Development and radiographic evaluation of a normalised guide-pin orientation abacus for anterior closing-wedge tibial osteotomy: Comparison with fixed-ratio and osteotomy-depth methods.

Purpose: To develop a simplified mathematical model and abacus estimating anterior wedge resection height during slope-reducing tibial osteotomy from patient-specific guide-pin length and normalised guide-pin orientation, and to evaluate its accuracy under simulated radiographic conditions against fixed-ratio and osteotomy-depth methods. It was hypothesised that normalised guide-pin orientation would provide wedge-height estimates comparable to radiographic planning in both configurations. Methods: Two hundred fifty-nine calibrated strict lateral knee radiographs from patients undergoing ACL reconstruction were retrospectively analysed in a single-centre radiographic simulation study. Supratuberosity and infratuberosity slope-reducing osteotomies were simulated with a standardised 10° correction, recording guide-pin length, orientation and corresponding anterior wedge height. Three models were compared: a trigonometric model with normalised mean angles, a fixed-ratio model and the osteotomy-depth method. Accuracy (mean absolute error, 90th percentile error) was assessed in-sample against radiographic reference measurements and confirmed by leave-one-out and five-fold cross-validation. Results: Mean guide-pin orientation angles were 67.4° ± 6.0° (supratuberosity) and 110.6° ± 4.7° (infratuberosity). The normalised-angle model produced mean absolute errors of 0.45 ± 0.41 mm (95% CI, 0.40-0.50) and 0.88 ± 0.79 mm (95% CI, 0.78-0.98), with 90th percentile errors of 0.91 and 1.77 mm and Bland-Altman bias of -0.17 and -0.06 mm, lower than both comparator models. Estimation error was not significantly influenced by sex or baseline posterior tibial slope, though the cohort's imbalanced sex distribution (194 men, 65 women) limited power to detect smaller effects in women. Conclusion: Within this model-development cohort, a patient-specific abacus based on guide-pin length and normalised guide-pin orientation produced low approximation errors under simulated radiographic conditions, without intraoperative radiographic calibration or complex calculations. These findings are exploratory and reflect in-sample performance; independent and clinical validation, including prospective intraoperative testing, are required before the method can be considered accurate, reproducible or ready for intraoperative use. Level of Evidence: Level IV, retrospective radiographic simulation/model-development study without clinical outcomes.