A mathematical taxonomy to evaluate the biomechanical quality of the human foot

Abstract

The relationship between a functional disorder of the foot and the geometric configuration of its anatomical structure has been a subject of continuing interest among clinicians who are concerned with the various biomechanical disabilities of the foot. A survey of the literature shows that various geometric criteria and models have been proposed to arrive at a diagnosis and select an appropriate plan of treatment. Although these models have been used in biomechanical evaluation with varying degrees of success, their verbal descriptions and measurements are considered as over-simplifications with respect to both classification and discrimination. A more realistic model should induce a classification of sufficient refinement to produce a differential diagnosis among clinically significant variations in the biostructure of the foot.Based on a rationale of anatomical, physiological, and clinical considerations, the one-quarter ellipsoid is selected as the model. Mathematical methods are used to classify human feet into a continuum of points representing the entire range of variations in foot shape. There is located an optimal point (foot) from which every other point is measured by means of a distance function. Each numerical deviation of a particular foot reflects the biomechanical quality of that foot.The concept of a biomechanically optimal foot which has ideal function as opposed to normal function offers the practitioner a quantitative rationale for the diagnosis and treatment of mechanical foot disorders.