Elsevier

Journal of Biomechanics

Volume 44, Issue 13, 2 September 2011, Pages 2489-2495
Journal of Biomechanics

Three-dimensional characterization of regional lung deformation

https://doi.org/10.1016/j.jbiomech.2011.06.009Get rights and content

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.

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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