1.    Introduction
Anterior cruciate ligament (ACL) rupture is a common orthopedic injury affecting male and female athletes of all ages (1). ACL tears typically occur during jumping and landing, sudden changes in direction, and acceleration or deceleration (2). One of the primary contributors to ACL injury is the complexity and dynamic nature of sports. In sports, athletes perform complex movements under constraints related to the individual, the task, and the environment—such as varying conditions, the presence of a defender, and time limitations. Athletes must rapidly perceive and predict environmental information and respond accordingly (3). Studies that have employed movement learning approaches have demonstrated significant benefits compared to protocols that focus solely on athletes' physical characteristics, such as strength, balance, and neuromuscular control (4-7). Among these approaches, variability-based exercises, which aim to retrain high-level movement control, facilitate the discovery of new movement patterns based on constraints, and enhance movement transfer in athletes, may represent the missing link in injury prevention programs. The findings of the present study could contribute to the improvement of rehabilitation programs and the reduction of ACL injury risk. We hypothesize that variability-based approaches are more effective in enhancing the kinematic and kinetic factors associated with ACL injury compared to other movement learning approaches. Therefore, this study aims to investigate the effect of variability-based motor learning approaches on kinetic and kinematic factors related to ACL injury in athletes.
2.    Methods
This systematic review was conducted in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA 2020) guidelines (8) and has been registered on the PROSPERO website under the code CRD42024617971. In the first step, articles published in reliable databases—including PubMed, Google Scholar, Scopus, Science Direct, Elsevier, and PEDro—between 2010 and 2024 were retrieved. The search was conducted using the following keywords: ("ACL" OR "Anterior cruciate ligament"), ("Differential learning"), ("Non-linear pedagogy"), ("Variability"), and ("Biomechanics" OR "Kinematics" OR "Kinetics"), both independently and in combination. For this review, studies were included if they combined variability-based strategies with injury prevention exercises or sport-specific skills. The inclusion criteria were as follows: clinical trial studies indexed in the specified databases, full-text, English-language articles (if the full text was unavailable, the corresponding author was contacted via email), and studies involving athletes as participants. Exclusion criteria included lack of access to the full text, review articles, non-research papers, duplicate studies, guidelines, and articles published in languages other than English. The eligibility of studies was assessed based on the PICOS model (Population, Intervention, Comparator, Outcome, Study type) (9).
3.    Results
After searching based on the title of the studies, abstract, and inclusion and exclusion criteria, 60 articles were initially identified. Among these, 30 studies focused on the conceptual aspects of variability, 15 studies involved subjects in the children's age group, and 9 studies examined different variables. Ultimately, 6 studies met the inclusion criteria and were included in Fig. 1. The participants in these studies consisted of football players (10), basketball players (11-13), and athletes from a combination of basketball, volleyball, and handball (5, 14). Notably, one study included athletes with a history of ACL reconstruction (14). Regarding educational approaches, two studies compared linear, non-linear, and differential learning (10, 11), two studies compared linear and non-linear learning (12, 13), one study compared differential learning with visual-motor exercises (14), and another study compared differential learning with an external focus of attention and self-controlled learning (5).

Regarding the training content, sport-specific skills were used in four studies (10-13), while injury prevention exercises were applied in two studies (5, 14). The kinematic variables examined in these studies included trunk flexion angle (10, 11, 13), hip flexion (5, 10, 11, 13, 14), knee flexion (5, 10, 11, 13, 14), knee valgus (10, 11, 13, 14), ankle dorsiflexion (10, 11, 13, 14), and knee abduction (5). The kinetic variables analyzed were ground reaction force (5, 10-12, 14), knee extension/flexion moment (10-12), knee valgus moment (10-12), ankle dorsiflexion moment (10-12), hip abduction and external rotation moment (5), and knee abduction moment (5). Regarding the quality assessment of the included studies, four studies received a score of 9 (5, 10, 11, 14), while two studies received a score of 6 (12, 13).
4.    Conclusion
This study aimed to investigate the effect of variability-based movement learning approaches on kinetic and kinematic factors related to ACL injury in athletes. The results indicated that variability-based exercises, including differential and non-linear pedagogy, lead to several biomechanical improvements that can significantly reduce the risk of ACL injury. These improvements include increased trunk and hip flexion, increased knee flexion, decreased knee valgus and abduction, increased ankle dorsiflexion, increased abduction moment and external rotation of the hip, increased ankle dorsiflexion moment, decreased knee valgus and abduction moment, and reduced ground reaction force. Although the non-linear approach is often considered more effective than differential learning due to its emphasis on variability, flexibility, and exploration, there is no direct evidence demonstrating that participants in non-linear training exhibited more variability, flexibility, or exploration. This conclusion remains primarily theoretical (15). The non-linear approach does not emphasize achieving an ideal movement pattern; instead, it focuses on manipulating constraints related to the individual, task, and environment. This approach encourages movement variability, allowing athletes to independently explore and discover movement solutions rather than following rigid instructions. For example, exercises may involve jumping and landing on obstacles of different heights, manipulating the sensorimotor system (e.g., vision, hearing, proprioception), or altering movement paths to the left or right of obstacles (10). In this way, variability is semi-structured, as it is slightly guided by task constraints (16). On the other hand, in the differential learning method, variability is introduced through random fluctuations in performance, exposing athletes to as many movement solutions as possible. Unlike non-linear learning, repetition is not allowed, as the goal is to maximize exploration rather than reinforce a particular movement pattern (15).

Ethical Considerations
Compliance with ethical guidelines
There were no ethical considerations to be addressed in this research.
Funding
This research did not receive any financial support from government, private, or non-profit organizations.
Authors' contributions
All authors contributed equally to preparing the article.
Conflicts of interest
The authors declare that there are no conflicts of interest associated with this article.