Martin Weiser, Stefan Zachow
01.01.2021 − 31.12.2022
Stability and longevity of tooth implants not only depend on the chosen implant type and its insertion but also on individual bite forces and bone density. We estimate bite forces from dental CT by machine learning, integrating simulation and measurements in a physics-informed approach. We compare smooth bias approaches and auxiliary task learning.
Complications with bone-anchored dental implants (inflammation, loosening, chipping) up to complete implant loss often occur due to unfavorable loading conditions within bone (at least 7.6% loss within 10 years). The objective of this project is therefore to increase the durability of bone-anchored dental implants, i.e. to minimize implant losses, by improved therapy planning taking into account individual bite forces (i.e. loading conditions in implant and bone).
So far, implant configuration and positioning is based on geometrical aspects only, as obtained from DVT/CBCT imaging. Individual forces acting from the occlusal surfaces of the tooth crowns via the implant into the bone are important, but neglected. The long-term application goal is therefore to enable load-dependent configuration and positioning of implant-supported dentures as well as the design of new modular implants.
The measurement of bite forces is elaborate and usually not performed in clinical routine. However, bite forces affect bone density due to remodeling. Hence, physiological bite force distributions can be inferred from the shape of the jawbone and the bone density distribution therein. The direct project goal is the estimation of bite forces from DVT data.
We will follow two strands of research:
(i) By utilizing the bone tendency to remodel till reaching a natural strain energy state, a finite element model can be established to produce density distributions based on the geometry and biting forces. After model calibration to fit real measured data, pairs of density and stress distribution can be generated. Since the remodeling process is not strictly mechanical, the FEM model is prone to errors on one hand, and on the other hand be too complex a procedure for routine application.
Thus, we will consider
(ii) physics-informed learning for directly learning the desired bone density to bite force mapping. Available measured training data will be scarce, so we aim at integrating measured data with simulated training data. Both data enrichment and auxiliary task learning are considered.
Bone adapts to the local mechanical situation induced by bite force loading and described by linearly elastic solid mechanics:
Bone remodeling is driven by the deviation from a homeostatic equilibrium stored energy density. Local averaging accounts for diffusion of biochemical signals and is necessary for a well-posed remodeling model.
Bone density adaptation follows the remodeling signal Θ. Lower and upper bounds on bone density are formulated as barrier function b. We assume the bone to be well-adapted to the bite forces before loss of the missing tooth, i.e. a stationary state, given by the fixed point of bone remodeling:
The system can be solved by Newton’s method or (pseudo-) time stepping after FE discretization.
a) Initial constant bone density. b) Resulting adapted density. c) Initial strain energy density w d) strain energy density after remodeling
Bite force measurements are expensive and complex, and therefore usually not available in clinical practice – in contrast to CBCT bone density data routinely acquired. Thus, bite forces can be reconstructed from bone density, assuming the remodeling is described correctly:
Necessary regularization can be done by (i) discretization, e.g., total forces left/right,front/back and/or (ii) nonnegativity. As a preliminary study, we investigated identifiability of bone density depending on spatial resolution and noise at a 2D setup.
2D inversion example. a) Ground truth for load on left boundary and resulting deformation. Color code: ρ,
isolines: Θ. b) Identification of boundary force with regularization by coarse discretization, n=2 and n=3.
Limited identifiability of spatially high-frequent force distributions from noisy bone density data. a) Simulated measurement with uniformyl distributed
pointwise noise. b) Identified force distribution for n=6.