Executive function (EF) is a multifaceted cognitive process predominantly governed by the prefrontal cortex, involving the integration of various cognitive tasks to achieve specific objectives in a flexible and efficient manner [1]. EF, as a higher-order cognitive function, orchestrates and modulates individuals' cognition, emotions, and behaviors, incorporating such components as working memory, inhibitory control, and cognitive flexibility [1,2]. These functions are critical for children's learning and social interactions, significantly influencing their overall achievement[3,4]. Recent research has indicated that contemporary challenges, such as increased sedentary behavior and screen time, have been linked to poorer EF development of children and adolescents' EF, and may undermine academic performance and long-term mental health[5,6]. Thus, identifying effective interventions to enhance EF during childhood and adolescence is imperative.

Physical activity (PA), as a non-pharmacological intervention, has garnered increasing attention for enhancing cognitive function in children and adolescents owing to its broad benefits. The relationship between PA and cognition has been extensively explored across neuroscience, psychology, and exercise science. Early studies have primarily established a positive link between habitual PA and cognitive performance through cross-sectional designs[7,8]. Spirduso's foundational work in the 1970s highlighted superior cognitive outcomes among physically active individuals [[9], [10], [11]]. Kramer et al.'s trials in 1999 provided compelling causal evidence that aerobic exercise enhances EF in older adults[12]. This study provided causal evidence and shifted research from global cognition to specific EF components. These findings catalyzed a wave of research into the cognitive benefits of PA across age groups.

Recent studies, with growing interest in child development, have increasingly focused on the impact of PA on EF in children and adolescents. Initially, research highlighted general cognitive benefits, but as the centrality of EF in learning and behavior became considerably clear [13], attention turned to how PA influences EF domains such as inhibitory control, working memory, and cognitive flexibility. Sibley and Etnier's systematic review provided early support for the positive link between PA and children's cognition [14]. Álvarez-Bueno et al. emphasized the value of high-intensity, cognitively demanding activities [15]. Later studies began distinguishing between PA types. Aerobic exercise showed consistent benefits, especially for inhibitory control and cognitive flexibility[16], while combined aerobic and resistance training improved EF and neural efficiency [17]. Cognitively engaging activities were particularly effective for cognitive flexibility [18,19]. A recent network meta-analysis also suggested that dance, ball games, and skill/coordinating activities may have the most significant effect on EF [20].

In recent years, understanding the precise dose–response relationship between PA and EF in children and adolescents has emerged as a critical research priority, yet most prior meta-analyses have relied on categorical “high vs. low” comparisons or treated each intensity level as a distinct node, thereby obscuring continuous dose–effect patterns [22]. To overcome the lack of standardized dosing metrics, we converted all interventions into metabolic equivalent minutes (METs-min), following the widely adopted Compendium[23], enabling consistent quantification of PA volume across studies. Traditional network meta-analysis approaches, although valuable for ranking interventions, either collapse dose levels into single categories or fragment them into isolated nodes, thereby failing to model how incremental increases in PA translate into EF improvements [24,25]. In response, we applied a Bayesian model-based network meta-analysis framework (MBNMA) that embeds continuous dose–response functions, such as restricted cubic splines and Emax models, directly within the evidence network, thus preserving the actual shape of the curve and enabling estimation of minimum effective and optimal doses [26]. This Bayesian approach borrows strength across sparse data points and dose levels, yielding markedly precise estimates and complete posterior distributions supporting probabilistic statements on clinically relevant thresholds [27]. This approach has been successfully used to characterize dose–response curves in such areas as cognitive decline in older adults and diabetes management [28,29]. To our knowledge, ours is the first to adapt MBNMA for PA interventions targeting EF in youth. This research provides continuous dose–response curves with credible intervals and probability thresholds that directly inform precise, actionable PA “prescriptions” for cognitive enhancement.