A stochastic biomechanical model for risk and risk factors of non-contact anterior cruciate ligament injuries

Abstract

Gender has been identified as a risk factor for non-contact anterior cruciate ligament (ACL) injuries. Although some possible biomechanical risk factors underlying the gender differences in the risk for non-contact ACL injuries have been identified, they have not been quantitatively confirmed yet because of the descriptive nature of the traditional epidemiological methods. The purpose of this study was to validate a stochastic biomechanical model for the risk and risk factors for non-contact ACL injuries. An ACL loading model was developed and instrumented to a Monte Carlo simulation to estimate the ACL injury rate for a stop–jump task in which non-contact ACL injuries frequently occur. Density distributions of independent variables of the ACL loading model were determined from in-vivo data of 40 male and 40 female athletes when performing the stop–jump task. A non-contact ACL injury was defined as the peak ACL loading being greater than 2250 N for males and 1800 N for females. The female-to-male non-contact ACL injury rate ratio was determined as the ratio of the probability of ACL ruptures of females to that of males. The female-to-male non-contact ACL injury rate ratio predicted by the stochastic biomechanical model was 4.96 (SD=0.22). The predicted knee flexion angle at the peak ACL loading in the simulated injury trials was 22.0 (SD=8.0) degrees for males and 24.9 (SD=5.6) degrees for females. The stochastic biomechanical model for non-contact ACL injuries developed in the present study accurately predicted the female-to-male injury rate ratio for non-contact ACL injuries and one of the kinematic characteristics of the injury.

Introduction

Anterior cruciate ligament (ACL) tear is one of the most common knee injuries in sports (Griffin et al., 2006). The majority of ACL injuries occur with a non-contact mechanism (Boden et al., 2000) and can be potentially prevented (Griffin et al., 2006). Significant research efforts have been made in the last decade to determine modifiable risk factors of sustaining non-contact ACL injuries so prevention strategies can be developed. Although previous studies have indicated that biomechanical factors such as increased knee valgus moment, quadriceps muscle activation, and proximal anterior tibia shear force may be risk factors for non-contact ACL injuries (Malinzak et al., 2001; Chappell et al., 2002; Ford et al., 2003; Sell et al., 2007), a recent extensive literature review (Yu and Garrett, 2007) failed to find any convincing scientific evidence to support a cause-and-effect relationship between those proposed risk factors and non-contact ACL injuries.

The lack of scientific confirmation of biomechanical risk factors for non-contact ACL injuries is mainly due to a lack of effective and efficient research methods for identifying risk factors. The longitudinal cohort research design is the most commonly used traditional epidemiological method for identifying risk factors for an injury or disease. The studies using the longitudinal cohort design are usually complicated, labor intensive, time consuming, and expensive because of the need to test and follow a large group of subjects for a long time period to obtain a certain number of injury cases (Portney and Watkins, 2000). In addition, the results of the studies using the traditional cohort design are descriptive and lack cause-and-effect relationships between risk factors and the risk of an injury or disease (Portney and Watkins, 2000).

Stochastic biomechanical modeling is an effective and efficient research method for investigating the random outcomes of human movement (Hughes and An, 1997). This method allows investigators to determine the risk for an injury without following subjects to obtain actual injury cases. This enables the execution of the study to be less complicated, less labor intensive, less time consuming, and less expensive in comparison to traditional epidemiological methods. Also, stochastic biomechanical modeling method allows investigators to identify risk factors with cause-and-effect relationships to the injury in the absence of any observed injuries.

Stochastic biomechanical modeling method has been successfully applied to studies on the variation of human movements and prevention of a variety of musculoskeletal system injuries (Davidson et al., 2004; Langenderfer et al., 2006; McLean et al., 2004; Mirka and Marras, 1993; Santos and Valero-Cuevas, 2004; Valero-Cuevas et al., 2003). Stochastic biomechanical modeling methods have also been applied to recent research pertaining to ACL injury prevention. McLean et al. (2004) estimated the variation of ACL loading in a sidestep cut task using a stochastic biomechanical model. Garrett and Yu (2004) also examined the effects of proximal tibia anterior shear force and knee valgus–varus and internal–external rotation moments on ACL loading using a stochastic biomechanical modeling approach.

The purpose of this study was to validate a stochastic biomechanical model to predict the risk (injury rate or probability for injury) and risk factors (factors that contribute to the risk) for non-contact ACL injuries. We hypothesized that the female-to-male non-contact ACL injury rate ratio estimated using the stochastic biomechanical model proposed in this study would be similar to that determined using traditional epidemiological methods. We also hypothesized that the injury characteristics estimated by the Monte Carlo simulation using the stochastic biomechanical model proposed in this study would be similar to those reported in the literature.