Three-dimensional characterization of regional lung deformation

Abstract

The deformation of the lung during inspiration and expiration involves regional variations in volume change and orientational preferences. Studies have reported techniques for measuring the displacement field in the lung based on imaging or image registration. However, means of interpreting all the information in the displacement field in a physiologically relevant manner is lacking. We propose three indices of lung deformation that are determinable from the displacement field: the Jacobian--a measure of volume change, the anisotropic deformation index--a measure of the magnitude of directional preference in volume change and a slab-rod index--a measure of the nature of directional preference in volume change. To demonstrate the utility of these indices, they were determined for six human subjects using deformable image registration on static CT images, registered from FRC to TLC. Volume change was elevated in the inferior-dorsal region as should be expected for breathing in the supine position. The anisotropic deformation index was elevated in the inferior region owing to proximity to the diaphragm and in the lobar fissures owing to sliding. Vessel regions in the lung had a significantly rod-like deformation compared to the whole lung. Compared to upper lobes, lower lobes exhibited significantly greater volume change (19.4% and 21.3% greater in the right and left lungs on average; p<0.005) and anisotropy in deformation (26.3% and 21.8% greater in the right and left lungs on average; p<0.05) with remarkable consistency across subjects. The developed deformation indices lend themselves to exhaustive and physiologically intuitive interpretations of the displacement fields in the lung determined through image-registration techniques or finite element simulations.

Figure 1

(A) Illustration of the shape change spectrum graph. Anisotropic deformation index (ADI) corresponds to the radius of a point from the origin. SRI corresponds to the angle from the x-axis. J is constant over the entire graph but regions undergoing expansion and contraction are separated into the first and third quadrants respectively. (B) Illustration of the meanings of the shape change indices by placing a deformed cube at different positions on the shape spectrum. Volume change is held constant. In human subjects studied, the ADI ranged from 0 to 2.4 (5th to 95th percentile) and SRI from 0 to 1.

Figure 2

Contour plots for Subject 1 showing the distribution of J, ADI and SRI on 6 sagittal slices from patient right to left.

Figure 3

Contour plots for Subject 2 showing the distribution of J, ADI and SRI on 6 sagittal slices from patient right to left.

Figure 4

Vector plot of maximum principal stretch orientation weighted with ADI. For clarity the vectors are plotted on 4 transverse slices. Only a fraction of the vectors in a given slice is shown for clarity.

Figure 5

Box plots of the distribution of J, ADI and SRI in the six study subjects stratified by lobe. The bounds of the box represent the 25^th and 75^th percentile; the horizontal line inside the box represents the median; and the error bars extend from the 5^th to 95^th percentile. The percentage above each box represents lobe volume as a fraction of the total lung volume at FRC for that subject. LLL – left lower lobe; LUL – left upper lobe; RLL – right lower lobe; RML – right middle lobe; RUL – right upper lobe. The sample sizes for the quartiles are roughly the number of voxels in the particular lung lobe and range between 175K and 700K.

Figure 6

Box plots showing the distribution of J, ADI and SRI throughout the lung, in the vessels and in the major vessels (roughly the vessels of the 5^th generation or lesser) only. The bounds of the box represent the 25^th and 75^th percentile; the horizontal line inside the box represents the median; and the error bars extend from the 5^th to 95^th percentile. The sample sizes for the quartiles are roughly the number of voxels in the associated data set and range between 33K (major vessels) and 2.7M (whole lung).