We have used three-dimensional reconstructions obtained with spiral computed tomography to measure total diaphragm length (L di ) and surface area (A di ), the length (L do ) and surface area (A do ) of the dome, and the length (L ap ) and surface area (A ap ) of the zone of apposition in 10 hyperinflated patients with severe chronic obstructive pulmonary disease, or COPD (FEV 1 ϭ 27% predicted: FRC ϭ 225% predicted) and 10 normal subjects matched for age, sex, and height. Measures of L di , A di , L ap , and A ap decreased linearly between FRC and TLC in the two groups, but L do and A do did not change. On average, patients' A di and A ap at FRC were reduced to 73% and 54% of normal values, whereas A do was unaffected. When compared at similar absolute lung volumes, mean diaphragm dimensions were similar in patients with COPD and normal subjects, but individual values were very variable in both groups. This variability was partly accounted for by differences in body weight: i.e., the greater the weight, the longer the diaphragm. We conclude that ( 1 ) patients with COPD have marked reductions in A di and A ap at FRC but have diaphragm dimensions similar to those of normal subjects when compared at similar absolute lung volumes, and ( 2 ) normal subjects and patients with COPD show substantial intersubject variability in diaphragm dimensions that is partly explained by differences in body weight. In patients with chronic obstructive pulmonary disease (COPD), hyperinflation of the lungs decreases the operating length of the diaphragm. As a result, the inspiratory function of the muscle is impaired. The magnitude of diaphragm shortening increases with the degree of hyperinflation, and it is generally assumed that, at a given absolute lung volume, diaphragm length and surface area are similar in patients with COPD and normal subjects.However, very few studies have investigated the effect of chronic hyperinflation on diaphragm dimensions. In two early studies using chest radiographs, Sharp and colleagues (1) reported that the diaphragm was 40% shorter at FRC in patients with COPD than in normal subjects, and Rochester and Braun (2) showed that diaphragm length was reduced by 28% in patients with COPD at residual volume (RV) compared with normal subjects at their RV; this difference, however, disappeared when diaphragm lengths were compared at similar absolute lung volumes. Interpretation of these results is difficult because measurements of diaphragm dimensions were obtained from two-dimensional analysis of chest radiographs, were generally performed at a single lung volume, and were not always compared with measurements obtained in adequately matched controls.In a previous study (3), we have described a technique of three-dimensional (3D) diaphragm imaging using spiral computed tomography (CT) that allowed accurate measurements of diaphragm length and surface area. In the present work, we have used this technique to compare diaphragm dimensions at different lung volumes in 10 hyperinflated patients with severe COPD...
We developed a technique of diaphragm imaging by using spiral computed tomography, and we studied four normal subjects who had been previously investigated with magnetic resonance imaging (A. P. Gauthier, S. Verbanck, M. Estenne, C. Segebarth, P. T. Macklem, and M. Paiva. J. Appl. Physiol. 76: 495-506, 1994). One acquisition of 15- to 25-s duration was performed at residual volume, functional residual capacity, functional residual capacity plus one-half inspiratory capacity, and total lung capacity with the subject holding his breath and relaxing. From these acquisitions, 20 coronal and 30 sagittal images were reconstructed at each lung volume; on each image, diaphragm contour in the zone of apposition and in the dome was digitized with the software Osiris, and the digitized silhouettes were used for three-dimensional reconstruction with Matlab. Values of length and surface area for the diaphragm, the dome, and the zone of apposition were very similar to those obtained with magnetic resonance imaging. We conclude that satisfactory three-dimensional reconstruction of the in vivo diaphragm may be obtained with spiral computed tomography, allowing accurate measurements of muscle length, surface area, and shape.
We study analytically the squeezing spectrum of second-harmonic generation in the self-pulsing regime. We prove that squeezing is still defined in the presence of a limit cycle. When the input field exceeds the self-pulsing threshold, the intensity spectrum remains smaller than the shot-noise limit in a frequency domain around the self-pulsing frequency.PACS numbers: 42.50.Dv, 42.65.Ky It has been known for some time that squeezing can be enhanced near a bifurcation point. 1 This property has been recently demonstrated for a class of nonlinear optical systems 2 and is especially relevant for parametric processes inside a resonant cavity. For instance, in subharmonic generation on resonance, perfect squeezing is obtained at the bifurcation point corresponding to the transition from the amplifier regime to the oscillator regime. 1(a) On both sides of the bifurcation point, the squeezing is large, though of a different nature. Below the bifurcation, a squeezed vacuum is produced, a)3 while above the bifurcation, the subharmonic field displays squeezed phase fluctuations. 1 In the case of subharmonic generation, the bifurcation point corresponds to a transition between steady states. Both regimes are characterized by time-independent intensities. In second-harmonic generation (SHG), a different kind of bifurcation occurs (known as Hopf bifurcation), which connects a steady state to a time-periodic solution. 4 It has been shown that perfect intensity squeezing can be reached when approaching the Hopf bifurcation from below. 1(a) Most nonlinear optical systems in resonant cavities display such Hopf bifurcations. The purpose of this Letter is to calculate analytically the squeezing spectrum above a Hopf bifurcation, in the self-pulsing regime. To our knowledge, no theoretical result has been published on squeezing of nonsteady states (such as stable periodic or quasiperiodic solutions) with constant input. In this line of temporal problems, the parametric amplifier submitted to a periodically pulsed input field has been considered by Yurke et al. 5 and it was demonstrated that squeezing can still be defined. This has been confirmed experimentally first by Slusher et al. 6 The problem that we analyze in this Letter is different since the input field amplitude remains constant while both output electric fields display stable spontaneous amplitude and phase modulations. Thus it is nonlinear dynamics which is the cause of the time periodicity in the response of the system. In this first analytic approach to the problem, we shall consider SHG because its analytical solution of the deterministic problem in the self-pulsing regime is known and simple to handle.There exist two main methods for calculating the squeezing spectra of nonlinear optical systems. The first one is an extension by Collett and Gardiner 7 of the fluctuation-dissipation theorem for nonlinear dissipative quantum systems. It was used by Collett and Walls 1(a) who published the first theoretical derivation of the squeezing spectrum in SHG below the Hopf...
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