Validation of musculoskeletal models through comparison with measurable human sEMG features is a well-established approach to ensure the reliability of simulation calculations (28). In this study, we compared the model-predicted muscle force during one movement cycle for six inclination angles of the push-up to the subjects' sEMG data. Biomechanical properties and motor performance of internal muscles and joints for different push-up variants were analyzed using trend analysis, mean absolute errors (MAEs), and correlation coefficients. Muscle force primarily depends on the number of active motor units (MUs), their size (cross-sectional area), and their firing rate (36). EMG surface electrodes detect potential changes in extracellular tissue induced by depolarization of muscle fiber membranes, representing the algebraic summation of motor unit action potentials (MUPs). Despite the relationship not always being entirely linear, previous studies have shown a strong correlation between EMG amplitude and true muscle strength, making it a frequently used estimation method for muscle strength (29).
Our findings revealed good agreement and strong correlations (correlation coefficient > 0.7) across all six angles for the pectoralis major, triceps brachii, anterior deltoid, and middle deltoid, which are the primary target muscles in push-up workouts (37). Approximately 86.1% of cases demonstrated such strong correlations (Table 3), and in 83.3% of cases, the mean absolute error (MAE) between the normalized muscle force prediction curve and the EMG curve was less than 0.1. However, we observed poor correlation, with negative and low correlations, for the lower trapezius bundle in decline 15° push-ups and the biceps in incline 15° push-ups. This may be attributed to the biceps EMG electrode piece shifting laterally during the movement in the experiment. Overall, the AnyBody model's prediction of muscle force was accurately verified by EMG data, demonstrating good agreement with the EMG curve. This musculoskeletal model reliably reflects the actual muscle activities during push-ups, providing a robust foundation for subsequent analyses of muscle force and joint loading.
The muscles activated during push-up variations are of particular interest to sports biomechanics researchers. In medium-distance push-ups (slightly larger than shoulder width, approximately 1.2 times shoulder width), the pectoralis major is prominently activated, along with the anterior deltoid and triceps. When comparing the current experiment with most existing studies involving push-ups with different body inclinations, our kinematic results for muscle activation in the triceps, anterior deltoid, and pectoralis major muscles were consistent with those reported by Borreani et al. (38). Similarly, the mean muscle activation trend of the lower trapezius observed in this study aligns with the findings of Lehman et al. (13), who investigated muscle activation on different stabilizing support surfaces. The anterior deltoid bundle, a crucial muscle for push-up movements, displayed predicted results that correspond to the trend of change in muscle strength during 0-degree push-ups as tested by McGill et al. (39). These previous studies provide robust validation for the accuracy of the EMG measurement and AnyBody muscle force simulation employed in our investigation.
Moreover, the notion that inclined push-ups are recommended for individuals with lower fitness levels is substantiated by the significant differences in mean EMG RMS for push-ups at various inclination angles. Among the six muscles examined in this study, no significant difference in activation effect was observed between − 15° and 0° inclinations, whereas significant differences in muscle activation were found when comparing decline push-ups or standard push-ups to larger inclination angles (incline 15° to 60°). This suggests that inclined push-ups are considerably less physically demanding than traditional push-ups, which aligns with the findings of Ebben et al. (17), who reported a decrease in muscle activation with increasing inclination angle.
Analyzing the peak of the EMG curve, we observed that the muscles were most activated during the − 15° push-up. However, the peak of the muscle force curve predicted by the AnyBody model mostly occurred at 0° inclination. This discrepancy could be attributed to the slightly lower accuracy of the − 15° model. During the modeling process of the − 15° push-up, conflicting orientations and mismatches between the wrist and elbow joints were frequent, leading to the arm posture in the final modeled − 15° push-up not being entirely perpendicular to the ground. Additionally, the angle between the upper and lower arm was distorted, further reducing the modeling accuracy.
For those solely aiming to achieve maximum muscle activation, both − 15° and 0° push-ups can be chosen to obtain an optimal workout for the muscles. Analyzing the EMG data, we observed the highest increase in activation for the pectoralis major (89.93%), followed by the biceps (169.50%), triceps (176.51%), anterior deltoid (301.28%), middle deltoid (188.54%), and lower trapezius (126.87%). Consequently, individuals can select the most suitable inclination angle for different muscles in push-ups based on the above results.
Push-ups are effective for strengthening the pectoral muscles, shoulders, and arms; however, improper force distribution in different joints can lead to shoulder pain after a push-up workout. During push-ups, the primary stress is concentrated on the shoulder and elbow joints. The upper extremities mainly undergo movements involving glenohumeral flexion/extension and adduction/abduction, as well as elbow flexion/extension. The shoulder joints, including the sternoclavicular, acromioclavicular, and glenohumeral joints, have the largest range of motion in the human body but are also more susceptible to instability compared to stable joints. Excessive joint loading can cause repeated wear and tear, leading to aseptic inflammation and shoulder pain. Improper posture during exercise can also subject the elbow joint to significant loads, potentially resulting in joint damage and discomfort.
The contact force curves for different incline push-up variations of the shoulder and elbow joints in three directions are depicted in Fig. 5. A similar trend to the EMG data can be observed in the joint force curves, indicating that relatively smaller joint forces are generated when performing push-ups at greater body inclination angles. Smaller joint forces were found during 45° and 60° push-ups, while maximum joint forces were observed during − 15°, 0°, and 15° push-ups. This is primarily due to the varying proportion of the body's gravity acting on the upper limb joints at different inclination angles. The overall trend direction of the joint force curve aligns with prior studies by (40, 41), suggesting that opting for push-ups with a greater positive angle between the body trunk and the ground would be less detrimental to the joints.
Notably, the magnitude and peak of the proximal-distal force of the elbow joint at -15° were paradoxically smaller than at 0°, 15°, and 30°, while the inferior-superior force of the shoulder joint at -15° were generally greater than at the other angles. Similarly, the anterior-posterior force of the shoulder joint at -15° appeared to be paradoxically smaller than some other angles, while the anterior-posterior force of the elbow joint at -15° seemed somewhat larger than at other angles. This phenomenon may be attributed to changes in the body's angle relative to the ground during − 15° push-ups compared to 0° push-ups, while the angle of the arm supporting the ground remains unchanged. Consequently, the force in specific directions at the shoulder or elbow joint is partially compensated by the other joints, leading to the observed variations in force magnitude and direction.
In this study, we introduced a novel proportional index, denoted as R, which represents the degree of muscle activation during push-ups at different inclination angles under the same joint stress conditions. Push-up exercises are commonly employed for sports injury rehabilitation, with variations of push-ups being utilized to reestablish proper scapular position to aid in shoulder injury rehabilitation (6). Therefore, studying the R index can ensure an increase in muscle activation while minimizing secondary joint damage, making it beneficial for rehabilitation purposes. Our findings indicated that higher R-values were observed in the triceps brachii, deltoideus, and pectoralis muscles compared to other muscles, suggesting that these muscles play a crucial role in the push-up exercise and validate their effectiveness in strength training.
The maximum R value for the pectoralis major and triceps brachii occurred at 45°, indicating that this inclination angle allowed for the most efficient activation of these muscles with minimal joint forces compared to other angles. Similarly, for exercises targeting the biceps brachii and anterior deltoideus, the 60° inclination angle appeared to be the most cost-effective option. Furthermore, the optimal inclination angle for exercising the middle deltoideus was found to be 0°, and for the trapezius ascendens, it was 30°. Analyzing the R index values of all six muscles in Fig. 6 revealed that under 0° and 30° inclination angles, the R index was highest for all muscles. Therefore, 0° and 30° can be considered as the "least costly" options for exercising all muscles. Although the R index values showed diversity across different push-up variants, this study provides valuable information and serves as a reference for future more precise investigations in related fields. The R index enables a comprehensive evaluation of push-up variations and their impact on muscle activation and joint loading, thus offering insights for optimizing push-up exercises for different purposes, including rehabilitation and strength training.
Several limitations may exist in the analysis of this study. While the proposed R index offers a valuable approach to evaluating push-up variations based on muscle activation and joint forces, further optimization could be achieved by considering the different contributions of various joints and directions of joint forces during the push-up process. This refinement could improve the reliability and accuracy of the R index. However, the paucity of available clinical reports and statistics on joint injuries related to push-ups hindered the inclusion of more comprehensive clinical data in this work.
Another limitation is that the musculoskeletal model used in the push-up simulation was based on a standard European human model, which did not account for the specific variations in height and weight among individuals from different regions worldwide. Despite this, the comparative analysis between the predicted muscle forces and the subjects' EMG data demonstrated good agreement, with joint forces expressed in terms of body weight multiples, which enhanced the comprehensiveness of the model's simulation calculations. The forward-driven approach employed in the simulation of push-up movement allowed for a greater degree of simulation realism. Moreover, compared to experimental methods involving human motion capture and ground reaction force testing, the inverse dynamics algorithm used in the simulation model reduced economic and time costs while ensuring satisfactory accuracy of the simulation results.
It is important to note that the present study focused solely on the activation effect of push-ups on specific upper body muscles and did not investigate the motor performance of abdominal and lower limb muscles. Exploring the changes in these muscles and their potential correlation with the upper limb muscles would be a valuable avenue for future research, especially as the number of collected muscles and the sample size of EMG data increase, allowing for more comprehensive investigations. Overall, while this study offers valuable insights, addressing these limitations can further enhance the understanding of push-up biomechanics and their potential applications in rehabilitation and strength training contexts.