A quantitative framework for interpreting rate and capacity effects in oral regenerative scaffolds

Successful oral and periodontal regeneration requires scaffolds that do more than host cells--they must regulate both the tempo and the extent of growth within healing tissues. While proliferation data are routinely quantified, comparisons across materials remain fragmented. We introduce the scaffold-augmented logistic (SAL) framework, a minimal quantitative formalism that organizes scaffold performance within a two-parameter space defined by the effective growth rate (reff) and the effective carrying capacity (Keff). Each scaffold can thus be positioned on an R/K design map, where R = reff/r0 reflects relative kinetic enhancement and K* = Keff/K0 expresses sustainable population capacity with respect to a 2D reference. Applied to in vitro and ex vivo data from oral and periodontal systems, the SAL framework distinguishes R-type (rate-dominated), K-type (capacity-dominated), and hybrid R + K scaffolds. By expressing complex biological outcomes through interpretable parameters, SAL provides a shared quantitative language for scaffold classification and design. It enables model-based reinterpretation of existing data and prediction of design sensitivities, offering a compact quantitative grammar for regenerative scaffold development in oral tissue engineering.