[A mathematical model for the treatment of root surfaces with rigid and flexible instruments]

The objective of this study was to assess the accessibility of root surfaces using stiff instruments in order to evaluate the advantages of a new flexible instrument-set for the treatment of periodontally diseased roots. 100 extracted human teeth were sectioned and histologically prepared. They were divided into two groups each containing 50 sections. Group I showing the interproximal, group II the buccal/lingual morphology. Slides were taken of each section under a constant magnification (3.2x) and a selected number of distances and angles were measured on each section. Using trigonometric functions the following parameters were calculated and set in relation with hypothetical probing depths ranging from 0-15 mm: 1.) instrument length; 2.) change of the instrument angulation; 3.) theoretical deflection of the gums. Statistical analysis was performed using Student's t-test. For a given probing depth the instrument length was independent of the sites and the deflection of the gums. When a deflection of the gums was assumed, the instrument angulation was constant; an exponential decrease of the angulation with increasing probing depth was found with gum deflection. The deflection was increasing with increasing probing depth, showing statistically significant differences between interproximal and buccal/lingual sites (p < or = 0.05). In conclusion the instrument length seems not to be an impeding factor for the accessibility of root surfaces in contrast to the instrument angulation and the fact that teeth are encircled by the gum. Due to morphological reasons stiff instruments seem to be inferior to flexible instruments when a non-surgical root treatment is performed.(ABSTRACT TRUNCATED AT 250 WORDS)