I came across this wonderful article of David C. Clarke and Philip F. Skiba on mathematical modeling and want to make sure the readers of the blog get access to it.

Clarke and Skiba have reviewed all the current knowledge on mathematical modeling to predict adaptations to training and to predict performance and have provided all the details about the different methods as well as the summary of all calculations with a spreadsheet.

The article is available here and below you can read the 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 vital 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.

This paper was published on Advances in Physiology Education which is a relatively new journal of the American Physiological Society.

Here is the full reference: 

Clarke DC, Skiba PF. rationale and resources for teaching the mathematical modeling of athletic training and performance. Adv Physiol Educ. 37(2):134-52. June 2013.

If you want to read more about Dr. Skiba’s work you can go here.

Great paper and most of all terrific supplementary material, excellent job @DrPhilipSkiba!

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