Automated Remodelling of Connectors in Fixed Partial Dentures
Abstract
:1. Introduction
2. Materials and Methods
2.1. CAD-Modelling
2.1.1. Automatic Connector Detection
- Find the smallest bounding box B0 (with faces focclusal, fgingival, fmesial, fdistal, flingual and fbuccal) for the FPD mesh geometry MFPD using the bounding box function in Grasshopper. Connect the centre of the smallest faces of B0 (fdistal and fmesial) with the line L1, see Figure 2a.
- Generate 300 equally spaced planes Ei along the line L1 that are perpendicular to L1. Find the intersection curves Ci between the planes Ei and the FPD mesh (MFPD), see Figure 2b.
- Define the plane Emid that lies in the middle between the faces focclusal and fgingival of Box B0. Define the plane Emid2 that lies in the middle between the faces flingual and fbuccal of Box B0.
- Create bounding rectangles Ri for all intersection curves Ci, with the rectangle’s sides parallel to the faces of the box B0, see Figure 2c.
- Divide each bounding rectangle Ri into an occlusal rectangle Ri-occlusal and a gingival rectangle Ri-gingival using Emid, see Figure 2c.
- Compute the surface areas (Ai-occlusal and Ai-gingival) of each bounding rectangle (Ri-occlusal and Ri-gingival). Find the local minima of Ai-occlusal (denoted as αj) and of Ai-gingival (denoted as βj), see Figure 2d. The minima are used to define the position of the connectors. As the connectors may be oblique, the minima for the occlusal and gingival sides are calculated separately.
2.1.2. Connector Adjustment
- Define Lo as the upper edge of the previously computed bounding rectangle Ri-occlusal at the position of αj (minimum detected in step 6 in the previous section). Define Lg as the lower edge of Ri-gingival at the position of βj. Define a plane EmidCon that contains Lo and Lg.
- Define a Cartesian coordinate system (xyz), whereas the origin is defined by the point, which lies in Emid, Emid2 (see step 3 in the previous section) and EmidCon. The x-axis points from the origin in the direction of the point that is obtained by Emid2 crossing Lo. The y-axis lies in EmidCon and points to the buccal side (defined by the previously computed bounding Box B0). The z-axis is chosen perpendicular to the x- and y-axis.
- Compute the distances of all points of the FPD mesh to the plane EmidCon and select all points that are closer to the plane than w ( < w), whereas w is a user-defined parameter (w = 1 mm in this study). These selected points are called Pi-C2 and their position is altered in the following steps to adjust the connectors.
- Starting from the point set Pi-C2 select all points with x > 0, which are the points close to the occlusal side, see Figure 3c. These selected points are called Pi-occlusal.
- For each point in Pi-occlusal calculate the distance to the x-y plane (equals EmidCon) and y-z plane. These distances are called and
- Compute a new x-coordinate xnew(i) for each point Pi-occlusal, see Figure 3b. B(t) is a bézier type function, x(i) is the old x-coordinate and k is a parameter chosen in step 7. The equations were:
- Calculate the cross-sectional area A2 of connector C2 and iteratively adjust the value of the parameter k in Equation (1) using Galapagos in Grasshopper until A2 matches the predefined input area value Ainput. The optimization was stopped after an accuracy of ± 0.001 mm2 was achieved.
- Reconstruct the FPD mesh using the updated vertices via the Grasshopper function construct mesh.
2.1.3. Implant Support for the FPD
2.2. Material Properties, Contact Models, Boundary Conditions and Mesh Size
Component | Material | Young’s Modulus [GPa] | Poisson’s Ratio |
---|---|---|---|
Implant 1 | Titanium grade 4 | 104.5 | 0.37 |
Abutment 1 | Titanium grade 4 | 104.5 | 0.37 |
Implant screw 1 | Titanium grade 5 | 114.0 | 0.33 |
Cement layer 2 | Glass ionomer cement | 14.3 | 0.33 |
FPD 3 | Zirconium dioxide | 210 | 0.27 |
Cortical bone 4 | - | 13.7 | 0.3 |
Transition zone | - | 13.7 to 1.37 (graded) | 0.3 |
Cancellous bone 4 | - | 1.37 | 0.3 |
2.3. Evaluation of Results
3. Results
4. Discussion
5. Clinical Relevance
6. Conclusions
- The proposed algorithm enables automatic detection of the connector position and parameterized adjustment of the cross-sectional area of the connectors from various directions.
- Reducing the connector area from the gingival side has a major influence on the tensile stresses, whereas the middle connector in a 4-unit FPD is most vulnerable regarding a cross-sectional area reduction.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Stress Increase in %, When Distal Connector Area 10% Reduced | Stress Increase in %, When Distal Connector Area 20% Reduced | |||||
---|---|---|---|---|---|---|
Dis. Con | Mid. Con | Mes. Con | Dis. Con | Mid. Con | Mes. Con | |
Iso | 36 | 0 | 1 | 77 | 0 | 1 |
Gin | 81 | 1 | −1 | 152 | 1 | 0 |
Occ | 9 | 0 | 0 | 27 | −1 | −1 |
Lin | 6 | 1 | 0 | 31 | 1 | 1 |
Buc | 64 | 0 | 1 | 123 | −1 | 0 |
Stress Increase in %, When Middle Connector Area 10% Reduced | Stress Increase in %, When Middle Connector Area 20% Reduced | |||||
---|---|---|---|---|---|---|
Dis. Con | Mid. Con | Mes. Con | Dis. Con | Mid. Con | Mes. Con | |
Iso | 0 | 33 | 0 | 3 | 71 | −1 |
Gin | 0 | 72 | −5 | 1 | 137 | −6 |
Occ | 1 | 13 | 3 | 4 | 36 | 6 |
Lin | 0 | 6 | 2 | 1 | 14 | 5 |
Buc | 1 | 44 | 0 | 2 | 101 | −3 |
Stress Increase in %, When Mesial Connector Area 10% Reduced | Stress Increase in %, When Mesial Connector Area 20% Reduced | |||||
---|---|---|---|---|---|---|
Dis. Con | Mid. Con | Mes. Con | Dis. Con | Mid. Con | Mes. Con | |
Iso | 1 | −1 | 19 | −1 | 0 | 55 |
Gin | −1 | −1 | 57 | 0 | −1 | 128 |
Occ | −1 | 0 | 11 | 0 | 4 | 24 |
Lin | 0 | 4 | 5 | 0 | 3 | 30 |
Buc | 0 | 2 | 36 | −1 | −1 | 91 |
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Jemaa, H.; Eisenburger, M.; Greuling, A. Automated Remodelling of Connectors in Fixed Partial Dentures. Dent. J. 2023, 11, 252. https://doi.org/10.3390/dj11110252
Jemaa H, Eisenburger M, Greuling A. Automated Remodelling of Connectors in Fixed Partial Dentures. Dentistry Journal. 2023; 11(11):252. https://doi.org/10.3390/dj11110252
Chicago/Turabian StyleJemaa, Hassen, Michael Eisenburger, and Andreas Greuling. 2023. "Automated Remodelling of Connectors in Fixed Partial Dentures" Dentistry Journal 11, no. 11: 252. https://doi.org/10.3390/dj11110252
APA StyleJemaa, H., Eisenburger, M., & Greuling, A. (2023). Automated Remodelling of Connectors in Fixed Partial Dentures. Dentistry Journal, 11(11), 252. https://doi.org/10.3390/dj11110252