Abstract
Intraoperative planning of knee replacement components, targeting a desired functional outcome, requires a calibrated patient-specific model of the patient's soft-tissue anatomy and mechanics. Previously, a surgical technique was demonstrated for measuring knee joint kinematics and kinetics consistent with modern navigation systems in conjunction with the development of a patient-customizable knee model. A data efficient approach for the model calibration task was achieved utilizing the sensitivity of the model to simulated clinical hand manipulations of the knee joint requiring 85% less computations.
For this numerical investigation a simplified knee joint model, based on the OpenKnee repository, consisting of bone (rigid), cruciate ligaments (single-bundle, nonlinear spring), collateral ligaments (multiple nonlinear springs), articular cartilage (rigid, pressure-over-closure relationship), and combined capsule/meniscus (linear springs) was created using a custom Matlab (MathWorks)-Abaqus (Dassault Systèmes) implicit finite element modeling framework (Figure 1). A sensitivity analysis was performed by applying constant loading along the anterior-posterior, medial-lateral, varus-valgus, and internal-external directions (30 N for forces and 3 Nm for moments) while perturbing each customizable parameter positively and negatively by 1 mm at 0, 25, 50, 75 and 100 degrees of flexion. A constant load of 150 N was maintained in compression. The change in static endpoint position was measured relative to the respective position without perturbation. Sensitivity results were then arranged by load direction and principal component analysis was subsequently performed (Table 1).
First a single optimization task was simulated including all model parameters and all loading sequences with the goal of minimizing the kinematic differences between the reference model and a perturbed model (Figure 2). Second, a piecewise optimization task was designed using only the sensitive parameters for a spanning set of loads for the same perturbed model. Parameters 3 and 4 were tuned using internal and external endpoints. Then parameters 1 and 5 were tuned using the anterior endpoints. Similarly, parameters 2 and 7 were tuned using the posterior endpoints. Finally, parameter 8 was tuned using the varus endpoints. All loadings were observed to be insensitive to parameter 6 (ACL-Y). The number of model evaluations required were 2520 and 390 for the single and piecewise optimizations, respectively. The single simulation task recovered all parameters within 0.57 mm on average compared to 0.64 mm on average for the piecewise task. Kinematic errors due to the calibration technique were within 0.001 mm and 0.18 deg compared to 0.001 mm and 0.04 deg.
Computational cost for the optimization task required to calibrate a patient-specific knee model was reduced while maintaining clinically relevant accuracy. This model reduction approach will further enable the rapid adoption of the technology for intraoperative planning of knee replacement components based on targeted functional outcomes.
