Musculoskeletal (MSK) models must accurately reflect anatomy and function to yield reliable biomechanical results. While muscle geometry in the TLEM 2.0 dataset is highly detailed, the skeletal kinematic chain in the original model relies on simple revolute joints that can produce joint distraction and bone copenetration and that do not reproduce physiological articular constraints. This work updates the TLEM 2.0 lower-limb articulations—tibio-femoral, patello-femoral, talo-tibial, and calcaneo-talar—by reconstructing 3D joint kinematics from bone morphology using joint congruence maximization, and by adding contact and ligament representations consistent with those motions.
Subchondral surfaces were manually selected from the CT-derived bone meshes in the TLEM 2.0 dataset. These surfaces were offset to simulate a constant-thickness cartilage layer; thickness values were chosen by averaging data reported in the literature and applied uniformly per articulation. The offset surfaces served both as cartilage approximations and as control volumes for congruence computations.
Joint motion was computed through congruence maximization, a method that assumes articular morphology evolves to minimize peak contact pressure and thus maximize congruence between mating surfaces. For kinematic description the study adopted tailored reference frames and rotation sequences to limit secondary motions: the tibio-femoral joint used a Cardanic z-x-y sequence, while ankle articulations used a z-y-x rotation order to minimize non-physiological components. Each joint was treated as having one independent degree of freedom (DOF): knee and talo-tibial used flexion as the free coordinate, and the calcaneo-talar joint used inversion (rotation about x). For each 1° increment within literature-derived ranges of motion, the independent coordinate was fixed and the remaining pose parameters were determined by maximizing congruence.
Patello-femoral kinematics were computed as dependent on tibio-femoral flexion. Because the patella is not fully engaged with the trochlea at low flexion angles, congruence maximization for the patello-femoral joint was restricted to flexion values >40°. The patellar trajectory from the CT-scan pose to the first congruence pose at 40° was represented by a finite helical axis calculated via Mozzi–Chasles’ theorem. Final kinematics were converted to TLEM 2.0 reference systems and provided as rototranslational matrices to avoid parametrization dependence.
The original TLEM 2.0 revolute-based neutral posture produced atypical orientations for several lower-limb segments. The neutral posture was redefined beginning with the calcaneo-talar pose that exhibited maximum congruence over the computed trajectory. Midfoot and forefoot meshes from TLEM 2.0 were treated as a rigid cluster and manually adjusted to eliminate bone copenetration and to obtain a foot posture compatible with neutral ground contact. The tibio-talar neutral pose was then chosen to minimize the angle between a ground normal (plane through the most distal calcaneus and first and fifth metatarsal heads) and the tibia y axis. The knee angle in neutral was set to minimize the angle between the femur and tibia y axes. Instantaneous helical axes (IHA) envelopes and mean helical axes (MHA) were computed for the resulting motions in both distal-on-proximal and proximal-on-distal observer frames.
Articular surfaces were divided regionally (medial/lateral for most joints; anterior/posterior for calcaneo-talar). Distance maps between simulated cartilage surfaces identified contact areas as regions with intersurface distance below a 2 mm threshold. For each contact region and pose, the centroid of the contact area was projected onto the articular surface to define a single contact point per bone; contact normals were computed as weighted averages of mesh normals within the contact area, weighting facet contributions by proximity to the mating surface.
Original TLEM 2.0 ligament attachments were single-point definitions for four principal knee ligaments and were inconsistent with the original axes, producing non-isometric behavior during passive flexion. The study remapped attachments to anatomical areas on bone meshes using atlases, creating origin and insertion point clouds for each ligament. Additional structures were added, including the anterior lateral ligament (ALL), deep MCL bundles, patello-femoral retinacular attachments (superior/inferior medial and lateral), and ankle ligaments (tibio-calcaneal and fibulo-calcaneal).
From each origin/insertion cloud, the single most isometric fiber was identified numerically using the computed congruence kinematics; isometry was assessed via fiber length variation along the motion. For ankle ligament evaluation the foot was kept in its neutral pose.
Compared with the original revolute-based TLEM 2.0 kinematics, the congruence-maximized motions produced notably different tibio-femoral behavior, especially in internal–external rotation, while patello-femoral rotations were largely similar with some differences in abduction–adduction. Visual comparisons at 90° flexion highlighted joint distraction and bone copenetration in the revolute-based model, whereas the congruence-based representation preserved physiological articular gaps and produced more physiological ligament elongation patterns. The computed motions align with trends reported in prior congruence- and anatomy-based studies cited in the manuscript.
The updated articular representation strengthens the anatomical fidelity of TLEM 2.0, enabling more reliable estimation of ligament lengths, contact points and normals, and providing a basis for implementing rigid or deformable joint mechanisms and subject-specific personalization when joint geometry is available. All modifications and results are included within the manuscript and supporting information; the updated TLEM 2.0 dataset is available on request from the contact reported in the source. The study did not update the hip joint definition in TLEM 2.0 and some modeling choices (e.g., constant cartilage thickness, single-DOF parametrization) reflect simplifying assumptions described in the manuscript.