Advanced Mathematical Methods in Dental Bioengineering and Biomaterials Machining.

This article presents a systematic analysis of the application of advanced mathematical and computational approaches in dental bioengineering, with a focus on biomaterials processing and machining-related technologies. The aim is to critically synthesize current knowledge on the use of numerical simulations, statistical modeling, and algorithm-based methods in the analysis and optimization of technological processes in dentistry. The review was conducted following the PRISMA framework to ensure a transparent and reproducible selection of relevant studies addressing the intersection of dental applications, manufacturing processes, and computational modeling. The results reveal that the current research does not constitute a unified modeling framework, but rather a heterogeneous set of approaches targeting specific aspects of biomaterial processing. The analyzed studies demonstrate the application of finite element analysis, empirical statistical models, and geometry-based computational methods, particularly in processes such as drilling and grinding of ceramic dental materials. These approaches enable detailed analysis of mechanical and thermal loading conditions, as well as partial optimization of process parameters. However, their applicability is often limited by their empirical nature, lack of integration, and insufficient linkage to real-time process control. The synthesis highlights a significant research gap in the development of integrated and multiphysics modeling frameworks capable of combining mechanical, thermal, and geometrical aspects of machining processes. Future research should focus on the implementation of digital twins, adaptive process control, and personalized modeling strategies to enhance the accuracy, efficiency, and predictability of dental biomaterial processing.