RA-Trabecular: A Percolation-Based Framework for Modeling Trabecular Bone Degradation in Rheumatoid Arthritis Using Voronoi Tessellation and Effective Mechanical Connectivity

RA-Trabecular is a conceptual and computational framework for modeling trabecular bone degradation as a topological and mechanical failure process rather than solely as a loss of bone mass. The framework integrates concepts from cellular solids theory, Voronoi tessellation, percolation theory, graph connectivity analysis, and finite element modeling to investigate how progressive trabecular erosion affects the structural competence of cancellous bone. A central contribution of this work is the introduction of the Index of Effective Mechanical Connectivity (IRCE), a dimensionless metric designed to quantify the relationship between mechanical stiffness, network connectivity, and trabecular anisotropy. The framework hypothesizes that trabecular degradation can be understood as a critical transition in which a load-bearing network loses structural continuity and fragments into disconnected clusters. Although initially developed in the context of rheumatoid arthritis, the proposed methodology is intended as a general computational framework applicable to multiple disorders involving trabecular deterioration, including osteoporosis, psoriatic arthritis, osteoarthritis, avascular necrosis, osteomyelitis, metastatic bone disease, peri-implant bone loss, and fragility fracture risk assessment. This deposit contains the conceptual paper describing the theoretical foundations of the RA-Trabecular framework, the formal definition of IRCE, the proposed simulation architecture, and the validation roadmap for future empirical studies based on micro-CT and biomechanical datasets. https://github.com/Vlattice/ra-trabecular Keywords: trabecular bone, rheumatoid arthritis, percolation theory, Voronoi tessellation, finite element analysis, biomechanics, computational rheumatology, network science, bone mechanics, structural connectivity.