Image Postprocessing

Image postprocessing was performed using MATLAB (MathWorks). Depolarization correction was performed by calculating signal decay in the static segments of each image sequence, as described previously (4,7). As two image acquisition rates were used in the MRI sequence, the latter half of the sequence was digitally upsampled using linear interpolation to generate a temporally homogeneous image sequence. The final image sequence was 44 images, each separated by 250 msec.

The time of expiration commencement was determined mathematically (as the minimum second-order differential of the image total-signal-time series) and confirmed by visual inspection of both images and total-signal-time series curves. The image section corresponding to expiration commencement was designated as the baseline image (t = 0 second). Images of the lungs at 1 second and 6 seconds were subsequently extracted from the image series with reference to the baseline image.

Index images at 1 second and 6 seconds were corrected for volume changes due to expiration using a nonrigid registration with the baseline image (t = 0 second). To achieve volume correction, the mathematical displacement field required to warp the index images to match the baseline reference image was calculated. This was done using a MATLAB implementation of a nonrigid registration based on Maxwell’s demon (8,9). To assist spatial coregistration in the setting of a reduced signal-to-noise ratio, global histogram-equalized versions of the index images were generated and used to derive the required image displacement field. Subsequently, the histogram-equalized images were discarded, and the derived displacement field applied to the original index images to generate volume-adjusted images. Any minor global signal gain or loss secondary to the volume correction was corrected by applying a constant multiplication factor to the image on a pixel-by-pixel basis.

Following volumetric correction, FEV₁^MRI, FVC^MRI, and FEV₁/FVC^MRI maps were derived on a pixel-by-pixel basis through direct image subtraction, using the following formulas: FEV₁^MRI = HPX^{t = 0s} − HPX^{t = 1s}, FVC^MRI = HPX^{t = 0s} − HPX^{t = 6s}, and FEV₁/FVC^MRI = (HPX^{t = 0s} − HPX^{t = 1s})/(HPX^{t = 0s} −HPX^{t = 6s}), where FEV₁^MRI, FVC^MRI and FEV₁/FVC^MRI are, respectively, FEV₁, FVC, and FEV₁/FVC derived with MRI spirometery, and HPX (hyperpolarized ¹²⁹Xe) is the volume-corrected image of the lungs at a given time point. A numerical, global FEV₁/FVC^MRI can be calculated by summing the total signal on the FEV₁^MRI image and dividing this by the total signal on the FVC^MRI image.

An initial noise filtration was performed on each image sequence using an implementation of the BM3D filter (10). Prior to FEV₁/FVC^MRI map generation, pixels on FEV₁^MRI maps that were very small in magnitude (empirically defined as the median signal in the extrapulmonary regions of the image) were set to zero.