{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T05:01:19Z","timestamp":1774414879757,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,7,26]],"date-time":"2019-07-26T00:00:00Z","timestamp":1564099200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["Post-graduation grant"],"award-info":[{"award-number":["Post-graduation grant"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Medicina"],"abstract":"<jats:p>Background and Objectives: This study considered the use of a generalized additive multilevel model to describe the joint-angle-specific functional hamstring to quadriceps ratio (H:Q ratio) in the knee, using all of the available truly isokinetic data within the range. Materials and Methods: Thirty healthy male basketball players aged 15.0 (1.4) years (average stature = 180.0 cm, SD = 11.1 cm; average body mass = 71.2, SD = 14.9 kg) years were considered. All players considered had no history of lower extremity musculoskeletal injury at the time of testing or during the 6 months before testing, and had been engaged in formal basketball training and competition for 5.9 (2.4) years. Moments of force of the reciprocal concentric and eccentric muscular actions for the knee extensors and flexors assessed by isokinetic dynamometry at 60\u00b0\u2219s\u22121 were used. Results: Maximum moments of force were attained at different angle positions for knee extension. For knee flexion, it was apparent that there was an ability to maintain high levels of moment of force between 30\u00b0 and 60\u00b0 in the concentric muscular action, corresponding to the concentric action of the hamstrings. However, for the eccentric knee flexion, corresponding to the quadriceps action, there was a marked peak of moment of force at about 55\u00b0. The functional H:Q ratio for the knee extension was non-linear, remaining higher than 1.0 (i.e., point of equality) from the beginning of the extension until approximately 40\u00b0 of the knee extension, leveling off below the point of equality thereafter. On average, the functional H:Q ratio for the knee flexion did not attain 1.0 across the range of motion. The functional H:Q ratio for the knee in the present sample peaked at 20\u00b0 and 80\u00b0, declining between these angle positions to below 0.50 at about 0.54. Conclusions: Estimating the form of the non-linear relationship on-the-fly using a generalized additive multilevel model provides joint-angle-specific curves and joint-angle-specific functional H:Q ratio patterns, allowing the identification and monitoring of strength development, with potential implications for injury and performance.<\/jats:p>","DOI":"10.3390\/medicina55080411","type":"journal-article","created":{"date-parts":[[2019,7,26]],"date-time":"2019-07-26T11:55:22Z","timestamp":1564142122000},"page":"411","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Modeling the Angle-Specific Isokinetic Hamstring to Quadriceps Ratio Using Multilevel Generalized Additive Models"],"prefix":"10.3390","volume":"55","author":[{"given":"Lucas A.","family":"Sousa","sequence":"first","affiliation":[{"name":"School of Physical Education, University of Campinas, Campinas, S\u00e3o Paulo 13083-851, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6629-656X","authenticated-orcid":false,"given":"Andr\u00e9 L. A.","family":"Soares","sequence":"additional","affiliation":[{"name":"Department of Physical Education, School of Sports, Federal University of Santa Catarina, Florian\u00f3polis, Santa Catarina 88040-900, Brazil"}]},{"given":"Ahlan B.","family":"Lima","sequence":"additional","affiliation":[{"name":"Department of Physical Education, School of Sports, Federal University of Santa Catarina, Florian\u00f3polis, Santa Catarina 88040-900, Brazil"}]},{"given":"Roberto R.","family":"Paes","sequence":"additional","affiliation":[{"name":"School of Physical Education, University of Campinas, Campinas, S\u00e3o Paulo 13083-851, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7312-2717","authenticated-orcid":false,"given":"Luiz R.","family":"Nakamura","sequence":"additional","affiliation":[{"name":"Department of Informatics and Statistics, School of Technology, Federal University of Santa Catarina, Florian\u00f3polis, Santa Catarina 88040-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2855-0296","authenticated-orcid":false,"given":"Humberto M.","family":"Carvalho","sequence":"additional","affiliation":[{"name":"Department of Physical Education, School of Sports, Federal University of Santa Catarina, Florian\u00f3polis, Santa Catarina 88040-900, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1177\/0363546504269937","article-title":"Anterior cruciate ligament injury in national collegiate athletic association basketball and soccer: A 13-year review","volume":"33","author":"Agel","year":"2005","journal-title":"Am. J. Sports Med."},{"key":"ref_2","first-page":"311","article-title":"Epidemiology of collegiate injuries for 15 sports: Summary and recommendations for injury prevention initiatives","volume":"42","author":"Hootman","year":"2007","journal-title":"J. Athl. Train."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1177\/0363546508314400","article-title":"Epidemiology of knee injuries among boys and girls in US high school athletics","volume":"36","author":"Ingram","year":"2008","journal-title":"Am. J. Sports Med."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1519\/SSC.0b013e31821a9833","article-title":"Injury Incidence, Body Site, and Severity in Soccer Players Aged 6\u201318 Years: Implications for Injury Prevention","volume":"34","author":"Rumpf","year":"2012","journal-title":"Strength Cond. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1016\/j.jbiomech.2003.11.009","article-title":"Frequency content asymmetry of the isokinetic curve between ACL deficient and healthy knee","volume":"37","author":"Tsepis","year":"2004","journal-title":"J. Biomech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"18","DOI":"10.2165\/00007256-199621010-00003","article-title":"The utility of isokinetic dynamometry in the assessment of human muscle function","volume":"21","author":"Gleeson","year":"1996","journal-title":"Sports Med."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1177\/036354658801600215","article-title":"Assessment of quadriceps\/hamstring strength, knee ligament stability, functional and sports activity levels five years after anterior cruciate ligament reconstruction","volume":"16","author":"Seto","year":"1988","journal-title":"Am. J. Sports Med."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1111\/j.1748-1716.1995.tb09927.x","article-title":"Isokinetic hamstring\/quadriceps strength ratio: Influence from joint angular velocity, gravity correction and contraction mode","volume":"154","author":"Aagaard","year":"1995","journal-title":"Acta Physiol. Scand."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1177\/03635465980260021201","article-title":"A new concept for isokinetic hamstring: Quadriceps muscle strength ratio","volume":"26","author":"Aagaard","year":"1998","journal-title":"Am. J. Sports Med."},{"key":"ref_10","first-page":"56","article-title":"Developments in the use of the hamstring\/quadriceps ratio for the assessment of muscle balance","volume":"1","author":"Coombs","year":"2002","journal-title":"J. Sports Sci. Med."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1097\/00042752-200409000-00005","article-title":"Hamstring and quadriceps strength balance in normal and hamstring anterior cruciate ligament-reconstructed subjects","volume":"14","author":"Hiemstra","year":"2004","journal-title":"Clin. J. Sport Med."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7269","DOI":"10.1038\/s41598-017-06601-5","article-title":"Isokinetic angle-specific moments and ratios characterizing hamstring and quadriceps strength in anterior cruciate ligament deficient knees","volume":"7","author":"Huang","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_13","unstructured":"Steindler, A. (1955). Kinesiology of the Human Body Under Normal and Pathological Conditions, Charles C Thomas. [1st ed.]."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1080\/02640414.2014.942680","article-title":"Angle-specific hamstring-to-quadriceps ratio: A comparison of football players and recreationally active males","volume":"33","author":"Evangelidis","year":"2015","journal-title":"J. Sports Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1016\/j.knee.2017.03.012","article-title":"The impact of joint angle and movement velocity on sex differences in the functional hamstring\/quadriceps ratio","volume":"24","author":"ElNagar","year":"2017","journal-title":"Knee"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1007\/s00167-015-3684-7","article-title":"Sex-related differences in joint-angle-specific functional hamstring-to-quadriceps strength ratios","volume":"25","author":"Carson","year":"2017","journal-title":"Knee Surg. Sports Traumatol. Arthrosc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1055\/a-0850-0016","article-title":"Discipline and Sex Differences in Angle-specific Isokinetic Analysis in Elite Skiers","volume":"40","author":"Alhammoud","year":"2019","journal-title":"Int. J. Sports Med."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Speelman, D., Heylen, K., and Geeraerts, D. (2018). Autocorrelated Errors in Experimental Data in the Language Sciences: Some Solutions Offered by Generalized Additive Mixed Models. Mixed-Effects Regression Models in Linguistics, Springer. [1st ed.].","DOI":"10.1007\/978-3-319-69830-4"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1643","DOI":"10.1002\/sim.4780131605","article-title":"Multilevel time series models with applications to repeated measures data","volume":"13","author":"Goldstein","year":"1994","journal-title":"Stat. Med."},{"key":"ref_20","unstructured":"Hastie, T., and Tibshirani, R. (1990). Generalized Additive Models, Chapman and Hall. [1st ed.]."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Wood, S.N. (2006). Generalized Additive Models: An Introduction with R, Chapman & Hall\/CRC. [1st ed.].","DOI":"10.1201\/9781420010404"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Simpson, G.L. (2018). Modelling Palaeoecological Time Series Using Generalised Additive Models. Front. Ecol. Evol., 6.","DOI":"10.3389\/fevo.2018.00149"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Gelman, A., and Hill, J. (2007). Data Analysis Using Regression and Multilevel\/Hierarchical Models, Cambridge University Press. [1st ed.].","DOI":"10.32614\/CRAN.package.arm"},{"key":"ref_24","unstructured":"McElreath, R. (2015). Statistical Rethinking: A Bayesian Course with Examples in R and Stan, Chapman & Hall\/CRC Press. [1st ed.]."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"395","DOI":"10.32614\/RJ-2018-017","article-title":"Advanced Bayesian Multilevel Modeling with the R Package brms","volume":"10","year":"2018","journal-title":"R J."},{"key":"ref_26","first-page":"e27320v1","article-title":"Hierarchical generalized additive models: An introduction with mgcv","volume":"6","author":"Pedersen","year":"2018","journal-title":"PeerJ Prepr."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/s11222-012-9314-z","article-title":"Straightforward intermediate rank tensor product smoothing in mixed models","volume":"23","author":"Wood","year":"2013","journal-title":"Stat. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1111\/j.1467-9868.2010.00749.x","article-title":"Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models","volume":"73","author":"Wood","year":"2011","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1515\/hukin-2015-0105","article-title":"Multilevel Models for the Analysis of Angle-Specific Torque Curves with Application to Master Athletes","volume":"49","author":"Carvalho","year":"2015","journal-title":"J. Hum. Kinet."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1055\/s-0043-124001","article-title":"Standards for Ethics in Sport and Exercise Science Research: 2018 Update","volume":"38","author":"Harriss","year":"2017","journal-title":"Int. J. Sports Med."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"446","DOI":"10.3390\/medicina47080063","article-title":"Assessment of reliability in isokinetic testing among adolescent basketball players","volume":"47","author":"Carvalho","year":"2011","journal-title":"Medicina"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"138","DOI":"10.2519\/jospt.1991.13.3.138","article-title":"Sources of error in isokinetic dynamometry: Effects of visual feedback on maximum torque","volume":"13","author":"Baltzopoulos","year":"1991","journal-title":"J. Orthop. Sports Phys. Ther."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"807","DOI":"10.2165\/00007256-200737090-00004","article-title":"Altering the length-tension relationship with eccentric exercise: Implications for performance and injury","volume":"37","author":"Brughelli","year":"2007","journal-title":"Sports Med."},{"key":"ref_34","first-page":"1","article-title":"Brms: An R Package for Bayesian Multilevel Models Using Stan","volume":"80","year":"2017","journal-title":"J. Stat. Softw."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Vehtari, A., Gelman, A., and Gabry, J. (2016). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. arXiv.","DOI":"10.32614\/CRAN.package.loo"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1123\/pes.23.1.1","article-title":"It\u2019s about time","volume":"23","author":"Rowland","year":"2011","journal-title":"Pediatr. Exerc. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1055\/s-0032-1311586","article-title":"Absolute reliability of hamstring to quadriceps strength imbalance ratios calculated using peak torque, joint angle-specific torque and joint ROM-specific torque values","volume":"33","author":"Ayala","year":"2012","journal-title":"Int. J. Sports Med."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Baumgart, C., Welling, W., Hoppe, M.W., Freiwald, J., and Gokeler, A. (2018). Angle-specific analysis of isokinetic quadriceps and hamstring torques and ratios in patients after ACL-reconstruction. BMC Sports Sci. Med. Rehabil., 10.","DOI":"10.1186\/s13102-018-0112-6"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1080\/17461391.2019.1574904","article-title":"Sex-related differences in joint-angle-specific hamstring-to-quadriceps function following fatigue","volume":"19","author":"Allardyce","year":"2019","journal-title":"Eur. J. Sport Sci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1689","DOI":"10.1016\/j.jbiomech.2004.02.005","article-title":"Angle- and gender-specific quadriceps femoris muscle recruitment and knee extensor torque","volume":"37","author":"Pincivero","year":"2004","journal-title":"J. Biomech."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/S0268-0033(99)00063-7","article-title":"Cruciate ligament forces in the human knee during rehabilitation exercises","volume":"15","author":"Toutoungi","year":"2000","journal-title":"Clin. Biomech."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1002\/ajpa.20356","article-title":"Modeling physiological and anthropometric variables known to vary with body size and other confounding variables","volume":"128","author":"Nevill","year":"2005","journal-title":"Am. J. Phys. Anthr."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1152\/jappl.1949.2.1.1","article-title":"Fallacy of per-weight and per-surface area standards, and their relation to spurious correlation","volume":"2","author":"Tanner","year":"1949","journal-title":"J. Appl. Physiol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2881","DOI":"10.1007\/s00421-011-2259-7","article-title":"Scaling lower-limb isokinetic strength for biological maturation and body size in adolescent basketball players","volume":"112","author":"Carvalho","year":"2012","journal-title":"Eur. J. Appl. Physiol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1111\/rssc.12068","article-title":"Generalized additive models for large data sets","volume":"64","author":"Wood","year":"2015","journal-title":"J. R. Stat. Soc. Ser. C Appl. Stat."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Wood, S.N. (2017). Generalized Additive Models: An Introduction with R, Chapman and Hall\/CRC. [2nd ed.].","DOI":"10.1201\/9781315370279"}],"container-title":["Medicina"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1648-9144\/55\/8\/411\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:10:10Z","timestamp":1760188210000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1648-9144\/55\/8\/411"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,26]]},"references-count":46,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["medicina55080411"],"URL":"https:\/\/doi.org\/10.3390\/medicina55080411","relation":{},"ISSN":["1648-9144"],"issn-type":[{"value":"1648-9144","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,26]]}}}