A mathematical model of knee joint line orientation: Independent effects of femoral and tibial coronal anatomy and limits on achieving a horizontal joint line.

Abstract

Purpose: Natural knee joint line orientation (JLO) relative to the ground remains poorly understood. A JLO parallel to the floor is commonly assumed to favour balanced medial-lateral compartment loading, but the independent influence of femoral and tibial coronal anatomy on JLO during bipodal and single-limb stance has not been quantified. This study aimed to quantify the independent effects of the medial proximal tibial angle (MPTA) and lateral distal femoral angle (LDFA) on knee JLO relative to the ground during bipodal and single-limb stance using a mathematical model.

Methods: A two-dimensional geometric model of the lower limb was developed using representative anthropometric parameters. MPTA and LDFA were varied independently across the native varus-valgus range, from neutral to 7°, in 1° increments, yielding 36 discrete anatomical configurations. For each configuration, knee JLO relative to the ground was calculated for bipodal and single-limb stance, along with the theoretical mediolateral centre of mass (COM) displacement required to achieve a horizontal JLO. The model is deterministic and closed-form; results are reported to 0.1° and 0.1 mm.

Results: Transition from bipodal to single-limb stance reduced JLO by 2.6° regardless of coronal anatomy. Each 1° change in MPTA or LDFA altered JLO by approximately 0.5° (0.54° and 0.46° per degree, respectively), indicating comparable effect magnitudes for tibial and femoral anatomy. However, MPTA and LDFA produced distinct geometric relationships, yielding different JLOs despite identical hip-knee-ankle alignment. Only a limited subset of configurations produced a horizontal JLO without theoretical COM displacement.

Conclusion: Femoral and tibial coronal anatomy independently and predictably influence knee JLO during bipodal and single-limb stance, and overall alignment alone does not predict JLO. Achieving a horizontal JLO would require substantial COM adaptation in most configurations. Whether a horizontal JLO is physiologically achievable, or the primary biomechanical objective in all individuals, remains unknown.

Level of evidence: Level V.