On the application of the mathematical method of dimensional analysis to the six-minute walk test

The six-minute walk test (SMWT) is one of the simplest and most widely available methods of assessing exercise tolerance. At the same time, the issues of presentation and interpretation of its results have not been fully studied yet.
It is known that in the case of unavailability of formal laws of the phenomenon, the method of dimensional analysis can be applied. This method, first proposed by Fourier and developed in the works of Rayleigh, Prandtl, Buckingham and others, is quite successfully used in physics, chemistry, engineering, economics and very rarely in biology and medicine.

The essence of the method is that the dependent variable is represented as a set of variables that are independent (or weakly dependent) on each other. This paper presents a general model of the dependence of the distance R traveled by a person on 8 variables: human parameters (mass, height, tolerance parameter), time and environmental characteristics (gravity potential, air density and viscosity, the coefficient of friction of the sole with the surface). Two
basic theorems of the dimensionality analysis method were applied to the general model: the dimensionality theorem of the quantity and Buckingham’s theorem (about finding the number of dimensionless complexes). Difficulties associated with the study of the general model do not allow us to form dependences on other quantities, which are much more difficult to vary in the experiment than others, for example, to control the density and viscosity of the medium, the gravitational potential of the Earth.
The possibility of reducing the number of model variables and forming a system of new, simpler models that allow explicit description of the motion process from all variables is shown.
A latent parameter is introduced into the model, i.e. a degree of tolerance of a person to motion which it is offered to characterize as an energy parameter. A method for its quantitative estimation and comparison of people by this parameter is proposed. In terms of assessing the dynamics of change in motion tolerance, it is necessary to further study the dependence of this parameter on time.

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