A systems model of training for patients in phase 2 cardiac rehabilitation

A Fitness-Fatigue Model of Performance in Peripheral Artery Disease: Predicted and Measured Effects of a Pain-Free Exercise Program

Banister impulse-response (IR) model estimates the performance in response to the training impulses (TRIMPs). In 100 patients with peripheral artery disease (PAD), we tested by an IR model the predictability of the effects of a 6-month structured home-based exercise program. The daily TRIMPs obtained from prescribed walking speed, relative intensity and time of exercise determined the fitness-fatigue components of performance. The estimated performance values, calculated from the baseline 6-min and pain-free walking distance (6MWD and PFWD, respectively) were compared with values measured at visits through regression models. Interval pain-free walking at controlled speed prescribed during circa-monthly hospital visits (5 ± 1) was safely performed at home with good adherence (92% of scheduled sessions, 144 ± 25 km walked in 50 ± 8 training hours). The mean TRIMP rose throughout the program from 276 to 601 a.u. The measured 6MWD and PFWD values increased (+33 m and +121 m, respectively) showing a good fit with those estimated by the IR model (6MWD: R² 0.81; PFWD: R² 0.68) and very good correspondence (correlation coefficients: 0.91 to 0.95), without sex differences. The decay of performance without training was estimated at 18 ± 3 weeks. In PAD, an IR model predicted the walking performance following a pain-free exercise program. IR models may contribute to design and verify personalized training programs.

An Improved Version of the Classical Banister Model to Predict Changes in Physical Condition

In this paper, we formulate and provide the solutions to two new models to predict changes in physical condition by using the information of the training load of an individual. The first model is based on a functional differential equation, and the second one on an integral differential equation. Both models are an extension to the classical Banister model and allow to overcome its main drawback: the variations in physical condition are influenced by the training loads of the previous days and not only of the same day. Finally, it is illustrated how the first model works with a real example of the training process of a cyclist.

Modeling the responses to resistance training in an animal experiment study

The aim of the present study was to test whether systems models of training effects on performance in athletes can be used to explore the responses to resistance training in rats. 11 Wistar Han rats (277 ± 15 g) underwent 4 weeks of resistance training consisting in climbing a ladder with progressive loads. Training amount and performance were computed from total work and mean power during each training session. Three systems models relating performance to cumulated training bouts have been tested: (i) with a single component for adaptation to training, (ii) with two components to distinguish the adaptation and fatigue produced by exercise bouts, and (iii) with an additional component to account for training-related changes in exercise-induced fatigue. Model parameters were fitted using a mixed-effects modeling approach. The model with two components was found to be the most suitable to analyze the training responses (R(2) = 0.53; P < 0.001). In conclusion, the accuracy in quantifying training loads and performance in a rodent experiment makes it possible to model the responses to resistance training. This modeling in rodents could be used in future studies in combination with biological tools for enhancing our understanding of the adaptive processes that occur during physical training.

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

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.