The standard fitness-fatigue model (FFM) is known to include several limitations described by the linearity assumption, the independence assumption and the deterministic assumption. These limitations ensure that the modelled response to chronic training does not match the complexity observed in practice. The purpose of part II of this review series was to describe previous extensions to the standard FFM to address these limitations, providing key mathematical insights and resources, to both explain technical elements and enable researchers and practitioners to fit these extended models to their own data. To address the linearity assumption of the standard FFM and the associated limitation that doubling the training load predicts twice the performance improvement, two distinct extensions are reviewed including the addition of a non-linear transform to training inputs and inclusion of non-linear terms within the system of differential equations. To address the independence assumption where the response to a training session is unaffected by previous sessions, a popular extension where fatigue is updated as an exponentially weighted moving average of previous training loads is reviewed. Finally, the review introduces the concept of state-space models where uncertainty in the estimates of fitness, fatigue and performance measurement can be directly modelled eliminating the unsuited deterministic assumption of the standard FFM. The review also highlights how state-space models can be further expanded to include features such as the Kalman filter where parameter estimates can be updated with incoming performance measurements to better predict and manipulate training to optimise performance. Collectively, the range of topics covered in this review series and the resources provided should enable researchers and practitioners to better investigate the extensive area of FFMs and determine in what contexts models can assist with training monitoring and prescription.
SWINTON, P., STEPHENS HEMINGWAY, B., RASCHE, C., PFEIFFER, M. and OGOREK, B. 2021. Traditional and contemporary approaches to mathematical fitness-fatigue models in exercise science: a practical guide with resources. Part II. SportRxiv [online]. Available from: https://doi.org/10.31236/osf.io/5qgc2