Purpose: Small airways disease (SAD), a major cause of airflow obstruction in COPD patients, has been identified as a precursor to emphysema. Nevertheless, there is a lack of clinical techniques that can quantify the progression of SAD. We aim to determine if our Parametric Response Mapping (PRM) method to quantify SAD offers insight into lung progression from healthy to emphysema. Materials and Methods: PRM metrics quantifying normal lung (PRMNorm) and functional SAD (PRMfSAD) were generated from CT scans collected as part of the COPDGene study (n=8956). Volume density (V) and Euler-Poincaré Characteristic (χ) maps, measures of extent and coalescence of pocket formations, respectively, were determined for both PRMNorm and PRMfSAD. Association with COPD severity, emphysema, and spirometric measures were assessed via multivariable regression models. Results: Across all GOLD, we observed a strong linear correlation between χfSAD and χNorm (ρ =-0.745, p<0.001). Values of χfSAD and χNorm were found to flip signs in unison between GOLD 2 and 4, demonstrating an inversion in parenchymal topology. For subjects with COPD, multivariable analysis showed that both χfSAD (β of 0.106, p<0.001) and VfSAD (β of 0.065, p=0.004) were independently associated with FEV1% predicted. V and χ measures for PRMfSAD and PRMNorm were independently associated with the amount of emphysema. Conclusions: We demonstrated that χ of fSAD and Norm have independent value when associated with lung function and emphysema, even when considering the amount of each (i.e., VfSAD, VNorm). Our approach for quantifying pocket formations of PRMfSAD from normal lung parenchyma (PRMNorm) may show promise as a CT readout of emphysema onset.