Arithmetic hip-knee-ankle angle (aHKA): An algorithm for estimating constitutional lower limb alignment in the arthritic patient population

AIMS: Once knee arthritis and deformity have occurred, it is currently not known how to determine a patient’s constitutional (pre-arthritic) limb alignment. The purpose of this study was to describe and validate the arithmetic hip-knee-ankle (aHKA) algorithm as a straightforward method for preoperative planning and intraoperative restoration of the constitutional limb alignment in total knee arthroplasty (TKA). METHODS: A comparative cross-sectional, radiological study was undertaken of 500 normal knees and 500 arthritic knees undergoing TKA. By definition, the aHKA algorithm subtracts the lateral distal femoral angle (LDFA) from the medial proximal tibial angle (MPTA). The mechanical HKA (mHKA) of the normal group was compared to the mHKA of the arthritic group to examine the difference, specifically related to deformity in the latter. The mHKA and aHKA were then compared in the normal group to assess for differences related to joint line convergence. Lastly, the aHKA of both the normal and arthritic groups were compared to test the hypothesis that the aHKA can estimate the constitutional alignment of the limb by sharing a similar centrality and distribution with the normal population. RESULTS: There was a significant difference in means and distributions of the mHKA of the normal group compared to the arthritic group (mean -1.33° (SD 2.34°) vs mean -2.88° (SD 7.39°) respectively; p < 0.001). However, there was no significant difference between normal and arthritic groups using the aHKA (mean -0.87° (SD 2.54°) vs mean -0.77° (SD 2.84°) respectively; p = 0.550). There was no significant difference in the MPTA and LDFA between the normal and arthritic groups. CONCLUSION: The arithmetic HKA effectively estimated the constitutional alignment of the lower limb after the onset of arthritis in this cross-sectional population-based analysis. This finding is of significant importance to surgeons aiming to restore the constitutional alignment of the lower limb during TKA. Cite this article: Bone Jt Open 2021;2(5):351–358.