Hydrodynamic Damping of Tooth Movement

¹ Department of Microbiology, College of Dentistry, New York University, New York, New York

The resistance to the axial intrusion of a tooth was due to the activity of viscous and inertial forces acting within the periodontium. Separation of the effects of these two forces was made by means of the Reynold's number and the spring constant. These dimensionless constants were derived from measurements of the oscillation of rat maxillary incisors in their sockets in living rats and within 5 minutes after sacrifice. Using mean values for the velocity under loads of 35 Gm. and 183 Gm. from 39 experiments, the Reynold's number R = p l v/v was found both in the living and in the dead animal to be 10^-4. The differences were not significant. The dynamic similitude of the responses demonstrated that the resistance was dominated by the viscous forces whether there was extracellular fluid flow or not. Using mean values for the period of oscillation under the different loads, the spring constant k = m (2/T)² for the living rat was 250 per cent and 2,000 per cent greater, respectively, than for the dead rat, showing that a spring mechanism was operated by fluid flow. With the small Reynold's number, the morphological conditions existing within the periodontium, and the rate of the intrusion under the different loads, it was suggested that a squeeze film involving the interstitial fluid was the first damping effect, which plays a part in the load carrying capabilities of the periodontium. As the squeeze film became depleted without being refed and as the pressure continued, the second damping effect was provided by the passage through the walls of the smaller blood vessels of fluid, entrapped because of constriction of the vessels by the stretched periodontal fibers during intrusion of the tooth.

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