also observed for the pair A_130SP-C_130SP.

We may interpret our findings with the combination of ICrA and standard data processing as evidence that the level of excitability is lower during the co-contraction of antagonist muscles than in the reciprocal activity of the agonist muscle. We suggest that ICrA results mark the relations between the pairs of MEP amplitudes, which reflect excitability structures involved in the different motor condition tasks. ICrA outcomes may successfully confirm the dependence of silent period duration on the TMS intensity and MEP amplitude sizes. We assume that ICrA results pointed to individual characteristics of EMG activity and responses to TMS, which were not marked by conventional statistics. Also, ICrA noticed subject characteristics of the excitability and inhibition, which were not highlighted by the statistical methods.

5. Conclusions

Here, the effects on evoked responses at different TMS intensities and three FDIM muscle conditions were assessed, applying both standard statistics and, for the first time, InterCriteria analysis. Three case studies were investigated applying ICrA. The relations between TMS intensities, MEP amplitudes, MEP latencies, and silent periods were obtained for relaxed muscle condition, isometric index finger abduction condition, and co-contraction of antagonist muscles condition, and different TMS intensities. Also, the dependencies between pairs of criteria themselves were examined.

The consonance relations between TMS intensity–MEP amplitude size, TMS intensity–SP duration, MEP amplitude size–SP duration, found using ICrA, may confirm that MEP amplitude and SP duration are jointly determined by the excitability of the corticospinal system when TMS is applied. In addition to the expected dependencies, ICrA found one interesting exception for the TMS-R_Lat at the relaxed muscle condition. The pair is in a consonance relation for six out of ten subjects. These findings assumed that ICrA is an appropriate tool for further analyses of EMG experimental data and has the potential to detect, as known from the literature, as well as non-observed relations in a complicated data set.