Abstract <p>This study quantitatively evaluated the effects of bulk porosity and the average surface roughness on curved surfaces. In this study, we investigate the effects of bulk porosity and surface roughness of TPMS-based Gyroid structures fabricated via selective laser melting on various biocompatibility factors through quantitative linear regression analysis. The results demonstrate that bulk porosity and surface roughness influence biocompatibility parameters in distinct and complementary ways. Bulk porosity exhibited a strong correlation (R² &gt; 0.9) with osteogenesis-related factors, including osteoblastic cell activity, BMM, ALP-p, and OPG, indicating its critical role in promoting cell adhesion, proliferation, and early-stage osteogenesis. The high correlation with OPG suggests that bulk porosity contributes significantly to bone tissue stability and regeneration by fostering a conducive microenvironment. Conversely, resorption-related markers (RANKL) and late-stage osteogenesis markers (OCL) showed relatively low correlations with bulk porosity, indicating its primary influence on early osteogenesis processes. In contrast, surface roughness demonstrated strong correlations (R² &gt; 0.9) with resorption-related markers (RANKL) and late-stage osteogenesis markers (OCL). This highlights the importance of curved surface characteristics in modulating bone remodeling processes. The strong correlation with OCL (R² &gt; 0.98) underscores the role of surface roughness in regulating late-stage osteogenesis, while moderate correlations with ALP-p and OPG (0.38 &lt; R² &lt; 0.53) suggest a limited impact on early-stage osteogenesis. These findings reveal that bulk porosity and surface roughness play complementary roles in biocompatibility. Bulk porosity enhances osteogenesis and tissue stability by providing expanded surface area and optimized pore structures, whereas surface roughness directly influences bone resorption and late-stage cellular activity, particularly on curved surfaces. The integration of bulk porosity and surface roughness as design parameters is crucial for optimizing the balance between bone formation and resorption.</p> Graphical Abstract <p></p>