imaging in chronic obstructive pulmonary disease using computational simulations with Relationship between structural changes and hyperpolarized gas magnetic resonance
imaging in chronic obstructive pulmonary disease using computational simulations with Relationship between structural changes and hyperpolarized gas magnetic resonance
The theory of Laplacian transport towards and across irregular surfaces is reformulated in terms ... more The theory of Laplacian transport towards and across irregular surfaces is reformulated in terms of the Dirichlet-to-Neumann operator and its spectral characteristics. This permits us to obtain an exact equivalent circuit for the impedance of a working interface of arbitrary shape. The important result is that only very few eigenmodes of this operator do govern the entire response of a macroscopic system. This property drastically simplifies the understanding of irregular or prefractal interfaces. The results can be applied in electrochemistry, physiology and chemical engineering, fields where exchange processes across surfaces with complex geometry are ubiquitous.
Flow and Sound Generation in Human Lungs: Models of Wheezes and Crackles
General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.-Diffusion-Reaction in Branched Structures: Theory and Application to the Lung Acinus
The localization subregions of stationary waves in continuous disordered media have been recently... more The localization subregions of stationary waves in continuous disordered media have been recently demonstrated to be governed by a hidden landscape that is the solution of a Dirichlet problem expressed with the wave operator. In this theory, the strength of Anderson localization confinement is determined by this landscape, and continuously decreases as the energy increases. However, this picture has to be changed in discrete lattices in which the eigenmodes close to the edge of the first Brillouin zone are as localized as the low energy ones. Here we show that in a 1D discrete lattice, the localization of low and high energy modes is governed by two different landscapes, the high energy landscape being the solution of a dual Dirichlet problem deduced from the low energy one using the symmetries of the Hamiltonian. We illustrate this feature using the one-dimensional tight-binding Hamiltonian with random on-site potentials as a prototype model. Moreover we show that, besides unveiling the subregions of Anderson localization, these dual landscapes also provide an accurate overall estimate of the localization length over the energy spectrum, especially in the weak disorder regime.
We propose an analytical approach to solving the diffusion-convection equations governing oxygen ... more We propose an analytical approach to solving the diffusion-convection equations governing oxygen transport in the human placenta. We show that only two geometrical characteristics of a placental cross-section, villi density and the effective villi radius, are needed to predict fetal oxygen uptake. We also identify two combinations of physiological parameters that determine oxygen uptake in a given placenta: (i) the maximal oxygen inflow of a placentone if there were no tissue blocking the flow and (ii) the ratio of transit time of maternal blood through the intervillous space to oxygen extraction time. We derive analytical formulas for fast and simple calculation of oxygen uptake and provide two diagrams of efficiency of oxygen transport in an arbitrary placental cross-section. We finally show that artificial perfusion experiments with no-hemoglobin blood tend to give a two-orders-of-magnitude underestimation of the in vivo oxygen uptake and that the optimal geometry for such setup ...
Proceedings of the National Academy of Sciences, 2002
The transfer of oxygen from air to blood in the lung involves three processes: ventilation throug... more The transfer of oxygen from air to blood in the lung involves three processes: ventilation through the airways, diffusion of oxygen in the air phase to the alveolar surface, and finally diffusion through tissue into the capillary blood. The latter two steps occur in the acinus, where the alveolar gas-exchange surface is arranged along the last few generations of airway branching. For the acinus to work efficiently, oxygen must reach the last branches of acinar airways, even though some of it is absorbed along the way. This ''screening effect'' is governed by the relative values of physical factors like diffusivity and permeability as well as size and design of the acinus. Physics predicts that efficient acini should be spacefilling surfaces and should not be too large. It is shown that the mammalian acini fulfill these requirements, small mammals being more efficient than large ones both at rest and in exercise. ‡ To whom reprint requests should be addressed.
In the human lung, the gas transfer between air and blood is achieved in terminal units that are ... more In the human lung, the gas transfer between air and blood is achieved in terminal units that are called 'acini'. Whereas convection is still the predominant transport phenomenon at the acinus entrance, most of the acinar surface is in fact accessed by diffusion. The transition between convection and diffusion, and thus the size of the diffusion unit, depends on the air velocity at the acinus entrance. In this paper, we present a gas transport model which takes into account both the diffusion into the acinus and the diffusion across the alveolar membrane. It is shown that the physiological sizes of the diffusion unit in the lung, at rest or at exercise, can be explained by physical arguments. In that sense, diffusion is the 'dimensioning criterion' of the lung at the acinar level. This approach shows that, due to diffusional screening at inspiration and at rest, there exists a permanent spatial inhomogeneity of oxygen and carbon dioxide partial pressure which reduces the effective surface efficiency of the human acinus to a value of only 30 to 40%. This model casts a new light on the properties of this physiological transport system. It permits in particular to understand how several diseases among which pulmonary edema may remain asymptomatic in their early stages.
A surprising similarity is found between the distribution of hydrodynamic stress on the wall of a... more A surprising similarity is found between the distribution of hydrodynamic stress on the wall of an irregular channel and the distribution of flux from a purely Laplacian field on the same geometry. This finding is a direct outcome from numerical simulations of the Navier-Stokes equations for flow at low Reynolds numbers in two-dimensional channels with rough walls presenting either deterministic or random self-similar geometries. For high Reynolds numbers, when inertial effects become relevant, the distribution of wall stresses on deterministic and random fractal rough channels becomes substantially dependent on the microscopic details of the walls geometry. In addition, we find that, while the permeability of the random channel follows the usual decrease with Reynolds, our results indicate an unexpected permeability increase for the deterministic case, i.e., "the rougher the better". We show that this complex behavior is closely related with the presence and relative intensity of recirculation zones in the reentrant regions of the rough channel.
A numerical study of the transfer across random fractal surfaces shows that their response are ve... more A numerical study of the transfer across random fractal surfaces shows that their response are very close to the response of deterministic model geometries with the same fractal dimension. The simulations of several interfaces with prefractal geometries show that, within very good approximation, the flux depends only on a few characteristic features of the interface geometry: the lower and higher cut-offs and the fractal dimension. Although the active zones are different for different geometries, the electrode responses are very nearly the same. In that sense, the fractal dimension is the essential "universal" exponent which determines the net transfer. Many random processes such as aggregation, diffusion, fracture and percolation, build fractal objects [1,2]. Fractal geometry essentially describes hierarchical structures . If properties of these random systems depend on the hierarchical character of their geometry, then the study of a deterministic structure with the same fractal dimension may provide a good approximation of the random system properties . The question is significant since fractal and pre-fractal geometries are widely used in mathematical approaches or numerical simulations as a convenient model of irregularity. They are also more simply addressed by algebraic calculations and incorporated into numerical models for computer simulation. It is then an important matter to decide whether simple deterministic, artificial, fractals could help determine the properties of random, natural, fractals . In particular, it is a question whether experiments performed on model fractal geometries [7] may help understand the behavior of real complex structures.
An exact ''branch by branch'' calculation of the diffusional flux is proposed for partially absor... more An exact ''branch by branch'' calculation of the diffusional flux is proposed for partially absorbed random walks on arbitrary tree structures. In the particular case of symmetric trees, an explicit analytical expression is found which is valid whatever the size of the tree. Its application to the respiratory phenomena in pulmonary acini gives an analytical description of the crossover regime governing the human lung efficiency.
Uploads
Papers by M. Filoche