This investigation presents the numerical development of a fully porous tibial knee implant that is suggested to alleviate the clinical problems associated with current prostheses that are fully solid. A scheme combining multiscale mechanics and topology optimization is proposed to handle the homogenized analysis and property tailoring of the porous architecture with the aim of reducing the stiffness mismatch between the implant and surrounding bone. The outcome of applying this scheme is a graded lattice microarchitecture that can potentially offer the implant an improved degree of load bearing capacity while reducing concurrently bone resorption and interface micromotion. Asymptotic Homogenization theory is used to characterize the mechanics of its building block, a tetrahedron based unit cell, and the Soderberg fatigue criterion to represent the implant fatigue resistance under multiaxial physiological loadings. The numerical results suggest that the overall amount of bone resorption around the graded porous tibial stem is 26% lower than that around a conventional, commercially available, fully dense titanium implant of identical shape and size. In addition, an improved interface micromotion is observed along the tibial stem, with values at the tip of the stem as low as 17 µm during gait cycle and 22 µm for deep bend compared to a fully dense implant. This decrease in micromotion compared to that of an identical solid implant made of titanium can reasonably be expected to alleviate post-operative end of stem pain suffered by some patients undergoing surgery at the present time.

这项研究提出了一种完全多孔的胫骨膝关节植入物的数值开发方法，可以缓解与目前完全牢固的假体相关的临床问题。提出了一种结合多尺度力学和拓扑优化的方案来处理多孔结构的均质化分析和特性调整，目的是减少植入物与周围骨骼之间的刚度不匹配。应用该方案的结果是渐变的晶格微体系结构，可以潜在地为植入物提供更高程度的负载能力，同时减少骨吸收和界面微运动。渐近均质化理论用于表征其构造块（基于四面体的晶胞）的力学特性，和Soderberg疲劳准则来表示多轴生理载荷下的植入物抗疲劳性。数值结果表明，梯度多孔胫骨干周围的骨吸收总量比形状和尺寸相同的常规，可商购的完全致密的钛植入物周围的骨吸收量低26％。此外，沿着胫骨茎部观察到界面微动得到了改善，与完全致密的植入物相比，步态周期中茎部尖端的值低至17 µm，深度弯曲时的值低至22 µm。与相同的钛制固体植入物相比，这种微动作的减少可以合理地预期减轻目前一些接受手术的患者所遭受的茎干疼痛。