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Deformation of the Dog Lung in the Chest Wall

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Deformation of the Dog Lung in the Chest Wall Deformation of the dog lung in the chest wall SHAOBO LIU, SUSAN S. MARGULIES, AND THEODORE A. WILSON Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis 55455; and Division of Thoracic Disease and Internal Medicine, Mayo Clinic, Rochester, Minnesota 55905 LIU, SHAOBO, SUSAN S. MARGULIES, AND THEODORE A. distribution and the distribution of strain that underlie WILSON. Deformation of the dog lung in the chest wall. J. Appl. the volume distribution with the use of radiopaque mark- Physiol. 68(5): 1979-1987, 1990.-Data on the shape of the ers embedded in the parenchyma. They found a variabil- chest wall at total lung capacity (TLC) and functional residual ity of ventilation in the prone dog but weak and variable capacity (FRC) were used as boundary conditions in an analysis spatial gradients of ventilation. The uniformly distrib- of the deformation of the dog lung. The lung was modeled as an elastic body, and the deformation of the lung from TLC to uted variability of ventilation has been traced to a vari- FRC caused by the change in chest wall shape and gravity were ability of parenchymal properties at small scale (10, 15). calculated. Parenchymal distortions, distributions of regional In the supine dog they found cephalocaudal and vertical volume at FRC as a fraction of the volume at TLC, and gradients of ventilation. Their data describe the distor- distributions of surface pressure at FRC are reported. In the tion of the parenchyma as well as the volume change. prone dog there are minor variations in fractional volume along For example, they found that the lateral dimensions of the cephalocaudal axis. In transverse planes opposing defor- an element of lung parenchyma in the upper lobe de- mations are caused by the change of shape of the transverse creased by more than the dorsoventral or cephalocaudal section and the gravitational force on the lung, and the result- dimensions as lung volume decreased. They reported ant fractional volume and pleural pressure distributions are magnitudes of the fractional length changes or strains in nearly uniform. In the supine dog, there is a small cephalocau- these three directions and spatial gradients of the three da1 gradient in fractional volume, with lower fractional volume components of strain. caudally. In transverse sections the heart and abdomen extend farther dorsally at FRC, squeezing the lung beneath them. The In one of the first mathematical analyses of lung gradients in fractional volume and pleural pressure caused by deformation, West and Matthews (13) and Vawter et al. shape changes are in the same direction as the gradients caused (12) computed the distortion of a body with an idealized by the direct gravitational force on the lung, and these two upright human lung shape by the gravitational body force factors contribute about equally to the large resultant vertical and by some idealized changes in chest wall shape. Sub- gradients in fractional volume and pleural pressure. In the sequently, the mechanical properties of lung parenchyma prone position the heart and upper abdomen rest on the rib that are needed to model the lung as a deformable body cage. In the supine posture much of their weight is carried by were measured (8), and lung deformations for simple the lung. This difference causes the difference between the local distortions and distortions of lobes under simple distributions of regional volume in the prone and supine posi- loading have been calculated (6). More recently, Bar- tions. Yishay et al. (1) analyzed a model of the whole lung that included heart weight. The computed dependence of the ventilation; pleural pressure; heart weight vertical distribution of pleural pressure on heart weight was consistent with the measurements of esophageal pressure in upright dogs reported by Hyatt et al. (5). THE DISTRIBUTION of ventilation in the human lung has The data on the shape of the chest wall of supine and been studied by measuring the dilution of test gases. It prone dogs at total lung capacity (TLC) and functional was indirectly measured by their concentration in ex- residual capacity (FRC) reported by Margulies and Ro- pired gas and directly measured by the y emission of a darte (9) provide the basis for more detailed modeling radioactive gas within the lung. The ventilation distri- and analysis of the deformation of the lung in the chest bution has been found to depend on posture, gravita- wall. In this paper, we report the results of an analysis tional field, and the state of the muscles of the chest of the deformation of the lung caused by gravity and by wall. These studies imply that the gravitational force on the boundary displacements imposed on the 11xng by t he the lung and the shape imposed on the lung by the chest chest wall. wall both affect the distribution of ventilation. The distortion of the lung of the dog has been studied METHODS in more detail. Hoffman (3) reported distributions of the percent air content in the lungs of dogs, prone and Data. The origin of the data on chest wal 1 shape is supine, obtained from measurements of X-ray opacity by described by Margulies and Rodarte (9). The aisplace-1* 1 fast multislice computed tomography. A strong vertical ment of the lung along the cephalocaudal axis was com- gradient was found in the supine dog and a nearly uni- puted from the data on transverse area vs. axial position form distribution was found in the prone dog. Hubmayr for all six dogs. The computed displacements for five of et al. (4) and Rodarte et al. (11) measured the ventilation the six dogs were similar. Deformations in the transverse 0161-7567/90 $1.50 Copyright 0 1990 the American Physiological Society 1979 1980 DEFORMATION OF THE DOG LUNG planes were computed for two of the group of five dogs, are the input data that appear in the equation that and the results were similar. Computed deformations for governs axial displacements, Eq. A9. The solution of this one dog are reported. equation provides the mapping of the position of trans- Analysis. The deformation of the lung that accompa- verse planes from TLC to FRC. The transverse section nies the change in volume from TLC to FRC is divided of the thorax at TLC and at the location of this slice of into two parts. First, the lung is imagined to shrink parenchyma at FRC was chosen from the data. For each isotropically from the volume at TLC (VT& to the posture the two slices marked by arrows in Fig. 1 were volume at FRC (VFRc). Then the deformations that are analyzed. The shape of each slice at TLC, the isotropi- caused by the change of boundary shape from the iso- tally reduced shape, and the shape at FRC are shown in tropically reduced lung shape to the observed shape at Fig. 2. The finite element method was used to find the FRC and by the gravitational body force on the lung are displacements in the transverse plane that are required computed. Local fractional volume at FRC, the ratio of to deform the plane section from the isotropically re- the volume of an element of parenchyma at FRC to its duced shape to the shape at FRC. The density of the volume at TLC, is the product of the uniform volume lung was assumed to be 0.3 g/cm3, and the gravitational ratio V&VTLc and the local volume ratio for the defor- body force on the lung was included in the analysis of mation of the isotropically reduced lung. Local pleural the deformation in the plane. pressure is the sum of a uniform transpulmonary pres- sure at FRC and the pressure that accompanies the RESULTS deformation. To compute the deformation of the isotropically re- The ratio of the thickness of a transverse lung slice at duced lung caused by the change of shape and gravity, FRC to its thickness at TLC is plotted vs. its position at the lung is modeled as an elastic solid. Transpulmonary FRC in Fig. 3. If the lung shrank isotropically from TLC pressure at FRC is assumed to be 3 cmHzO and values to FRC, the thickness ratio would equal the cube root of of the shear modulus p and bulk modulus K appropriate the volume ratio, 0.72. Regions in which the thickness for this transpulmonary pressure are used: lu.= 2 cmH20, ratio is >0.72 are stretched in the axial direction by the deformation from the isotropically reduced shape to the K = 10 cmHZO (8). The entire lung is modeled as a single body, and lobar fissures are not represented. It is as- shape at FRC. The ratio of the area of a slice at FRC to sumed that the lung slides freely at the pleural surface its area at TLC is also shown in Fig. 3. If the lung shrank and that the shear stress on this surface is zero. isotropically, the area ratio would equal the two-thirds Approximations are made in analyzing the deforma- power of the volume ratio, 0.52. Around the mediastinum the lung is stretched in the axial direction and com- tion from the isotropically reduced lung shape to the pressed in transverse area, compared with an isotropic shape at FRC. It is assumed that the shape of the volume change. The distortions are in the opposite di- transverse cross section of the isotropically reduced lung rection at the apex of the lung and between the heart changes slowly along the cephalocaudal axis and that the and the dome of the diaphragm. The ratio of the volume difference between this shape and the true cross-sec- of a slice at FRC to its volume at TLC shown in Fig.
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