Association of respiratory integer and fractional-order models with structural abnormalities in silicosis

Integer and fractional-order models have emerged as powerful methods for obtaining information regarding the anatomical or pathophysiological changes that occur during respiratory diseases. However, the precise interpretation of the model parameters in light of the lung structural changes is not known. This study analyzed the associations of the integer and fractional-order models with structural changes obtained using multidetector computed tomography densitometry (MDCT) and pulmonary function analysis.

Integer and fractional-order models were adjusted to data obtained using the forced oscillation technique (FOT). The results obtained in controls (n = 20) were compared with those obtained in patients with silicosis (n = 32), who were submitted to spirometry, body plethysmograph, FOT, diffusing capacity of the lungs for carbon monoxide (DLCO), and MDCT. The diagnostic accuracy was also investigated using ROC analysis.

The observed changes in the integer and fractional-order models were consistent with the pathophysiology of silicosis. The integer-order model showed association only between inertance and the non-aerated compartment (R = -0.69). This parameter also presented the highest associations with spirometry (R = 0.81), plethysmography (-0.61) and pulmonary diffusion (R = 0.53). Considering the fractional-order model, the increase in the poorly aerated and non-aerated regions presented direct correlations with the fractional inertance (R = 0.48), respiratory damping (R = 0.37) and hysteresivity (R = 0.54) and inverse associations with its fractional exponent (R = -0.62) and elastance (-0.35). Significant associations were also observed with spirometry (R = 0.63), plethysmography (0.37) and pulmonary diffusion (R = 0.51). Receiver operator characteristic analysis showed a higher accuracy in the FrOr model (0.908) than the eRIC model (0.789).

Our study has shown clear associations of the integer and fractional-order parameters with anatomical changes obtained via MDCT and pulmonary function measurements. These findings help to elucidate the physiological interpretation of the integer and fractional-order parameters and provide evidence that these parameters are reflective of the abnormal changes in silicosis. We also observed that the fractional-order model showed smaller curve-fitting errors, which resulted in a higher diagnostic accuracy than that of the eRIC model. Taken together, these results provide strong motivation for further studies exploring the clinical and scientific use of these models in respiratory medicine.