PDL Fiber Slack and the Geometry of Immediate Extrusion

Ecco la descrizione, pronta da incollare nel campo Description di Zenodo (accetta HTML base — grassetto, paragrafi): PDL Fiber Slack and the Geometry of Immediate Extrusion: A Working Hypothesis on Anchorage Loss During Canine Root Distalization This working paper proposes an original geometric model of periodontal ligament (PDL) oblique fiber kinematics and its consequences for anchorage control during canine root distalization, contrasting fixed appliance and clear aligner mechanics. Collagen fibers of the PDL are tension-only elements: a fiber loaded past its working configuration does not resist displacement in the reverse direction, it simply goes slack. Modeling a single oblique fiber (bone-to-cementum, ~45°) under axial tooth displacement shows that reaching a fully re-engaged, oppositely-oriented tension state after extrusive movement requires a total coronal displacement on the order of twice the PDL width (≈300–500 μm) — during which the fiber offers essentially no resistance. This excursion is the same order of magnitude as a single clear aligner stage activation (150–330 μm), but one to two orders of magnitude smaller than the elastic range of a fixed appliance wire or auxiliary spring (1–3 mm). Applied to differential-moment mechanics for canine root distalization, this predicts a structural divergence between the two appliance systems: in fixed mechanics, the wire's elastic range comfortably outlasts the reactive tooth's slack zone, so the intended moment is delivered despite the well-recognized extrusive side effect on the reactive unit (typically the lateral incisor). In aligner mechanics, the shell's usable range per stage is comparable to the slack zone itself, so the reactive unit may fail to develop resistance before the aligner's stored elastic energy is spent — predicting that the couple decays before completing its intended work, independent of attachment design on the canine. The model further distinguishes this immediate, single-activation mechanism from aligner material relaxation and creep, which act on a much slower timescale (hours to days) and cannot account for the same failure mode. A supporting literature review of clinical extrusion rates (≈1–2 mm/week, forced-eruption protocols) versus compression-limited retraction rates (≈0.5–1 mm/month) shows roughly an order-of-magnitude asymmetry, consistent with the mechanistic distinction proposed (apposition-only vs. resorption-limited tooth movement). This is an original theoretical/geometric model, presented as a testable working hypothesis. It has not been experimentally or numerically (FE) validated, and several input parameters (PDL fiber crimp extensibility) are extrapolated from non-PDL collagenous tissue. It is deposited here to establish priority and invite discussion; a fiber-network finite-element model incorporating tension-only elements is proposed as the natural next step for validation. Keywords: periodontal ligament biomechanics; PDL fiber kinematics; orthodontic tooth movement; canine distalization; differential moment mechanics; clear aligners; anchorage control; oblique fibers; tension-only elements