Biomedical subjects

D S Grebenkov

Publications and source records attributed to D S Grebenkov.

8 recordsLinked to original sources

PubMed2006

Restricted diffusion in a model acinar labyrinth by NMR: theoretical and numerical results.

A branched geometrical structure of the mammal lungs is known to be crucial for rapid access of oxygen to blood. But an important pulmonary disease like emphysema results in partial destruction of the alveolar tissue and enlargement of the distal airspaces, which may reduce the total oxygen transfer. This effect has been intensively studied during the last decade by MRI of hyperpolarized gases like helium-3. The relation between geometry and signal attenuation remained obscure due to a lack of realistic geometrical model of the acinar morphology. In this paper, we use Monte Carlo simulations of restricted diffusion in a realistic model acinus to compute the signal attenuation in a diffusion-weighted NMR experiment. We demonstrate that this technique should be sensitive to destruction of the branched structure: partial removal of the interalveolar tissue creates loops in the tree-like acinar architecture that enhance diffusive motion and the consequent signal attenuation. The role of the local geometry and related practical applications are discussed.

Animals↗

PubMed2006

Brownian flights over a fractal nest and first-passage statistics on irregular surfaces.

The diffusive motion of Brownian particles near irregular interfaces plays a crucial role in various transport phenomena in nature and industry. Most diffusion-reaction processes in confining interfacial systems involve a sequence of Brownian flights in the bulk, connecting successive hits with the interface (Brownian bridges). The statistics of times and displacements separating two interface encounters are then determinant in the overall transport. We present a theoretical and numerical analysis of this complex first-passage problem. We show that the bridge statistics is directly related to the Minkowski content of the surface within the usual diffusion length. In the case of self-similar or self-affine interfaces, we show and check numerically that the bridge statistics follows power laws with exponents depending directly on the surface fractal dimension.

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PubMed2006

Multiexponential attenuation of the CPMG spin echoes due to a geometrical confinement.

The CPMG multi-echo technique is often used to investigate the translational motion of diffusing nuclei in a confining medium. Henceforth, periodically repeated RF pulses with a diffusion-sensitizing gradient yield a formation of spin echoes of gradually decreasing amplitudes. The parameters of their exponential fits may characterize the structure of porous materials or biological tissue. In this paper, a multiexponential character of the CPMG measurements is rigorously demonstrated, once a geometrical confinement is present. Based on the multiple propagator approach, we derived a spectral representation for the echo amplitudes under external magnetic field of an arbitrary gradient profile. The multiple relaxation times and their spectral weights were found in a general form. The study of simple restrictive media allowed to obtain a quantitative condition under which the multiexponential attenuation is reduced to a monoexponential one.

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PubMed2006

Mathematical basis for a general theory of Laplacian transport towards irregular interfaces.

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.

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PubMed2005

What makes a boundary less accessible.

For the growth and transport processes driven by Laplacian fields, the accessibility of an interface for Brownian motion is characterized by the harmonic measure. Its multifractal properties help one to understand how the irregular geometry of biological membranes, metallic electrodes, porous catalysts, or growing aggregates is "seen" by diffusing particles. To clarify this point, we performed an extensive numerical study of the harmonic measure on two families of self-similar triangular Koch curves of variable Hausdorff dimension which may represent branched pore networks or fjordlike rough interfaces. Although these structures are apparently different, the multifractal properties of the harmonic measure in two cases are found to be very close for curves of small Hausdorff dimensions and to differ for higher irregularity. This provides new insight into optimization problems in chemical engineering.

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PubMed2005

Multifractal properties of the harmonic measure on Koch boundaries in two and three dimensions.

The multifractal properties of the harmonic measure on quadratic and cubic Koch boundaries are studied with the help of a new fast random walk algorithm adapted to these fractal geometries. The conjectural logarithmic development of local multifractal exponents is guessed for regular fractals and checked by extensive numerical simulations. This development allows one to compute the multifractal exponents of the harmonic measure with high accuracy, even with the first generations of the fractal. In particular, the information dimension in the case of the concave cubic Koch surface embedded in three dimensions is found to be slightly higher than its value D1 =2 for a smooth boundary.

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PubMed2005

Diffusion-reaction in branched structures: theory and application to the lung acinus.

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.

Animals↗

PubMed2002

Parametric equations of the theory of formation of spherical micelles.

Using the notion of aggregation work, we construct a system of differential equations for the aggregation number of micelles which is a function of the parameters of micellization (parametric equations). There are explicit solutions for two important models of spherical micelles. Based on these solutions, we obtain an analytical expression for the equilibrium concentration of surfactant monomers and consequently for the whole spectrum of equilibrium concentrations of molecular aggregates in this framework. Accuracy of these expressions is discussed, and they are applied to an example of micelles formed by sodium dodecyl sulfate.

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