This paper presents a semi-analytical model to describe the action of vertical and 16°-inclined toothbrush filaments onto flat tooth surfaces and into approximal areas. The theory is based on the analytical solution of the beam equation about normal and transversal (shear) forces that deform the filaments. A 15% increase of penetration depth (approximal area model) and a 60% increase of transversal force (tooth surface model) for an inclination angle of 16° compared to a vertical filament were determined. Furthermore, that 16°-inclined filaments are able to transfer higher shear forces to the tooth compared to vertical ones was shown experimentally, which could account for the higher efficiency of plaque removal by inclined filaments compared to vertical filaments. The theoretical findings for manual and oscillating-rotating toothbrushes are discussed, and implications for their design are drawn.
vertical and inclined toothbrush filaments; shear forces; penetration depth; power toothbrush; mechanical plaque removal; oscillating-rotating technology