Advertisement
Browse Subject Areas
?

Click through the PLOS taxonomy to find articles in your field.

For more information about PLOS Subject Areas, click here.

  • Loading metrics

Open Access

Peer-reviewed

Research Article

Is there a relationship between isometric hamstrings-to-quadriceps torque ratio and athletes’ plyometric performance?

  • Farideh Babakhani ,

    Roles Conceptualization, Data curation, Investigation, Supervision, Writing – original draft

    Farideh_babakhani@yahoo.com

    Affiliation Department of Sport Injuries and Corrective Exercises, Faculty of Physical education, Allameh Tabataba’i University, Tehran, Iran

    ⨯
  • Mohamadreza Hatefi,

    Roles Data curation, Investigation, Software, Writing – original draft

    Affiliation Department of Sport Injuries and Corrective Exercises, Faculty of Physical education, Allameh Tabataba’i University, Tehran, Iran

    ⨯
  • Ramin Balochi

    Roles Conceptualization, Data curation, Visualization

    Affiliation Department of Sport Injuries and Corrective Exercises, Faculty of Physical education, Allameh Tabataba’i University, Tehran, Iran

    ⨯

Abstract

Background

The application of the modified reactive strength index (RSImod) and isometric hamstrings to quadriceps (H:Q) torque ratio to monitoring the athletes’ performance is well established, but their relationship to each other still remains unknown. Therefore, the purpose of this investigation was to clarify whether there is a relationship between RSImod and the isometric H:Q torque ratio.

Methods

Twenty-one male recreational athletes (age, 24.89 ± 4.46 years; weight, 74.11 ± 8.66 kg; height, 179.78 ± 6.76 cm) volunteered to participate in this research. Their isometric H:Q torque ratio via hand-held dynamometer and jumping performance variables during the stop jump (STJ), double leg-drop vertical jump (DL-DVJ), and single leg-drop vertical jump (SL-DVJ) tasks were measured. Also, the RSImod was calculated by dividing the vertical jump height by the time to take-off. Pearson correlation coefficients were used to determine the relationship between the RSImod and jumping performance variables.

Results

The result showed a significant strong positive relationship between the H:Q torque ratio and STJ performance based on the RSImod (p = .027, r = .724). Although, there was a moderate positive relationship between the H:Q torque ratio and jumping height of the STJ task, but it wasn’t statistically significant (p = .096, r = .588). Also, no significant relationship was found between the H:Q torque ratio and all jumping performance variables of the DL-DVJ and SL-DVJ tasks (p ≥ .05).

Conclusion

The current study exhibited that the isometric H:Q torque ratio correlates to STJ performance based on RSImod but not to SL-DVJ and DL-DVJ. Notably, the difference in results between jumping tasks can be attributed to the complexity of the movement, which means that the RSImod is probably related to other factors. Therefore, the isometric H:Q torque ratio used to monitor the athletes’ performance couldn’t independently represent the jumping performance that is determined by RSImod.

Citation: Babakhani F, Hatefi M, Balochi R (2023) Is there a relationship between isometric hamstrings-to-quadriceps torque ratio and athletes’ plyometric performance? PLoS ONE 18(11): e0294274. https://doi.org/10.1371/journal.pone.0294274

Editor: Esedullah Akaras, Erzurum Technical University: Erzurum Teknik Universitesi, TURKEY

Received: July 20, 2023; Accepted: October 30, 2023; Published: November 16, 2023

Copyright: © 2023 Babakhani et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the paper and its Supporting Information files.

Funding: The authors received no specific funding for this work.

Competing interests: The authors declare that they have no conflicting interests.

Introduction

Muscle strength is one of the key components of athletes’ performance, and in many sports due to the necessity of performing maximal repeated jumps during the activities, it has been shown that there is a direct relationship between the strength of the knee extensor muscles and the jumping performance and subsequently sport successes [1–3]. In this regard, various exercises have been designed to increase knee extensor strength, and the effectiveness of these exercises is often measured by using different methods of muscle strength measurement, directly by an isokinetic dynamometer and hand-held manual dynamometer (HHD), as an inexpensive, portable, and more clinically applicable devices, or indirectly by using functional movement tests such as jump-landing tasks. On the other hand, it has been well proven that muscle strength should be considered as an important factor in reducing the risk of non-contact injuries among athletes, and improving it has been also recommended as a component of an injury prevention program [4].

In movement tasks with high-velocity conditions including jump-landing, the quadriceps muscle plays an important role to produce explosive force and also controlling the knee flexion acceleration with the collaboration of the hamstring muscle as a hip extensor, and also reducing the shearing force on the anterior cruciate ligament (ACL) and controlling hip flexion and knee extension accelerations [5]. Deficient in the hamstrings and quadriceps muscles strength, as well as the change in their strength ratio to each other (as an indicator of the strength balance between the antagonistic muscle groups (extensor and flexor) around the axes of knee rotation) has been identified as a modifiable intrinsic risk factor for ACL injuries and hamstring strains; Which should be considered in injury prevention programs, and subsequently, if necessary, the hamstring (H)-to-quadriceps (Q) torque ratio (H:Q) should be improved [6–8]. For this reason, in addition to muscle strength, or more specifically the ability to produce torque (force times the moment arm) by muscles, the H:Q torque ratio is considered an integral part of evaluating the athletes’ performance or monitoring the rehabilitation process of people with various injuries [6].

In contrast, the modified reactive strength index (RSImod) is introduced as a valid index to evaluate the athletes’ plyometric performance as well as neuromuscular readiness, which is calculated by dividing the vertical jump height by the time to take-off [9, 10]. RSImod is defined as the ability to quickly and efficiently change eccentric contraction to concentric contraction, which is used to measure the lower extremity explosive power for evaluating the athletes’ plyometric performance [11]. Basically, using the RSImod is considered vital for high-performance athletes, because it can be used as a motivational tool by providing the athletes with immediate feedback about their own achieved RSImod score, and if necessary improving their movement performance with a skill and injury prevention approach during training programs [12]. Actually, the RSImod is used 1) as a practical method to quantify the stretching-shortening cycle during jump-landing movement tasks [13], 2) to monitor the quality of training of sports teams [14], and 3) or as a diagnostic test to evaluate the functional ability of subjects with ACL deficient [15]. In this regard, it has been reported that there is a direct relationship between extensor muscle strength [16], triple hop performance test [3], change-of-direction speed [17], and agility [18] with the RSImod. However, no study was found that evaluate the relationship between isometric H:Q torque ratio and athletes’ plyometric performance by using RSImod.

In summary, both RSImod and the H:Q torque ratio variables as performance criteria are considered for monitoring athletes with the approaches of movement performance, injury prevention, and returning to sports after an injury, or evaluating the effectiveness of training interventions in athletes with different conditions; But there is no evidence if these two variables are related to each other. Therefore, the current research question is whether there is an relationship between the isometric H:Q torque ratio and the jumping performance variables of athletes or not? Notably! we hypothesized that isometric H:Q torque ratio would be positively correlated with jumping performance.

Methods

Participants

According to G. Power software version 3.1.0 (Franz Faul, University of Kiel, Germany), based on a Pearson correlation statistical test and assuming a power of 0.80, an effect size of 0.8, and a two-tailed alpha level of 0.05, twenty-one male recreational athletes (10 football, 6 basketball, 4 volleyball, and 1 handball players) were voluntarily participate to this investigation (age, 24.89 ± 4.46 years; weight, 74.11 ± 8.66 kg; height, 179.78 ± 6.76 cm); Which were selected according to the study criteria. Participants were recruited for the current study through the board of the faculty of physical education and sports sciences since May 1, 2023, for a month. In this study, a recreational athlete was defined as a subject who participates in sports activities at least three times a week for at least 30 minutes. Inclusion criteria were to: be active physically, be aged 18 to 30 years, have a body mass index (BMI) between 18 and 24, and have a normal ankle dorsiflexion range of motion at least 20° based on the ankle lunge test [19]. Participants were excluded if they: had any musculoskeletal injury in the previous two months or lower-extremity injury in the previous six months, had a lower limb surgery or fractures within the past year, and had any neurological and pathological conditions.

Prior to the test, ethical approval was obtained by the ethical committee of Allameh Tabataba’i University (IR.ATU.REC.1402.008), and all participants provided written informed consent.

Procedures

In the present study, participants were referred to the athletic training laboratory on one occasion and completed a single half-hour testing session. They were asked to wear comfortable sports clothing and their own sport shoes. Overall, first, the strength of the quadriceps and hamstring muscles of the participants was measured by an HHD, and after that, they were asked to perform the stop jump (STJ), double leg-drop vertical jump (DL-DVJ), and single leg-drop vertical jump (SL-DVJ) tasks on a force plate with 1 min rest between two consecutive repetitions and 2 min rest between tasks. Also, a 5 min rest was considered between the muscle strength test and performance tests. Before performing the strength test, the participant performed a 5 min warm-up routine of stretching and aerobic exercises with moderate intensity. Also, they were asked to perform the jumping tasks before data capturing for familiarization.

The hamstring-to-quadriceps (H:Q) torque ratio measurement

The quadriceps and hamstring muscle strength of the dominant leg was measured by HHD as a valid and reliable device [20, 21] (Nicholas Manual Muscle Tester, Lafayette Instrument Company, Lafayette, Indiana, USA) and then the recorded maximum value was multiplied by the distance between the center of the dynamometer and the rotation axis of the knee; Which was measured by tape measure. To measure the isometric hamstring strength, the participants were asked to lay in a prone position with knees and hips in 90° flexion and hands freely behind the body. In the next step, the HHD was placed 2 cm above the lateral malleus in the posterior part of the tibia, and the participants were asked to produce maximum force for 5 s in the knee flexion direction. To measure the isometric quadriceps strength, the participants were asked to sit on the table with knees and hips in 90° flexion and hands crossed over the chest. In the next step, the HHD was placed 2 cm above the lateral malleus in the anterior part of the tibia, and the participants were asked to produce maximum force for 5 s in the knee extension direction.

It should be noted that each test was performed for two trials with a 30-s resting period interval between them and a 2-min between muscles, and the highest value was considered as the maximum isometric strength; Notably, the participants were verbally encouraged to perform the maximum effort during the test, and if the difference between two measurements was more than 10%, the test was repeated. Also, if pain and discomfort are reported during the test, the test was stopped and repeated.

Finally, the quadriceps and hamstrings muscles torque (Nm/kg) was calculated by multiplying the force, acceleration of gravity, and lever arm: [force (kg) × 9.81 × lever arm (m)] and normalized by the body mass (kg) of each subject. Also, isometric H:Q torque ratio for each participant was calculated by dividing hamstring torque by the quadriceps torque multiplied by 100.

Jump tasks procedures

To perform the STJ task, the participants were asked to run towards the force plates, quickly decelerate and jump with both feet on the force plate, then immediately perform a two-footed maximal vertical jump (Fig 1A). To perform the DL-DVJ task, first, the participants were asked to stand with feet shoulder-width apart on the 30-cm height step which was placed at a distance equal to half of the subject’s height in relation to the center of force plate; Then, they were asked to land with both feet on a force plate, and immediately perform a maximal vertical jump as fast as they can (Fig 1B). To perform the SL-DVJ task, the participants were asked to do the same task as the DL-DVJ with the difference that landing and jumping must be done with the dominant leg (Fig 1C); The dominant leg was defined as the leg that was chosen in the sudden landing.

thumbnail
Download:
Fig 1. The illustration of the method of the jumping tests.

A: Stop jump (STJ), B: Double leg-drop vertical jump (DL-DVJ), and C: Single leg-drop vertical jump (SL-DVJ).

https://doi.org/10.1371/journal.pone.0294274.g001

The modified reactive strength index (RSImod) measurement

RSImod is used as a method to measure the lower extremity explosive strength to assess the athletes’ jumping performance. RSImod was calculated by dividing the vertical jump height by the time to take-off which indicates the athlete’s jump ability relative to the duration of the applied force or time to take-off [22]; Jump height was calculated by the vertical force-time graph of the force plate device sampling at 1200 Hz based on this formula: [9/81× (flight time)^2) /8]; Time to take-off was defined as the duration length of force-time between the landing and take-off (vertical force threshold was defined as 10% of the subject’s body weight by using MATLAB software) [22–24]. Notably, the RSImod has been shown to be a reliable and valid measure [22], a practical way to assess the lower limb explosive performance [13].

Statistical analysis

Regarding the normality of data distribution based on the Shapiro-Wilk test, the Pearson correlation coefficient statistical test was used to determine the relationship between the H:Q torque ratio and jumping performance. All data were calculated by use of the SPSS software Version 22.0 (Microsoft Corp., Redmond, WA), and the significance level was set at .05.

Results

The mean and SD values for jumping performance tests’ variables and the hamstring-to-quadriceps strength ratio of participants can be found in Table 1. The result of the Pearson correlation coefficient test showed a significant strong positive relationship between the H:Q torque ratio and STJ performance based on the RSImod (p = .027; r = .724 [95% CI, .446 to .946]). Although, there was a moderate positive relationship between the H:Q torque ratio and jumping height of the STJ task, but it wasn’t statistically significant (p = .096; r = .588 [95% CI, .188 to .869]). Also, no significant relationship was found between the H:Q torque ratio and all jumping performance variables of the DL-DVJ and SL-DVJ tasks (Table 2).

thumbnail
Download:
Table 1. Jumping performance tests’ variables values and the hamstring-to-quadriceps (H:Q) torque ratio score of participants^.

https://doi.org/10.1371/journal.pone.0294274.t001

thumbnail
Download:
Table 2. Correlation (r) between isometric hamstring-to-quadriceps (H:Q) torque ratio and jumping performance.

https://doi.org/10.1371/journal.pone.0294274.t002

Discussion

Several factors including extensor muscle strength, triple hop performance test, change-of-direction speed, and agility are related to athletes’ jumping performance based on RSImod [3, 16, 18]; Notably, there is some study that evaluated the relationship between dynamic/mixed type of the H:Q torque ratio and RSImod in various tasks with different conditions [25–27]. Although, the gold standard method to quantify muscle strength utilizes an isokinetic dynamometer, However, this option lacks clinical applicability due to cost and size. HHD is a portable and more clinically applicable device well establishes as a valid and reliable testing alternative. To date, the relation of the isometric H:Q torque ratio, especially in various jumping tasks has not been well investigated. The purpose of this study was to determine the relationship between the isometric H:Q torque ratio and jumping performance variables. Our results indicated that the isometric H:Q torque ratio significantly had a strong positive correlation with RSImod of the STJ task. But, no significant relationship was found between the isometric H:Q torque ratio and all jumping performance variables of the DL-DVJ and SL-DVJ tasks. Although, the relationship between the H:Q torque ratio and the RSImod of the DL-DVJ task wasn’t statistically significant, but, there was a moderate positive relationship between them; Notably, the correlation between the H:Q torque ratio and the RSImod of the SL-DVJ task was poor; These results suggest that the RSImod can be attributed to a much more complex process than to H:Q torque ratio, especially in tasks with high complexity, including SL-DVJ task.

In this regard, recent similar studies have shown that the correlation of the H:Q torque ratio with jumping performance variables is different in various tasks with different conditions, which means that it could be related to movement task demand [26, 27]; Diker et al. demonstrated that, although, the H:Q torque ratio was correlated with 30 m sprint time but it wasn’t with countermovement jump or squat jump height tasks [26]; Struzik and Pietraszewski showed a different correlation of the H:Q torque ratio with jumping performance variables by changing the velocity changes-based isokinetic H:Q torque ratio or box height of the drop jump task [27]. It is worth noting that the difference between these studies and our study was that they defined jump height as a jumping performance and also measured the dynamic/mixed type of the H:Q torque ratio. According to the finding of the current study and considering the results of previous similar studies in regard to the relationship between the H:Q torque ratio and jumping performance in different task conditions, the authors hypothesize that as much as the complexity of the movement is increase, the correlation between H:Q torque ratio and RSImod decreases; In other words, the jumping performance rate is probably more related to other factors. In this context, various studies well have proven that the physical demands are not the same in different movement tasks or different conditions which can be attributed to the results of the current study [28–31]. Therefore, the isometric H:Q torque ratio used to monitor the athletes’ performance couldn’t independently represent the jumping performance that is determined by RSImod. Authors recommend that monitoring strength balances along with other factors may provide a better understanding of the association between H:Q torque ratio and jumping performance variables.

In summary, according to the strong correlation of the isometric H:Q torque ratio with the RSImod of the STJ task, calculated RSImod during the STJ task, but not during DL-DVJ and SL-DVK tasks, can be used as an additional tool for the recognition of the isometric H:Q torque ratio. However, it should be noted that even in this case, we investigated the isometric H:Q ratio, and this correlation value might have been different if the H:Q ratio was calculated based on the dynamic or mixed type of ratio. In this regard, some research has shown a significant association between a different type of H:Q torque ratio and injuries [6]. Also, it is reported that the dynamic strength tests may be more practical methods of assessing the relationships between relative strength levels and dynamic performance especially in athletes [32]. Although, in this regard, it has been shown that the dynamic H:Q torque ratio is also related to jumping performance based jumping height and should be considered in strength-based training programs which was similar to our finding [33]. However, it seems that a comprehensive study is needed to investigate the dynamics H:Q torque ratio on jumping performance during different jumping tasks.

We acknowledge that the current study had limitations that should be considered; First, we used the isometric H:Q torque ratio, and the other type of ratio may have a different correlation with RSImod; Second, the participants in this study were healthy male recreational athletes, so these results may not be generalizable to everyone; Gender differences may play an important role in jumping movements pattern and, of course, the results may have been affected if athletes of different sports were evaluated.

Conclusion

In summary, we investigated the relationship between isometric H:Q torque ratio and athletes’ jumping performance; The findings of the current study indicated that the isometric H:Q torque ratio correlates to STJ performance based on RSImod but not to SL-DVJ and DL-DVJ. Notably, the difference in results between jumping tasks can be attributed to the complexity of the movement, which means that the RSImod is probably related to other factors. Therefore, the isometric H:Q torque ratio used to monitor the athletes’ performance couldn’t independently represent the jumping performance that is determined by RSImod.

Acknowledgments

The authors would like to thank all participants and athletic training laboratory staff for the collaborations to make this study.

References

  1. 1. McKay CD, Merrett CK, Emery CA. Predictors of FIFA 11+ implementation intention in female adolescent soccer: an application of the health action process approach (HAPA) model. International journal of environmental research and public health. 2016;13: 657. pmid:27399746
  2. 2. McKay CD, Steffen K, Romiti M, Finch CF, Emery CA. The effect of coach and player injury knowledge, attitudes and beliefs on adherence to the FIFA 11+ programme in female youth soccer. British Journal of Sports Medicine. 2014;48: 1281–1286. pmid:24928848
  3. 3. Birchmeier T, Lisee C, Geers B, Kuenze C. Reactive strength index and knee extension strength characteristics are predictive of single-leg hop performance after anterior cruciate ligament reconstruction. The Journal of Strength & Conditioning Research. 2019;33: 1201–1207. pmid:30844991
  4. 4. Hewett TE. Neuromuscular and hormonal factors associated with knee injuries in female athletes: strategies for intervention. Sports medicine. 2000;29: 313–327.
  5. 5. Askling CM, Tengvar M, Saartok T, Thorstensson A. Acute first-time hamstring strains during slow-speed stretching: clinical, magnetic resonance imaging, and recovery characteristics. The American journal of sports medicine. 2007;35: 1716–1724. pmid:17567821
  6. 6. Kellis E, Sahinis C, Baltzopoulos V. Is hamstrings-to-quadriceps torque ratio useful for predicting anterior cruciate ligament and hamstring injuries? A systematic and critical review. Journal of Sport and Health Science. 2022. pmid:35065297
  7. 7. Opar DA, Williams MD, Shield AJ. Hamstring strain injuries: factors that lead to injury and re-injury. Sports medicine. 2012;42: 209–226. pmid:22239734
  8. 8. Peek K, Gatherer D, Bennett KJM, Fransen J, Watsford M, Fransen AJ. Muscle strength characteristics of the hamstrings and quadriceps in players from a high-level youth football Academy. Research in Sports Medicine. 2017.
  9. 9. Šarabon N, Milinović I, Dolenec A, Kozinc Ž, Babić V. The Reactive Strength Index in Unilateral Hopping for Distance and Its Relationship to Sprinting Performance: How Many Hops Are Enough for a Comprehensive Evaluation? Applied Sciences. 2022;12: 11383.
  10. 10. Rebelo A, Pereira JR, Martinho D V, Duarte JP, Coelho-e-Silva MJ, Valente-dos-Santos J. How to Improve the Reactive Strength Index among Male Athletes? A Systematic Review with Meta-Analysis. Healthcare. MDPI; 2022. p. 593. pmid:35455771
  11. 11. Ramirez-Campillo R, Thapa RK, Afonso J, Perez-Castilla A, Bishop C, Byrne PJ, et al. Effects of Plyometric Jump Training on the Reactive Strength Index in Healthy Individuals Across the Lifespan: A Systematic Review with Meta-analysis. Sports Medicine. 2023;53: 1029–1053. pmid:36906633
  12. 12. Flanagan EP, Comyns TM. The use of contact time and the reactive strength index to optimize fast stretch-shortening cycle training. Strength & Conditioning Journal. 2008;30: 32–38.
  13. 13. Ebben WP, Petushek EJ. Using the reactive strength index modified to evaluate plyometric performance. The Journal of Strength & Conditioning Research. 2010;24: 1983–1987. pmid:20634740
  14. 14. McClymont D, Hore A. Use of the reactive strength index (RSI) as an indicator of plyometric training conditions. Science and Football V: The proceedings of the fifth World Congress on Sports Science and Football, Lisbon, Portugal. 2003. p. 16.
  15. 15. Flanagan EP, Harrison AJ. Lower limb performance in anterior cruciate ligament reconstructed individuals. ISBS-Conference Proceedings Archive. 2006.
  16. 16. Beckham GK, Suchomel TJ, Bailey CA, Sole CJ, Grazer JL. The relationship of the reactive strength index-modified and measures of force development in the isometric mid-thigh pull. ISBS-Conference Proceedings Archive. 2014.
  17. 17. Young WB, Miller IR, Talpey SW. Physical qualities predict change-of-direction speed but not defensive agility in Australian rules football. The Journal of Strength & Conditioning Research. 2015;29: 206–212.
  18. 18. Young WB, Murray MP. Reliability of a field test of defending and attacking agility in Australian football and relationships to reactive strength. The Journal of Strength & Conditioning Research. 2017;31: 509–516. pmid:28129280
  19. 19. Lima YL, Ferreira VMLM, de Paula Lima PO, Bezerra MA, de Oliveira RR Almeida GPL. The association of ankle dorsiflexion and dynamic knee valgus: A systematic review and meta-analysis. Physical Therapy in Sport. 2018;29: 61–69. pmid:28974358
  20. 20. Lesnak J, Anderson D, Farmer B, Katsavelis D, Grindstaff TL. Validity of hand-held dynamometry in measuring quadriceps strength and rate of torque development. International journal of sports physical therapy. 2019;14: 180. pmid:30997270
  21. 21. Chamorro C, Armijo-Olivo S, De la Fuente C, Fuentes J, Javier Chirosa L. Absolute reliability and concurrent validity of hand held dynamometry and isokinetic dynamometry in the hip, knee and ankle joint: systematic review and meta-analysis. Open medicine. 2017;12: 359–375. pmid:29071305
  22. 22. Suchomel TJ, Bailey CA, Sole CJ, Grazer JL, Beckham GK. Using reactive strength index-modified as an explosive performance measurement tool in Division I athletes. The Journal of Strength & Conditioning Research. 2015;29: 899–904. pmid:25426515
  23. 23. Kipp K, Kiely MT, Giordanelli MD, Malloy PJ, Geiser CF. Biomechanical determinants of the reactive strength index during drop jumps. International Journal of Sports Physiology and Performance. 2018;13: 44–49. pmid:28422586
  24. 24. Beckham GK, Suchomel TJ, Sole CJ, Bailey CA, Grazer JL, Kim SB, et al. Influence of sex and maximum strength on reactive strength index-modified. Journal of Sports Science & Medicine. 2019;18: 65. pmid:30787653
  25. 25. Crotty NMN, Daniels KAJ, McFadden C, Cafferkey N, King E. Relationship between isokinetic knee strength and single-leg drop jump performance 9 months after ACL reconstruction. Orthopaedic journal of sports medicine. 2022;10: 23259671211063800. pmid:35005049
  26. 26. Diker G, Struzik A, Ön S, Zileli R. The Relationship between the Hamstring-to-Quadriceps Ratio and Jumping and Sprinting Abilities of Young Male Soccer Players. International Journal of Environmental Research and Public Health. 2022;19: 7471. pmid:35742720
  27. 27. Struzik A, Pietraszewski B. Relationships between hamstrings-to-quadriceps ratio and variables describing countermovement and drop jumps. Applied Bionics and Biomechanics. 2019;2019. pmid:31281414
  28. 28. Taylor JB, Ford KR, Nguyen A-D, Shultz SJ. Biomechanical comparison of single-and double-leg jump landings in the sagittal and frontal plane. Orthopaedic Journal of Sports Medicine. 2016;4: 2325967116655158. pmid:27482527
  29. 29. de Oliveira HLC, Costa Alvim F, Menegaldo LL. Exploring Hip and Knee Biomechanical Differences Between Horizontal and Vertical Single Leg Jumps. XXVI Brazilian Congress on Biomedical Engineering: CBEB 2018, Armação de Buzios, RJ, Brazil, 21–25 October 2018 (Vol 1). Springer; 2019. pp. 207–212.
    • 30. Chinnasee C, Weir G, Sasimontonkul S, Alderson J, Donnelly C. A biomechanical comparison of single-leg landing and unplanned sidestepping. International Journal of Sports Medicine. 2018;39: 636–645. pmid:29902807
    • 31. Cushion EJ, Warmenhoven J, North JS, Cleather DJ. Task demand changes motor control strategies in vertical jumping. Journal of Motor Behavior. 2021;53: 471–482. pmid:32744143
    • 32. Thomas C, Jones PA, Rothwell J, Chiang CY, Comfort P. An Investigation into the Relationship between Maximum Isometric Strength and Vertical Jump Performance. Journal of Strength and Conditioning Research. 2015;29: 2176–2185. pmid:25647649
    • 33. Schons P, Da Rosa RG, Fischer G, Berriel GP, Fritsch CG, Nakamura FY, et al. The relationship between strength asymmetries and jumping performance in professional volleyball players. Sports Biomechanics. 2018. pmid:29578379