Analytical Modeling of the Interaction of a Four Implant-Supported Overdenture with Bone Tissue

Abstract

Today, an interdisciplinary approach to solving the problems of implantology is key to the effective use of intraosseous dental implantations. The functional properties of restoration structures for the dentition depend significantly on the mechanical stresses that occur in the structural elements and bone tissues in response to mastication loads. An orthopedic design with a bar fixation system connected to implants may be considered to restore an edentulous mandible using an overdenture. In this study, the problem of the mechanics of a complete overdenture based on a bar and four implants was formulated. A mathematical model of the interaction between the orthopedic structure and jawbone was developed, and a methodology was established for the analytical study of the stress state of the implants and adjacent bone tissue under the action of a chewing load. The novelty of the proposed model is that it operates with the minimum possible set of input data and provides adequate estimates of the most significant output parameters that are necessary for practical application. The obtained analytical results are illustrated by two examples of calculating the equivalent stresses in implants and the peri-implant tissue for real overdenture designs. To carry out the final assessment of the strength of the implants and bone, the prosthesis was loaded with mastication loads of different localization. In particular, the possibilities of loading the prosthesis in the area of the sixth and seventh teeth were investigated. Recommendations on the configuration of the distal cantilever of the overdenture and the acceptable level and distribution of the mastication load are presented. It was determined that, from a mechanical point of view, the considered orthopedic systems are capable of providing long-term success if they are used in accordance with established restrictions and recommendations.

Keywords: bar fixation system; contact interaction; dental implant; distal cantilever; overdenture; stress state.

Figure 1

Four implant-retained mandibular bar overdenture scheme: 1—implant; 2—bar; 3—screw; 4—removable overdenture; H and d are the length and the diameter of implant.

Figure 2

Individual components of the bar structure during the manufacturing process: (a) bar, (b) secondary overdenture frame, and (c) removable overdenture.

Figure 3

Calculation scheme of the force interaction of the elements of the bar structure as an assembly (implants–bar–overdenture).

Figure 4

Original coordinate system (the $$OZ$$ axis is directed at the reader): red—implants, blue—pole.

Figure 5

Central coordinate system (the $$Cz$$ axis is directed at the reader): red—implants, blue—pole.

Figure 6

Scheme of the interaction of the implant with bone tissue: h is small layer thickness, d is the implant diameter.

Figure 7

Numbering scheme and determination of the coordinates of the teeth and implants of a removable overdenture (the first variant of implant placement): red—implant number, white—tooth number.

Figure 8

Dependence of the maximum equivalent stresses in implants on the location of the mastication load (the first variant of implant placement).

Figure 9

Comparative analysis of maximum equivalent stresses in implants at different mastication load locations (the first variant of implant placement).

Figure 10

Dependence of maximum equivalent stresses in bone tissue on the location of the mastication load (the first variant of implant placement).

Figure 11

Comparative analysis of maximum equivalent stresses in bone tissue at different localizations of mastication load (the first variant of implant placement).

Figure 12

Numbering scheme and determination of the coordinates of the teeth of a removable overdenture (the second variant of implant placement): red—implant number, white—tooth number.

Figure 13

Dependence of maximum equivalent stresses in implants on the localization of the mastication load (the second variant of implant placement).

Figure 14

Comparative analysis of maximum equivalent stresses in implants at different localizations of the mastication load (the second variant of implant placement).

Figure 15

Dependence of maximum equivalent stresses in bone tissue on the location of the mastication load (the second variant of implant placement).

Figure 16

Comparative analysis of maximum equivalent stresses in bone tissue at different localizations of the mastication load (the second variant of implant placement).