The utility of mathematical fitness-fatigue models for assisting with the planning of physical training for sport: from in silico experiments employing synthetic data, lower-bound operational conditions and model estimation, to the development of software resources for future research.

Stephens Hemingway, Benedict H.

Abstract

The greatest potential application of mathematical models in sport science is to predict future performance of individual athletes in response to training, with sufficient accuracy to assist with planning of training programs and short tapering periods. The most widely known and investigated set of mathematical models include the fitness-fatigue models (FFMs). However, despite over 45 years of FFM study, problems remaining within the research base and gaps in existing knowledge have limited interpretation of prior research, and prevented progression toward practical implementation. These limitations include: 1) inadequate study of model validity in prior experimental study as a result of unsatisfactory model testing; 2) a disorganised literature body without a connective narrative linking previous research and providing consistent recommendations for the requirements and direction of future study; 3) limitations in the structure of basic FFMs matched by little awareness of extensions that have been proposed to address them; 4) no consideration of experimental factors and methods that may interact with model accuracy (e.g. measurement error, testing frequency, parameter estimation); 5) limited practical resources elucidating key concepts, and no tools available to facilitate processes required to fit and evaluate more promising FFMs. Subsequently the aims of this PhD were to: 1) systematise the FFM literature body, providing sufficient detail and structure to the point where there exists a consistent narrative threading the historical literature, pertinent concepts, and contemporary work to address limitations in basic FFM structure; 2) conduct original study of key experimental factors (measurement error and testing-frequency) and methods of model estimation that may affect model accuracy or utility; 3) identify and raise awareness of alternative FFMs - beyond the standard model and advanced methods - that reflect more promising avenues for future research; 4) develop flexible code tools that facilitate future study and address the current gap in available resources. The first aim was achieved by comprehensive review, balancing mathematical rigor with clarity in the communication of concepts and methods, ranging from the standard model to the most advanced FFMs. The second aim was achieved by two novel studies that developed in silico experimental designs, and which represented prerequisite work prior to any further study of model validity. Study 1 quantified the effects of key experimental factors (measurement noise and testing-frequency) on lower-bound model accuracy in the standard FFM, demonstrating that testing practices comprising high error will provide unsatisfactory results and that greater deleterious effects of error exist at lower testing frequencies. Study 2 focused on suitability of a traditional quasi-Newton algorithm for fitting FFMs, by assessing starting point sensitivity and existence/implications of local extrema. Study 2 demonstrated that the model-fitting problem is more challenging than researchers have previously acknowledged and that the presence of many local extrema even in the standard FFM may now necessitate global optimisation approaches. The third and fourth aims were achieved by development of extensive code resources in the R programming language for fitting and evaluating FFMs, facilitating future study under the most promising models/methods. The original research and systematised literature body provides clearer direction for future FFM research, guidance with respect to key experimental factors/methods (e.g. measurement practices, estimation, model testing), and reflects the most up-to-date resource available for researchers interested in FFMs. The developed code tools meet the need for flexible practical resources for researchers, and the novel experimental designs developed for the two studies provide a unique and cost-effective approach to study FFMs and potentially other phenomena in sport science.

Citation

STEPHENS HEMINGWAY, B.H. 2021. The utility of mathematical fitness-fatigue models for assisting with the planning of physical training for sport: from in silico experiments employing synthetic data, lower-bound operational conditions and model estimation, to the development of software resources for future research. Robert Gordon University, PhD thesis. Hosted on OpenAIR [online]. Available from: https://doi.org/10.48526/rgu-wt-1603154

• Thesis Type: Thesis
• Deposit Date: Feb 23, 2022
• Publicly Available Date: Feb 23, 2022
• Keywords: Fitness-fatigue models; Literature organisation; Knowledge organisation; Experimental methods; Sport sciences
• Public URL: https://rgu-repository.worktribe.com/output/1603154
• Publisher URL: https://doi.org/10.48526/rgu-wt-1603154
• Award Date: May 31, 2021