Three-dimensional characterization of regional lung deformation
Introduction
Volume change is the primary metric for assessing lung expansion and its health. But volume change in the lungs is not regionally homogeneous (Olson and Rodarte, 1984). The practice of image-guided radiotherapy brought a need for regional characterizations of lung deformations as lung pathology and the effects of interventions (radiological or otherwise) are essentially region-specific. Methods have been developed to determine regional volume change from the displacement field using deformable image registration and MRI-grid tagging (Reinhardt et al., 2008, Cai et al., 2009). Finite element simulations of lung deformation also yield a displacement field and, consequently, regional volume changes.
Regional deformation of the lung during inspiration and expiration is more than just volume change. Volume change may also have orientational preference—anisotropy of deformation (West and Matthews, 1972, Rodarte et al., 1985). Volume change and deformation anisotropy are independent quantities as a region may undergo no volume change, but still has deformed significantly, say, when the lengthening in one orientation is compensated by contraction along another orientation. Devoid of orientational preference, regional volume change alone may not do full justice to characterization of lung deformation, and this may have clinical implications. For example, consider two cases: one, a lung with fibrosis at its inferior region (close to the diaphragm); two, a healthy lung but with poorly functioning diaphragm. In both the cases, the volume change may conceivably be lower at the inferior regions. But the anisotropy of deformation will likely be significantly affected only in the latter. Or perhaps, regions closest to the diaphragm are likely to experience more volume change in the vertical orientation, or regions closest to the heart may be more constrained from expanding normal to the heart.
In classical mechanics, deformation of structures is characterized by the regional distribution of a strain or stretch tensor. Previous reports have addressed lung deformation using the traditional methods employed in mechanics. West and Matthews (1972) computed and reported lung regional strains along the anatomical orientations using an idealized 3D finite element model under the influence of gravity. They made visual observations of shape changes that occurred in the inferior portion of the model, but stopped short of quantifying it. Rodarte et al. (1985) used parenchymal markers to quantify regional strains along the anatomical orientations. A comparison of strain magnitudes revealed a dominant transverse strain throughout the lung, though mean strains tended to be greater in the lower lobes. Napadow et al. (2001) quantified strains using spin-inversion MRI. In addition to reporting strains along the standard anatomical orientations, they also reported the difference between strains in the coronal and sagittal axes – noted as in-plane shear strain. Cai et al. (2009) used MRI-grid tagging to report regional ventilation and principal strains in two dimensions. Others have estimated point-wise displacements in the lung, but are often concerned only with accuracy of registration (verified using landmark error), which can be used for image-guided radiotherapy (Reinhardt et al., 2007, van Beek and Hoffman, 2008, Brock, 2010). While strains entirely capture the deformation, use of strains themselves (be it principal strains or strain components based on an intuitive coordinate system) to interpret the nature of lung deformation may not be the best approach for a few reasons. One, strain components lump the effect of volume change with the preferential directionalities involved in volume change rendering independent interpretations difficult. Two, strains are not physiologically intuitive within the context of lung deformation which is essentially about volume change. Three, the lungs do not have an intuitive coordinate system based on which individual strain components could be interpreted.
We submit that, regional lung deformation is best interpreted by indices that independently capture different aspects of lung deformation. The objective of this work is to develop indices of lung deformation that independently capture volume change and the level and nature of orientational preferences that occur in volume change and that these indices be intuitive and relevant to the physiology of lung function. Such indices will permit future studies on regional lung deformation (both experimental and computational) to make physiologically relevant interpretations from displacement fields determined by image registration or numerical modeling.
Section snippets
Development of indices
We propose quantification of regional lung deformation using three independent measures determined from the displacement field, such that their physical meanings accommodate the essentially volumetric nature of deformation in the lungs. The indices are volume change (J), an anisotropic deformation index (ADI) and a slab-rod index (SRI)—defined and explained subsequently.
To understand the rationale and definitions behind these indices, consider that a point at position X in a body moves to a
Results
Regional variations exist in J, ADI and SRI for subjects as seen on sequential sagittal slices from right to left (see Fig. 2, Fig. 3). Regionally, J is elevated at the inferior and dorsal ends of the lungs. ADI is elevated at the inferior region close to the diaphragm and also roughly along lobar fissures. SRI is not elevated predominantly in any particular localized region, but rather appears elevated at various localized spots in the lung. The maximum principal stretch vectors weighted with
Discussion
Lung parenchymal deformation is primarily about local volume change. It can vary regionally, especially in the presence of localized pathologies. A complete description of local volume change must consider the amount of volume change as well as orientational preferences in volume change.
Conventionally, lung deformation is characterized by the amount of tissue ‘stretching’. But note that the term stretch may be used loosely when referencing the lung. Mechanically, tissue stretch is often
Conflict of Interest Statement
Dr. Reinhardt is a founder and shareholder of VIDA Diagnostics, Inc.
Acknowledgments
This work was supported in part by NIH Grant HL079406 (to JMR).
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