Rationale and resources for teaching the mathematical modeling of athletic training and performance

Abstract

A number of professions rely on exercise prescription to improve health or athletic performance, including coaching, fitness/personal training, rehabilitation, and exercise physiology. It is therefore advisable that the professionals involved learn the various tools available for designing effective training programs. Mathematical modeling of athletic training and performance, which we henceforth call "performance modeling," is one such tool. Two models, the critical power (CP) model and the Banister impulse-response (IR) model, offer complementary information. The CP model describes the relationship between work rates and the durations for which an individual can sustain them during constant-work-rate or intermittent exercise. The IR model describes the dynamics by which an individual's performance capacity changes over time as a function of training. Both models elegantly abstract the underlying physiology, and both can accurately fit performance data, such that educating exercise practitioners in the science of performance modeling offers both pedagogical and practical benefits. In addition, performance modeling offers an avenue for introducing mathematical modeling skills to exercise physiology researchers. A principal limitation to the adoption of performance modeling is a lack of education. The goal of this report is therefore to encourage educators of exercise physiology practitioners and researchers to incorporate the science of performance modeling in their curricula and to serve as a resource to support this effort. The resources include a comprehensive review of the concepts associated with the development and use of the models, software to enable hands-on computer exercises, and strategies for teaching the models to different audiences.

Quantification of Training and Competition Loads in Endurance Sports: Methods and Applications

“…Attempts have been made over the past 4 decades to describe training adaptations and predict competition performance by means of mathematical models that rely on training quantification and performance outcomes. 17,35,36,49,50 Nevertheless, no single physiological marker has been identified that can accurately quantify the fitness and fatigue responses to training or predict competition performance. This implies that sport scientists probably need to direct their efforts toward the measurement of markers that reflect an athlete's global capacity to respond or adapt to training.…”

Modeling Physical Activity Behavior Change

“…Indeed, Clarke and Skiba [1] argue that there remains a "dearth of longitudinal studies to guide long-term training program designs." There remain many challenges in integrating diverse sensor data, as well as challenges related to what to do with the information derived from these data.…”

A nonlinear model for the characterization and optimization of athletic training and performance

“…Conceptually, this constraint ensures that a longer period of training sufficiently prepares an individual for more intense short-term training effects. CTL can be calculated as (8) where the chronic training load C n and the daily training stress σ n on the n th day were used along with the time constant τ = 42 days to determine the chronic training load C n + 1 on day n + 1.…”

“…The model accounted for two primary physiological components: the positive effects of training, called fitness, and the negative effects of training, called fatigue. Several studies have built upon the Banister model with promising results [5,6,8,10,12,15]. However, these studies also recognized that the Banister model was based on linear systems theory, which limits its accuracy and applicability.…”

“…It is the incorporation of these well-known phenomena into a performance modeling framework that provides a more realistic and necessary counter balance; the inclusion of these phenomena also allows performance to be optimized. However, despite the potential concerns associated with the linear modeling approach, it has been used to successfully inform training strategies for many athletes by approximating optimal recovery times between workouts, predicting the success of training regimens, and determining how an athlete should taper before a competition [5,7,8,10,12,13,15].…”