Perimeter growth of a branched structure: Application to crackle sounds in the lung (original) (raw)

Scaling Behavior in Crackle Sound during Lung Inflation

During slow inflation of lung lobes, we measure a sequence of short explosive transient sound waves called ''crackles,'' each consisting of an initial spike followed by ringing. The crackle time series is irregular and intermittent, with the number of spikes of size s following a power law, n(s)ϰs Ϫ␣ , with ␣ϭ2.77Ϯ0.05. We develop a model of crackle wave generation and propagation in a tree structure that combines the avalanchelike opening of airway segments with the wave propagation of crackles in a tree structure. The agreement between experiments and simulations suggests that ͑i͒ the irregularities are a consequence of structural heterogeneity in the lung, ͑ii͒ the intermittent behavior is due to the avalanchelike opening, and ͑iii͒ the scaling is a result of successive attenuations acting on the sound spikes as they propagate through a cascade of bifurcations along the airway tree.

Fluid transport in branched structures with temporary closures: A model for quasistatic lung inflation

Physical Review E, 2003

We analyze the problem of fluid transport through a model system relevant to the inflation of a mammalian lung, an asymmetric bifurcating structure containing random blockages that can be removed by the pressure of the fluid itself. We obtain a comprehensive description of the fluid flow in terms of the topology of the structure and the mechanisms which open the blockages. We show that when calculating averaged flow properties of the fluid, the tree structure can be partitioned into a linear superposition of one-dimensional chains. In particular, we relate the pressure-volume P-V relationship of the fluid to the distribution ⌸(n) of the generation number n of the tree's terminal branches, a structural property. We invert this relation to obtain a statistical description of the underlying branching structure of the lung, by analyzing experimental pressure-volume data from dog lungs. The ⌸(n) extracted from the experimental P-V data agrees well with available data on lung branching structure. Our general results are applicable to any physical system involving transport in bifurcating structures with removable closures.

Avalanche Dynamics of Crackle Sound in the Lung

We analyze a sequence of short transient sound waves, called "crackles," which are associated with explosive openings of airways during lung inflation. The distribution of time intervals between consecutive crackles Dt shows two regimes of power law behavior. We develop an avalanche model which fits the data over five decades of Dt. We find that the regime for large Dt is related to the dynamics of distinct avalanches in a Cayley tree, and the regime for small Dt is determined by the dynamics of crackle propagation within a single avalanche. We also obtain a mean-field solution of the model which provides information about lung inflation.

Avalanches in the Lung: A Statistical Mechanical Model

Physical Review Letters, 1996

We study a statistical mechanical model for the dynamics of lung inflation which incorporates recent experimental observations on the opening of individual airways by a cascade or avalanche mechanism. Using an exact mapping of the avalanche problem onto percolation on a Cayley tree, we analytically derive the exponents describing the size distribution of the first avalanches and test the analytical solution by numerical simulations. We find that the treelike structure of the airways, together with the simplest assumptions concerning opening threshold pressures of each airway, is sufficient to explain the existence of power-law distributions observed experimentally.

Models of cluster growth on the Cayley tree

Physical Review B, 1984

We study the diffusion-controlled process of cluster growth, introduced by Witten and Sander, on a Cayley tree. We show that it is then equivalent to the Eden model where growth occurs at any boundary site with equal probability. The mean level number and the square gyration radius of an N-particle aggregate both increase as [K/(ICl)]lnN on a tree of branching ratio K. The case of biased diffusion is studied numerically: an attractive bias does not change the logarithmic behavior of the size, but a repulsive bias leads to a different behavior, presumably with a mean level number of order N.

Growing Cayley trees described by a Fermi distribution

Physical Review E, 2002

We introduce a model for growing Cayley trees with thermal noise. The evolution of these hierarchical networks reduces to the Eden model and the invasion percolation model in the limit T → 0, T → ∞ respectively. We show that the distribution of the bond strengths (energies) is described by the Fermi statistics. We discuss the relation of the present results with the scale-free networks described by Bose statistics.

Models of lung branching morphogenesis

Journal of biochemistry, 2015

Vertebrate airway has a tree-like-branched structure. This structure is generated by repeated tip splitting, which is called branching morphogenesis. Although this phenomenon is extensively studied in developmental biology, the mechanism of the pattern formation is not well understood. Conversely, there are many tree-like structures in purely physical or chemical systems, and their pattern formation mechanisms are well-understood using mathematical models. Recent studies correlate these biological observations and mathematical models to understand lung branching morphogenesis. These models use slightly different mechanisms. In this article, we will review recent progress in modelling lung branching morphogenesis, and future directions to experimentally verify the models.

Avalanches in the Lung: A Statistical Mechanical Approach

Diffusion-Reaction in Branched Structures: Theory and Application to the Lung Acinus

Physical Review Letters, 2005

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.

Perimeter growth of a branched structure: Application to crackle sounds in the lung (original) (raw)

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