Predicting Knee Joint Instability Using a Tibio-Femoral Statistical Shape Model

Abstract

Statistical shape models (SSMs) are a well established computational technique to represent the morphological variability spread in a set of matching surfaces by means of compact descriptive quantities, traditionally called “modes of variation” (MoVs). SSMs of bony surfaces have been proposed in biomechanics and orthopedic clinics to investigate the relation between bone shape and joint biomechanics. In this work, an SSM of the tibio-femoral joint has been developed to elucidate the relation between MoVs and bone angular deformities causing knee instability. The SSM was built using 99 bony shapes (distal femur and proximal tibia surfaces obtained from segmented CT scans) of osteoarthritic patients. Hip-knee-ankle (HKA) angle, femoral varus-valgus (FVV) angle, internal-external femoral rotation (IER), tibial varus-valgus (TVV) angles, and tibial slope (TS) were available across the patient set. Discriminant analysis (DA) and logistic regression (LR) classifiers were adopted to underline specific MoVs accounting for knee instability. First, it was found that thirty-four MoVs were enough to describe 95% of the shape variability in the dataset. The most relevant MoVs were the one encoding the height of the femoral and tibial shafts (MoV #2) and the one representing variations of the axial section of the femoral shaft and its bending in the frontal plane (MoV #5). Second, using quadratic DA, the sensitivity results of the classification were very accurate, being all >0.85 (HKA: 0.96, FVV: 0.99, IER: 0.88, TVV: 1, TS: 0.87). The results of the LR classifier were mostly in agreement with DA, confirming statistical significance for MoV #2 (p = 0.02) in correspondence to IER and MoV #5 in correspondence to HKA (p = 0.0001), FVV (p = 0.001), and TS (p = 0.02). We can argue that the SSM successfully identified specific MoVs encoding ranges of alignment variability between distal femur and proximal tibia. This discloses the opportunity to use the SSM to predict potential misalignment in the knee for a new patient by processing the bone shapes, removing the need for measuring clinical landmarks as the rotation centers and mechanical axes.