Predictive Performance Models in Long-Distance Runners: A Narrative Review

variables such as maximal oxygen uptake (VO2max), velocity at maximal oxygen uptake (vVO2max), running economy (RE) and changes in lactate levels are considered the main factors determining performance in long-distance races. The aim of this review was to present the mathematical models available in the literature to estimate performance in the 5000 m, 10,000 m, half-marathon and marathon events. Eighty-eight articles were identi ed, selections were made based on the inclusion criteria and the full text of the articles were obtained. The articles were reviewed and categorized according to demographic, anthropometric, exercise physiology and eld test variables were also included by athletic specialty. A total of 58 studies were included, from 1983 to the present, distributed in the following categories: 12 in the 5000 m, 13 in the 10,000 m, 12 in the half-marathon and 21 in the marathon. A total of 136 independent variables associated with performance in long-distance races were considered, 43.4% of which pertained to variables derived from the evaluation of aerobic metabolism, 26.5% to variables associated with training load and 20.6% to anthropometric variables, body composition and

in the 5000 m, 13 in the 10,000 m, 12 in the half-marathon and 21 in the marathon. A total of 136 independent variables associated with performance in long-distance races were considered, 43.4% of which pertained to variables derived from the evaluation of aerobic metabolism, 26.5% to variables associated with training load and 20.6% to anthropometric variables, body composition and somatotype components. The most closely associated variables in the prediction models for the half and full marathon specialties were the variables obtained from the laboratory tests (VO2max,vVO2max), training variables (training pace, training load) and anthropometric variables (fat mass, skinfolds). A large gap exists in predicting time in long-distance races, based on eld tests. Physiological e ort assessments are almost exclusive to shorter specialties (5000 m and 10,000 m). The predictor variables of the half-marathon are mainly anthropometric, but with moderate coe cients of determination. The variables of note in the marathon category are fundamentally those associated with training and those derived from physiological evaluation and anthropometric parameters. Keywords:prediction equations; performance; long-distance runners Int. J. Environ. Res. Public Health2020,17, 8289; doi:10.3390 /ijerph17218289 /journal/ijerph

Int. J. Environ. Res. Public Health2020,17, 8289 2 of 23 1. Introduction The great popularity of long-distance running has seen an unprecedented increase in the last 10 years. This has generated, in coaches and athletes, a great interest in the development of performance prediction models based on linear regression equations, with the aim of helping many athletes in their preparation for competitions. These predictions are based on a combination of physiological, anthropometric, nutritional and training factors (modifying frequency, volume and intensity), most obtained in exercise physiology laboratories, through variables related to training load [1,2]. Performance in long-distance disciplines can be de ned as the nal time or race time, and its understanding is important both for designing training programs and for determining scheduled training and race pace. However, accurate knowledge is frequently di cult to obtain, especially in long-distance races, as it would involve high training loads, which can, at times, indicate poor race planning in inexperienced runners who normally use polarized training methods [3]. This and other factors associated with the control of training, result in predictive models being recognized and useful for coaches or professional runners. The physiological adaptations produced by training in amateur runners are well understood and are generally those performed at submaximal intensities with continuous training strategies [4]. In high-level athletes, these improvements are seen particularly with tempo runs and short-interval training, as methods to improve performance [5]. Therefore, transferring the results and conclusions obtained from amateur athletes to high-level athletes is not advisable [6]. Performance in endurance running is in uenced by a variety of factors, both anthropometric and training. Morphological (somatotype components) and anthropometric characteristics such as skinfolds, body fat percentage, circumferences, lower limb length, weight, height and body mass index appear to in uence performance. Accordingly, certain characteristics have a better relationship between energy expenditure and performance [7,8]. There are numerous studies on physiological factors in the literature on performance prediction in long-distance runners. Classically, maximal oxygen uptake (VO2max), running economy (RE) and anaerobic threshold (AT) stand out as the main variables that have been used to predict performance in long-distance races

in uence performance. Accordingly, certain characteristics have a better relationship between energy expenditure and performance [7,8]. There are numerous studies on physiological factors in the literature on performance prediction in long-distance runners. Classically, maximal oxygen uptake (VO2max), running economy (RE) and anaerobic threshold (AT) stand out as the main variables that have been used to predict performance in long-distance races [9,10], but a large gap exists in the eld of performance prediction based on eld tests. The aim of this narrative review was to undertake a descriptive, analytical and detailed analysis of the determinants and predictive ability of anthropometric, physiological (laboratory test), training and combined variables, as well as eld assessments ( eld tests), to estimate performance in specialties of long-distance races (5000 m, 10,000 m, half–marathon and marathon). 2. Materials and Methods This document is classi ed as a narrative review and was carried out under a framework of assigning key attributes based on Search, Appraisal, Synthesis and Analysis (SALSA) [11]. Accordingly, the search was exhaustive. The synthesis is a tabular exposition of the data and the analysis may be chronological, conceptual or thematic [11]. In general terms, this narrative review presents all the known published works that include runners of di erent levels: all of these in di erent types of runner (amateur, moderately trained, highly trained, high-level and elite) with the common denominator that they are generally trained both in length of time and number of weekly sessions. Also included are all studies that found associations between anthropometric and physiological parameters and performance in the middle-distance (5000 m and 10,000 m) and long-distance (half-marathon and marathon) events. 2.1. Search The abstracts of original English articles registered in the Pubmed, SciELO (Scienti c Electronic Library On line), ScienceDirect and SportDiscus databases were reviewed. The terms entered in the

Int. J. Environ. Res. Public Health2020,17, 8289 3 of 23 search engines were as follows: “runners”, “long distance runners”, “performance”, “performance prediction”, “anthropometric”, “physiological determinants”, “performance determinants”, “5000 m”, “10,000 m”, “half-marathon” and “marathon”, as well as the combinations of all of them, depending on the specialty examined. 2.2. Selection Criteria The selection criteria were all relevant articles, as well as books and monographs. The rst evaluation consisted of reading the abstract and the full text of the selected studies, followed by an analysis of the results. 2.3. Exclusion Criteria Case studies, duplicate articles and abstracts without clear and su cient information were excluded. 3. Results The ow chart (Figure) shows the nal selection of 58 articles, with 12 articles identi ed for the 5000 m modality, 13 for the 10,000 m, 12 for the half-marathon and 21 for the marathon.Int. J. Environ. Res. Public Health 2020 16, x 3 of 21 m”, “10,000 m”, “half-marathon” and “marathon”, as well as the combinations of all of them, depending on the specialty examined. 2.2. Selection Criteria The selection criteria were all relevant articles, as well as books and monographs. The first evaluation consisted of reading the abstract and the full text of the selected studies, followed by an analysis of the results. 2.3. Exclusion Criteria Case studies, duplicate articles and abstracts without clear and sufficient information were excluded. 3. Results The flow chart (Figure 1) shows the final selection of 58 articles, with 12 articles identified for the 5000 m modality, 13 for the 10,000 m, 12 for the half-marathon and 21 for the marathon. Figure 1. Diagram of study search and selection process. In Table 1, the variables are grouped as demographic, laboratory assessments, field test, training, anthropometric and others. Table 1. Partial and total figures for performance prediction variables in long-distance specialties. Long-Distance Specialties Variables 5000 m 10,000 m HM M Total % of Total Demographic 4 1 1 1 7 5.1 Aerobic Metabolism 26 14 3 16 59 43.4 Training 1 5 2 28 36 26.5 Anthropometry 2 5 16 5 28 20.6 Field test 0 1 2

Table 1. Partial and total figures for performance prediction variables in long-distance specialties. Long-Distance Specialties Variables 5000 m 10,000 m HM M Total % of Total Demographic 4 1 1 1 7 5.1 Aerobic Metabolism 26 14 3 16 59 43.4 Training 1 5 2 28 36 26.5 Anthropometry 2 5 16 5 28 20.6 Field test 0 1 2 0 3 1.47 Others 0 1 0 3 4 2.94 Figure 1.Diagram of study search and selection process. In Table, the variables are grouped as demographic, laboratory assessments, eld test, training, anthropometric and others. Table 1.Partial and total gures for performance prediction variables in long-distance specialties. Long-Distance Specialties Variables 5000 m 10,000 m HM M Total % of Total Demographic 4 1 1 1 7 5.1 Aerobic Metabolism 26 14 3 16 59 43.4 Training 1 5 2 28 36 26.5 Anthropometry 2 5 16 5 28 20.6 Field test 0 1 2 0 3 1.47 Others 0 1 0 3 4 2.94 Subtotals/Total 33 27 24 51 137 100 HM: Half-marathon, M: Marathon.

Int. J. Environ. Res. Public Health2020,17, 8289 4 of 23 3.1. Demographic Variables Of the seven demographic variables, the most notable is age, which is included in all the specialties studied. Gender is only recorded in the 5000 m specialty [12]. 3.2. Aerobic Metabolism Assessment Variables In this section, the variables were classi ed into two groups: 1. Maximum range (VO2max, velocity at maximal oxygen uptake [vVO2max], maximum heart rate, maximum lactate,vVO2with the University of Montreal Track Test, anaerobic capacity and oxygen de cit, etc.). 2. Submaximal range (VO2at lactate threshold, lactate threshold, velocity at lactate levels of 2.5–3 and 4 mmol/L, RE, heart rate at individual anaerobic threshold (IAT), velocity at heart rate de ection point, VO2and % VO2at AT, velocity at AT, lactate level at AT and % of peak velocity at AT). Of particular note arevVO2max and VO2max, RE, understood as oxygen uptake at speci c velocity, VO2at AT and velocity at the level of 4 mmol/L lactate. Thirty-one of these studies include mL/kg/min among the variables that are associated with or are predictive factors of running performance from middle to long distance. Additionally, 24 studies include variables such as km/h, m/min, m/s associated with conditions obtained at VT2 (anaerobic threshold), velocity at heart rate de ection, IAT, ATLab (AT in laboratory test), etc. 3.3. Training Variables The training variables were grouped into two categories: quantitative (mean race duration, number of training sessions per week, miles per week, km per week, training volume, miles in 8 weeks, training in 9 weeks, years of training) and qualitative (training pace, record for 1 mile, 5 miles, 10 miles, half-marathon time and having nished a marathon). 3.4. Field Test Variables Only two studies measuring AT using the University of Montreal Track test [13], and covered distance in the Cooper test [14,15] 3.5. Anthropometric Variables These variables are classi ed into three categories: (i) basic measurements (height, weight, body mass index, skinfolds and muscle circumferences), (ii) body composition fractions (fat mass, fat-free mass and skeletal muscle mass) and (iii) somatotype components (endomorphy, mesomorphy and ectomorphy). Other important performance-related variables are body

Track test [13], and covered distance in the Cooper test [14,15] 3.5. Anthropometric Variables These variables are classi ed into three categories: (i) basic measurements (height, weight, body mass index, skinfolds and muscle circumferences), (ii) body composition fractions (fat mass, fat-free mass and skeletal muscle mass) and (iii) somatotype components (endomorphy, mesomorphy and ectomorphy). Other important performance-related variables are body mass index, fat mass percentage, and skinfolds as regional indicators of adiposity associated with performance. Fifteen of the 26 studies were conducted in the half-marathon specialty by Knechtle's research group [8,16,17]. 3.6. Other Variables Noteworthy are also the use of a biochemical variable such as transferrin levels, as well as a model based on data collection through a post-competition survey [14] and leg volume and heart rate changes during the Ru er test recovery period [15]. 3.7. Data Management and Presentation Tables–5 (half-marathon and marathon) respectively and structured to display: Author, year of publication, sex, number of participants, athletic level, dependent variable, independent variable(s) associated with performance (correlation coe cient,p-value) or if the independent variables comprise a signi cant model (equation): the coe cient of determination (R 2 ) and the standard error of the estimate (SEE), the limits of agreement of the Bland–Altman plot (only in half-marathon) and the predictive equation.

Int. J. Environ. Res. Public Health2020,17, 8289 5 of 23 Table 2.Multiple regression models associated with performance in 5000 m races. Author Year Sex n Level Dependent Variable Independent Variable r p R 2 SEE Foster 1983 1 28 Well-trained 3 Miles VO 2max 0.92Training volume Intensity Tanaka 1984 1 21 Trained 5000 m vVO 2max 0.78 <0.001 0.62 nr Ramsbottom 1987 1 55 University VO 2max 5000 m 0.85 <0.01 0 43 5000 m 0.80 <0.01 1987 1 55 University 5000 m RE 0.39 <0.01 0 43 RE 0.34 <0.05 Fay 1989 0 13 Mod-Highly 5000 m (m /min) Vlact 4 mMol /L (m/min) 0.94 0.940–0.97 nr VO 2max (ml/kg/min) Oxygen cost of running 0.4–( 0.63) Velocity (m/min)=0.346 (vLac 4 mMol/L)+1.899 (VO2max) Kenney 1985 1 8 Elite 5000 (time in sec) Age +VT2 (mL/kg/min) <0.02 0.98 nr Time (sec)=11555 5.1 (age) 2.9 (VT2) Weyand 1994 1–0 22–19 Competitive 5000 m Peak O 2Def (POD) 0.4 VO 2max High %VO 2AT RE at 3.6 m/s Gender (1=male; 2=female) Specialty Time (sec)=0.38 (POD) 1.29 (VO2max)+1.25 AT(%VO2) +4.42 (RE)+55.9 (Gender) 47.4 (specialty) (1 sprinter, 2 long-distance runner)+1664.9 nr nr Takeshima 1995 1 51 Popular 5000 m (m /s) VO 2LT (ml/kg/min) 0.87 Age ARD 0.89 VO 2LT (ml/kg/min) 0.79 Age VO 2LT (ml/kg/min) 0.82Age ARD Velocity (m/s)=4.436+0.045 (VO2LT) 0.033 (Age)+0.005 (ARD) 0.89 0.27

Int. J. Environ. Res. Public Health2020,17, 8289 6 of 23 Table 2.Cont. Author Year Sex n Level Dependent Variable Independent Variable r p R 2 SEE Roecker 1998 1–0 339–88 Competitive 5000 m (m /s) vPeak (km /h) 0.91 <0.001 0.940–0.97 IAT (m/s) 0.91 % Fat Mass nr MHR (bpm) Max Lact (mMol/L) Velocity (m/s)=3.404+0.683 (vPeak)+0.274 (IAT) 0.05 (%FM) (MHR) 0.079 (Max Lact) Nummela 2006 1 18 Well-trained Velocity (m /s) VO 2max 0.55 <0.05 MART Vel (m/s)=0.066 (VO2max)+0.048 (MART) 0.549 0.728 nr Stratton 2009 1–0 17–22 Untrained 5000 m (km /h) VO 2max (ml/kg/min) 0.55 <0.01 V LT (km/h) 0.73 <0.01 V Max (km/h) 0.89 <0.01 Run velocity (km/h)= 1.124+0.514 (Vmax)+0.267 (V LT) 0.812 2009 1–0 17–22 Trained 5000 m (km /h) VO 2max (ml/kg/min) 0.51 <0.01 V LT (km/h) 0.76 <0.01 V Max (km/h) 0.83 <0.01 Run velocity (km/h)= 2.629+0.546 (Vmax)+0.345 (V LT) 0.738 Mendes de Souza 2014 1 10 5000 m vVO 2max Lab 0.05 0.35 nr 1 10 5000 m vVO 2max Montreal 0.002 0.66 nr Dellagrana 2015 1 23 Moderately trained 5000 (time) vVT (km /h) 0.64 0.001 RE at 11.2 km/h (L/min) 0.44 0.035 Fat-free mass (kg) 0.57 <0.005 5 km T (min)=25.64 0.71 (vVT) 3.38 (RE 11.2)+0.21 (FFM) 0.71 0.67r: correlation coe cient;p: signi cance level; R 2 : coe cient of determination; SEE: standard error of estimation;vVO2max: max velocity in VO2max; RE: running economy; VLact4: velocity at 4mMol/L; AT: anaerobic threshold; POD: peak oxygen de cit; LT: lactate threshold; ARD: average running duration; IAT: individual anaerobic; threshold; MHR: maximal heart rate; Max Lact: maximal lactate; MART: maximal anaerobic running test;vVO2maxLab: maximal velocity at exercise laboratory test:vVO2max Montreal: maximal velocity on Montreal eld test. vVT: velocity at ventilatory threshold.

Int. J. Environ. Res. Public Health2020,17, 8289 7 of 23 Table 3.Multiple regression models associated with performance in 10,000 m races. Author Year Sex n Level Dependent Variable Independent Variable r p R 2 SEE Foster 1983 1 17 Well-trained 3 Miles VO 2max 0.94Training volume Intensity Tanaka 1984 1 21 Trained 10,000 m vVO 2max 0.96 nr 1 21 Trained 10,000 m vAT (ml /kg/min) 0.80 <0.001 Bale 1986 1 60 Elite & Good Time 10,000 m Workouts (WO)per week 0.87 0.75 2.28 Time (min)=44.27 1.44 (WO) WO+Miles (MW) per week 0.84 Time (min)=46.32 0.91 (WO) 0.11 (MW) 0.8 2.08 WO+MW+Running years (RY) 0.80 Time (min)=46.45 0.68 (WO) 0.11 (MW) 0.38 (RY) 0.83 1.92 WO+MW+RY+ Ectomorphy 0.40 Time (min)=47.93 0.68 (WO) 0.10 (MW) – 0.38 (RY) 0.68 (Ectomorphy) 0.86 1.78 Brandon 1987 Middle 10,000 (m /s) VO 2max (ml/kg/min) Anaerobic Capacity (AC) Height (cm) 10,000 (m/s)=127.39+0.64 (VO2)+0.21 (AC)+0.4 (Height) Fay 1989 0 13 Moderate 10,000 m (m /min) Vlact 4 mmol /L(m/min) 0.840–0.94High VO 2max (ml/kg/min) Vlact 2 mmol/L(m/min) 10,000 (m/min)=0.437 (vLA 4 mmol/L)+2.082 (VO2max)+8.698 10000 (m/min)=0.728 (vLac 4 mmol/L)+57.926 10,000 (m/min)=0.407 (vLac 2 mmol/L)+2.276 (VO2max)+12.706 Morgan 1989 1 10 Well-trained Time (min) VO 2max 0.45 >0.05 vVO 2max 0.87 <0.01 Vel at 4 mmol/L 0.82 <0.01 RE 0.64 <0.05

Int. J. Environ. Res. Public Health2020,17, 8289 8 of 23 Table 3.Cont. Author Year Sex n Level Dependent Variable Independent Variable r p R 2 SEE Petit 1997 1 15 Trained Vel Ventilatory threshold 0.95 0.96 Vel HR def (km/h) 10,000 (km/h)=1.03 (Vel De ection HR) Berg 1998 1 34 Mod trained Time 10,000 m BMI and Mesomorphy 0.61 0.38 7.3 10,000 (min)=4.12 (BMI) 4.5 (Mesomorphy) 29.1 0 19 Mod trained Time 10,000 m Endomorphy 0.64 0.41 6.5 10,000 (min)=37+3.3 (Endomorphy) Evans 1995 0 31 Highly trained 10,000 Pace (m/min) VO 2max 0.89 0.05 0.8 Lac Threshold 0.89 0.05 0.8 VO 2(ml/kg FFM/min) 0.81 0.05 0.66 VO 2in LT 0.84 0.05 0.71 Takeshima 1995 1 51 Trained 10,000 vel (m /s) VO 2in LT (ml/kg/min) 0.78 0.62 nr Age VO 2in LT 0.81 0.67Age nr Workout (min) 10,000 (m/s)=4.371+0.037 (VO2in LT) 0.031 (Age)+0.005 (Workout) 0.82 0.335 r: correlation coe cient;p: signi cance level; R 2 : coe cient of determination; SEE: standard error of the estimate; VO2max: maximal oxygen uptake;vVO2max: velocity at VO2max; WO: workouts; vAT: velocity at anaerobic threshold; Lact 4: velocity at 4 mmol/L; vLact 2: velocity at 2 mmol/L; RE: running economy; vHR def: velocity at heart rate de ection; BMI: body mass index; FFM: fat-free mass; LT: lactate threshold; AT: anaerobic threshold; IAT: individual anaerobic threshold; HR: heart rate; Max Lact: maximal lactate; SK: skinfold.

This review presents mathematical models to estimate performance in long-distance running events.