This study aims to create a novel computational workflow for frontal plane laxity evaluation which combines a rigid body knee joint model with a non-linear implicit finite-element model wherein collateral ligaments are anisotropically modelled using subject-specific, experimentally calibrated Holzpfel-Gasser-Ogden (HGO) models.

The framework was developed based on CT and MRI data of three cadaveric post-TKA knees. Bones were segmented from CT-scans and modelled as rigid bodies in a multibody dynamics simulation software (MSC Adams/view, MSC Software, USA). Medial collateral and lateral collateral ligaments were segmented based on MRI-scans and are modelled as finite elements using the HGO model in Abaqus (Simulia, USA). All specimens were submitted varus/valgus loading (0-10Nm) while being rigidly fixed on a testing bench to prevent knee flexion. In subsequent computer simulations of the experimental testing, rigid bodies kinematics and the associated soft-tissue force response were computed at each time step. Ligament properties were optimised using a gradient descent approach by minimising the error between the experimental and simulation-based kinematic response to the applied varus/valgus loads. For comparison, a second model was defined wherein collateral ligaments were modelled as nonlinear no-compression spring elements using the Blankevoort formulation.

Models with subject-specific, experimentally calibrated HGO representations of the collateral ligaments demonstrated smaller root mean square errors in terms of kinematics (0.7900° +/− 0.4081°) than models integrating a Blankevoort representation (1.4704° +/− 0.8007°).

A novel computational workflow integrating subject-specific, experimentally calibrated HGO predicted post-TKA frontal-plane knee joint laxity with clinically applicable accuracy. Generally, errors in terms of tibial rotation were higher and might be further reduced by increasing the interaction nodes between the rigid body model and the finite element software. Future work should investigate the accuracy of resulting models for simulating unseen activities of daily living.

To unravel the relation between mechanical loading and biological response, cell-seeded hydrogel constructs can be used in bioreactors under multi-axial loading conditions that combines compressive with torsional loading. Typically, considerable biological variation is observed. This study explores the potential confounding role of mechanical factors in multi-directional loading experiments. Indeed, depending on the material properties of the constructs and characteristics of the mechanical loading, the mechanical environment within the constructs may vary. Consequently, the local biological response may vary from chondrogenesis in some parts to proteoglycan loss in others.

This study uses the finite element method to investigate the effects of material properties of cell-seeded constructs and multiaxial loading characteristics on local mechanical environment (stresses and strains) and relate these to chondrogenesis (based on maximum compressive principal strain (MCPS) - Zahedmanesh et al., 2014) and proteoglycan loss (based on fluid velocity (FV) - Orozco et al., 2018).

The construct was modelled as a homogenized poro-hyperelastic (using a Neohookean model and Darcys law) cylinder of 8mm diameter and equal height using Abaqus. The bottom surface was fully constrained and dynamic unconfined compression and torsion loading were applied to the top surface. Free fluid flow was allowed through the lateral surface. We studied the sensitivity of the maximum values of the target parameters at 9 key locations to the material parameters and loading characteristics. Six input parameters were varied in preselected ranges: elastic modulus (E=[20,80]kPa), Poissons ratio (nu=[0.1,0.4]), permeability (k=[1,4]e-12m4/Ns), compressive strain (Comp=[5,20]%), rotation (Rot=[5,20]°) and loading frequency (Freq=[1,4]Hz). A full-factorial design of experiment method was used and a first-order polynomial surface including the interactions fitted the responses.

MCPS varies between 7.34% and 33.52% and is independent of the material properties (E, nu and k) and Freq but has a high dependency on Comp and a limited dependency on Rot. The maximum value occurs centrally in the construct, except for high values of Rot and low Comp where it occurs at the edges. FV vary between 0.0013mm/sec and 0.1807mm/sec and dominantly depends on E, k and Comp, while its dependency on Rot and Freq is limited. The maximum value usually occurs at the edges, although at high Freq it may move towards the center of the superficial and deep zones. This study can be used as a guideline for the optimized selection of mechanical parameters of hydrogel for cell-seeded constructs and loading conditions in multi-axial bioreactor studies. In future work, we will study the effect in intact and injured cartilage explants.