Mathematical analysis of running performance and world running records

The objective of this study was to develop an empirical model relating human running performance to some characteristics of metabolic energy-yielding processes using A, the capacity of anaerobic metabolism (J/kg); MAP, the maximal aerobic power (W/kg); and E, the reduction in peak aerobic power with the natural logarithm of race duration T, when T greater than TMAP = 420 s. Accordingly, the model developed describes the average power output PT (W/kg) sustained over any T as PT = [S/T(1 - e-T/k2)] + 1/T integral of T O [BMR + B(1 - e-t/k1)]dt where S = A and B = MAP - BMR (basal metabolic rate) when T less than TMAP; and S = A + [Af ln(T/TMAP)] and B = (MAP - BMR) + [E ln(T/TMAP)] when T greater than TMAP; k1 = 30 s and k2 = 20 s are time constants describing the kinetics of aerobic and anaerobic metabolism, respectively, at the beginning of exercise; f is a constant describing the reduction in the amount of energy provided from anaerobic metabolism with increasing T; and t is the time from the onset of the race. This model accurately estimates actual power outputs sustained over a wide range of events, e.g., average absolute error between actual and estimated T for men's 1987 world records from 60 m to the marathon = 0.73%. In addition, satisfactory estimations of the metabolic characteristics of world-class male runners were made as follows: A = 1,658 J/kg; MAP = 83.5 ml O2.kg-1.min-1; 83.5% MAP sustained over the marathon distance. Application of the model to analysis of the evolution of A, MAP, and E, and of the progression of men's and women's world records over the years, is presented.     

An analysis of world records in three types of locomotion

The record history of running, swimming and ice-skating, over various distances, was analyzed. A mean period of about 66 years for the 18 male events and of about 50 years for the 14 female events was studied. Over a given distance the velocity (v) was related to the dates of the records minus 1900 (T) according to polynomial functions like: v = a0 + a1T + a2T2 + ..... + anTn. In 21 out of the 32 events equations of first or second degree fitted the experimental data. The mean correlation coefficient was 0.979 +/- 0.019 (+/- S.D.). The ratio between predicted (vlp) and actual value (vl) of the last records was 0.999 +/- 0.010. For T corresponding to v1 (Tl), the rate of record growth was slowing down in 5 events. Hence up to June 1981 a tendency towards an asymptotic v was not yet a general phenomenon. At Tl the range of the relative rate of increase of v (dvp/dT . vlp) was 0.9 . 10(-3) per year (800 m - female running) and 12.4 . 10(-3) per year (800 m - female swimming). dv/dT . vlp in swimming and skating was similar in both sexes but 4 times faster than in male running. Less marked differences were found for female running. A lowering of the cost of transport was probably the main reason of the fast growth of swimming and skating records. The numerical constants calculated from linear regression of v versus the time of the races over different distances did not seem to have a clear physiological meaning, as reported in the previous literature.     

Sprint,agility, strength and endurance capacity in wheelchair basketball players

The aims of the present study were, firstly, to determine the reliability and reproducibility of an agility T-test and Yo-Yo 10 m recovery test; and secondly, to analyse the physical characteristics measured by sprint, agility, strength and endurance field tests in wheelchair basketball (WB) players. 16 WB players (33.06 ± 7.36 years, 71.89 ± 21.71 kg and sitting body height 86.07 ± 6.82 cm) belonging to the national WB league participated in this study. Wheelchair sprint (5 and 20 m without ball, and 5 and 20 m with ball) agility (T-test and pick-up test) strength (handgrip and maximal pass) and endurance (Yo-Yo 10 m recovery test) were performed. T-test and Yo-Yo 10 m recovery test showed good reproducibility values (intraclass correlation coefficient, ICC = 0.74-0.94). The WB players’ results in 5 and 20 m sprints without a ball were 1.87 ± 0.21 s and 5.70 ± 0.43 s and with a ball 2.10 ± 0.30 s and 6.59 ± 0.61 s, being better than those reported in the literature. Regarding the pick-up test results (16.05 ± 0.52 s) and maximal pass (8.39 ± 1.77 m), players showed worse values than those obtained in elite players. The main contribution of the present study is the characterization of the physical performance profile of WB players using a field test battery. Furthermore, we demonstrated that the agility T-test and the aerobic Yo-Yo 10 m recovery test are reliable; consequently they may be appropriate instruments for measuring physical fitness in WB.     

Modelling human power and endurance

A generalised three component hydraulic model has been proposed to represent the human bioenergetic processes relating internal energy stores to performance during exercise, and into recovery. Further development of the model allows testable predictions to be made. In particular in this paper I examine certain hypotheses of chemical fuel shortage as a subgroup of the potential causes of fatigue, and their implications for maximal power and for endurance. The assumption that the limitation to sustainable power is direct proportionality to the glycogen store remaining, appears the most feasible. Based on this assumption, equations for the decline in maximum attainable power over time, the endurance at fixed workrates and the endurance at incremental tests (as a function of the increment slope) are obtained. Using published data for fit males, the maximum exertable power declines after about 6 s at 972 W to very low levels after about 2 min. For constant powers selected between 208 and 927 W, endurance declines from ad infinitum to only 6 s. Endurance at VO2max is predicted to be about 9 min. For incremental exercise tests of slope ranging from 30 W/min to 60 W/min, endurance lessens from 14 to 9 min. In these tests the anaerobic threshold is reached in times between 6 and 3 min. Although the power at termination of a test increases with incremental slope, terminal oxygen consumption is effectively constant. Almost all these model predictions are observed to correspond well with published experimental findings. These results suggest that the model can be used to represent an adequate overview of the operation of the human bioenergetic system.     

Elite endurance athletes and the ACE I allele – the role of genes in athletic performance

Genetic markers that might contribute to the making of an elite athlete have not been identified. Potential candidate genes might be found in the renin-angiotensin pathway, which plays a key role in the regulation of both cardiac and vascular physiology. In this study, DNA polymorphisms derived from the angiotensin converting enzyme (ACE), the angiotensin type 1 receptor (AT1) and the angiotensin type 2 receptor (AT2) were studied in 64 Australian national rowers. Compared with a normal population, the rowers had an excess of the ACE I allele (P<0.02) and the ACE II genotype (P=0.03). The ACE I allele is a genetic marker that might be associated with athletic excellence. It is proposed that the underlying mechanism relates to a healthier cardiovascular system. Received: 20 October 1997 / Accepted: 10 March 1998     

Sprint interval and traditional endurance training induce similar improvements in peripheral arterial stiffness and flow-mediated dilation in healthy humans

Low-volume sprint interval training (SIT), or repeated sessions of brief, intense intermittent exercise, elicits metabolic adaptations that resemble traditional high-volume endurance training (ET). The effects of these different forms of exercise training on vascular structure and function remain largely unexplored. To test the hypothesis that SIT and ET would similarly improve peripheral artery distensibility and endothelial function and central artery distensibility, we recruited 20 healthy untrained subjects (age: 23.3 +/- 2.8 yr) and had them perform 6 wk of SIT or ET (n = 5 men and 5 women per group). The SIT group completed four to six 30-s "all-out" Wingate tests separated by 4.5 min of recovery 3 days/wk. The ET group completed 40-60 min of cycling at 65% of their peak oxygen uptake (Vo2peak) 5 days/wk. Popliteal endothelial function, both relative and normalized to shear stimulus, was improved after training in both groups (main effect for time, P < 0.05). Carotid artery distensibility was not statistically altered by training (P = 0.29) in either group; however, popliteal artery distensibility was improved in both groups to the same degree (main effect, P < 0.05). We conclude that SIT is a time-efficient strategy to elicit improvements in peripheral vascular structure and function that are comparable to ET. However, alterations in central artery distensibility may require a longer training stimuli and/or greater initial vascular stiffness than observed in this group of healthy subjects.     

Noncompatibility of power and endurance training among college baseball players

Exercise professionals seeking to develop evidence-based training programs rely on several training principles demonstrated through research and professional experience. In an effort to further research examining these principles, an investigation was designed and completed to evaluate the compatibility of cardiovascular endurance and neuromuscular power training. Sixteen Division-I collegiate baseball players were divided into two training groups with lower body power measured before and after their college playing season. The two groups differed in training in that one group performed moderate- to high-intense cardiovascular endurance training 3-4 days per week throughout the season, while the other group participated in speed/speed endurance training. A significant difference between groups (P < .05) was identified in the change in lower body power during the baseball season. During the season, the endurance training group decreased an average of 39.50 +/- 128.03 watts while the speed group improved an average of 210.63 +/- 168.96 watts. These data demonstrate that moderate- to high-intense cardiovascular endurance and neuromuscular power training do not appear to be compatible when performed simultaneously. For baseball players, athletes who rely heavily on power and speed, conventional baseball conditioning involving significant amounts of cardiovascular endurance training should be altered to include more speed/power interval training.     

Factors in maximal power production and in exercise endurance relative to maximal power

The relationship of muscle fiber type and mass to maximal power production and the maintenance of power (endurance time to exhaustion) at 36%, 55%, and 73% of maximal power was investigated in 18 untrained but physically active men. Power output was determined at constant pedalling rate (60 rev.min-1) on a cycle ergometer instrumented with force transducers and interfaced with a computer. Maximal power was determined for each subject as the highest one-revolution average power. Fat-free mass was determined by hydrostatic weighing, fat-free thigh volume by water displacement and skinfold measurement, and percentage and area of type II fibers from biopsy specimens taken from the vastus lateralis. Maximal power averaged 771 +/- 149 W with a range of 527-1125 W. No significant correlations were found among percentage of type II fibers, relative area of type II fibers, or fat-free thigh volume and maximal power or endurance times to exhaustion at any percentage of maximal power. Weak but significant relationships were found for fat-free mass with both maximal power (r = 0.57) and endurance time at 73% of maximal power (r = -0.47). These results show maximal power to be more dependent on factors related to body size than muscle-fiber characteristics. The low correlations for so many of the relationships, however, suggest that individuals employ either different combinations of these factors or utilize other strategies for the generation of high power.     

Evaluating the impact of flexible practices on the master surgical scheduling process: an empirical analysis

This study focuses on the master surgical scheduling problem and adds two main contributions. First, it presents a novel mixed integer programming model to support the master surgical schedule production. Second, it uses the model to investigate the impact, in terms of scheduled surgeries, of the flexible management of three critical resources, namely surgical teams, operating rooms and surgical units. Our analysis revealed that to maximise the number of surgeries scheduled, it is sufficient to introduce flexibility with respect to surgical teams and ORs. In fact, if both these resources are managed flexibly, then introducing flexibility with respect to surgical units carries no additional advantages. However, if surgical teams or ORs (or both) are not managed flexibly, then managing surgical units flexibly produces significant benefits. In addition, our study shows that if surgical teams cannot be managed flexibly, then introducing flexibility with respect to ORs yields significant benefits. Similarly, it reveals that if ORs cannot be managed flexibly, then introducing flexibility with respect to surgical teams yields significant benefits as well. The work is based on real data from the Meyer University Children’s Hospital in Florence.     

Towards an e-biology of ageing: integrating theory and data

Ageing is a highly complex process; it involves interactions between numerous biochemical and cellular mechanisms that affect many tissues in an organism. Although work on the biology of ageing is now advancing quickly, this inherent complexity means that information remains highly fragmented. We describe how a new web-based modelling initiative is seeking to integrate data and hypotheses from diverse biological sources.