| The loss of individual free-end posterior tooth is very common in clinical practice. Removable partial denture, fixed restoration and implant restoration are the three main types of restoration for it. Removable partial denture has the disadvantages of inconvenience and discomfort, and the indication and high fee are the problems for implant restoration. Patients tend to choose fixed restoration as their first choice due to the advantages of small size, similarity to natural teeth in morphology, comfort, beauty, and high efficiency of mastication. However, because of the particularity of free-end posterior teeth loss, we can only choose the free-end posterior tooth as the abutment of restoration. The application of cantilever bridges restoration has yet to be disputed due to torque force of the abutment. The key point is the rational selection of free-end fixed bridge which is the main subject studied by domestic and foreign scholars.In the study, a 3-D finite-element model included the mandibular 43, 44,45,46,47 was constructed by spiral CT scanning, the software of reverse engineering and finite element analysis. Firstly, construct a 3-D finite-element model of the mandibular 43, 44,45,46,47 and their surface supporting tissues. Secondly, to obtain two sets of models: 1. Free-end fixed bridge prosthetic designs in the case of loss of free-end 47 by modifying the prosthetic design based on the 3-D finite-element model. Model 1: mandibular⑥7 restoration. Model 2: mandibular⑤⑥7 restoration. Model 3: mandibular④⑤⑥7 restoration. Model 4: mandibular⑥7'restoration(7':pontics reduced 1/2 of its mesiodistal diameter). Model 5: mandibular⑤⑥7'restoration. 46,47 respectively Model 6: mandibular④⑤⑥7'restoration; 2. Free-end fixed bridge prosthetic designs in the case of loss of free-end 46 and 47. Model 1: mandibular④⑤6 7 restoration. Model 2: mandibular③④⑤6 7 restoration. Model 3: mandibular④⑤67'restoration. Model 4: mandibular③④⑤67'restoration. To observe the stress distribution of periodontal surface supporting tissues in different prosthetic design with central concentrated loads and oblique distributing load. To analyze the effect of different abutments and the reduction in mesiodistal diameter of the pontics on stress of abutments when the free-end 46 and free-end 45, and to get the rational choice of restoration and offer reference for in clinical work. The results indicate: The 3-D finite element models, which have a good agreement with natural teeth, have the similarity in both morphology and geometric, which provide a further reliable theoretical basis for biomechanics analysis. Stress distribution of periodontal surface supporting tissues in different prosthetic design when 47 is the free-end: in model 1, the stress of periodontal membrane is much greater than the pericementum potential, which is not favorable to the health of supportive periodontal tissues. In addition, it is not recommended in clinical work. In model 2, the stress distribution of abutments near the edentulous space is dramatically reduced, and it is favorable to the health of supportive periodontal tissues. The occlusal force in model 3 is dispersed better than that in model 2, but the distribution of stress do not change significantly. And the need of the preparation of another molar does not meet the principle of prosthetic design. It is reasonable in model 4 to reduce the mesiodistal diameter. Stress distribution of periodontal surface supporting tissues in different prosthetic design when 46, 47 are the free-end: in model 1, 2, 3, the stress of periodontal membrane is much greater than the pericementum potential, which is not favorable to the health of supportive periodontal tissues and it is not recommended in clinical work. The stress of periodontal membrane is 2 times as that of normal loading, so it is not recommended except when the proximal space is narrow with good condition of periodontal tissues or occulsal teeth is removable partial denture.Conclusion: to obtain 3-D finite-element model of the mandibular 43, 44,45,46,47, and analyze the stress distribution of periodontal surface supporting tissues in different prosthetic design when the loss of individual free-end posterior tooth. The conclusions are as follows:1. Compare to different prosthetic designs of free-end fixed bridge when the periodontal tissues are healthy, the rational choice is taking 45,46 as the abutment when 47 is the free-end. Increasing the number of splinted abutments and reduction of the mesiodistal diameter would reduce the stress on root tips of the abutments. As a result, reduction of the mesiodistal diameter is necessary to reduce the stress of the abutments.2. The stress of supportive bone tissues gets dramatically uniform when increasing the number of splinted abutment from 1 to 2. However, there is no significantly change when increasing the number of splinted abutments from 2 to 3. It is can be indicated in the study that although the increasing only in the number of splinted abutments would reduce the concentration of stress, the stress of periodontal tissues would not have a dramatically change. As a result, we should not increase the number of abutments unreasonable, or on the contrary, it would be difficult to get the common path of insertion.3. It indicates that the abutment will suffer more with oblique distributing load than with central concentrated loads. Compare to different loading conditions and loading capacity, the direction of loading will have more impact on stress distribution. It can not only influence the value of stress, but also the distribution. So it would be better to avoid the lateral load which can do more harm to the fixed bridge.4. The stress distribution mainly focuses on root tip and cervix of the abutments. It indicates that it does not fit for the patients who get absorption of alveolar bone and periodontal lesion to take the fixed bridge restoration.5. The health of periodontal tissues of abutment near the absence area is important, because the maximum stress usually distribute on the periodontal tissues near the absence area.
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