## 4 Discussion
The range of strain observed in this state was between 1000 \(\upmu\)e and 1500 \(\upmu\)e, which is the range where the balance of bone resorption and formation becomes equal and the bone remodeling process occurs. However, in the cases of weak bone, the octahedral shear strain was observed to be above 3000 \(\upmu\)e, which is the pathologic overload stage that may lead to bone damage. It is important to note that weak bone can be a result of various factors [51] such as age, disease, or previous trauma, and it can significantly affect the success of dental implants. Additionally, the atrophied state, which is the state of bone that is not well adapted to the implant, was found to include the bulk Ti, P76, and P53 implants with the lower octahedral shear strain of less than 1000 \(\upmu\)e. In this case, the stress shielding phenomenon may occur, where the implant takes on most of the load and the surrounding bone experiences reduced stress. This can lead to bone resorption and implant loosening over time. It's important to keep in mind that the mechanostat hypothesis is just one theory for explaining bone remodeling, and other factors such as hormonal changes and local cytokine signaling can also influence bone adaptation to implants [52]. Further research is needed to fully understand the complex interplay between these factors and how they affect the long-term success of dental implants. Bulk Ti implants have a significantly higher elastic modulus (114 GPa) than human bones, which can result in stress shielding and eventually lead to bone resorption and aseptic loosening of the implants [53]. It is essential to consider the stiffness of implants when planning implant procedures, as using implants with low stiffness can improve long-term implant stability and prevent complications. It's important to take into consideration the state of osseointegration and bone quality, as partial osseointegration can pose a potential risk to the longevity of dental implants and may cause damage to the surrounding bone tissue [7]. People who suffer from osteoporosis will inevitably have less bone stiffness, are more prone to fracture [54]. Bone quality has been examined in many studies using finite element methods [55; 56; 57]. Our findings concur with their conclusion that deterioration in bone quality precedes a worsening of stress and strain. Recent studies have suggested that 3D-printed porous titanium implants can be a suitable choice for improving osseointegration capacity and prolonging the functional life of the implant [58; 59]. This is mainly due to the ability of porous implants to promote bone ingrowth and osseointegration, leading to better long-term outcomes. With the advances in computer-assisted design and topological optimization technologies, 3D printing has become a revolutionary process that allows for the precise fabrication of porous titanium implants with tailored porosity and pore size, which can further enhance their performance. However, it's important to note that enhancing secondary stability at the bone-implant interface remains a challenge in implant dentistry. Several approaches have been proposed to improve implant stability, including surface modifications and coating techniques, as well as the use of growth factors and stem cells to promote bone regeneration [60]. Further research is needed to fully understand the mechanisms underlying implant stability and to develop more effective strategies for enhancing osseointegration and reducing implant failures. Selecting the appropriate implant material and design is critical for ensuring the long-term success of dental implants. The use of porous implants with low stiffness can be an effective approach for improving implant stability and promoting osseointegration. Advances in 3D printing technology have enabled the precise fabrication of such implants, opening up new possibilities for improving the outcomes of implant procedures.