PerioMechanics

Module 04 / 6

Occlusal force vectors

von Mises, principal stress, crestal bone, and regeneration under load

Magnitude without direction is an incomplete load. Most periodontal failures are not 'too many newtons'. They are newtons arriving at an angle the remaining attachment cannot turn into compression.
Plate IV — occlusal force vectorsF at angle θAxial vs shear at the crestF cos θ → distributed in PDLF sin θ → crestal concentrationHotspot: crestal lip
Plate IV — An oblique occlusal vector resolved at the crest: axial compression through the PDL, shear and tensile peaks at the crestal ligament and cortical lip.

We chart mobility. We rarely chart the vector that produced it.

Occlusal force is a vector. It has a point of application, a magnitude, and an angle relative to the long axis. The PDL is reasonably good at turning axial load into a distributed compressive field. It is much less forgiving of a shear component that leverages the crest. This is undergraduate statics. It is also why an apparently modest restoration can undo a careful regenerative procedure.

Two stress measures are worth keeping apart in a teaching lab.

von Mises (or an equivalent scalar) is useful for a heatmap. It answers: where is the material 'working hard'? It does not answer whether that work is compression the graft can live with, or tension that opens a wound.

Principal stress answers the second question. Tension at the crestal PDL, tension at a thin buccal plate, tension across a papilla that was sutured under a lateral vector — these are surgical facts wearing tensor clothing.

The teaching formula used in the simulator is deliberately simple:

  • axial component F cos θ is spread along the ligament,
  • shear component F sin θ is concentrated toward the crest,
  • an equivalent scalar is plotted so a student can see the hotspot move as the angle changes.

It is not a constitutive law. It is a caption you can argue with. That is the correct status of a teaching model.

Regeneration under load is the clinical sting. We do not regenerate in a museum. We regenerate in a mouth that will occlude tomorrow morning. A virtual regenerative plan that never meets a vector is a plan for a patient who does not chew.

In the chair

Do not ask only how hard the patient bites. Ask where the resultant points, and which wall of the defect is in tension when they do.

Educational and illustrative teaching models. Not a medical device. Not for diagnosis, treatment planning, or patient-specific simulation.