## 1 Introduction  
Ruptures of the anterior cruciate ligament (ACL), one of the most serious injuries in sports, affect female athletes at an incidence rate 2.2 times higher than males [1]. Prevention of ACL injuries is the ideal goal as fewer than half of competitive athletes return to the same or higher activity level two years post-surgery following an ACL rupture [2]. ACL tears often occur in a non-contact manner when an individual quickly decelerates to change direction or lands from a jump [3]. About two thirds of ACL injuries occur during a knee valgus or varus injury mechanism [3], and the mechanics of the landing and cutting maneuvers that may result in these injuries are thoroughly studied [4, 5, 6]. However, almost one-third of the injuries occur during a hyperextension event [3], and this kind of injury has hardly been studied at all.  
The forces that tear the ACL are well understood from cadaveric studies that apply various loads to knee specimens in order to assess their effects on ACL strain [7]. Such studies are valuable as measurements taken from strain transducers implanted in the ACL allow for the effects of potential loading mechanisms to be studied directly. As a result, the multi-planar loading of the knee with abduction and internal rotation moments has been shown to result in higher ACL strains compared to that of uni-planar loading [8]. These findings have been used in motion capture studies to identify potential risk factors for ACLinjury [5; 6; 9]. However, both cadaver and motion capture studies have inherent limitations. Cadaver studies are limited in the number of tests that can be conducted due to wear on the specimens and the struggle to account for the role of the muscles during dynamic loading. Motion capture studies are limited to studying movements where no ACL injury occurs, and the forces acting on the ACL are largely unknown. Computer simulation studies (in silico) are well suited to exploring the complex interactions of external moments and muscle forces that produce high ACL strain values during injurious situations such as a single leg hyperextension landing.  
Through programs such as OpenSim, forward dynamic (FD) simulations can be used to study various aspects of gait under conditions not typically available in experimental approaches [10]. Model parameters such as ligament properties and muscle activations can be manipulated at will, and the number of tests that can be performed is limited only by computation time. As a result, the interest in musculoskeletal modeling has increased in recent years, with researchers advancing towards anatomically correct knee models [11; 12; 13].  
Although previous studies have used OpenSim modeling to assess knee kinematics under various conditions [14; 15; 16], no study has used these models for dynamic serial simulations to assess multi-planar loading during knee hyperextension on the ACL despite having been identified as a potential injury mechanism and a predictive tool for ACL injuries [17]. Therefore, the aim of this study was to explore the effects of various external moments and muscle activations on ACL loading using serial FD simulations of single leg, hyperextension landings in OpenSim.