The benefits of physical activity (PA) and cardio-respiratory fitness (CRF) for children's and adolescents' physical [1, 2] and psychological health [3] are well established. However, only 33% of British boys and 21% of British girls aged 4-15 years meet PA guidelines when PA is objectively assessed [4]. Meanwhile, British children spend on average between 3.4 - 4.1 hours in sedentary pursuits outside of their school time and the amount of time spent sedentary increases with age [4]. Sedentary behaviours such as TV viewing and passive travel negatively predict CRF [5, 6] and are associated with increased adiposity [6]. Data also indicates that British youth have become alarmingly unfit in the course of the last decade [7]. Inactive lifestyles not only pose a health concern during adolescent years, but also track relatively well into adulthood, thus increasing adult risk of morbidity and mortality [8].

The emerging body of evidence suggests that low levels of PA, CRF and fatness are not only associated with adverse physical health outcomes but negatively affect brain and cognitive development, as well as academic achievement in youth [9-12]. Conversely, CRF, short bouts of exercise and exercise interventions have been associated with superior cognitive performance [10, 13-15] and larger volumes in brain structures sub-serving memory and learning [13], as well as with higher academic achievement in youth and children [10, 16]. Investigating the relationships among PA, CRF, cognitive function and academic outcomes in school-aged children and youth is important, as these relationships can contribute to long term positive educational sequel [17].

A number of studies using neurophysiological and behavioural measures of cognition indicate that pre-adolescent children with higher levels of CRF perform significantly better on cognitive tasks requiring executive control (mental processes regulating goal directed behaviour, which include working memory, inhibition, and cognitive flexibility), attention and relational memory [13, 18-20]. Superior cognitive performance was linked to greater volumes in brain structures supporting learning and memory: (i) basal ganglia [19, 21, 22], and (ii) hippocampus [18], thus indicating structural physiological underpinnings for the effects of CRF on children's cognition. Working memory and inhibition in particular are thought to be important for academic achievement and are linked to achievement in mathematics and reading [23-25]. Likewise teachers' ratings of pupils' attention show a strong association with academic achievement in mathematics and reading [26-28]. However, studies employing objective cognitive measures of attention in relation to academic achievement are sparse [29, 30]. Likewise, only a paucity of studies investigated the effects of PA (exercise intervention) or CRF on children's attention and these results are promising [20, 31]. Thus the relationship between PA, CRF, attention and academic achievement warrants further investigation.

Evidence is emerging linking childhood and adolescent overweight and obesity to the declines in cognitive function and academic achievement [11, 12]. Research also suggests that exercise can positively affect this relationship and improve executive function and academic performance in overweight and sedentary children [32-34]. Thus it is possible that PA, CRF and adiposity interact in producing different cognitive and academic outcomes in youth. Further research investigating complex associations between PA, CRF, adiposity and cognition as well as academic achievement is warranted.

Studies to date focused on the effects of CRF [10] and broadly defined PA, including time spent in physical education (PE) [10, 35, 36], self-reported PA, or the effects of a particular exercise intervention as a proxy for PA [10, 15, 35]. Such methodological approaches taken together with the heterogeneity of PA measures and definitions do not allow for any inferences about what patterns of habitual PA (intensity, frequency and duration, as well as the number of PA bouts) are most strongly associated with positive cognitive and academic outcomes in youth and children. Evidence linking objectively measured habitual PA to these outcomes is lacking [13, 14]. Furthermore, none of the studies to date assessed the unique effects of sedentary time on cognitive function and academic achievement in children or adolescents. Although few studies reported positive effects of short bouts of exercise during class on children's concentration and engagement with learning tasks [37, 38], these data do not inform our knowledge of how sedentary time independent of moderate to vigorous PA uniquely contribute to gains in cognitive function and, possibly, academic achievement. The knowledge of how patterns of habitual PA and sedentary time uniquely contribute to various aspects of adolescents' cognitive function in comparison to their effects on academic achievement is important. Such knowledge will afford mapping of complex pathways through which habitual PA can affect processes supporting learning as well as learning outcomes.

Present study proposes to address these gaps in research and to investigate:

1) the mediated effects of cognition (working memory, inhibition, selective attention, divided attention, attentional control) on the relationship between habitual PA (and sedentary behaviour) on academic achievement at age 11 years;

Research question (RQ) 1: Is the relationship between the total and accumulated bouts (e.g. greater than 10 minutes) of PA (and time sedentary) and academic achievement (in reading, spelling, English, mathematics and science) at age 11 mediated by cognitive performance on the tests of working memory and inhibition at age 10 years, and divided attention, selective attention and attentional control at age 11 years?

2) the longitudinal effects of habitual PA (and sedentary behaviour) at age 11 years on youth's cognition at age 15.5 years (inhibition), and academic achievement at 13 years (Key Stage 3), after controlling for academic achievement at age 11 years and habitual PA (and sedentary behaviour) at age 13 and 15.5 years;

RQ 2: What is the effect of the total and accumulated bouts (e.g. greater than 10 minutes) of PA (and time sedentary) at age 11 years on inhibition at age 15.5 years?

RQ3: What is the effect of the total and accumulated bouts (e.g. greater than 10 minutes) of PA (and time sedentary) at age 11 years on academic achievement (in reading, spelling, English, mathematics and science) at age 13 years?

3) and to test complex effects models to elucidate the mediating and moderating effects of CRF and adiposity, on the proposed relationships between habitual PA (and sedentary behaviour) and cognition (selective attention, divided attention, attentional control, working memory and inhibition).

RQ4: Does cardio-respiratory fitness at age 15.5 mediate or moderate the relationship between the total and accumulated bouts (e.g. greater than 10 minutes) of PA (and time sedentary) and cognition (inhibition) at age 15.5 years?

RQ5: Does adiposity at age 11 and 15.5 years mediate or moderate the relationship between the total and accumulated bouts (e.g. greater than 10 minutes) of PA (and time sedentary) and cognitive performance at age 10 years (working memory, inhibition), 11 years (selective attention, divided attention and attentional control) and 15.5 years (inhibition)?

PA and sedentary behaviour will be objectively measured by the Actigraph accelerometer (please refer to Appendix 2A for further details of the proposed use of the accelerometer data). The objective measures of components of executive function most consistently associated with academic outcomes (working memory, inhibition), as well as the measures of attention (selective attention, divided attention and attentional control) will be taken using validated computer and pen and paper tasks. Inhibition will be measured with Stop Signal Task [39] and working memory with a computerised Counting Span Task [40]. The Test of Everyday Attention for Children (TEACh) (adapted from the adult version by Robertson [41]) will be employed to test various aspects of attention. Scores from the Standard Assessment Tests (SATS) of the National Curriculum at Key Stages 2 and 3 (after controlling for child's results at Key Stage 1) in mathematics, reading, spelling, English and science will be used as outcome measures of academic achievement. Heart rate taken during an exercise bike session will be used as a proxy measure of cardio-respiratory fitness. Percent body fat will be assessed with the whole Dual X-Ray Absorptiometry (DXA) and BMI. BMI will be used to classify children into normal weight, overweight and obese categories in accordance with the criteria recommended by the Centre for Disease Control (CDC) [42] to test moderating effects model. Biological maturation has been related to body composition [43-47] as well as academic achievement [48, 49] in adolescent boys and girls, and its sequel affects maturation of brain structures involved in cognitive function [50]. Therefore biological maturation will be controlled for in all the analyses. Measures of sexual maturation (stage of pubic hair development in boys and girls, breast development and the onset of menses in girls, and genital development in boys), and somatic maturation (predicted age at peak height velocity (APHV)) will be used as maturity indicators.

There is strong evidence to suggest that very pre-term (<= 33 weeks gestation) and/or very low birth weight (VLBW; <= 1500 g) children have academic difficulties and more subtle cognitive impairments [51]. Recent meta-analysis of neurobehavioural outcomes in very preterm and VLBW children suggests that these effects are especially prominent for academic achievement in mathematics (d= -0.60) and spelling (d= - .76), with medium effect sizes reported for executive function (effect sizes range from

- 0.36 to - 0.57), and attention (effect sizes range from -0.43 to -0.59) [51]. Thus it is important to control for gestational age and weight at birth in the analyses relating to both adolescents' cognition and their academic performance.

Likewise, there is epidemiological evidence linking attention-deficit/hyperactivity disorder (AD/HD) and depression to the declines in cognitive [52, 53] and academic performance in youth [54-57]. Therefore, AD/HD and depression will be controlled for in the analyses based on the scores from the Development and Well-being Assessment (DAWBA, [58]), and, at time points when these are not available, by the hyperactivity score from Strength and Difficulties Questionnaire (SDQ) [59, 60] and a computerised depression questionnaire. Cases with IQ below 85, special educational needs, learning disabilities and physical disabilities will be excluded from the analyses. Please refer to appendix 2C for the exhaustive list of exposure, outcome, and confounding variables, as well as for mediators/moderators and exclusion criteria.

Statistical analyses:

Statistical analyses will include descriptive statistics, Pearson product moment correlations, and the assessments of mutlicollinearity. Exploratory multiple regression models including all the confounders (age at test, sex, SES, IQ, handedness, gestational age, birth weight, biological maturation, AD/HD, depression, accelerometer wear, adiposity and CRF) and predictors (frequency and duration of light, moderate, moderate to vigorous and vigorous PA, as well as the number of PA bouts, duration and frequency of sedentary time and sedentary bouts) will be first assessed to ensure that the direct relationships exist among PA, cognitive and academic outcomes. To test the mediating effects model (RQ1) the subtracting method as outlined by Judd and Kenny [61] will be employed. This approach allows for testing the significance of the indirect effect as opposed to Barron and Kenny's [62] method. The test of statistical significance for the indirect effect will be based on the method designed by McKinnon et al. [63] and outlined in [64]. To answer research questions 2 and 3, mixed effects models for longitudinal data analysis will be employed [65]. To address research questions 4 and 5, the complex moderating and mediating effects models including CRF and adiposity will be assessed by pathway analyses with Structural Equation Modelling [53].

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