Development and validation of a computational model of the knee joint for the evaluation of surgical treatments for osteoarthritis

Abstract

A three-dimensional (3D) knee joint computational model was developed and validated to predict knee joint contact forces and pressures for different degrees of malalignment. A 3D computational knee model was created from high-resolution radiological images to emulate passive sagittal rotation (full-extension to 65°-flexion) and weight acceptance. A cadaveric knee mounted on a six-degree-of-freedom robot was subjected to matching boundary and loading conditions. A ligament-tuning process minimised kinematic differences between the robotically loaded cadaver specimen and the finite element (FE) model. The model was validated by measured intra-articular force and pressure measurements. Percent full scale error between FE-predicted and in vitro-measured values in the medial and lateral compartments were 6.67% and 5.94%, respectively, for normalised peak pressure values, and 7.56% and 4.48%, respectively, for normalised force values. The knee model can accurately predict normalised intra-articular pressure and forces for different loading conditions and could be further developed for subject-specific surgical planning.

Keywords: in vitro cadaveric test; knee joint contact mechanics; lower limb malalignment; model validation; osteoarthritis; subject-specific finite element knee model.

Figure 1.

MRI images of the frontal view of the knee joint in (a) CUBE sequence for representation of meniscus and ligament and (b) SPGR sequence for representation of cartilage and bone.

Figure 2.

3D LiveWire algorithm used to create geometries of the different tissues.

Figure 3.

The use of the ‘non-manifold algorithm’ to create common contact areas between adjacent tissue, such as the distal femur and femoral cartilage. (a) The inner geometry of the cartilage was overestimated to protrude into the femur and eliminate any gap at the femur-cartliage boundary. (b) The non-manifold assembly technique superimposed the accurately identified femur with the overestimated cartilage image to remove overlaps between the femur and cartilage, creating a common boundary between the adjacent femur and cartilage surfaces.

Figure 4.

3D solid geometry of the knee joint assembly created in CATIA CAD package.

Figure 5.

Model preparation for hexagonal meshing. (a) A 3D spline was created near the edge of the cartilage surface. (b) The 3D spline was used to truncate the very thin edge to produce a finite thickness that would accommodate hexahedral elements.

Figure 6.

(a) Boundary and loading conditions on the FE knee joint model: tied contact pair between (1) cartilage–bone, (2) ligament–bone and (3) tibia–fibula; contact pairs between (4) cartilage–meniscus and (5) cartilage–cartilage. The proximal femur was fixed in 6 degrees of freedom. A 374-N axial load was applied along the tibia, and varus/valgus bending moments, ranging from 0 to 15 Nm, were applied about the knee joint centre. (b) Anterior and (c) posterior views and of the knee joint FE model, displaying the hexagonal and tetrahedral mesh elements for the soft tissues and bones, respectively.

Figure 7.

(a) Taylor Spatial Frame fixed to cadaveric leg for subsequent simulations of lower limb malalignments and corrections by HTO; (b) cadaveric knee, mounted on a 6-degree-of-freedom robot for controlled loading; (c) TekScan IScan sensor equilibration before calibration; (d) sensors fixed in vitro to the cruciate ligaments between the tibial cartilage and the femur; (e) pressure distribution in the knee joint during in vitro loading.

Figure 8.

The ligament tuning process: the ligament properties were adjusted in an iterative process until the kinematics of the tibia relative to the femur in the model closely matched those in vitro in all six degrees of freedom for (a) translational and (b) rotational kinematics during a sagittal rotation from full extension to 65° flexion, and (c) translational and (d) rotational kinematics during a 374-N axial load and a 0–15-Nm valgus/varus bending moment.

Figure 9.

Material properties for the LCL, MCL, ACL and PCL at every angle of flexion, following the ligament tuning process.

Figure 10.

Evaluation of FE model. Pressure distributions in the tibio-femoral joint in response to a 374-N axial load and a 15-Nm varus/valgus bending moment for (a) in vitro testing and (b) FE model predictions. A, anterior; P, posterior; L, lateral; M, medial.

Figure 11.

In vitro and FE-predicted medial and lateral compartment loading in response to a 374-N axial load and 0–15 Nm varus and valgus bending moments for (a) normalised peak pressure and (b) normalised force.

Figure 12.

In vitro and FE-predicted forces in the medial and lateral compartments as a percentage of the total axial force during 0–15 Nm varus and valgus bending moments.

Figure 13.

Static equilibrium diagrams showing forces and bending moment acting on the knee joint during (a) varus and (b) valgus lift off. F_MCL = internal force in the MCL; F_MCL = internal force in the LCL; M = bending moment.