Spirometric assessment of emphysema presence and severity as measured by quantitative CT and CT-based radiomics in COPD

Background The mechanisms underlying airflow obstruction in COPD cannot be distinguished by standard spirometry. We ascertain whether mathematical modeling of airway biomechanical properties, as assessed from spirometry, could provide estimates of emphysema presence and severity, as quantified by computed tomography (CT) metrics and CT-based radiomics. Methods We quantified presence and severity of emphysema by standard CT metrics (VIDA) and co-registration analysis (ImbioLDA) of inspiratory-expiratory CT in 194 COPD patients who underwent pulmonary function testing. According to percentages of low attenuation area below − 950 Hounsfield Units (%LAA-950insp) patients were classified as having no emphysema (NE) with %LAA-950insp < 6, moderate emphysema (ME) with %LAA-950insp ≥ 6 and < 14, and severe emphysema (SE) with %LAA-950insp ≥ 14. We also obtained stratified clusters of emphysema CT features by an automated unsupervised radiomics approach (CALIPER). An emphysema severity index (ESI), derived from mathematical modeling of the maximum expiratory flow-volume curve descending limb, was compared with pulmonary function data and the three CT classifications of emphysema presence and severity as derived from CT metrics and radiomics. Results ESI mean values and pulmonary function data differed significantly in the subgroups with different emphysema degree classified by VIDA, ImbioLDA and CALIPER (p < 0.001 by ANOVA). ESI differentiated NE from ME/SE CT-classified patients (sensitivity 0.80, specificity 0.85, AUC 0.86) and SE from ME CT-classified patients (sensitivity 0.82, specificity 0.87, AUC 0.88). Conclusions Presence and severity of emphysema in patients with COPD, as quantified by CT metrics and radiomics can be estimated by mathematical modeling of airway function as derived from standard spirometry. Electronic supplementary material The online version of this article (10.1186/s12931-019-1049-3) contains supplementary material, which is available to authorized users.


Supplemental Material: Theoretical background and description of ESI method
In the past many studies in human subjects have shown the presence of a functional association between the airflow at mouth, the instantaneous volume of the lung, and the pressure applied on the surface of the lung. [1][2][3] In particular the analysis of the maximum expiratory flow-volume (MEFV) curve has been used for many years to characterize the functional behavior of the bronchial tree and the surrounding parenchyma.
In this study we tested a parametric biomechanical model representing a theoretical approximation of the shape of the descending limb of the MEFV curve to assess the severity of emphysema in patients with COPD by spirometry. The Emphsyema Severity Index (ESI) application software is based on a mathematical model developed to approximate the MEFV curve of each subject to ultimately provide a quantitative score ranging from 1 to 10. The ESI score represents a practical application of a biomechanical model developed a priori. No retrospective statistical inference or standardization of input parameters was required.
The main physical principle inspiring this approach is that the pressure lost (Pl) at a given time t along an airway segment could be considered proportional to a specific friction factor (Ff), the air density (d) and the air velocity (v), similarly to the theory of the circular ducts. An inverse relationship between the pressure lost and the mean diameter (D) of the airway is also supposed obtaining the following equation (better known as Darcy equation): (1) By considering the hypothesis of laminar flow, the calculus of the friction factor depends uniquely on the Reynolds number Rn k1 is a constant and the variable vis is the dynamic viscosity of the air fluid.
Substituting equations (2) and (3) into equation (1) we obtain the pressure drop in the case of laminar flow as: Considering a circular airway section we can write the air velocity in the segment as: where Φ is the resulting flow and D is the mean inner diameter of the airway segment. Substituting equation (6) into (5) we obtain the association between the airflow and the pressure lost, as of laminar flow hypothesis.
Equation (7) shows that the relationship between the pressure lost and the airflow seems to be linear in laminar flow approximation.
In the past some authors proposed lumped parametric models to fit the MEFV curve acquired during maximal effort test, taking into account linear association profiles between airways resistance and airflow. The studies obtained acceptable waveforms and good fitting of the curve. 3 At variance with past models, we proposed a mathematical model for the approximation of the MEFV curve developed under the hypothesis that the airflow measured at the mouth through standard spirometry could not be considered as a laminar flow. As a consequence the Ff variable could not be where K3 and Ff are constant values for a specific patient and airway segment, d is the air density, Φ is the resulting flow and D is the mean inner diameter.
One interesting observation deriving from these mathematical models is that the pressure drop Pl along a segment is inversely proportional to the diameter of the airway power 4 or 5. It follows that a minimal variation in airway diameter is amplified to cause a significant pressure drop along the whole segment.
This shows how the regulation of the respiratory airways walls efficiently modulates the airflow.
Another important characteristic of the non-laminar flow hypothesis is the quadratic association between the airflow and the pressure lost along the airways, while this relationship would be linear if the measured flow at the mouth was hypothesized as laminar.
As a consequence the lumped parametric model of a maximal flow volume curve implemented in the ESI model is based on the following non-linear equation: (10) where the numerator represents a simple model of the quadratic pressure profile during a maximal function test and the denominator represents the model of the exhaled volume-dependent quadratic airways resistance profiles. The best a1, a2 and a3 coefficients are estimated iteratively by the software, which performs a Least Mean Squares fitting of the descending limb of the MEFV curve.
Once the best mathematical model fitting the raw data is obtained, the software then proceeds to the calculus of the first and second derivatives for the specific fitted MEFV curve. This procedure is performed to search the inflection point Vf of the descending limb of the MEFV curve.
The point Vf is very important in assessing emphysema severity, as its abscissa represents the lung volume (in liters) at which the resistance profile becomes influenced by the lost in elastic recoil due to the parenchymal destruction. This creates an inversion in the concavity of the descending limb of the MEFV curve.
This type of analysis was not possible before because of the hypothesis of the above-mentioned linear models. Indeed, in those models the second derivatives profiles did not admit acceptable solutions to the equation (11).
After the solutions of equation (11)  The Figure 1S shows a box-plot representing the %LAA -950insp distribution (I-III quartiles) in the validation dataset in three subgroups: no emphysema (NE, %LAA -950insp <6), moderate emphysema (ME, 6≤ %LAA -950insp <14), and severe emphysema (SE, %LAA -950insp ≥14). The intersection of the ESI values (red line) with the corresponding box indicates the most probable severity class for the case analyzed. In this example the case analyzed had a low probability of having SE. Figure 2S. ROC curve over the range of FEV 1 to differentiate NE from ME. AUC 0.74, 0.62 sensitivity and 0.80 specificity. Figure 3S. ROC curve over the range of FEV 1 to differentiate ME from SE. AUC 0.77, 0.77 sensitivity and 0.67 specificity. Figure 4S. ROC curve over the range of FEV 1 /FVC to differentiate NE from ME. AUC 0.83, 0.68 sensitivity and 0.88 specificity. Figure 5S. ROC curve over the range of FEV 1 /FVC to differentiate ME from SE. AUC 0.82, 0.82 sensitivity and 0.76 specificity.