Fractal Structure and Fractal Measurement of Pulmonary Vascular Systems

This article is devoted to determining the fractal structure and fractal size of organs. There is a detailed description of the various mathematical methods for determining the size of fractal organs, and an analysis of errors in determining the fractal size of organs. In the article, the fractal structure, fractal size, properties of human organs were determined using the Mandelbrot-Richardson scale (or cell method). The fractal structure of the human lung was also studied by comparing the fractal structure of tree branches. In particular, tree branches, vascular systems in the human retina, and fractal measurements of the lungs were calculated. In determining the fractal scale, changes in human body parts were not taken into account. Most articles have used fractal measurement only in relation to geometric shapes. In this article, the fractal structure of human organisms is studied on the basis of mathematical formulas and special methods are used to calculate fractal dimensions, as well as the results of an appropriate number of experiments. In addition, based on these measurements, fractal measurements of the pulmonary vascular system of patients have been evaluated in several studies, widely used to describe vascular networks in various diseases, and data on their practical application have been provided.

Predicting Electrokinetic Coupling and Electrical Conductivity in Fractured Media Using a Fractal Distribution of Tortuous Capillary Fractures

Electrokinetics methods have attracted increasing interest to characterize hydrogeological processes in geological media, especially in complex hydrosystems such as fractured formations. In this work, we conceptualize fractured media as a bunch of parallel capillary fractures following the fractal size distribution. This conceptualization permits to obtain analytical models for both the electrical conductivity and the electrokinetic coupling in water saturated fractured media. We explore two different approaches to express the electrokinetic coupling. First, we express the streaming potential coupling coefficient as a function of the zeta potential and then we obtain the effective charge density in terms of macroscopic hydraulic and electrokinetic parameters of porous media. We show that when the surface electrical conductivity is negligible, the proposed models reduces to the previously proposed one based on a bundle of cylindrical capillaries. This model opens up a wide range of applications to monitor the water flow in fractured media.

Predicting Electrokinetic Coupling and Electrical Conductivity in Fractured Media Using a Bundle of Tortuous Capillary Fractures

The electrokinetics methods have a great potential to characterize hydrogeological processes in geological media, especially in complex hydrosystems such as fractured formations. In this work, we conceptualize fractured media as a bunch of parallel capillary fractures following the fractal size distribution. This conceptualization permits to obtain analytical models for both the electrical conductivity and the electrokinetic coupling in water saturated fractured media. We explore two different approaches to express the electrokinetic coupling. First, we express the streaming potential coupling coefficient as a function of the zeta potential and then we obtain the effective charge density in terms of macroscopic hydraulic and electrokinetic parameters of porous media. We show that when the surface electrical conductivity is negligible, the proposed models reduces to the previously proposed one based on a bundle of cylindrical capillaries. This model opens up a wide range of applications to monitor the water flow in fractured media.