Sensitivity of the load-velocity relationship variables to discriminate the level of fatigue induced by multiple sets of the smith-machine squat exercise

Abstract

Background

The aim of the research was to examine the sensitivity of load-velocity (L-V) relationship parameters (L₀, v₀, and A_line (area under the L–V line; A_line = L₀×v₀/ 2)) in detecting fatigue after different fatigue protocols as well as their correlation with changes in 1-repetition maximum (1RM).

Methods

After a familiarization and preliminary testing session which was used for 1RM smith-machine squat (SMS) determination and performing a set of repetition to failure with 70%1RM load, 28 resistance-trained men randomly performed three fatigue protocols. All fatigue protocols were carried out between two incremental loading tests, conducted at the beginning (pre-session) and end (post-session) of the training session. The characteristics of the fatigue protocols were as follows: (i) control protocol: no training, (ii) moderate-fatigue protocol: 5 sets of the SMS exercise at 70%1RM performing half the maximum possible number of repetitions, and (iii) high-fatigue protocol: 5 sets of the SMS exercise performed to failure against the 70%1RM.

Results

Post-session declines in 1RM (p < 0.001), L₀ (p = 0.001) and A_line (p < 0.001) were the greatest after the high fatigue protocol, followed by the moderate fatigue protocol and finally the control protocol. Changes in v₀ did not differentiate between the fatigue protocols (p = 0.325). The post-session percentage change in 1RM was significantly correlated with the percentage change in A_line (r = 0.832) and L₀ (r = 0.764), but not with the percentage change in v₀ (r= -0.012).

Conclusions

These results suggest that L-V relationship variables offer a highly sensitive and practical solution for fatigue monitoring. Trial registration: ClinicalTrials.gov, NCT07307963 (First posted: 27/11/2025; retrospectively registered).

Introduction

Muscle fatigue can be defined as the loss of the ability of a specific muscle or muscle group to produce strength and power due to exercise-induced stress [1]. It is acknowledged that muscle fatigue can result from multiple mechanisms with the key contributing factors including (a) disruptions in ionic balance and neural stimulation, (b) accumulation of metabolic byproducts, and (c) reduced motor unit activation [2]. The level of fatigue induced during resistance training (RT) significantly influences how the neuromuscular system adapts in response to RT stimuli [3]. Therefore, the periodic assessment of RT-induced fatigue is paramount in optimizing strength adaptations and enhancing training efficacy [4]. Countermovement jump (CMJ) height [5], mean velocity (MV) against a fixed absolute load [6], and isometric maximal strength [7] are among the most commonly used metrics for monitoring fatigue. However, assessing fatigue based on a single mechanical variable is problematic, as it does not indicate whether the reduction in maximal power (P_max) [8] is due to impaired force (F₀) or velocity (v₀) capabilities [9]. This situation underscores the necessity of a more comprehensive evaluation of the fatigue process and its impact on performance variables.

A potential solution to this problem is the modeling of the force-velocity (F-V) relationship and the computation of the F-V parameters (F₀, v₀ and P_max) under different fatigue conditions. For example, Garcia-Ramos et al. [10] found that a reduction in v₀ was the primary cause of the decrease in P_max following a light-load fatigue protocol involving bench press performed to failure at 60% of the one-repetition maximum (1RM). Conversely, the decline in P_max during the non-failure high-load traditional (HLT) protocol involving bench press sets at 80% 1RM was mainly due to a decrease in F₀, with no significant change in v₀. Another study by Li et al. [11] examined the sensitivity of the F-V parameters in detecting fatigue under a HLT protocol consisting of five squat repetitions at 80% 1RM and a light-load ballistic (LLB) protocol comprising five squat jump repetitions at 30% 1RM. Even though both RT protocols resulted in a decline in P_max (10.1% and 12.2% for HLT and LLB, respectively), F₀ and v₀ contributed to this reduction to varying extents. In the LLB squat protocol, the decline in v₀ (9.7%) was more pronounced than the minimal decrease in F₀ (0.4%), whereas during the HLT squat protocol, F₀ showed a greater reduction (8.4%) compared to v₀ (4.1%). The findings of both studies consistently indicate that, in low-load, high-velocity exercises, the decline in P_max is predominantly attributed to a reduction in v₀. Conversely, in high-load, low-velocity exercises, the decrease in P_max is attributed to a decrease in F₀. These observations substantiate the hypothesis that monitoring fatigue through a sole mechanical parameter may lack adequate sensitivity.

Although F–V modeling provides a comprehensive framework to characterize neuromuscular mechanical capacities [12] some applications show substantial variability in v₀, which may limit its usefulness for certain exercises [13]. For example, González-Hernández et al. [14] explored the sensitivity of F-V parameters to selectively detect fatigue before and after three RT involving full squats and bench presses. Each session consisted of five repetitions at 10 RM, with varying inter-set rest durations in each session (1, 3, or 5 min). Contrary to predictions, the v₀ significantly increased after RT sessions. For example, in the CMJ test conducted following a one-min recovery period, v₀ rose from a pre-training baseline of 3.46 ± 0.93 m·s⁻¹ to 3.61 ± 0.77 m·s⁻¹ post-training. Similar increase was observed in the bench press throw test, where v₀ rose from 2.51 ± 0.34 m·s⁻¹ to 2.60 ± 0.27 m·s⁻¹ after a 3-min rest period. The high variability in v₀ observed in this and similar studies when performing exercises against gravity is likely explained by the large extrapolation needed from the experimental point representing the lowest load (e.g., unloaded jump) to the velocity-axis [15].

To address the issue of high v₀ variability, load-velocity (L-V) modelling may offer a more suitable alternative to traditional F-V modelling, when it comes fatigue assessment as previous studies have established validity and reliability of the L-V modelling in exercises such as bench press throw [16] and squat [17]. The parameters related to the L-V modelling include theoretical maximal load (L₀: load at 0 m·s⁻¹), theoretical maximal velocity (v₀: velocity at 0 kg), and the area under the L-V relationship line (A_line = L₀ × v₀/2). Recently, Pérez-Castilla et al. compared four VBT back-squat protocols combining 60% and 80% 1RM with 10% and 30% velocity loss (VL) thresholds, and reported post-exercise decreases in v₀ and Aline, whereas L₀ showed no change [18]. Similarly, Li et al. implemented back squats at 80% 1RM with sets terminated at a 20% VL threshold across 3, 4, or 6 sets, and observed reductions in v₀ and A_line without a meaningful change in L₀ [19]. On the other hand, Şentürk et al. examined acute changes in L–V variables during the hexagonal barbell deadlift within a three-session design positioned between two incremental loading tests after establishing 1RM (control: no training; moderate fatigue: five sets at 70% 1RM, with the number of repetitions in each set to half of the repetitions achieved in the set-to-failure determined during the preliminary testing session. high fatigue: five sets at 70% 1RM to failure), and reported decreases in L₀, v₀, and A_line following both fatigue conditions, although v₀ did not clearly discriminate between moderate- and high-fatigue protocols [20]. Overall, these results suggest that there is currently no clear consensus in the literature on how L-V relationship variables respond to fatigue.

Therefore, to address the shortcomings of the previous studies, the objective of this study was (i) to compare how L-V relationship parameters (L₀, v₀, and A_line) change after two fatigue protocols involving several sets of smith-machine squat (SMS) exercises. One protocol aimed to induce moderate fatigue (performing half the maximum number of repetitions), and the other aimed to induce high fatigue (performing sets to exhaustion), and (ii) to determine whether changes in L₀, v₀, and A_line following the fatigue protocols significantly correlate with the SMS one-repetition maximum (1RM) test, a traditional measure of maximal strength. We hypothesized that (i) all L–V parameters would decrease after the fatigue protocols, with larger decreases in L₀ and A_line than in v₀, particularly after the high-fatigue protocol; and (ii) percentage changes in 1RM would correlate strongly with changes in L₀ and A_line, but not with v₀.

Methods

Subjects

An a priori power analysis (G*Power v3.1.9.7) indicated that n = 27 subjects were required (repeated-measures ANOVA, within–between interaction; f = 0.30, α = 0.05, power = 0.95). Therefore, the final sample (n = 28) was sufficient. Twenty-eight physically trained males, with an average age of 23.3 years (standard deviation [SD]: 3.0 years; range: 20–36 years), voluntarily participated in the study. The subjects exhibited a mean body mass of 78.1 kg (SD: 9.3 kg), a body height of 177.2 cm (SD: 3.3 cm), and 1RM for smith-machine squat (SMS) exercise of 150.9 kg (SD: 12.5 kg). All subjects possessed prior RT experience, averaging 5.0 years (SD: 2.6 years), and demonstrated proficiency in executing the SMS exercise during the familiarization session. Note that all athletes were using the SMS exercise in their RT programs. None of the subjects exhibited any physical limitations or neuromuscular injuries that could impede their safe participation in the study. Subjects were explicitly instructed to refrain from engaging in strenuous lower-body exercises throughout the study and were required to arrive at each testing session in a rested state. Prior to commencement, all subjects received a comprehensive verbal explanation of the testing procedures and subsequently provided informed consent by signing a consent form, acknowledging their willingness to participate in the study. The research protocol strictly adhered to the principles outlined in the Declaration of Helsinki and was approved by the Ethics Committee of Istanbul Gelisim University (Approval no: IGU2024/04/67). The study was retrospectively registered at ClinicalTrials.gov (Identifier: NCT07307963; First posted: 27/11/2025).

Study design

A crossover study design was applied to investigate the sensitivity of L-V relationship variables in distinguishing the extent of fatigue caused by multiple sets of SMS exercise. Subjects were required to visit the laboratory on five separate occasions. There was 72 h of rest after the familiarization session and 96 h of rest after each testing sessions. The initial session aimed to familiarize subjects with the SMS exercise, during which they performed the exercise at their maximal intended velocity while dealing with varying external loads. In the second session, subjects underwent an incremental loading test to establish their SMS 1RM, after which subjects rested 5 min and then performed one set to failure with 70% of their 1RM. The subsequent three experimental sessions were conducted in a randomized sequence. A consistent element across these experimental sessions was that, at the beginning and end of each experimental testing session, subjects underwent a complete incremental loading test using the SMS exercise, with the loads ranging from 30% of the 1RM determined in the second session to the actual 1RM. This test aimed to determine both the 1RM and L-V relationship parameters (L₀, v₀, and A_line). The total duration of the singe L–V profiling procedure was approximately 15 min (including the standardized inter-set rest intervals across loads). The difference among the experimental sessions lay in the nature of the activity undertaken by subjects during the 30 min interval that separated the two incremental loading tests (Fig. 1). These activities included control, moderate-fatigue, and high-fatigue protocols. All sessions were meticulously conducted at the university research laboratory, supervised by the same researcher (DS), and maintained at approximately 22–24 °C with humidity of approximately 60%.

Fig. 1.

General overview of the study protocol. L-V, load-velocity; L₀, theoretical maximal load; v₀, theoretical maximal velocity, A_line, area under the L-V relationship line; SMS, smith-machine squat; 1RM, 1-repetition maximum

Familiarization session (session 1)

Following a general warm-up that included jogging and joint mobilization exercises, subjects performed a series of the SMS exercise against four different loads (30%, 50%, 70%, and 80% of their self-estimated 1RM) for three repetitions and one repetition against a load corresponding to 90% and 100% of their self-estimated 1RM. The subjects initiated the exercise from a fully extended posture, maintaining a shoulder-width stance with the barbell positioned across the back at the acromion level, commonly referred to as the “high-bar position.” Instructed to execute a continuous descent, they were guided to lower themselves until their thighs were parallel to the ground. Upon reaching this bottom position, subjects were required to swiftly return to the initial position as fast as possible [21]. To ensure the adherence to prescribed technique, an iPad 10th generation (Apple Inc., Cupertino, CA, USA) was thoughtfully positioned on a tripod with a height of 0.5 m, located 1.5 m away from the subjects, diagonally behind them. This configuration facilitated the continuous observation of hip movements during all repetitions, which were diligently captured in slow-motion recordings. Any repetitions deviating from the desired technique were promptly identified and repeated for accuracy. The standardized technique requirements and instructions were consistently applied across all sessions throughout the course of this study. Emphasis was placed on maintaining constant downward pressure on the barbell throughout the entirety of the movement, and subjects were explicitly prohibited from utilizing any jumping motions. After a 5-min rest period, subjects performed six consecutive repetitions against the 70% of their self-estimated 1RM using eccentric-concentric technique.

Preliminary testing session (Session 2)

After the completion of the identical general warm-up routine implemented in the familiarization session, which encompassed jogging and joint mobilization exercises, subjects underwent a specific warm-up protocol. This entailed one set each of 8, 5, and 2 repetitions against loads corresponding to 40%, 60%, and 80% of their self-estimated 1RM, respectively. Subsequently, the load was incrementally augmented until reaching the 1RM for eccentric-concentric SMS. Load increments were determined by assessing the mean velocity (MV) of the repetitions, with increases of 20–40 kg for MV above 0.80 m·s⁻¹, 10–20 kg for MV ranging from 0.80 m·s⁻¹ to 0.40 m·s⁻¹, and 1–10 kg for MV below 0.40 m·s⁻¹. Performance involved three repetitions with light loads (MV > 0.80 m·s⁻¹), two repetitions with medium loads (MV = 0.50–0.80 m·s⁻¹), and one repetition with heavy loads (MV < 0.50 m·s⁻¹). Subjects adhered to rest intervals of 2, 3, and 5 min when lifting light, medium, and heavy loads, respectively.

Experimental testing sessions (sessions 3–5)

The three experimental sessions commenced with the implementation of the identical general and specific warm-up routines delineated in the preliminary testing session. Subsequently, subjects undertook the initial incremental loading test of the experimental session (pre-session L-V assessment): 3 repetitions at 30%1RM, 2 repetitions at 50%1RM and 70%1RM, and 1 repetition at 80%1RM and 90%1RM. Following the 90%1RM trial, subjects executed single 1RM attempts until they were unable to complete a repetition. The maximal load lifted with proper technique was considered the 1RM. Recovery time was set at 1 min for loads of 20–50%, 2 min for loads of 70–80%, 3 min for loads of 90%, and 5 min for 1RM attempts. An identical incremental loading test was conducted at the conclusion of the experimental session (post-session L-V assessment).

The three experimental sessions differed in the activity subjects engaged in during the 30 min interval that separated pre-session and post-session incremental loading tests: (i) control protocol: passive rest for 30 min; (ii) After completing the pre-session 1RM test, 5 min of rest was provided. subjects then performed 5 sets of the SMS exercise at 70% of 1RM, each set consisting of half of the maximum number of repetitions determined during Session 2, with 2 min inter-set rest. After the final set, 15 min of rest was provided before the post-session incremental loading 1RM test; and (iii) high-fatigue protocol: identical to the moderate-fatigue protocol, except that all sets of the SMS exercise at 70% of 1RM were performed to failure. It is worth noting that in the medium fatigue protocol subjects executed only half of the maximum number of repetitions performed in the set up to 70% failure determined during preliminary testing session (session 2), while in the high fatigue protocol all sets were executed up to failure.

Data acquisition and analysis

The SMS exercise was executed utilizing a 10 kg smith-machine bar along with calibrated weight discs (Technogym; Italy, Europe) ranging from 0.5 to 25 kg. To capture the MV of all repetitions, a validated linear position transducer (GymAware RS PowerTool, Kinetic Performance Technologies, Canberra, Australia) was affixed to the right side of the barbell using a velcro strap, as detailed by [22]. The data acquired from the device were wirelessly transmitted through BluetoothTM to a tablet (iPad, Apple Inc., Cupertino, CA) via the GymAware v4.1.6 app, and subsequently, to an online cloud platform. Following this, the data were exported to Microsoft Excel (Microsoft Corporation, Redmond, WA) and prepared for subsequent analysis.

The L-V relationship was established based on individual values of MV and the external load lifted (kg) across five loading conditions (30%, 50%, 70%, 80%, and 90% of 1RM). After the fatigue protocols, when participants were unable to successfully lift the 90% 1RM load, the highest load successfully completed was used for the L–V modelling. For each load, only the trial with the highest MV was considered in determining the individual L-V relationship. Utilizing a least-square linear regression model (L[v] = L₀ – sv), where L₀ represents the load at zero velocity and s is the slope of the L-V relationship, the individual coefficients of determination (R²) for the L–V regressions ranged from 0.96 to 1.00. Subsequently, the theoretical maximal velocity (v₀) and the area under the L-V relationship line (A_line) were calculated as v₀ = L₀/s and A_line = L₀·v₀/2. Hence, four dependent variables were taken into account in this study including the actual 1RM, and three variables derived from the L-V relationship (L₀, v₀, and A_line).

Statistical analyses

Descriptive statistics are reported as means and standard deviations. The normality of the data distribution was verified through the Shapiro-Wilk test (p > 0.05). Reliability evaluation for the 1RM and L-V relationship parameters (L₀, v₀, and A_line) involved a comparison of the pre-session incremental loading tests between the first two experimental sessions. The coefficient of variation (CV% = standard error of measurement / subjects’ mean score × 100) and the intraclass correlation coefficient (ICC; model 3.1) were computed as indices of absolute and relative reliability, respectively. ICC values above 0.90 were considered excellent, values between 0.80 and 0.90 were regarded as high, and values from 0.70 to 0.79 were interpreted as acceptable reliability, while CV values below 10% were taken to indicate good measurement consistency [21]. A two-way repeated measures analysis of variance (ANOVA; protocol [control, moderate-fatigue, and high-fatigue] × time [pre-session and post-session]) with Bonferroni post hoc corrections was applied to each dependent variable. Subsequently, the Pearson’s correlation coefficient (r) was utilized to quantify the association between the percentage changes in 1RM and the corresponding percentage changes in L₀, v₀, and A_line. The criteria employed to interpret the magnitude of the r coefficients were as follows: trivial (0.00–0.09), small (0.10–0.29), moderate (0.30–0.49), large (0.50–0.69), very large (0.70–0.89), nearly perfect (0.90–0.99), and perfect (1.00) (1). The CV assessments was conducted using Excel (Microsoft Corporation, Redmond, WA), while other statistical analyses were carried out with the statistical software (JASP version 0.18.3, Amsterdam, The Netherlands).

Result

The reliability outcomes were as follows: 1RM (CV = 1.16%, 95% CL: 0.92–1.58; ICC = 0.98, 95% CL: 0.95–0.99), L₀ (CV = 1.96%, 95% CL: 1.55–2.66; ICC = 0.98, 95% CL: 0.95–0.99), v₀ (CV = 1.41%, 95% CL: 1.12–1.92; ICC = 0.93, 95% CL: 0.86–0.97), and A_line (CV = 1.55%, 95% CL: 1.25–2.11; ICC = 0.99, 95% CL: 0.98–1.00). Both fatigue protocols induced fatigue, as evidenced by the gradual decline in the fastest MV within each set with increasing number of sets (Table 1). As anticipated, the high-fatigue protocol exhibited a greater VL and a more pronounced reduction in the fastest MV of the set compared to the moderate-fatigue protocol.

Table 1.

Description of the training variables for the moderate- and high-fatigue protocols

Protocol	Set number	Number of repetitions	Fastest MV (m·s− 1)	Final MV (m·s− 1)	Velocity loss (%)
Moderate-fatigue	1	6 ± 0.04	0.57 ± 0.03	0.46 ± 0.05	-20.1 ± 7.5
	2	6 ± 0.04	0.54 ± 0.04	0.43 ± 0.04	-20.6 ± 6.3
	3	6 ± 0.04	0.52 ± 0.04	0.41 ± 0.05	-21.8 ± 8.6
	4	6 ± 0.04	0.50 ± 0.04	0.38 ± 0.06	-22.9 ± 10.3
	5	6 ± 0.04	0.49 ± 0.04	0.35 ± 0.05	-27.4 ± 8.4
High-fatigue	1	13.7 ± 1.7	0.58 ± 0.02	0.25 ± 0.03	-56.6 ± 4.9
	2	8.2 ± 1.5	0.51 ± 0.05	0.26 ± 0.03	-49.3 ± 6.5
	3	6.3 ± 1.4	0.47 ± 0.05	0.26 ± 0.03	-44.2 ± 7.6
	4	5.3 ± 1.2	0.43 ± 0.06	0.25 ± 0.04	-40.2 ± 10.4
	5	4.2 ± 1.4	0.40 ± 0.07	0.26 ± 0.03	-34.2 ± 12.7

MV, mean velocity; Velocity loss (%) = (Final MV – Fastest MV) / Fastest MV × 100

The 1RM and the three L-V relationship variables (L₀, v₀, and A_line) decreased at post-session compared to pre-session with the only exception of v₀ for the control protocol (Table 2). The interaction effect between protocol and time yielded significance for the 1RM, L₀, and A_line, as their decline at post-session was more pronounced for the high-fatigue protocol, followed by the moderate-fatigue protocol, and finally for the control protocol (Fig. 2). No significant interaction between protocol and time was observed for v₀. Additionally, the percent change in 1RM was strongly associated with the percent changes in L₀ (r = 0.764) and A_line (r = 0.832), but not with v₀ (r = −0.012) (Fig. 3).

Table 2.

Comparison of the 1-repetition maximum (1RM) and load-velocity relationship parameters between the fatigue protocols

Variable	Protocol	Pre-session	Post-session	ANOVA
1RM (kg)	Control	153.6 ± 23.4*	149.9 ± 23.6 a, b	Protocol: F = 16.6; p = 0.001 Time: F = 749.9; p < 0.001 Protocol × Time: F = 143.9; p < 0.001
	Moderate-fatigue	153.6 ± 22.9*	143.2 ± 22.6 b
	High-fatigue	153.3 ± 21.6*	134.0 ± 20.8
L0 (kg)	Control	205.2 ± 26.4	202.9 ± 25.8 a, b	Protocol: F = 452.0; p = 0.001 Time: F = 32.1; p < 0.001 Protocol × Time: F = 112.4; p = 0.001
	Moderate-fatigue	205.0 ± 26.2*	188.2 ± 28.1 b
	High-fatigue	203.8 ± 27.3*	171.2 ± 23.3
v0 (m·s− 1)	Control	1.18 ± 0.06	1.17 ± 0.06	Protocol: F = 0.4; p = 0.610 Time: F = 32.9; p < 0.001 Protocol × Time: F = 1.1; p = 0.325
	Moderate-fatigue	1.18 ± 0.06*	1.16 ± 0.05
	High-fatigue	1.19 ± 0.05*	1.16 ± 0.05
Aline (kg·m·s− 1)	Control	121.9 ± 17.9*	119.3 ± 17.7 a, b	Protocol: F = 28.7; p = 0.001 Time: F = 719.5; p < 0.001 Protocol × Time: F = 184.3; p < 0.001
	Moderate-fatigue	121.3 ± 18.2*	109.3 ± 17.9 b
	High-fatigue	121.3 ± 17.5*	99.8 ± 14.8

ANOVA analysis of variance, L₀ maximal theoretical load, v₀ maximal theoretical velocity, A_line area under the load-velocity relationship line

* Significantly different than post-session

^a Significantly different than moderate-fatigue

^b Significantly different than high-fatigue

Fig. 2.

Individual pre- and post-session responses for 1RM, L₀, v₀, and A_line across the three experimental conditions, arranged by columns as follows: left = control, middle = moderate-fatigue, and right = high-fatigue. Each dot represents an individual subject, and grey lines connect paired observations (pre to post). Boxplots summarize group-level data (central line = median; box = interquartile range; whiskers = range), while the half-violin density plots illustrate the distribution of values at each time point. Units are shown on the y-axes

Fig. 3.

The association between the percent changes in 1-repetition maximum (1RM) and the percent changes in theoretical maximal load (L₀; upper panel), theoretical maximal velocity (v₀; middle panel), and the area under the load–velocity relationship line (A_line; lower panel). Symbols represent the experimental protocols (Control: orange circles; Moderate-fatigue: green circles; High-fatigue: blue circles). Solid lines indicate the fitted linear regression (trendline). r, Pearson correlation coefficient

Discussion

This study was designed to examine the sensitivity and utility of the L-V parameters (L₀, v₀, and A_line) in identifying instances of fatigue in response to diverse fatigue protocols (control, moderate-fatigue, and high-fatigue). Although muscle fatigue can arise from central and peripheral mechanisms at various levels, the present study primarily focused on post-fatigue changes in performance-based mechanical outcomes that are predominantly associated with peripheral fatigue [9]. The primary hypothesis of this study was confirmed by the findings that the L-V variables demonstrated sensitivity in detecting fatigue at varying levels, leading to two key conclusions. Firstly, significant decrements were observed between the pre- and post-session for all variables and fatigue protocols, with the exception of v₀ and L₀ in the control protocol. The decreases in 1RM and A_line observed in the control protocol may be attributed to the incremental 1RM test performed at the beginning of the session, which can elicit acute neuromuscular fatigue and, consequently, lead to a modest reduction in post-test outcomes [23] Secondly, the L-V variables showed the most pronounced decrease in the high-fatigue, followed by the moderate-fatigue, and control protocols, with the exception of v₀. Supporting our second hypothesis, very large correlations were observed between changes in 1RM and changes in L₀ and A_line, but not with v₀. These results collectively reveal that L-V relationship variables offer a highly sensitive and practical solution for fatigue monitoring.

The present findings suggest that, in comparison with the moderate-fatigue protocol, the high-fatigue protocol resulted in a greater reduction in the fastest mean velocity (fastest MV) across sets (Δ: moderate-fatigue 14%, high-fatigue 31%) and a higher magnitude of VL (Δ: moderate-fatigue 22%, high-fatigue 44%). These findings corroborate earlier findings in the literature, demonstrating that high-fatigue protocols involving greater VL elicit greater neuromuscular fatigue and lead to a more progressive reduction in the fastest MV across sets [24]. Additionally, while 1RM, A_line, L₀, and v₀ showed high inter-session reliability, v₀ also exhibited strong test–retest reliability in our data (ICC = 0.93). This contrasts with previous research [20], which reported lower reliability for v₀ during the HBD exercise (ICC: 0.48). Previous studies have attributed the variability in v₀ to the biomechanical characteristics of exercises performed with low loads, which cause the extrapolation point to be positioned farther from F₀ [15]. However, the discrepancy between our findings and previous studies utilizing the HBD under identical protocols may be attributed to the following technical and mechanical differences between the two exercises. In the previous study, subjects were instructed to avoid shoulder elevation during the HBD exercise w hile Previous studies have attributed the variability in v₀ to the biomechanical characteristics of exercises performed with low loads, which cause the simultaneously performing all lifts at maximal velocity. Although all lifts were monitored throughout the study, this combination may have led subjects, particularly under low-load, high-velocity conditions, to instinctively elevate their shoulders to maximize lifting velocity, thereby increasing variability across sessions [20]. In contrast, during the SMS exercise, subjects can comfortably perform a standardized lift with low loads while maintaining their hips parallel to the ground, which likely reduces v₀ test-retest variability across different days [25].

A significant decline in 1RM and all L-V variables (L₀, v₀, and A_line) following the different fatigue protocols aligns with the findings of several studies with the similar design [26–28]. A key aspect of our findings is that, while the L₀ and A_line were sensitive enough to detect different levels of fatigue induced by the protocols (control > moderate-fatigue > high-fatigue), v₀ failed to do so, implying that the sensitivity of L-V parameters is different when it comes to detecting fatigue levels during the SMS exercise. The present findings align with those of Şentürk et al. [29] indicating that L₀ and A_line are highly sensitive markers capable of discriminating between different levels of neuromuscular fatigue, as they consistently decreased in a graded manner following high- and moderate-fatigue protocols, while v₀ failed to show such discriminatory capacity in both SMS and HBD exercises. However, two recent studies reported significant decreases in the A_line and v₀ variables after fatigue protocols were followed, but not in the L₀ variable [18, 19]. This difference may be attributed to variations in the load ranges and methodological approaches used to determine the L–V relationship variables across studies. One study determined the L–V variables using a load corresponding to 20% of 1RM and a velocity of 0.55 m/s based on the individual L-V profile [18]. The other study, however, calculated the L–V relationship variables using loads in the 20–80% 1RM range [19]. In the present study, the L–V variables were determined using loads in the 30–90% 1RM range. Furthermore, the decrease in 1RM values following the fatigue protocol in the present study resulted in modelling of the L–V relationship within the 30–100% 1RM range after moderate and high-fatigue protocol. This suggests that the decrease in L₀ observed after fatigue may have occurred in the 90–100% 1RM range, where higher force is required, rather than at loads below 80% 1RM. Taken together, the results of the present study align with the findings of previous studies that indicated that the changes in the A_line are influenced to varying degrees by the L₀ and v₀ variables depending on the source of fatigue (e.g., high load-low velocity vs. low load-high velocity). This finding underscores the practical utility of A_line as a sensitive method for detecting different levels of fatigue.

Confirming our second hypothesis, a significant correlation was observed between changes in 1RM and the A_line and L₀ variables following fatigue protocols, while no significant relationship was found with v₀. Once again, our results align with previous studies that have reported a strong relationship between 1RM and L₀ in both fatigued [30] non-fatigued [17] conditions, as well as with research examining the relationship between changes in these variables [20]. A key contribution of our study is its demonstration of the interaction between changes in 1RM and L-V variables during the SMS exercise, a frequently utilized movement pattern for monitoring lower-limb fatigue [31]. The findings presented above offer the following key conclusions regarding methods of fatigue monitoring. Traditionally, the 1RM test, which is commonly used to assess dynamic maximal strength [29, 32] is impractical for daily fatigue monitoring due to technical challenges, the fatigue-inducing effects of the test [33] and the risk of injury [34]. Consequently, the L₀ and A_line parameters have emerged as prominent indicators, as they not only detect statistically significant changes following different fatigue protocols but also exhibit a high correlation with 1RM values. It is notable that the test-retest reliability of the A_line parameter is higher than that of L₀, and its sensitivity varies depending on the source of fatigue. This highlights the importance of the A_line parameter in comprehensively addressing a broader range of mechanical factors contributing to fatigue, underscoring the necessity for a more holistic approach in its evaluation. Notably, because VL and repetition number co-varied across the protocols and were not manipulated independently, the present design cannot isolate their respective contributions to the observed changes in L₀.

This study provides a novel and valuable contribution to both sports scientists and practitioners involved in RT programs by highlighting the importance of detailed analyses of mechanical performance decline (i.e., fatigue assessment) following training sessions. Nevertheless, several limitations should be acknowledged. First, the L–V parameters were assessed only 15 min after the fatigue protocols, limiting the understanding of longer-term recovery dynamics. Given that neuromuscular fatigue can persist beyond this acute phase [35]. future studies should examine changes in 1RM and L–V parameters over extended recovery periods (e.g., 24, 48, and 72 h). Second, fatigue was assessed exclusively in the lower-body musculature, limiting the generalizability of the findings to other muscle groups, such as those in the upper body. Third, the study focused solely on mechanical aspects of fatigue (declines in 1RM and L–V parameters), without evaluating biomarkers that could provide additional insight into fatigue-related mechanisms particularly in high-fatigue conditions [7, 10, 20]. Fourth, this study did not compare the sensitivity of L–V parameters with other commonly used fatigue assessment tools such as the CMJ and other ballistics tests [5]. Ballistic tests provide directly measured velocity-based outcomes (MV) that align conceptually with the velocity-axis intercept derived from the L-V relationship [31], whereas maximal isometric strength tests provide directly measured force-based outcomes (maximal force) that align conceptually with the load-axis intercept [36]. In this context, directly measured performance outcomes are related to L–V derived parameters, but they are not strictly interchangeable. This is because directly measured outcomes typically reflect performance at a single load or measurement point, whereas extrapolated variables model the L-V relationship using multiple loads and thus provide a more holistic summary of the neuromuscular capacity to produce force across the entire L–V spectrum. A practical advantage of extrapolated indicators is that they integrate information from several loads and may be less dependent on a single measurement point. Accordingly, future studies comparing directly measured and extrapolated metrics within the same fatigue protocols and assessing the extent to which fatigue-induced changes in L–V variables are associated with concurrent changes in directly measured test outcomes may help establish the convergent validity of these parameters for fatigue monitoring and clarify whether they reflect similar underlying fatigue mechanisms. Lastly, as lifting maximal loads and performing multiple-point tests with 5–6 loads may not always be feasible during training or routine testing, future studies should aim to identify the optimal combination of load and repetitions that enables accurate L-V assessment with minimal effort. This would improve the practicality and applicability of fatigue-monitoring protocols in athletic settings [15].

Conclusions

The results of this study demonstrate that among the L–V relationship variables, L₀ and A_line possess the sensitivity to detect and discriminate between different levels of neuromuscular fatigue, showing a progressive decrease in the order of control > moderate-fatigue > high-fatigue and exhibiting strong correlations with changes in 1RM. In contrast, v₀ was unable to distinguish between different fatigue levels and showed no significant relationship with changes in 1RM, indicating its limited sensitivity during submaximal and slow-velocity exercises. These findings collectively support L–V profile variables as a non-fatiguing, reliable, and informative practical alternative to traditional 1RM testing for integration into routine athlete monitoring protocols. In particular, A_line provides a more holistic representation of fatigue-induced mechanical performance decline by integrating both force- and velocity-related components, making it especially valuable for practical applications.

Abbreviations

1RM

One repetition maximum

A_line

Area under the load-velocity relationship line

ANOVA

Analysis of variance

CMJ

Countermovement jump

CV

Coefficient of variation

SMS

Smith-machine squat

HBD

Hexagonal barbell deadlift

HHT

Heavy-load traditional

LLB

Light-load ballistic

F₀

Maximal theoretical force

L₀

Maximal theoretical load

L-V

Load-velocity

P_max

Maximal theoretical power

v₀

maximal theoretical velocity

MV

Mean velocity

RT

Resistance training

Authors’ contributions

Deniz Senturk (DS): Conceptualization, methodology, project administration, supervision, and writing original draft preparation. Aliasker Kumak (AK): Investigation, data curation, formal analysis, writing, review and editing. Danica Janicijevic (DJ): Statistical analysis, visualization, writing, review and editing. All authors read and approved the final manuscript.

Funding

This research received no external funding.

Data availability

The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

The study protocol was approved by the Ethics Committee of Istanbul Gelisim University (Approval no: IGU2024/04/67). The study was conducted in accordance with the Declaration of Helsinki. All subjects provided written informed consent prior to participation. Trial registration: ClinicalTrials.gov, NCT07307963 (First posted: 27/11/2025; retrospectively registered).

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.