Development and validation of subject-specific pediatric multibody knee kinematic models with ligamentous constraints

Computational knee models that replicate the joint motion are important tools to discern difficult-to-measure functional joint biomechanics. Numerous knee kinematic models of different complexity, with either generic or subject-specific anatomy, have been presented and used to predict three-dimensional tibiofemoral (TFJ) and patellofemoral (PFJ) joint kinematics of cadavers or healthy adults, but not pediatric populations. The aims of this study were: (i) to develop subject-specific TFJ and PFJ kinematic models, with TFJ models having either rigid or extensible ligament constraints, for eight healthy pediatric participants and (ii) to validate the estimated joint and ligament kinematics against in vivo kinematics measured from magnetic resonance imaging (MRI) at four TFJ flexion angles. Three different TFJ models were created from MRIs and used to solve the TFJ kinematics: (i) 5-rigid-link parallel mechanism with rigid surface contact and isometric anterior cruciate (ACL), posterior cruciate (PCL) and medial collateral (MCL) ligaments (ΔL_null), (ii) 6-link parallel mechanism with minimized ACL, PCL, MCL and lateral collateral ligament (LCL) length changes (ΔL_min) and (iii) 6-link parallel mechanism with prescribed ACL, PCL, MCL and LCL length variations (ΔL_match). Each model's geometrical parameters were optimized using a Multiple Objective Particle Swarm algorithm. When compared to MRI-measured data, ΔL_null and ΔL_match performed the best, with average root mean square errors below 6.93° and 4.23 mm for TFJ and PFJ angles and displacements, respectively, and below 2.01 mm for ligament lengths (<4.32% ligament strain). Therefore, within these error ranges, ΔL_null and ΔL_match can be used to estimate three-dimensional pediatric TFJ, PFJ and ligament kinematics and can be incorporated into lower-limb models to estimate joint kinematics and kinetics during dynamic tasks.