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.