The ability to predict the systematic decrease of power during physical exertion gives valuable insights into health, performance, and injury. This review surveys the research of power-based models of fatigue and recovery within the area of human performance. Upon a thorough review of available literature, it is observed that the twoparameter critical power model is most popular due to its simplicity. This two-parameter model is a hyperbolic relationship between power and time with critical power as the power-asymptote and the curvature constant denoted by W′. Critical power (CP) is a theoretical power output that can be sustained indefinitely by an individual, and the curvature constant (W′) represents the amount of work that can be done above CP. Different methods and models have been validated to determine CP and W′, most of which are algebraic manipulations of the twoparameter model. The models yield different CP and W′ estimates for the same data depending on the regression fit and rounding off approximations. These estimates, at the subject level, have an inherent day-today variability called intra-individual variability (IIV) associated with them, which is not captured by any of the existing methods. This calls for a need for new methods to arrive at the IIV associated with CP and W′. Furthermore, existing models focus on the expenditure of W′ for efforts above CP and do not model its recovery in the sub-CP domain. Thus, there is a need for methods and models that account for (i) the IIV to measure the effectiveness of individual training prescriptions and (ii) the recovery of W′ to aid human performance optimization.
Purpose This study (i) investigates the effect of recovery power (Prec) and duration (t rec) on the recovery of the curvature constant (W′) of the power–duration relationship, (ii) compares the experimentally measured W′ balance to that predicted (W′ bal) by two models (SK2 and BAR), and (iii) presents a case of real-time performance optimization using the critical power (CP) concept. Methods Seven competitive amateur cyclists performed a ramp test to determine their V˙O2peak and gas exchange threshold, two to four 3-min all-out tests to determine CP and W′, and nine intermittent cycling tests to investigate W′ recovery. The intermittent cycling tests involved a 2-min constant work-rate interval above CP, followed by a constant work-rate recovery interval below CP (Prec and t rec were varied), followed by a 3-min all-out interval. Results There was a significant two-way interaction between Prec and t rec on W′ recovery, P = 0.004 (η 2 = 0.52). Simple main effects were present only with respect to Prec at each t rec. The actual W′ balance at the end of the recovery interval was less than the W′ bal predicted by both SK2 (P = 0.035) and BAR (P = 0.015) models. The optimal strategy derived from the subject-specific recovery model reduced the race time by 55 s as compared with the self-strategy. Conclusions This study has shown that in a recovery interval, Prec has a greater influence than t rec on W′ recovery. The overprediction of W′ bal from SK2 and BAR suggests the need for individualized recovery parameters or models for sub-CP exercise. Finally, the optimal strategy results provide encouraging signs for real-time, model-based performance optimization.
Improving a cyclist performance during a timetrial effort has been a challenge for sport scientists for several decades. There has been a lot of work on understanding the physiological concepts behind it. The concepts of Critical Power (CP) and Anaerobic Work Capacity (AWC) have been discussed often in recent cycling performance related articles. CP is a power that can be maintained by a cyclist for a long time; meaning pedaling at or below this limit, theoretically, can be continued for infinite amount of time. However, there is a limited source of energy for generating power above CP. This limited energy source is AWC. After burning energy from this tank, a cyclist can recover some by pedaling below CP. In this paper we utilize the concepts of CP and AWC to mathematically model muscle fatigue and recovery of a cyclist. Then, the models are used to formulate an optimal control problem for a time trial effort on a 10.3 km course located in Greenville SC. The course is simulated in a laboratory environment using a CompuTrainer. At the end, the optimal simulation results are compared to the performance of one subject on CompuTrainer.
Fatigue has been proposed to increase the risk of knee injury. This study tracked countermovement jump, knee isometric strength, and kinetics and kinematics in 8 female soccer players (experimental group) during an anticipated sidestep maneuver before and after two matches played over a 43-h period. Time points were: Before and after match 1 (T0 and T1), 12 h after the first match (T2), and immediately after the second match (T3). A control group participated only in practice sessions. Isometric knee extension strength decreased by 14.8% at T2 (p = 0.003), but knee flexion was not affected until T3, declining by 12.6% (p = 0.018). During the sidestep maneuver, knee joint degrees of flexion at initial contact was increased by 17.1% at T3, but maximum knee and hip angle at initial contact were unchanged. Peak resultant ground reaction force (GRF) increased by 12.6% (p = 0.047) at T3 (3.03 xBW) from 2.69 xBW at T0, while posterior GRF was significantly higher than T0 at all three subsequent time points (T1 = 0.82 ± 0.23 xBW, T2 = 0.87 ± 0.22 xBW, T3 = 0.89 ± 0.22 xBW). Anterior tibial shear force increased significantly (p = 0.020) at T3 (1.24 ± 0.12 xBW) compared to T1 (1.15 ± 0.13 xBW), an 8.8% increase. Lateral tibial shear force was significantly higher at both T1 (0.95 ± 0.20 xBW) and T3 (1.15 ± 0.38 xBW) compared to T0 (0.67 ± 0.25 xBW). These findings suggest that participation in a soccer match has significant effects on both physical performance parameters and kinetics/kinematics during a sidestep cut, but these can be more pronounced after a second match with short rest.
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