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 ( r eff ) and the effective carrying capacity ( K eff ). Each scaffold can thus be positioned on an R/K design map, where R = r eff / r 0 reflects relative kinetic enhancement and K * = K eff / K 0 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.