The study is being conducted in accordance with Good Clinical Practice standards. The participating sites received favourable opinion from the local ethics committee and approval from the Administration of Radioactive Substances Advisory Committee. All patients provide informed written consent before enrolment in accordance with the Declaration of Helsinki.

### Patients and healthy volunteers

Baseline dynamic ^{18}F-FDG PET/CT scans obtained from the EVOLUTION (COPD, *N* = 10) and the EVOLVE (HV, *N* = 10) studies were used for this methodological assessment. The subset of ten subjects with COPD from EVOLUTION were chosen to be matched for age and gender with the ten HV used from EVOLVE. These COPD subjects were aged between 50 and 85 years, with a body mass index less than 35 kg/m^{2} and a plasma fibrinogen level greater than 2.8 g/l at screening. The same acquisition protocol was applied in all scans.

The EVOLUTION trial (Evaluation of losmapimod in COPD patients stratified by fibrinogen [18], ClinicalTrials.gov, NCT01541852) is a double-blinded placebo-controlled multicentre randomised controlled trial which incorporates ^{18}F-FDG PET/CT imaging of the lungs, aorta and carotids at baseline and approximately 16 weeks following treatment with losmapimod (p38 mitogen-activated protein kinase inhibitor: (GW856553, GlaxoSmithKline, Brentford, UK)) or placebo.

The EVOLVE study (REC 13/EE/0165, UK CRN ID 1513) is a cross-sectional multicentre study designed to evaluate lung and vascular inflammation by imaging subjects with COPD secondary to cigarette smoke compared with subjects with COPD secondary to alpha-1 antitrypsin deficiency and to compare these with subjects with obstructive sleep apnoea, healthy smokers and healthy never smoking controls (HV).

### Image acquisition

Each subject underwent a low-dose CT scan and a 60-min dynamic ^{18}F-FDG PET scan following a bolus injection of 237.3 ± 10.4 MBq (2.81 ± 0.54 MBq/kg) of radiotracer (full details of the image acquisition are provided in Additional file 1).

### Image processing

The analysis pipeline (Fig. 1) was common to all PET-CT data. Except for the whole lung and pulmonary artery segmentation, the post-processing of the images and kinetic modelling was achieved using the Molecular Imaging and Kinetic Analysis Toolbox (MIAKAT™, www.miakat.org), a Matlab (The MathWorks Inc., Natick, MA, USA) toolbox. Description of the delineation of the whole lung (WL) mask can be found in the Additional file 1.

#### Regional time activity curves (TACs)

To study regional differences of ^{18}F-FDG uptake, the downsampled WL mask was automatically subdivided into three regions of similar volume along the axial direction. The upper (UL), middle (ML) and lower (LL) lung masks were generated so that approximately each region equals one third of the total whole lung mask volume. Using the WL mask and the three subdivisions mentioned above, four time activity curves (TACs) were generated by calculating the mean regional activity for each time frame of the dynamic PET.

The standard uptake value (SUV) outcome measure was calculated for each TAC by dividing the average activity between 30 and 60 min by the injected dose per kg (kBq/kg).

#### CT-derived estimation of the fractional air volume

At the regional level, the fractional air volume in a given region R (WL, UL, ML and LL) was estimated [12]:

$$ {V}_A^{\mathrm{CT}}=1-\frac{\left({\overline{HU}}_R- H{U}_{\mathrm{air}}\right)}{\left( H{U}_{\mathrm{tissue}}- H{U}_{\mathrm{air}}\right)} $$

(3)

where \( {V}_A^{CT} \) is the estimated fractional air volume, \( {\overline{HU}}_R \) is the mean Hounsfield Unit (HU) in region R, *HU*
_{air} is the HU of air (−1024), and *HU*
_{tissue} is an approximation of the HU of lung tissue (40, taken from [12]). The air volume in a region can be computed by multiplying \( {V}_A^{CT} \) by the volume of the region.

#### Estimation of the lung input function

An image-derived input function (IDIF) was estimated as follows: a volume of interest was defined in the descending aorta (DA). Guided by an averaged early frame (0–5 min) PET and the downsampled CT-AC, the centre of the DA was manually drawn on a slice-by-slice basis (axial slices) using a 1-cm (5 voxel)-diameter disk mask starting at the aorta arch. To minimise the partial volume effect, the ROI was drawn very centrally in the DA over a large range of axial slices. The aorta mask was then applied to the dynamic PET image, and the DA time activity curve (TAC) was extracted. The actual blood input function used, C_{B}(t), included a correction for the plasma to whole blood ratio (1.056 ± 0.015) which was determined from venous samples collected after 5 min.

For each scan, a global time delay was estimated to account for the time separation between the radioactivity passing in the tissue of interest and the descending aorta: for delays spanning from −50 to 50 s, a one tissue compartmental model was fitted between the first 5 min of the delayed blood IF and the first 5 min of the WL TAC. The estimated delay was the delay generating the lowest residual sum of squares on the model fit.

### Kinetic modelling

Kinetic modelling was performed combining Eq. (2) (that describes the tissue concentration of FDG within the ROI composed of air, blood and tissue) with the irreversible two tissue compartmental model describing the kinetics of FDG in the lung tissue itself. Combining these two levels of description is necessary to accurately estimate the metabolic rate of FDG in lung tissue only (Fig. 2). Because the method is a *q*uantitative analysis correcting for *a*ir and *b*lood in *l*ung tissue, the acronym *qABL* will be used to refer to this method.

The irreversible two tissue compartmental model (Fig. 2) is composed of a component with reversible kinetics characterised by the rate constant *K*
_{1} and *k*
_{2} and a component with irreversible kinetics (*k*
_{3}). The qABL method was implemented using a fitted fractional blood volume contribution leading to the estimation of four parameters (*K*
_{1}, *k*
_{2}, *k*
_{3}, *V*
_{
B
}) that were obtained by weighted least squares fitting. The metabolic rate constant of ^{18}F-FDG corrected for air and blood, *K*
_{
i
} (ml cm^{−3} min^{−1}), was then calculated as

$$ {K}_i=\frac{K_1{k}_3}{k_2+{k}_3} $$

(4)

To enable comparison with previous studies [6,7,8], the Patlak graphical analysis [19] was also implemented with a linear start time (*t**) fixed to 10 min. The slope (Pat^{slope}) and the intercept (Pat^{intcpt}) of the regression were extracted. The normalised metabolic rate \( n{K}_i^{\mathrm{Pat}} \), used in previous studies [6,7,8] for quantifying lung tissue metabolism, was calculated as the ratio between the slope and intercept was calculated. As a consequence of the ROI containing air and blood (see Appendix 1), the outcome parameter \( n{K}_i^{\mathrm{Pat}} \) is a composite measure that includes terms for the fractional air volume, fractional blood volume and the metabolic rate of ^{18}F-FDG in lung tissue:

$$ n{K}_i^{\mathrm{Pat}}=\frac{{\mathrm{Pat}}^{\mathrm{slope}}}{{\mathrm{Pat}}^{\mathrm{intcpt}}}=\frac{\left(1-{V}_B-{V}_A\right){K}_i}{\left(1-{V}_B-{V}_A\right){V}_{\mathrm{ss}}+{V}_B} $$

(5)

with *K*
_{
i
} being the tissue metabolic rate constant of 18F-FDG and *V*
_{ss} the steady-state partition coefficient between tissue and plasma of non-phosphorylated FDG.

### Statistics

Differences between groups were assessed using the standardised corrected (or unbiased) effect size calculated using the Hedge’s g (abbreviated *g*) metric reported with the analytical 95% confidence interval (CI) measured using the Measures of Effect Size Toolbox [20]. Effect sizes are defined as small (*g* ≤ 0.2), medium (0.2 < *g* ≤ 0.8) and large (0.8 < *g*). Correlation was measured using Pearson’s correlation coefficient reported with the analytical 95% CI. A null hypothesis of zero effect between groups was rejected if the 95% CI did not contain the value 0. In this case, the group difference was named significant.