A survey of mathematical models of human performance using power and energy

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 two-parameter 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 two-parameter 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-to-day 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

An Experimental Protocol to Model Recovery of Anaerobic Work Capacity

Models of fatigue are based on physiological parameters such as Critical Power (CP) and Anaerobic Work Capacity (AWC). CP is a theoretical threshold value that a human can generate for an indefinite amount of time and AWC represents a finite expendable amount of anaerobic energy at intensities above CP. There is an increasing interest in developing mathematical models of energy expenditure and recovery for athletic training and human performance. The objective of this research is to propose and validate a model for recovery of AWC during a post exertion recovery interval of cycling. A cycling ergometer study is proposed which involves a VO2max ramp test to determine gas exchange threshold, a 3-min all-out intensity test to determine CP and AWC, and exertion-recovery interval tests to understand recovery of AWC. The results will be used to build a human in the loop control system to optimize cycling performance

Modeling the Expenditure and Recovery of Anaerobic Work Capacity in Cycling

The objective of this research is to model the expenditure and recovery of Anaerobic Work Capacity (AWC) as related to Critical Power (CP) during cycling. CP is a theoretical value at which a human can operate indefinitely and AWC is the energy that can be expended above CP. There are several models to predict AWC-depletion, however, only a few to model AWC recovery. A cycling study was conducted with nine recreationally active subjects. CP and AWC were determined by a 3-min all-out test. The subjects performed interval tests at three recovery intervals (15 s, 30 s, or 60 s) and three recovery powers (0.50CP, 0.75CP, and CP). It was determined that the rate of expenditure exceeds recovery and the amount of AWC recovered is influenced more by recovery power level than recovery duration. Moreover, recovery rate varies by individual and thus, a robust mathematical model for expenditure and recovery of AWC is needed