Modelling the Relationships between Training, Anxiety, and Fatigue in Elite Athletes

Modelling the Relationships between Training, Anxiety, and Fatigue in Elite Athletes G. P. Millet 1 A. Groslambert 2 B. Barbier 2 J. D. Rouillon 2 R. B. Candau 1 Abstract This study investigated the effects of 40-week training on anxiety and perceived fatigue in four elite triathletes. Anxiety and perceived fatigue were self-reported by the subjects twice a week by the way of a specific questionnaire and were linked by a mathematical model to the training loads calculated from the exercise heart rate. A significant relationship (r = 0.32; p < 0.001) between the training loads and anxiety was identified using a two-component model: a first, negative (i.e., anxiety decreased) short-term (τ 1 = 23 days) function and a second, positive longterm (τ 2 = 59 days) function. The relationship between the training loads and perceived fatigue was significant (r = 0.30; p < 0.001), with one negative function (τ 1 = 4 days). This mathematical model can potentially describe the relationships between training loads and anxiety or perceived fatigue and may improve both the adjustment of the duration of tapering and the early detection of staleness. Key words Mathematical model periodisation training loads triathletes 492 Introduction The literature about the relationships between physical activity and anxiety is quite extensive (for a review: [22]). Most of the studies support the viewpoint that moderate exercise is associated with a reduction in anxiety, but mainly for aerobic forms of exercise [2, 35]. Most of the studies showed a low to moderate/ high effect of aerobic training in reducing state and trait anxiety [29]. Chronic exercise reduced trait anxiety to a greater extent with exercise sessions lasting 21 30 or 40 min, when compared to < 21 min, or with training periods longer than 10 or 15 weeks, when compared to < 10 weeks [29]. Studies conducted on the effect of acute exercise in trained subjects have reported high variability of several psychological variables (anxiety, fear, self-image, perceived competence) [32]. The relationships between hard endurance training and fatigue have been extensively studied but remain partly unexplained [19, 28, 31]. Overtraining (i.e., under-performance, under-recovery) is described as a decrease in performance related to physiological, psychological, biochemical, immunological, and behavioural alterations (for a review: [14]). It has been reported that intense training may affect mood states, leading to anxiety, depression, feelings of fatigue, low self-esteem [16]. Evidences of relationships between change in neurotransmitters or brain monoamines (e.g., decrease in brain serotonin or GABA) and central fatigue during and after exercise are numerous [10,12]. These mechanisms may also explain partly the positive mood following low-intensity exercise. The psychological assessment by psychometric questionnaires (i.e., POMS; RESTQ-Sport; Recovery-Cue) has been shown to be an efficient method for monitoring overtraining (or underrecovery) [21]. Due to the difficulty of access- Affiliation 1 Laboratoire UPRES-EA 3759 «Approche bio-psycho-sociale du dopage», Faculté des Sciences du Sport, Montpellier, France 2 Laboratoire des Sciences du Sport, Besançon, France Correspondence Grégoire Millet Faculté des Sciences du Sport 700 Avenue du pic St Loup 34000 Montpellier France Phone: + 33 4 67415749 Fax: + 33 4 67415708 E-mail: g.millet@univ-montp1.fr Accepted after revision: April 25, 2004 Bibliography Int J Sports Med 2005; 26: 492 498 Georg Thieme Verlag KG Stuttgart New York DOI 10.1055/s-2004-821137 Published online September 10, 2004 ISSN 0172-4622

ing elite athletes for regular self-report questionnaires and for quantifying their training programs, the modelling of the training effects on the anxiety and perceived fatigue has not yet been performed. Modelling the effects of training on performance has been done for a variety of endurance sports, including running [3, 4, 26], swimming [27], cycling [6], and triathlon [25]. This modelling procedure used to link the variations of the training amounts to the changes in performance has also been used to associate training loads and haematological variables [3, 9] throughout first order transfer functions. The number of transfer functions retained was tested statistically. In this modelling method, two fundamental aspects of training are taken into account; first, the cumulative effects of the training loads. Secondly, the fact that the training effect decreases as a function of time is also included in the transfer functions. The decay time constant of each function characterizes the duration of a training effect; so, a decrease of 63% and 98% of the initial value (prior to the training load) under the effect of training occurs after a duration of onefold and 4-fold the value of the time constant, respectively. Moreover, this modelling method can define other characteristics of the training process as the sensitivity to training (i.e., the proportional responses to the training loads) described by the amplitude coefficients of the transfer functions, or the time necessary to return to the initial (pre-training) values. To the best of our knowledge, this modelling procedure has never been used to associate characteristics of endurance training and psychological variables. To summarize, the modelling approach described above aimed to identify the relationships between psychological variables and training loads; in other words, the psychological alterations in response to training. From a general point of view, this kind of approach could help to better understand the nature of the relationships between the dynamics of the training loads and psychological alterations. Such a model would, for example, allow the determination of parameters of the relationships between training loads and self-estimated fatigue or anxiety. Modelling the relationship between training loads and change in psychological variables may represent a new and valuable method for assessing the effects of training on the psychological status of the athletes. Moreover, this method could improve the adjustment of the duration of tapering prior to major competitions and aid in the early detection of staleness or overtrained status in elite athletes. Thus, the purpose of the present study was to model the effects of training loads on anxiety and perceived fatigue in elite endurance athletes. Methods Subjects Four professional triathletes (3 females, 1 male) of international level volunteered to take part in this experiment. Three of the athletes were members of the elite national team, which became long-distance (4 km swimming 120 km cycling 30 km running) World champion at day 237 (week 34) of the studied period (Fig. 1). Selected characteristics of the subjects are shown in Table 1. The study was approved by the institutional ethics committee and all subjects provided written, voluntary, informed consent prior to participate in this study. Experimental design An entire 40-week season was analysed. The period analysed was from the beginning of the season in early November until the last important competition in early September. All the athletes participated in two altitude-training camps during weeks 10 12 and 19 21. Quantification of training amount The training stimulus (W) is calculated separately for each discipline (swimming, cycling, running) and for miscellaneous training, based on the method described by Banister et al. [4]. The sum is defined as the total training amount W ˆ Xj ˆ T X j d k j ˆ 1 Where X j = (HR j HR rest ) (HR max HR rest ) 1, j = time varying between 0 and the end of the session (T), d = 5 s (time elapsed between two samples in the heart rate monitor), HR j is the exercise heart rate at j, HR rest is the resting HR value, HR max is maximum heart rate and k is a coefficient used to enhance the value of training amounts completed at high intensity (k = 0.86x j e 1.67Xj for women, k = 0.64x j e 1.92Xj for men) [4]. HR was recorded during every swimming, cycling, and running session with a HR monitor (Sport-tester PE4000, Polar Electro, Finland) and downloaded to a laptop computer every day. HR rest was self-measured everyday, in a supine position. Evaluation of anxiety and perceived fatigue Twice a week, the athletes completed a specific questionnaire (Table 2). The questionnaire was administered at the same time (in the morning) prior to a training session by the same observer. It was explained to the subjects that this questionnaire was a means of better monitoring their training program. According to Spielberger [29], a modified STAI A-State scale was used to perform multiple repeated measures. This modified scale consisted of 8 items that measured somatic anxiety (items 3, 4, 6, and 7) and cognitive anxiety (items 1, 2, 5, and 8). Subjects responded to each STAI item by rating themselves on a four-point Likert scale (1 = Not at all; 2 = Somewhat; 3 = Moderately so; 4 = Very much). Some of the modified STAI items are worded in such a manner that a rating of 4 indicated a high level of anxiety (i.e., items 2, 4, 6, 8), while other items (i.e., items 1, 3, 5, 7) are worded so that a high rating indicated low anxiety. For items on which a high rating indicated low anxiety, the scoring weight was reversed. The range of possible score for the modified STAI varied from 8 to 32. Evaluation of the perceived fatigue Perceived fatigue was evaluated by nine items (9 17 in Table 2). Items on which a high rating indicated high fatigue were items 9, 13, 14, and 15. Items on which a high rating indicated a low fatigue were items 10, 11, 12, 16, and 17. The range of possible score for the perceived fatigue varied from a minimum score of 9 to a 493 Millet GP et al. Modelling the Relationships Int J Sports Med 2005; 26: 492 498

Anxiety and Fatigue 8 7 6 5 4 Fig.1 Below: weekly training loads (arbitrary units). Top: Scores of anxiety and perceived fatigue averaged per week and expressed over a scale from 2to 8. The arrow indicates the long-distance World championship. 3 Training load(a.u.) 2 3500 3000 2500 2000 1500 1000 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 Fatigue Anxiety 500 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 Week 494 Table 1 Selected characteristics of the subjects Variables Subjects S1 S2 S3 S4 Mean ± SD Age (yr) 33 2 7 33 36 32.3±3.8 Height (cm) 151 165 174 175 166.3 ± 11.1 Mass (kg) 50 59 65 68 60.5 ± 7.9 V O 2max (ml kg 1 min 1 ) 74 68 66 76 71.0 ± 4.8 DT (yr) 9 8 10 10 9.3 ± 1.0 V O 2max = maximal oxygen uptake; DT = duration of training for triathlon maximum score of 36. Finally, anxiety and fatigue scores were expressed over the same scale from 2 to 8, respectively by dividing their scores by 4 and 4.5. In order to evaluate the reliability of the questionnaire, a test-retest (separated by 3 hours) was performed by 20 triathletes. The correlation coefficient between test and retest were 0.86 and 0.89 for the anxiety score and the fatigue score, respectively. The correlation coefficient between the test retest was 0.75 ± 0.10 for the 8 items of the anxiety score and 0.76 ± 0.11 for the 9 items of the anxiety score. The subscales of anxiety and fatigue showed good internal consistencies with coefficients alpha [11] of 0.82 and 0.83, respectively. Item Not at all Table 2 Anxiety (items 1 to 8) and fatigue (items 9 to 17) questionnaire Somewhat Moderately so Very much 1. I feel self-confident & & & & 2. I feel depressed & & & & 3. I feel relaxed & & & & 4. I feel nervous & & & & 5. I feel happy & & & & 6. I feel anxious & & & & 7. I feel peaceful & & & & 8. I feel irritable & & & & 9. I feel tired & & & & 10. I feel able to think & & & & 11. I feel on form & & & & 12. I feel energetic & & & & 13. I feel sleepy & & & & 14. I feel awkward & & & & 15. I have sore legs while training & & & & 16. I have a strong will in training 17. I have the desire to train & & & & & & & & Millet GP et al. Modelling the Relationships Int J Sports Med 2005; 26: 492 498

Modelling the effects of training on anxiety and perceived fatigue The relation between training and anxiety or perceived fatigue was described mathematically by a system where the input is the training load W(t) and the output is the level of anxiety/perceived fatigue p(t), all as a function of time t. A first-order system is described mathematically by g(t) = k e t/τ where τ is the decay time constant and k a positive or negative factor inducing an increase or a decrease in anxiety or perceived fatigue, respectively. The first studies described the relation between the training loads and performances either with two antagonistic system models ascribed as the fitness (positive function) and fatigue (negative function) responses [3, 4]; or with a more complex model, where the number of functions was tested statistically [7,8]. As shown by Busso et al. [8], the response of the system can be described by the convolution product of the training loads w(t) with the impulse responses of each system g r (t) with r varying from 1 to R. p(t) = p* + w(t) g 1 (t) + w(t) g 2 (t) + w(t) g r (t) where p* is the initial level of the athlete at the beginning of the studied period. Therefore the response of the system (i.e., in this study, the level of anxiety or of perceived fatigue), on day n is estimated by: ^P XrˆR n ˆ STR r n rˆ1 where STR r (n) = k n 1 P r w i e n i = R kp e n= R iˆ1 R is the number of components of the system, P n is the predicted level of anxiety or perceived fatigue at the day n, K r is the multiplying factor, τ R the decay time constant, expressed in days, for each of the transfer functions. The set of model parameters is determined by minimizing the residual sum of squares (RSS) between predicted and real (i.e., measured by questionnaire) levels of anxiety or perceived fatigue: RSS N ˆX ^p n p n 2 n The statistical significance was tested by an F-ratio on the mean RSS between the predicted and measured values. The addition of a first-order function was accepted only when it improved the explanation of the model. The model has been tested for a set of decay time constants τ between 0 and 100 days and a set of number of components between 1 and 3 [7,8]. This method was retained to identify the relationships between training loads (T all ) and anxiety (L anx ) or perceived fatigue (L fat ). As described previously [15], a duration (t n ), where the positive function of training overcomes the negative one, can be defined. Thus, t n is the time needed after a training stimulus for the negative effects of training to be dissipated sufficiently to allow the effects of training to return a variable to the initial (pre-training) level [6]. In a bi-exponential model (i.e., R = 2), t n ˆ 1 2 1 2 ln k 2 k 1 [6, 7]. In a mono-exponential model (i.e., R = 1), the decrease of the effects of training is directly related to τ R (= τ 1 ); and t n is assumed to be the time to return a variable to 98% of the initial level. Therefore, t n =4 τ 1. In the present study therefore, t n was the time needed for anxiety or perceived fatigue, respectively, to return to the pre-training level. The goal of the present study was not to assess the individualized changes of anxiety or perceived fatigue under the training influence but to model the relationship between training loads and these psychological variables. Thus, the global responses of the squad were analysed instead of the classical method based on individual responses. Statistical analysis Means and standard deviations were calculated for all variables. The normality and the homogeneity of variance were tested and accepted. Correlation coefficients between modelled and actual values of anxiety or perceived fatigue were also determined. A variance analysis was used to test whether the addition of a second transfer function significantly increased the variance of the model by taking into account the supplementary degrees of freedom introduced in the model [7]. An autocorrelation function was applied to the series of anxiety and perceived fatigue data of each subject in order to analyse the stability of the scores (Statistica 5.5, Statsoft, Tulsa, OK, USA). In all analyses, the level of significance was fixed at p < 0.05. Results Succession of the training loads and changes of anxiety and perceived fatigue over the period analysed are shown in Fig. 1. The highest level of perceived fatigue was at weeks 35 36, following the World championship. The highest level of anxiety were at weeks 7 9 due to illness of three of the four subjects, at week 23 following an altitude training camp, and at week 34 immediately preceding the World championship (Fig. 1). A slow decay of the autocorrelation function was observed for all subjects. The autocorrelation function remained significant for 6 to 8 lags in the 4 series of fatigue data and in three series of anxiety data. In one series of anxiety data, the autocorrelation remained significant for only 2 lags. All the parameters of the model describing the training influences on the level of anxiety and perceived fatigue are presented in Table 3. A significant relationship (r = 0.32; p < 0.001) between the training loads (T all ) and the anxiety (L anx ) was identified by using a two-component model. The first function was negative (i.e., anxiety decreased) and had a decay time constant (τ 1 )of23 days. The second function was positive (i.e., anxiety increased) with τ 2 = 59 days. t n for anxiety was 28 days. The relationships between T all and the perceived fatigue (L fat )was significant (r = 0.30; p < 0.001) with a one-component model (i.e. a single negative exponential transfer function). The time to return L fat to the pre-training level was 15 days (i.e. 4 folds the value of the time constant). 495 Millet GP et al. Modelling the Relationships Int J Sports Med 2005; 26: 492 498

496 Table 3 Parameters of the model describing the influence in training on the anxiety and perceived fatigue in four elite triathletes TrainingParameters Anxiety Fatigue Overall Functions (n) Two- Oneτ 1 (days) 23 4 K 1 0.0002 0.0002 τ 2 (days) 59 K 2.00009 p(f) < 0.001 < 0.001 r.32.30 t n (days) 28 15 Model based on 299 scores of anxiety and perceived fatigue measured by questionnaire. τ 1 and τ 2 are the decay time constants; K 1 and K 2 are the multiplying factors for the positive and negative transfer functions. p(f) is the level of significance of the F-test estimating the fit of the relationship between training responses and anxiety or fatigue. r is the correlation coefficient between the training responses and anxiety or fatigue Discussion The main finding of the present study is that anxiety is significantly related to the training loads by two mono-exponential functions, one negative and one positive (the time to return to the pre-training level was 28 days). Perceived fatigue, on the other hand, is related to the training loads by a single mono-exponential negative function. The time to return fatigue to its initial level was 15 days. In other words, training loads were associated with a short-term decrease concomitant to a longer-term increase in anxiety, whereas fatigue that was maximal at the end of the training load decreased exponentially. This is the first time this type of mathematical model has been used for linking training loads and psychological variables that does not reflect the individual responses analysed one-by-one. The scores measured by the questionnaires were quite stable as indicated by a slow delay of the autocorrelation function in almost all of the series concerned. This means that the subject response was relatively reproducible. However, the strength of the correlation that was observed between training load and anxiety or fatigue was low in both cases. This highlights the fact that, in a given athlete, both of the latter will be modulated by factors in addition to, and excluding, training stress. The proposed mathematical model may be a useful adjunct, however, to the development of understanding of the general influence of training on psychological variables in elite athletes. The data presented here highlighted two opposite effects i.e., a short term decreasing effect (A) and a long-term increasing effect (B) of training on anxiety. These are discussed separately below. The positive effects of acute exercise on state anxiety Most of the meta-analyses carried out on the relationships between exercise and anxiety reported that a single moderate exercise session was associated to reduction in state anxiety [29, 35]. The greatest effects were observed when the duration of the training program was at least 10 weeks (with the greatest benefits being observed over a 15-week period) [2, 35]. Acute exercise sessions appear to be most effective at reducing state anxiety when they are aerobic (i.e., at 70% of maximal HR and at least a 20-min duration), as was the case for the majority of the sessions in the training programmes of our subjects. The low state anxiety values that we observed immediately after each training session support this observation. The psycho-physiological changes between before and after acute exercise that have been suggested to contribute to such a possible anxiety reducing effect include increases in temperature, increases in beta endorphins, reductions in muscle tension [13], increases in parasympathetic activity, and reduced excitability of the central nervous system [29, 30]. However, Taylord has reported that the HR response may reflect changes in anxiety, and be influenced by such psycho-physiological changes [35]. However, Alfermann and Stoll [1] reported also no change in trait anxiety after six months of aerobic exercise in sedentary adults. Another mechanism proposed for anxiety-reducing effects has been the distraction hypothesis. According to Bahrke and Morgan [5], any distracting activity may result in reduced anxiety. However, the anxiety-reducing effects of exercise are stable [35]. Raglin and Morgan [31] observed that state anxiety decreased during two hours after the end of exercise and increased to the baseline level after 24 hours. In the present study, the daily training program sustained by the athletes may explain partly the low state anxiety level observed after acute exercise. The negative effects of chronic exercise on state anxiety There has been relatively little examination of the long-term effects of accumulated training loads and competitions on statetrait-anxiety in elite endurance athletes. Meyers and Whelan [24] reported that there is a dose-response relationship between training and mood that is common in all sports and that the stale athletes demonstrate symptoms similar to those seen in clinical depression. The effects of chronic exercise on state anxiety have been previously observed by Murphy et al. [28] who reported that, compared to the baseline values, a 10-week training program significantly increased competitive anxiety in high level judo players. The results of the present study carried out over 40 weeks reveal negative effects of chronic exercise on state anxiety in high level triathletes. This response was different than the one observed in sedentary subjects and may be caused partly by the cognitive competitive anxiety [23]. Authors reported that this specific form of anxiety, usually assessed by the CSAI-2, is linked to the perception of threat. Threat may be caused by perceived uncertainty of outcome (i.e., probabilities of success or defeat) or perception of the importance of the competition. Therefore, it is not surprising that the period preceding the World championship (week 34) was associated with higher anxiety (L anx = 5.1 ± 1.3) than usual. However, illness or a high level of fatigue can also lead to an increase in anxiety. Triathletes could also be affected by the performance evaluation of parents or the trainers [33]. Furthermore, it has been reported that overtraining and burnout have a significant long-term effect on mood state, self confidence, and state anxiety of subjects [16,17]. In the present study, the athletes did not exhibit any signs of overtraining. Moreover, since the team became World champion at day 237, the hypothesis that the long-term increase in anxiety was induced by staleness is not supported by the data. Millet GP et al. Modelling the Relationships Int J Sports Med 2005; 26: 492 498

In opposition to sedentary subjects, our results suggest that training load might have a positive short-term (τ 1 = 23 days) and a negative long-term effect on anxiety in high level triathletes (τ 2 = 59 days). The t n value corresponding to 28 days represents the cumulative effects of both functions. Fatigue In the present study, the time for perceived fatigue to return to its initial level was 15 days. The time constant decay of the negative function in the two-component model associating training and performance with the same subjects was 10 days and the time to return performance to its initial level, calculated from the same data [25] was 13.9 days. In other words, the time to decrease the fatigue evaluated by questionnaire was similar to the time required to return performance to its initial level. The time to recover performance after training loads, calculated with time-invariant models, has been reported to range between 8 and 15 days in endurance athletes training regularly; i.e., 12.2 days for elite swimmers [27], 8 11 days in runners [26], 10 14 days in subjects cycling 5 times a week [6]. However, this time to recover performance has been shown to be lower for a given group of athletes when it trained less frequently. For example, t n ranged from 1 3 days in athletes training four times a week [8]. t n increased when workloads and training frequency increased [6]. Although it is assumed that elite athletes could tolerate and recover more quickly from a training load than their sub-level counterparts, in fact t n was not reported to be lower in elite athletes than in recreational ones [6, 8,25 27]. The values of the time constant decay of the negative function, assumed to be the modelled fatigue, were reported to range between 6 and 13 days [6, 25 27]. The magnitude of the fatiguing effect of training increased as training frequency increased. All these parameters explain the difficulty in predicting the best duration that would lead to an optimal reduction of fatigue prior to a competition. The present results showing that the self-perceived fatigue measured by questionnaire decreased to its initial value in a time close to the time modelled previously as optimal for tapering [6, 7,15] may have important practical applications. Practicality of the method These results show how convenient and useful the regular monitoring of the perceived fatigue could be for adjusting the optimal duration of tapering. This period can last for a few days to 3 weeks [6]. This method would also improve the early detection of staleness or overtrained status in elite athletes since the selfreported ratings of well-being have previously been shown to be an efficient way [19] due to the fact that the psychological changes precede the biological alterations under the effect of fatigue. Beyond the nomothetic procedure used in the present study, the modelling technique allows also an individualized approach if the number of data collected for each variable is greater than 30. Obviously, the greater the number of points, the more accurate is the determination of the model parameters. Mathematical description of training responses applied to each athlete offers the possibility to determine the individual relationships between training loads, performance, anxiety, and fatigue. Of interest is that it becomes possible to assess the optimal time to reach a peak performance (i.e., tapering period), that is one of the key factors of training technique, and probably one of the most difficult to define. Several studies focused on this topic but did not take into account psychological variables in the training process. The present method focuses on the temporal variation in anxiety and perceived fatigue and is complementary to the IZOF model elaborated by Hanin [18], which proposes to distinguish individually zones of anxiety (IZOF = Individual Zone of Optimal Functioning, IZdy = Individual Zone of dysfunction) associated to optimal or poor performances, respectively. The IZOF anxiety model was shown to be realistic in predicting at which level of anxiety optimal performance will occur [20]. Potential issues of this model are: 1) that it is based on a single recall of anxiety prior personal best performance in the past; 2) that the temporal patterns of optimal anxiety are neglected [20]; and 3) that emotional intensities are not conceptualised as a continuum but as categories. The modelling procedure used in the present study did not aim to determine the anxiety associated to an optimal performance, but, by defining the temporal change of anxiety prior to an event, the optimal duration of tapering. Conclusion The use of transfer functions allows one to study systematically the effects of training on psychological variables as it has been achieved previously for physiological responses. This kind of model offers the possibility to better understand the psychological responses to training and the mechanisms of adaptation to chronic exercise. The present study showed that the long-term effects of accumulated training loads and competitions on state-trait-anxiety in competitors was associated with a singular response. In addition to the positive effect generally reported, a negative effect of training, with a different time constant, was identified. It may be caused by heavy training loads completed by the elite athletes and by cognitive competitive anxiety. Otherwise, the present results showed that the self-perceived fatigue decreased to its initial value in a time close to the optimal time previously found for tapering. Therefore, the use of a simple questionnaire could have important practical applications to adjust the optimal duration of tapering and to improve the early detection of staleness in elite athletes. However, the low strengths of the relationships between training loads and anxiety or fatigue highlight the influence of the other factors (i.e., perception by the athletes of the threat of the competition, personal or emotional life of the subjects, illness, ). Therefore this type of mathematical analysis is complementary to the clinical approach. References 1 Alfermann D, Stoll O. Effects of physical exercise on self-concept and well-being. Int J Sport Psycho 2000; 30: 47 65 2 Asci FH. The effects of physical fitness training on trait anxiety and physical self-concept of female university students. Psychol Sport Exerc 2003; 4: 255 264 3 Banister EW, Hamilton CL. Variations in iron status with fatigue modelled from training in female distance runners. Eur J Appl Physiol 1985; 54: 16 23 4 Banister EW, Good P, Holman G, Hamilton CL. Modeling the training response in athletes. In: Landers DM (ed). The 1984 Olympic Scientific 497 Millet GP et al. Modelling the Relationships Int J Sports Med 2005; 26: 492 498

498 Congress Proceedings Sport and Elite Performers. Champaign, IL: Human Kinetics, 1986: 7 23 5 Bahrke MS, Morgan WP. Anxiety reduction following exercise and meditation. Cogn Ther Res 1978; 2: 323 334 6 Busso T, Benoit H, Bonnefoy R, Feasson L, Lacour JR. Effects of training frequency on the dynamics of performance response to a single training bout. J Appl Physiol 2002; 92: 572 580 7 Busso T, Candau R, Lacour JR. Fatigue and fitness modelled from the effects of training on performance. Eur J Appl Physiol 1994; 69: 50 54 8 Busso T, Carasso C, Lacour JR. Adequacy of a systems structure in the modelling of training effects on performance. J Appl Physiol 1991; 71: 2044 2049 9 Candau R, Busso T, Lacour JR. Effects of training on iron status in crosscountry skiers. Eur J Appl Physiol 1992; 64: 497 502 10 Chaouloff F. Effects of acute physical exercise on central serotonergic systems. Med Sci Sports Exerc 1997; 29: 58 62 11 Cronbach LJ. Coefficient alpha and the internal structure of tests. Psychometrika 1951; 16: 297 334 12 Davis JM. Carbohydrates, branched-chain amino acids, and endurance: the central fatigue hypothesis. Int J Sport Nutr 1995; 5: S29 38 13 De Vries HA. Tranquilizer effects of exercise: a critical review. Phys Sportsmed 1981; 36: 373 389 14 Eichner ER. Overtraining: Consequences and prevention. J Sports Sci 1995; 13: S41 48 15 Fitz-Clarke JR, Morton RH, Banister EW. Optimizing athletic performance by influence curves. J Appl Physiol 1991; 71: 1151 1158 16 Fry RW, Grove JR, Morton AR, Zeroni PM, Gaudieri S, Keast D. Psychological and immunological correlates of acute overtraining. Br J Sports Med 1994; 28: 241 246 17 Hackney AC, Perlman SN, Nowacki JM. Psychological profiles of overtrained and stale athletes: a review. J Appl Sport Psychol 1990; 2: 2 33 18 Hanin YL. A cognitive model of anxiety in sports. In: Straub WF (ed.) Sport Psychology: An Analysis of Athletic Behavior. Ithaca, NY: Movement Publications, 1980: 236 249 19 Hooper SL, MacKinnon LT, Howard A, Gordon RD, Bachmann AW. Markers for monitoring overtraining and recovery. Med Sci Sports Exerc 1995; 27: 106 112 20 Jokela M, Hanin YL. Does the individual zones of optimal functioning model discriminate between successful and less successful athletes? A meta-analysis. J Sports Sci 1999; 17: 873 887 21 Kellmann M. Psychological assessment of underrecovery. In: Kellmann M (ed). Enhancing Recovery: Preventing Underperformance in Athletes. Champaign, IL: Human Kinetics, 2002: 37 55 22 Landers D. Performance, stress, and health: overall reaction. Quest 1994; 46: 123 135 23 Martens R, Vealey RS, Burton D. Competitive Anxiety in Sport. Champaign, IL: Human Kinetics, 1990: 117 190 24 Meyers AW, Whelan JP. A systemic model for understanding psychosocial influences in overtraining. In: Kreider RB, Fry AC, O Toole ML (eds). Overtraining in Sport. Champaign, IL: Human Kinetics, 1998: 335 369 25 Millet GP, Candau RB, Barbier B, Busso T, Rouillon JD, Chatard JC. Modelling the transfers of training effects on performance in elite triathletes. Int J Sports Med 2002; 23: 55 63 26 Morton RH, Fitz-Clarke JR, Banister EW. Modeling human performance in running. J Appl Physiol 1990; 69: 1171 1177 27 Mujika I, Busso T, Lacoste L, Barale F, Geyssant A, Chatard JC. Modeled responses to training and taper in competitive swimmers. Med Sci Sports Exerc 1996; 28: 251 258 28 Murphy SM, Fleck SJ. Psychological and performance concomitants of increased volume training in elite athletes. J Appl Sports Psychol 1990; 2: 34 50 29 Petruzzello SJ, Landers DM, Hatfield BD, Kubitz KA, Salazar W. A meta-analysis on the anxiety-reducing effects of acute and chronic exercise. Outcomes and mechanisms. Sports Med 1991; 11: 143 182 30 Petruzzello SJ, Landers DM. State anxiety reduction and exercise: does hemispheric activation reflect such changes? Med Sci Sports Exerc 1994; 26: 1028 1035 31 Raglin JS, Morgan WP. Development of a scale for use in monitoring training-induced distress in athletes. Int J Sports Med 1994; 15: 84 88 32 Raglin JS. Anxiety and sport performance. Exerc Sport Sci Rev 1992; 20: 243 274 33 Sinclair DA, Vealey RS. Effects of coaches expectations and feedback on the self perception of athletes. J Sport Behav 1992; 11: 77 91 34 Spielberger CD, Gorsuch RL, Lushene RE. Manual for the State-Trait Anxiety Inventory. Palo Alto, CA: Consulting Psychologists Press, 1970 35 Taylor AH. Physical activity, anxiety and stress. In: Biddle SJH, Fox KR, Boutcher SH (eds). Physical Activity and Psychological Well-Being. London: Routledge, 2000: 10 45 Millet GP et al. Modelling the Relationships Int J Sports Med 2005; 26: 492 498