Osseous condition of the mandible was regarded as a key factor influencing stability of implants in the early stage. Finite element analysis was used to assess the effect of bone mass density and alveolar bone resorption (double factors) on stress in a four-unit implant restoration of a free-end edentulous posterior mandible. A 3D finite element model was constructed for a single-sided free-end edentulous mandible (from mandibular first premolar to mandibular second molar) containing threaded dental implants. Mandible sensitivity modes were constructed with different alveolar bone resorption levels for normal conditions as well as mild, moderate and severe periodontitis, respectively. Based on the mass density of cancellous bone for four types of bones as the sensitivity parameter, two implant design modes were constructed: Model A (four-unit fixed bridge supported by three implants, implant positions were 34, 36 and 37) and model B: 34 × 36, 37 (37: a single implant crown) (34 × 36: three-unit fixed bridge supported by two implants, implant positions were 34 and 36). A total of 32 sensitivity-based finite element models, grouped in two groups, were constructed. Stress distribution and maximum von Mises stress on cortical bone and cancellous bone around the implant, as well as the surface of implant were investigated by using ABAQUS when vertical loading and 45° oblique loading were applied, respectively. When vertical loading was applied on the implant, maximum von Mises stress on the cortical bone around the implant was assessed to be 4.726 MPa - 13.15 MPa and 6.254 MPa - 13.79 MPa for groups A and B, respectively; maximum stress on the cancellous bone around the implant was 2.641 MPa - 3.773 MPa and 2.864 MPa - 4.605 MPa, respectively; maximum stress on the surface of implant was 14.7 MPa - 21.17 MPa and 21.64 MPa - 30.70 MPa, respectively. When 45° oblique loading was applied on the implant restoration, maximum von Mises stress on the cortical bone around the implant was assessed to be 42.08 MPa - 92.71 MPa and 50.84 MPa - 102.5 MPa for groups A and B, respectively; maximum stress on the cancellous bone around the implant was 4.88 MPa - 25.95 MPa and 5.227 MPa - 28.43 MPa, respectively; maximum stress on the surface of implant was 77.91 MPa - 124.8 MPa and 109.2 MPa - 150.7 MPa, respectively. Stress peak on the cortical bone and that on cancellous bone around the implant increased and decreased with the decrease in bone mass density, respectively. Stress peak on alveolar bone increased with alveolar bone resorption when oblique loading was applied. 1. Both alveolar bone resorption and bone mass density (double factors) are critical to implant restoration. Bone mass density may exhibit a more pronounced impact than alveolar bone resorption. 2. From the biomechanical perspective, types I and II bones are preferred for implant restoration, while implantation should be considered carefully in the case of type III bones, or those with less bone mass density accompanied by moderate to severe alveolar bone loss. 3. Splinting crowns restoration is biomechanically superior to single crown restoration.

中文翻译：

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骨密度和牙槽骨吸收对下颌后牙游离牙颌种植体修复应力的影响：双因素敏感性有限元分析

早期下颌骨骨质状况被认为是影响种植体稳定性的关键因素。有限元分析用于评估骨量密度和牙槽骨吸收（双因素）对游离端无牙颌后下颌骨四单元种植修复体应力的影响。为包含螺纹牙种植体的单侧游离端无牙颌（从下颌第一前磨牙到下颌第二磨牙）构建了 3D 有限元模型。分别针对正常情况以及轻度、中度和重度牙周炎，用不同的牙槽骨吸收水平构建下颌敏感性模式。以四种骨的松质骨质量密度为敏感参数，构建了两种种植体设计模式：模型A（四单元固定桥，三个种植体支撑，种植体位置分别为34、36和37）和模型B ：34 × 36、37（37：单个种植体冠）（34 × 36：由两个种植体支撑的三单元固定桥，种植体位置分别为 34 和 36）。总共构建了 32 个基于灵敏度的有限元模型，分为两组。利用ABAQUS分别研究了垂直加载和45°倾斜加载时种植体周围皮质骨、松质骨以及种植体表面的应力分布和最大von Mises应力。当对种植体施加垂直载荷时，A组和B组种植体周围皮质骨的最大von Mises应力分别为4.726 MPa - 13.15 MPa和6.254 MPa - 13.79 MPa；种植体周围松质骨的最大应力分别为2.641 MPa - 3.773 MPa和2.864 MPa - 4.605 MPa；种植体表面最大应力分别为14.7 MPa - 21.17 MPa和21.64 MPa - 30.70 MPa。当对种植体修复体施加45°倾斜加载时，A组和B组种植体周围皮质骨的最大von Mises应力分别为42.08 MPa - 92.71 MPa和50.84 MPa - 102.5 MPa；种植体周围松质骨的最大应力分别为4.88 MPa - 25.95 MPa和5.227 MPa - 28.43 MPa；种植体表面最大应力分别为77.91 MPa - 124.8 MPa和109.2 MPa - 150.7 MPa。随着骨密度的降低，皮质骨和种植体周围松质骨的应力峰值分别增大和减小。当施加倾斜载荷时，牙槽骨上的应力峰值随着牙槽骨吸收而增加。 1. 牙槽骨吸收和骨量密度（双重因素）对于种植体修复至关重要。骨质量密度可能比牙槽骨吸收表现出更明显的影响。 2. 从生物力学的角度来看，I型和II型骨优先用于种植修复，而III型骨则应慎重考虑种植，或骨量密度较低并伴有中度至重度牙槽骨丢失的患者。 3. 夹板冠修复在生物力学上优于单冠修复。