Restricted accessResearch articleFirst published online 2026-1
Influence of intrinsic and extrinsic conditions on the knee joint loading during double-leg landing using a musculoskeletal model in the sagittal plane
Knee injuries are prevalent in the sports world, particularly during single and double-leg landings. These injuries can affect various structures of the knee, including ligaments, menisci, condyles, the patellar tendon and others. While body posture at the time of ground impact plays a significant role in the occurrence of such injuries, extrinsic factors such as fall height, contact conditions and landing surface properties are also critical. Additionally, the stiffness-damping characteristics of the human joints may contribute to the risk of knee injury. This paper proposes a new dynamic model to investigate the influence of intrinsic and extrinsic parameters on knee joint forces and moments during a double-leg landing task. The model considers the mass, posture and movement of the body segments, the stiffness-damping of the joints, the ground reaction force and the landing surface conditions. The calibration of the model is based on ground reaction force behaviour reported in the literature. A sensitivity analysis using the Morris method is conducted to evaluate the influence of intrinsic and extrinsic parameters on knee joint forces. The results indicate that foot, shank and thigh posture, as well as the fall height, have the most significant influence on the knee joint forces and moments. This study provides valuable insights into the mechanisms of knee injuries and highlights the importance of considering both intrinsic and extrinsic factors in injury prevention strategies.
Fernández-GalvánLMHernández SantanaCLópez-NuevoC, et al. Injuries in female futsal players: a systematic review. Sports2024; 12: 311.
2.
KleinCLuigPHenkeT, et al. Nine typical injury patterns in German professional male football (soccer): a systematic visual video analysis of 345 match injuries. Br J Sports Med2020; 55: 390–396.
3.
Della VillaFBuckthorpeMGrassiA, et al. Systematic video analysis of ACL injuries in professional male football (soccer): injury mechanisms, situational patterns and biomechanics study on 134 consecutive cases. Br J Sports Med2020; 54: 1423–1432.
4.
D’HooghePGrassiAVillaFD, et al. The injury mechanism correlation between MRI and video-analysis in professional football players with an acute ACL knee injury reveals consistent bone bruise patterns. Knee Surg Sports Traumatol Arthrosc2023; 31: 121–132.
5.
TsarbouCLiverisNITsimeasPD, et al. The effect of fatigue on jump height and the risk of knee injury after a volleyball training game: a pilot study. Biomed Hum Kinet2021; 13: 197–204.
6.
CrossERLynchSMMillerPE, et al. Injury patterns in fencing athletes - a retrospective review. Int J Sports Phys Ther2024; 19(9): 1108–1115.
7.
BodenBPSheehanFT.Mechanism of non-contact ACL injury: OREF Clinical Research Award 2021. J Orthop Res2022; 40: 531–540.
8.
OkoyeMWissmanAWissmanRD.Review of extensor mechanism injuries in the dislocated knee. J Knee Surg2022; 35: 498–501.
9.
QiuLShengBLiJ, et al. Mechanisms of non-contact anterior cruciate ligament injury as determined by bone contusion location and severity. Quant Imaging Med Surg2021; 11: 3263–3273.
10.
MakkiARKTahirMAminU, et al. Mechanism of meniscal injury and its impact on performance in athletes. Heal J Physiother Rehabil Sci2022; 2: 232–237.
11.
OlivieriRLasoJIFranulicN, et al. Evaluating the impact of biological augmentation on failure rates and complications in acute patellar tendon rupture surgery compared with isolated repair. Orthop J Sports Med2024; 12: 23259671241288848.
12.
AbulhasanJGreyM.Anatomy and physiology of knee stability. J Funct Morphol Kinesiol2017; 2(4): 34.
13.
LarwaJStoyCChafetzRS, et al. Stiff landings, core stability, and dynamic knee valgus: a systematic review on documented anterior cruciate ligament ruptures in male and female athletes. Int J Environ Res Public Health2021; 18(7): 3826.
14.
PoulsenEGoncalvesGHBriccaA, et al. Knee osteoarthritis risk is increased 4-6 fold after knee injury - a systematic review and meta-analysis. Br J Sports Med2019; 53: 1454–1463.
15.
MarieswaranMJainIGargB, et al. A review on biomechanics of anterior cruciate ligament and materials for reconstruction. Appl Bionics Biomech2018; 2018: 4657824.
16.
TandoganRNTerziEGomez-BarrenaE, et al. Extensor mechanism ruptures. EFORT Open Rev2022; 7: 384–395.
17.
BackxFJGErichWBMKemperABA, et al. Sports injuries in school-aged children. Am J Sports Med1989; 17: 234–240.
18.
HewettTEMyerGDFordKR, et al. Biomechanical measures of neuromuscular control and valgus loading of the knee predict anterior cruciate ligament injury risk in female athletes: a prospective study. Am J Sports Med2005; 33: 492–501.
19.
ThambyahA. A biomechanical interpretation of the non-contact anterior cruciate ligament injury. In: 2012 IEEE-EMBS conference on biomedical engineering and sciences, IECBES2012, 2012, pp.460–464. IEEE.
20.
PurevsurenTDorjAKimK, et al. Prediction of medial and lateral contact force of the knee joint during normal and turning gait after total knee replacement. Proc Inst Mech Eng H J Eng Med2016; 230: 288–297.
21.
PurevsurenTKwonMSParkWM, et al. Fatigue injury risk in anterior cruciate ligament of target side knee during golf swing. J Biomech2017; 53: 9–14.
22.
PurevsurenTKhuyagbaatarBLeeS, et al. Biomechanical factors leading to high loading in the anterior cruciate ligament of the lead knee during golf swing. Int J Precis Eng Manuf2020; 21: 309–318.
23.
NhaKWDorjAFengJ, et al. Application of computational lower extremity model to investigate different muscle activities and joint force patterns in knee osteoarthritis patients during walking. Comput Math Methods Med2013; 2013: 314280.
24.
DelpSLAndersonFCArnoldAS, et al. OpenSim: open-source software to create and analyze dynamic simulations of movement. IEEE Trans Biomed Eng2007; 54: 1940–1950.
25.
AoDLiGShourijehMS, et al. EMG-Driven musculoskeletal model calibration with wrapping surface personalization. IEEE Trans Neural Syst Rehabil Eng2023; 31: 4235–4244.
26.
XuHBloswickDMerryweatherA.An improved OpenSim gait model with multiple degrees of freedom knee joint and knee ligaments. Comput Methods Biomech Biomed Eng2015; 18: 1217–1224.
27.
ChenLJiangZYangC, et al. Effect of different landing actions on knee joint biomechanics of female college athletes: based on opensim simulation. Front Bioeng Biotechnol2022; 10: 1–11.
28.
MarieswaranMSikidarAGoelA, et al. An extended OpenSim knee model for analysis of strains of connective tissues. Biomed Eng Online2018; 17: 42.
Cerda-LugoAGonzalezACardenasA, et al. Experimental estimation of a second order, double inverted pendulum parameters for the study of human balancing. In: Annu Int Conf IEEE Eng Med Biol Soc, July2019, pp.4117–4120. IEEE. DOI: 10.1109/EMBC.2019.8857611.
31.
Cerda-LugoAGonzálezACardenasA, et al. Modeling the neuro-mechanics of human balance when recovering from a fall: A continuous-time approach. Biomed Eng Online2020; 19(1): 24.
32.
RamalingasettySTDannerSMArreguitJ, et al. A whole-body musculoskeletal model of the mouse. IEEE Access2021; 9: 163861–163881.
33.
PiovesanDPierobonAMussa IvaldiFA.Critical damping conditions for third order muscle models: implications for force control. J Biomech Eng2013; 135: 101010.
34.
MeirovitchL.Fundamentals of vibrations. Waveland Press, Illinois, USA, 2010.
35.
HuntKHCrossleyFRE. Coefficient of restitution interpreted as damping in vibroimpact. J Appl Mech1975; 42: 440–445.
36.
HertzH. On the contact of solids—on the contact of rigid elastic solids and on hardness. In: Miscellaneous papers. Macmillan and Co., New York, 1896, pp.146–183.
37.
PflumMAShelburneKBTorryMR, et al. Model prediction of anterior cruciate ligament force during drop-landings. Med Sci Sports Exerc2004; 36: 1949–1958.
38.
LiLSongYJenkinsM, et al. Prelanding knee kinematics and landing kinetics during single-leg and double-leg landings in male and female recreational athletes. J Appl Biomech2023; 39: 34–41.
39.
MothersoleG.Ground reaction force profiles of specific jump - landing tasks in females. Doctoral dissertation, Auckland University of Technology, 2013.
40.
JanzKFRaoSBaumannHJ, et al. Measuring children’s vertical ground reaction forces with accelerometry during walking, running, and jumping: the Iowa bone development study. Pediatr Exerc Sci2003; 15: 34–43.
41.
McNitt-GrayJL.Kinematics and impulse characteristics of drop landings from three heights. Int J Sport Biomech1991; 7: 201–224.
42.
ZadpoorAANikooyanAA.The effects of lower-extremity muscle fatigue on the vertical ground reaction force: a meta-analysis. Proc Inst Mech Eng H J Eng Med2012; 226: 579–588.
43.
SaltelliATarantolaSCampolongoF.Sensitivity analysis as an ingredient of modeling. Stat Sci2000; 15: 377–395.
44.
MohammadiABianchiLKorganbayevS, et al. Thermomechanical modeling of laser ablation therapy of tumors: sensitivity analysis and optimization of influential variables. IEEE Trans Biomed Eng2022; 69: 302–313.
45.
KarabelasELongobardiSFuchsbergerJ, et al. Global sensitivity analysis of four chamber heart hemodynamics using surrogate models. IEEE Trans Biomed Eng2022; 69: 3216–3223.
46.
MorrisMD.Factorial sampling plans for preliminary computational experiments. Technometrics1991; 33: 161–174.
47.
WinterDA.Biomechanics and motor control of human movement. Elsevier, 2009.
48.
Cerda-LugoAGonzalezACardenasA, et al. Estimation of hip and ankle visco-elastic parameters during quiet standing. In: ASME international mechanical engineering congress and exposition, proceedings (IMECE). 2018. DOI: 10.1115/IMECE201887585.
McKayHTsangGHeinonenA, et al. Ground reaction forces associated with an effective elementary school based jumping intervention. Br J Sports Med2005; 39: 10–14.
51.
RiemannBLSchmitzRJGaleM, et al. Vertical ground reaction forces during jogging. J Orthop Sports Phys Ther2002; 32: 628–636.
52.
Ponce-ZambranoMRGordónDPAlejanoLR, et al. Geotechnical characterization of the site and stability of a tailings dam in Ecuador. In: Rock engineering and rock mechanics: structures in and on rock masses - proceedings of EUROCK 2014, ISRM European Regional Symposium. Taylor and Francis - Balkema, 2014, pp.1165–1170.
53.
ChiţescuCLNicolauAIRömkensP, et al. Quantitative modelling to estimate the transfer of pharmaceuticals through the food production system. J Environ Sci Health B2014; 49: 457–467.
54.
MasrurHKhanKRAbumelhaW, et al. Efficient energy delivery system of the CHP-PV based microgrids with the economic feasibility study. Int J Emerg Electric Power Syst2020; 21(1): 20190144.
55.
SouzaRBPowersCM.Differences in hip kinematics, muscle strength, and muscle activation between subjects with and without patellofemoral pain. J Orthop Sports Phys Ther2009; 39: 12–19.
56.
SheehanFTSipprellWHBodenBP.Dynamic sagittal plane trunk control during anterior cruciate ligament injury. Am J Sports Med2012; 40: 1068–1074.
57.
BonnerTJNewellNKarunaratneA, et al. Strain-rate sensitivity of the lateral collateral ligament of the knee. J Mech Behav Biomed Mater2015; 41: 261–270.
58.
ZhouT.Analysis of the biomechanical characteristics of the knee joint with a meniscus injury. Healthc Technol Lett2018; 5: 247–249.
59.
BaniasadMMartinRCrevoisierX, et al. Knee adduction moment decomposition: toward better clinical decision-making. Front Bioeng Biotechnol2022; 10: 1017711.
60.
WilczyńskiBZorenaKŚlęzakD.Dynamic knee valgus in single-leg movement tasks. Potentially modifiable factors and exercise training options. A literature review. Int J Environ Res Public Health2020; 17: 1–17.
61.
LinJDos’SantosTLiW, et al. Is there a Performance-Injury conflict between maximum horizontal deceleration and surrogates of noncontact anterior cruciate ligament injury?Eur J Sport Sci2025; 25(8): e70014.
62.
Dos’SantosTMcBurnieAThomasC, et al. Biomechanical determinants of the modified and traditional 505 change of direction speed test, www.nsca.com (2019).
