Structural differences in the diaphragm of patients following controlled vs assisted and spontaneous mechanical ventilation.

PURPOSE: Ventilator-induced diaphragm dysfunction or damage (VIDD) is highly prevalent in patients under mechanical ventilation (MV), but its analysis is limited by the difficulty of obtaining histological samples. In this study we compared diaphragm histological characteristics in Maastricht III (MSIII) and brain-dead (BD) organ donors and in control subjects undergoing thoracic surgery (CTL) after a period of either controlled or spontaneous MV (CMV or SMV). METHODS: In this prospective study, biopsies were obtained from diaphragm and quadriceps. Demographic variables, comorbidities, severity on admission, treatment, and ventilatory variables were evaluated. Immunohistochemical analysis (fiber size and type percentages) and quantification of abnormal fibers (a surrogate of muscle damage) were performed. RESULTS: Muscle samples were obtained from 35 patients. MSIII (n = 16) had more hours on MV (either CMV or SMV) than BD (n = 14) and also spent more hours and a greater percentage of time with diaphragm stimuli (time in assisted and spontaneous modalities). Cross-sectional area (CSA) was significantly reduced in the diaphragm and quadriceps in both groups in comparison with CTL (n = 5). Quadriceps CSA was significantly decreased in MSIII compared to BD but there were no differences in the diaphragm CSA between the two groups. Those MSIII who spent 100 h or more without diaphragm stimuli presented reduced diaphragm CSA without changes in their quadriceps CSA. The proportion of internal nuclei in MSIII diaphragms tended to be higher than in BD diaphragms, and their proportion of lipofuscin deposits tended to be lower, though there were no differences in the quadriceps fiber evaluation. CONCLUSIONS: This study provides the first evidence in humans regarding the effects of different modes of MV (controlled, assisted, and spontaneous) on diaphragm myofiber damage, and shows that diaphragm inactivity during mechanical ventilation is associated with the development of VIDD.

Continued fraction solution for the radiative transfer equation in three dimensions

Starting from the radiative transfer equation, we obtain an analytical solution for both the free propagator along one of the axes and an arbitrary phase function in the Fourier-Laplace domain. We also find the effective absorption parameter, which turns out to be very different from the one provided by the diffusion approximation. We finally present an analytical approximation procedure and obtain a differential equation that accurately reproduces the transport process. We test our approximations by means of simulations that use the Henyey-Greenstein phase function with very satisfactory results.

Occupancy of a single site by many random walkers

We consider an infinite number of noninteracting lattice random walkers with the goal of determining statistical properties of the time, out of a total time T, that a single site has been occupied by n random walkers. Initially the random walkers are assumed uniformly distributed on the lattice except for the target site at the origin, which is unoccupied. The random-walk model is taken to be a continuous-time random walk and the pausing-time density at the target site is allowed to differ from the pausing-time density at other sites. We calculate the dependence of the mean time of occupancy by n random walkers as a function of n and the observation time T. We also find the variance for the cumulative time during which the site is unoccupied. The large-T behavior of the variance differs according as the random walk is transient or recurrent. It is shown that the variance is proportional to T at large T in three or more dimensions, it is proportional to T(3/2) in one dimension and to T ln T in two dimensions.

Persistent random walk model for transport through thin slabs.

We present a model for transport in multiply scattering media based on a three-dimensional generalization of the persistent random walk. The model assumes that photons move along directions that are parallel to the axes. Although this hypothesis is not realistic, it allows us to solve exactly the problem of multiple scattering propagation in a thin slab. Among other quantities, the transmission probability and the mean transmission time can be calculated exactly. Besides being completely solvable, the model could be used as a benchmark for approximation schemes to multiple light scattering.