From Static Material Design to Predictive Open-Loop Control via Chemistry–Architecture Coupling in a Moving-Boundary Reaction–Diffusion Framework

Abstract

Bioactive silicate ceramics, wollastonite (CaSiO3), diopside (CaMgSi2O6), and apatite–wollastonite glassceramics constitute a unique class of bone-regeneration materials whose therapeutic action is intrinsically coupled to their own degradation. Yet the field continues to design these materials as static objects, optimizing initial composition, porosity and elastic modulus while evaluating outcomes at fixed endpoints, tacitly ignoring the central fact that the physicochemical microenvironment they create evolves continuously and irreversibly. We argue that this temporal evolution is not a side effect but the therapeutic mechanism itself, and that it can be engineered predictively. This review consolidates and mathematically hardens the emerging paradigm of spatiotemporal trajectory engineering: the pre-encoded, open-loop programming of a degrading scaffold’s full physicochemical trajectory through coupled control of ceramic network chemistry and pore-network architecture. Three advances over prior treatments are delivered. First, the solid-state chemistry foundation is deepened: Qn speciation from 29Si MAS-NMR is mapped onto hydration versus hydrolysis activation barriers; the incongruent dissolution cascade (cation exchange → silica-gel layer → hydroxycarbonate apatite nucleation) is formalized as a coupled surface–gel-layer–precipitation problem; and the autocatalytic OH−-feedback loop that drives local pH spikes is quantified, together with surface-specific XPS O 1s BO/NBO deconvolution as the front-tracking metric. Second, the static reaction–diffusion model is upgraded to a moving-boundary erosion formulation: an explicit porosity-evolution law, a dynamically self-consistent effective diffusivity, and interstitial convective (Brinkman) transport are introduced, yielding a two-dimensional Damköhler–Péclet regime map that delineates four phenomenologically distinct trajectory regimes, reaction-limited, diffusion-limited, convective washout, and convection-amplified dosing, plus a coupled design corridor where trajectory classes diverge maximally. Third, biological admissibility is replaced from discrete endpoint thresholds to a continuous phase-indexed Regenerative Target Zone (RTZ) envelope incorporating M1-gating, M2-switch, and HCA-maturation kinetics; and the computational pipeline is extended with functional data analysis (fPCA, DTW), neural ordinary differential equations, physicsinformed neural networks, Hamiltonian Monte Carlo credible tubes, and Bayesian-optimal experimental design. The resulting framework is fully specified, falsifiable, and implementable with open-source tools and standard instrumentation. It reclassifies the design problem from optimizing a material to programming an evolving microenvironment, and because the temporal program is pre-encoded without biological sensing, it qualifies as a passive implant under current regulatory frameworks.