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General Orthopaedics

A QUANTIFIABLE RISK FACTOR FOR ANTERIOR CRUCIATE LIGAMENT INJURY: APPLIED MATHEMATICS TO MODEL THE POSTEROLATERAL TIBIAL PLATEAU SURFACE GEOMETRY

The Canadian Orthopaedic Association (COA) and The International Combined Orthopaedic Research Societies (ICORS) Meeting, Montreal, Canada, June 2019. Part 2.



Abstract

Anterior cruciate ligament (ACL) injuries are frequent among athletes and a leading cause of time away from competition. Stability of the knee involves the ACL for limiting anterior tibial translation and the ALL (anterolateral ligament) to restrain internal rotation of the tibia. Present indications for treatment with a combined ACL-ALL reconstruction remain unclear and mostly subjective. We mathematically modeled the tibial plateau geometry to try and identify patients at risk of ACL injury, and develop an objective trigger point for the decision to proceed with additional surgery to optimize rotational stability in these higher risk patients. We hypothesized that an increased convexity and steepness of the posterior aspect of the lateral plateau would subject knees to higher rotational torques leading to potentially a higher risk of ACL injury.

The study design was a case-control study involving ACL reconstruction cases (n=68) and matched controls (n=68) between 2008–2015 at our institution. We used a two-dimensional approach, evaluating sagittal MRI images of the knee to model the posterior convexity of the lateral tibial plateau. Points were selected along the articular surface, and a least-squares regression was used to curve-fit a power function (y = a xn). In the equation, larger coefficient a and n represented steeper slopes. The cases and controls were compared using a Mann-Whitney-U test, and the statistical significance was set at α < 0.05. A subgroup analysis for females and males was also performed for the curve-fit coefficients.

We observed a significant difference in the tibial surface geometry between our ACL reconstruction cases and matched controls (Figure 1). The modeled power equation for our ACL cases had larger coefficients compared to controls for all groups. For all pooled subjects, coefficient a (ACL recon cases = 0.90 vs controls = 0.68, p < 0.0001) and coefficient n (ACL recon cases = 0.34 vs controls = 0.30, p = 0.07) (Table 1). For the statistically significant coefficient a, we found it had a sensitivity of 78.9% and specificity of 77.5% for the statistically significant coefficient a, we found it had a sensitivity of 78.9% and specificity of 77.5% for predicting injury, using a cut off coefficient of a = 0.78. The odds ratio was 12.6 [5.5 – 29].

The posterolateral cartilaginous slope of the tibial plateau was mathematically modeled in patients with ACL injury. Patients with ACL injury demonstrated abnormally steep and fast slopes compared to controls that may play predispose to ACL injury by increasing anterior translation forces and internal rotation torques sustained by their knee joint. A steeper slope may also explain high-grade pivot shifts on physical exam that are thought to be a relative indication for adding an associated ALL reconstruction. Our findings are promising for adding more objectivity to surgical decision-making, especially with identifying high-risk patients that may be candidates for combined ACL-ALL reconstructions.

For any figures or tables, please contact the authors directly.


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