The curve of dental arch in normal occlusion

The development of human dentition from adolescence to adulthood has been the subject of extensive study by numerous dentists, orthodontists and other experts in the past. While prevention and cure of dental diseases, surgical reconstitution to address teeth anomalies and research studies on teeth and development of the dental arch during the growing up years has been the main concerns across the past decades, in recent years, substantial effort has been evident in the field of mathematical analysis of the dental arch curve, particularly of children from varied age groups and diverse ethnic and national origins. The proper care and development of the primary dentition into permanent dentition is of major importance and the dental arch curvature, whose study has been related intimately by a growing number of dentists and orthodontists to the prospective achievement of ideal occlusion and normal permanent dentition, has eluded a proper definition of form and shape. Many eminent authors have put forth mathematical models to describe the teeth arch curve in humans. Some have imagined it as a parabola, ellipse or conic while others have viewed the same as a cubic spline. Still others have viewed the beta function as best describing the actual shape of the dental arch curve. Both finite mathematical functions as also polynomials ranging from 2nd order to 6th order have been cited as appropriate definitions of the arch in various studies by eminent authors. Each such model had advantages and disadvantages, but none could exactly define the shape of the human dental arch curvature and factor in its features like shape, spacing and symmetry/asymmetry. Recent advances in imaging techniques and computer-aided simulation have added to the attempts to determine dental arch form in children in normal occlusion. This paper presents key analysis models & compares them through some secondary research study.