Abstract
In this work, a nonlinear strain rate dependent plugin developed for the OpenSim® platform was used to estimate the instantaneous strain rate (ISR) and the forces on the ACL’s anteromedial (aACL) and posterolateral (pACL) bundles during walking and sudden change of direction of running termed as ‘plant-and-cut’ (PC). The authors obtained the kinematics data for walking via optical motion capture. PC movements, along with running kinematics, were obtained from the literature. A nonlinear plugin developed for ligaments was interfaced with OpenSim® platform to simulate walking and PC motions with a flexed knee and an extended knee. PC phase is sandwiched between an approach phase and take-off phase and was studied at various event velocities (1.8, 3, and 4.2 m s−1), and angles of PC (23°, 34°, and 45°) as encountered in adult ball games. In both cases of PC-with-extended knee and PC-with-flexed-knee, the maximum forces on both the ACL bundles were observed after the take-off phase. A maximum force of ~ 35 N kg−1 of body weight (BW) was observed on aACL after the take-off phase for an event velocity of 4.2 m s−1. In the posterolateral bundle (pACL), the maximum forces (~ 40 N kg−1 of BW) were observed towards the end of the mid-swing phase (after the take-off phase) for the various combinations of the parameters studied. The forces observed in the simulation of PC-with-flexed-knee and PC-with-extended-knee has resulted in magnitude higher than sustainable by the adults. This study is novel in attempting to incorporate differing rates-of-strain that have been shown to alter soft tissue properties into the OpenSim® musculoskeletal model. The proposed model can be used by researchers to predict the forces during various kinematic activities for other soft tissues.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
All the necessary information has been included in the main script as well as the supplementary section. For additional queries, the readers can contact the corresponding author.
Abbreviations
- ACL:
-
Anterior cruciate ligament
- FATC:
-
Femur-anterior cruciate ligament-tibial complex
- aACL:
-
Anteromedial bundle of anterior cruciate ligament
- pACL:
-
Posterolateral bundle of anterior cruciate ligament
- BW:
-
Body weight
- r st :
-
Strain rate
- ISR:
-
Instantaneous strain rate
- GRF:
-
Ground reaction force
- IR:
-
Internal rotation
- ER:
-
External rotation
- IC:
-
Initial contact
- PC:
-
Plant-and-cut
- PC-with-flexed-knee:
-
Plant-and-cut With flexed knee
- PC-with-extended-knee:
-
Plant-and-cut With extended knee
- RHS:
-
Right heel strike
- RTO:
-
Right toe-off
- LHS:
-
Left heel strike
- LTO:
-
Left toe-off
- PCA:
-
Angle of plant-and-cut
References
Ahsanizadeh S, Li L (2015) Visco-hyperelastic constitutive modeling of soft tissues based on short and long-term internal variables. Biomed Eng Online 14:29. https://doi.org/10.1186/s12938-015-0023-7
Ali AA, Harris MD, Shalhoub S et al (2017) Combined measurement and modeling of specimen-specific knee mechanics for healthy and ACL-deficient conditions. J Biomech 57:117–124. https://doi.org/10.1016/j.jbiomech.2017.04.008
Amiel D, Billings E, Harwood FL (1990) Collagenase activity in anterior cruciate ligament: protective role of the synovial sheath. J Appl Physiol 69:902–906
Bach JM, Hull ML, Patterson HA (1997) Direct measurement of strain in the posterolateral bundle of the anterior cruciate ligament. J Biomech 30:281–283. https://doi.org/10.1016/S0021-9290(96)00132-7
Christophy M, Senan NAF, Lotz JC, O’Reilly OM (2012) A Musculoskeletal model for the lumbar spine. Biomech Model Mechanobiol 11:19–34. https://doi.org/10.1007/s10237-011-0290-6
Dai B, Garrett WE, Gross MT et al (2019) The effect of performance demands on lower extremity biomechanics during landing and cutting tasks. J Sport Heal Sci 8:228–234. https://doi.org/10.1016/j.jshs.2016.11.004
Dargel J, Gotter M, Mader K et al (2007) Biomechanics of the anterior cruciate ligament and implications for surgical reconstruction. Strateg Trauma Limb Reconstr 2:1–12. https://doi.org/10.1007/s11751-007-0016-6
Davis FM, De Vita R (2012) A nonlinear constitutive model for stress relaxation in ligaments and tendons. Ann Biomed Eng. https://doi.org/10.1007/s10439-012-0596-2
De Vita R, Slaughter WS (2006) A structural constitutive model for the strain rate-dependent behavior of anterior cruciate ligaments. Int J Solids Struct 43:1561–1570. https://doi.org/10.1016/j.ijsolstr.2005.04.022
De Vita R, Slaughter WS (2007) A constitutive law for the failure behavior of medial collateral ligaments. Biomech Model Mechanobiol 6:189–197. https://doi.org/10.1007/s10237-006-0054-x
DeFrate LE, Li G (2007) The prediction of stress-relaxation of ligaments and tendons using the quasi-linear viscoelastic model. Biomech Model Mechanobiol 6:245–251. https://doi.org/10.1007/s10237-006-0056-8
Donnelly CJ, Lloyd DG, Elliott BC, Reinbolt JA (2012) Optimizing whole-body kinematics to minimize valgus knee loading during sidestepping: implications for ACL injury risk. J Biomech 45:1491–1497. https://doi.org/10.1016/j.jbiomech.2012.02.010
Gazendam MGJ, Hof AL (2007) Averaged EMG profiles in jogging and running at different speeds. Gait Posture 25:604–614. https://doi.org/10.1016/j.gaitpost.2006.06.013
Holden JP, Grood ES, Korvick DL et al (1994) In vivo forces in the anterior cruciate ligament: direct measurements during walking and trotting in a quadruped. J Biomech. https://doi.org/10.1016/0021-9290(94)90063-9
Koga H, Muneta T (2016) ACL injury mechanisms. ACL injury and its treatment. Springer, Tokyo, pp 113–125
Lee JH, Asakawa DS, Dennerlein JT, Jindrich DL (2015) Extrinsic and intrinsic index finger muscle attachments in an opensim upper-extremity model. Ann Biomed Eng. https://doi.org/10.1007/s10439-014-1141-2
Malkin AY, Isayev A (2017) Viscoelasticity. Rheology. Elsevier, pp 45–128
Marieswaran M, Jain I, Garg B et al (2018a) A review on biomechanics of anterior cruciate ligament and materials for reconstruction. Appl Bionics Biomech 2018:1–14
Marieswaran M, Sikidar A, Goel A et al (2018b) An extended OpenSim knee model for analysis of strains of connective tissues. Biomed Eng Online. https://doi.org/10.1186/s12938-018-0474-8
Marieswaran M, Sikidar A, Rana A et al (2020) A cadaveric study on the rate of strain dependent behaviour of human anterior cruciate ligament. Acta Bioeng Biomech 23:1–23. https://doi.org/10.37190/ABB-01672-2020-05
Nadeau SE, Wu SS, Dobkin BH et al (2013) Effects of task-specific and impairment-based training compared with usual care on functional walking ability after inpatient stroke rehabilitation: leaps trial. Neurorehabil Neural Repair 27:370–380. https://doi.org/10.1177/1545968313481284
Nagai K, Gale T, Chiba D et al (2019) The complex relationship between in vivo ACL elongation and knee kinematics during walking and running. J Orthop Res 37:1920–1928. https://doi.org/10.1002/jor.24330
Nagai K, Gale T, Herbst E et al (2018) Knee hyperextension does not adversely affect dynamic in vivo kinematics after anterior cruciate ligament reconstruction. Knee Surg Sport Traumatol Arthrosc 26:448–454. https://doi.org/10.1007/s00167-017-4653-0
Nasseri A, Khataee H, Bryant AL et al (2020) Modelling the loading mechanics of anterior cruciate ligament. Comput Methods Programs Biomed 184:105098. https://doi.org/10.1016/j.cmpb.2019.105098
Quatman CE, Kiapour AM, Demetropoulos CK et al (2014) Preferential loading of the ACL compared with the MCL during landing. Am J Sports Med 42:177–186. https://doi.org/10.1177/0363546513506558
Rajagopal A, Dembia CL, DeMers MS et al (2016) Full-body musculoskeletal model for muscle-driven simulation of human gait. IEEE Trans Biomed Eng 63:2068–2079. https://doi.org/10.1109/TBME.2016.2586891
Roelker SA, Caruthers EJ, Baker RK et al (2017) Interpreting musculoskeletal models and dynamic simulations: causes and effects of differences between models. Ann Biomed Eng. https://doi.org/10.1007/s10439-017-1894-5
Sanders TL, Maradit Kremers H, Bryan AJ et al (2016) Incidence of anterior cruciate ligament tears and reconstruction: a 21-year population-based study. Am J Sports Med 44:1502–1507. https://doi.org/10.1177/0363546516629944
Schmitz A, Piovesan D (2016a) Development of an open-source, discrete element knee model. IEEE Trans Biomed Eng 63:2056–2067. https://doi.org/10.1109/TBME.2016.2585926
Schmitz A, Piovesan D (2016b) Development of an open-source cosimulation method of the knee. In: 2016 38th annual international conference of the IEEE engineering in medicine and biology society (EMBC). IEEE, pp 6034–6037
Shelburne KB, Pandy MG, Anderson FC, Torry MR (2004) Pattern of anterior cruciate ligament force in normal walking. J Biomech 37:797–805. https://doi.org/10.1016/j.jbiomech.2003.10.010
Sikidar A, Kalyanasundaram D (2019) An open-source plugin for OpenSim® to model the non-linear behaviour of dense connective tissues of the human knee at variable strain rates. Comput Biol Med. https://doi.org/10.1016/j.compbiomed.2019.05.021
Sikidar A, Kalyanasundaram D (2019) An open-source plugin for OpenSim® to model the non-linear behaviour of dense connective tissues of the human knee at variable strain rates. Comput Biol Med 110:186–195. https://doi.org/10.1016/j.compbiomed.2019.05.021
Skelley NW, Castile RM, York TE et al (2015) Differences in the microstructural properties of the anteromedial and posterolateral bundles of the anterior cruciate ligament. Am J Sports Med. https://doi.org/10.1177/0363546514566192
Suzuki Y, Ae M, Takenaka S, Fujii N (2014) Comparison of support leg kinetics between side-step and cross-step cutting techniques. Sport Biomech. https://doi.org/10.1080/14763141.2014.910264
Taylor DC, Dalton JDJ, Seaber AV, Garrett WEJ (1990) Viscoelastic properties of muscle-tendon units. The biomechanical effects of stretching. Am J Sports Med 18:300–309
Taylor KA, Cutcliffe HC, Queen RM et al (2013) In vivo measurement of ACL length and relative strain during walking. J Biomech 46:478–483. https://doi.org/10.1016/j.jbiomech.2012.10.031
Vanrenterghem J, Venables E, Pataky T, Robinson MA (2012) The effect of running speed on knee mechanical loading in females during side cutting. J Biomech. https://doi.org/10.1016/j.jbiomech.2012.06.029
Verbruggen SW, Loo JHW, Hayat TTA et al (2016) Modeling the biomechanics of fetal movements. Biomech Model Mechanobiol 15:995–1004. https://doi.org/10.1007/s10237-015-0738-1
Wu JL, Hosseini A, Kozanek M et al (2010) Kinematics of the anterior cruciate ligament during gait. Am J Sports Med 38:1475–1482. https://doi.org/10.1177/0363546510364240
Xu H, Bloswick D, Merryweather A (2015) An improved OpenSim gait model with multiple degrees of freedom knee joint and knee ligaments. Comput Methods Biomech Biomed Eng 18:1217–1224. https://doi.org/10.1080/10255842.2014.889689
Funding
No funding was received for this work.
Author information
Authors and Affiliations
Contributions
AS developed the plugin, simulated the dynamic activities and drafted the manuscript, MM edited the manuscript and DK edited the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors have no conflict of interest in this work.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Sikidar, A., Marieswaran, M. & Kalyanasundaram, D. Estimation of forces on anterior cruciate ligament in dynamic activities. Biomech Model Mechanobiol 20, 1533–1546 (2021). https://doi.org/10.1007/s10237-021-01461-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10237-021-01461-5