Background: Predictions of the forces transmitted by the redundant force-bearing\r\nstructures in the knee are often performed using optimization methods considering\r\nonly moment equipollence as a result of simplified knee modeling without ligament\r\ncontributions. The current study aimed to investigate the influence of model\r\ncomplexity (with or without ligaments), problem formulation (moment equipollence\r\nwith or without force equipollence) and optimization criteria on the prediction of\r\nthe forces transmitted by the force-bearing structures in the knee.\r\nMethods: Ten healthy young male adults walked in a gait laboratory while their\r\nkinematic and ground reaction forces were measured simultaneously. A validated 3D\r\nmusculoskeletal model of the locomotor system with a knee model that included\r\nmuscles, ligaments and articular surfaces was used to calculate the joint resultant\r\nforces and moments, and subsequently the forces transmitted in the considered\r\nforce-bearing structures via optimization methods. Three problem formulations with\r\neight optimization criteria were evaluated.\r\nResults: Among the three problem formulations, simultaneous consideration of\r\nmoment and force equipollence for the knee model with ligaments and articular\r\ncontacts predicted contact forces (first peak: 3.3-3.5 BW; second peak: 3.2-4.2 BW;\r\nswing: 0.3 BW) that were closest to previously reported theoretical values (2.0-4.0 BW)\r\nand in vivo data telemetered from older adults with total knee replacements (about\r\n2.8 BW during stance; 0.5 BW during swing). Simultaneous consideration of moment\r\nand force equipollence also predicted more physiological ligament forces (< 1.0 BW),\r\nwhich appeared to be independent of the objective functions used. Without\r\nconsidering force equipollence, the calculated contact forces varied from 1.0 to 4.5 BW\r\nand were as large as 2.5 BW during swing phase; the calculated ACL forces ranged from\r\n1 BW to 3.7 BW, and those of the PCL from 3 BW to 7 BW.\r\nConclusions: Model complexity and problem formulation affect the prediction of the\r\nforces transmitted by the force-bearing structures at the knee during normal level\r\nwalking. Inclusion of the ligaments in a knee model enables the simultaneous\r\nconsideration of equations of force and moment equipollence, which is required for\r\naccurately estimating the contact and ligament forces, and is more critical than the\r\nadopted optimization criteria.
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