## 1 Introduction  
Dental implants made of dense titanium alloys (Ti) are widely used to restore damaged tooth functionality due to their excellent biocompatibility [1, 2]. Despite numerous advantages of these implants, such as natural appearance, improved speech and comfort, and ability to prevent bone loss in the jaw [3], they may cause stress shielding and bone resorption which depends on many factors such as bone quality, mechanical stimulus, implant design, and so on. Bone quality refers to the overall health of bone tissue and is determined by several factors, including bone volume fraction and microarchitecture. The mechanical properties of bone, such as elasticity modulus and yield strength, are also important indicators of bone quality. [PERSON] et al. [4] have used high-resolution micro-CT images and micro-finite-element analysis to examine the microarchitecture of trabecular bone and its effect on mechanical stimuli. They have quantified the changes in the apparent Young's modulus of bone tissue with varying levels of porosities and found that as porosity increases, there is a decrease in the apparent Young's modulus. Another study comparing osteoporoptic and healthy bone elastic properties [5] has shown that the yield strength of osteoporoptic bone tissue is lower than that of healthy bone tissue. This indicates that the bone tissue of individuals with osteoporosis may be weaker and more susceptible to fractures. These studies provide insights into the complex relationship between bone microarchitecture, including porosity and mechanical properties [6]. So dense implant designs are not the best choice for different bone qualities. After implantation, osseointegration (fusion of the dental implant with the surrounding bone) occurs at peri-implant which depends on the bone health, design of the implant, loadings, and other biological factors. Ossointegration, the process of direct structural and functional connection between living bone and the surface of the implant, is a critical factor in the long-term success of dental implants. Although full osseointegration, where the implant becomes completely integrated with the surrounding bone tissue, is the desired outcome. A previous study showed that partial osseointegration can pose a potential risk that may compromise implant stability and reliability [7] and that unfavorable changes in trabecular bone architecture due to bone remodeling can lead to implant failure as well. Dental implants present challenges for researchers and clinicians due to their high mismatch material properties between implant and host bones. One of the most significant complications is stress shielding [8; 9], which occurs when the high Young's modulus of the dense Ti implant does not match the lower Young's modulus of the surrounding bone, leading to a reduced load on the bone and a subsequent decrease in bone density [10; 11]. To overcome these challenges, researchers are continuously exploring innovative strategies to minimize the risk of stress shielding and improve the longevity and success of implants [12; 13]. One potential solution is the use of materials with lower Young's modulus, such as porous Ti, which could provide a better match with the bone and reduce the risk of implant failure [14; 15]. Porous Ti has become increasingly important in modern dentistry due to its low Young's modulus, strong biocompatibility, great corrosion resistance, and highly interconnected porous structure to aid osseointegration [16]. The advancement of additive manufacturing (AM) has paved the way for the creation of complex-shaped architectures from CAD data [17], enabling the production of topologically optimized porous implants [18]. The impact of porosity and osseointegration on mechanical performance (i.e., strength and stiffness) of topologically optimal designs of implants has been assessed in numerous studies [19; 20]. Porosity and performance are crucial design parameters that affect the overall performance of implants [21].