# Extramedullary tibial guide orientation in TKA personalized alignment: validation of a trigonometric method

## TL;DR

A new trigonometric formula is validated to help surgeons accurately position knee implants using standard X-rays and conventional tools.

## Contribution

The study introduces a novel trigonometric method for calculating tibial guide lateralization in personalized TKA alignment.

## Key findings

- 97.2% of lateralization measurements fell within the defined safety zone with high inter-observer reliability (ICC 0.91).
- The formula-derived measurements showed no significant difference from true radiographic lateralization.
- The method achieves high accuracy without requiring specialized software or robotic assistance.

## Abstract

Achieving personalized alignment in total knee arthroplasty (TKA) with conventional instrumentation remains challenging. This study validates a novel trigonometric formula that calculates the exact lateralization needed for the tibial extramedullary guide based on preoperative weight-bearing X-rays.

We retrospectively analysed 196 patients who underwent TKA between November 2018 and June 2023. Inclusion criteria: patients with preoperative weight-bearing AP lower limb X-rays aged 18 or older. Exclusion criteria: previous total hip arthroplasty, those without consent. The formula LAT = LENG(S) × sin α angle calculated tibial guide lateralization, where LAT was the lateralization distance, LENG(S) was the tibial length from radiographs, and α angle was the tibial coronal correction angle. The true radiographic lateralization was measured to validate the formula’s accuracy and defined a “safety zone” representing acceptable surgical margins to validate the formula’s accuracy and defined a “safety zone” representing acceptable surgical margins. The Intraclass Correlation Coefficient (ICC) was used to test for the measurement consistency among observers. 95% Clopper-Pearson Confidence Interval was calculated for the frequency of lateralization falling within a “safety zone”. A T-test compared LAT measurements with true radiographic lateralization.

ICC showed that 97.2% of lateralization measurements fell within the defined “safety cone” (95% CI 93.9–98.9%). Inter-observer reliability was high (ICC 0.91). No differences were found between the formula-derived measurements and the true radiographic lateralization. The 95% Clopper-Pearson Confidence Interval was 93.9–98.9%. LAT was found to fall outside the safety cone with a total mean of 2.3° (range 1–5) in 2.8% of the cases, with a mean error in the degree of proximal tibial cut of -0.67° (range − 1 - +1). No association between CPAK and cases within or outside the safety cone was found (χ²= 5.014, p = 0.658).

This validated trigonometric formula enables surgeons to accurately calculate tibial guide lateralization for personalized alignment using only conventional instrumentation and standard radiographs. The method’s 97.2% accuracy within safe surgical margins supports its use as a reliable preoperative planning tool for personalized TKA alignment without requiring specialized software or robotic assistance.