Evidence That Cigarette Smoking Alters Alveolar Type I Cell Nuclear Fractal Dimension

A large number of alveolar type I and II cells from the lungs of both smokers and non-smokers was collected using 40x magnification histological images from our digital archive. These images underwent a transformation into binary images of nuclear contours, followed by the application of the box-counting method. Statistical analysis revealed a significant difference in the mean box-counting dimension values between type I cells of smokers and non-smokers. However, no significant difference was observed in the mean fractal dimensions of alveolar type II cells. This study provides preliminary evidence of the impact of cigarette smoking on the nuclear shape of alveolar type I cells. Given the high toxicity of cigarette smoke to lung cells and the interconnection between morphology and function, further study is needed to understand its impact on the nuclear shape of these cells. Future research should also explore the effects of second-hand smoke on cell shape.

Fractal Characteristic-Induced Optimization of the Fixed Abrasive Lapping Plate in Fabricating Bipolar Plate of Proton-Exchange Membrane Fuel Cells

Purpose: A bipolar plate with fractal-characterized microstructures can realize intelligent energy transmission and obtain a high efficiency of proton-exchange membrane fuel cells. In this paper, fixed abrasive lapping technology is proposed to fabricate a surface microstructure on a bipolar plate with fractal characteristics. Methodology: The kinematics of the fixed abrasive lapping process was developed and employed to numerically investigate the particle trajectories moving on the target surface by considering the different arraying forms of diamonds on the lapping plate. Findings: It was found from an analysis of both the uniformity and the fractal characteristics that the arraying form of diamonds on the lapping plate, with the distribution of latitude and longitude with an angle of 30° and a gap of concentric circles of 40 mm with a minimum radius of 70 mm and maximum radius of 190 mm, can be used to obtain the best uniformity and fractal characteristics in the fixed abrasive lapping of a bipolar plate. Conclusions: The distribution of the latitude and longitude of 40° and 30° considered in this study is expected to realize the best machining performance in the bipolar plate and present good cell performance.

Fractal Analysis of Human Gait Variability via Stride Interval Time Series

Fractal analysis of stride interval time series is a useful tool in human gait research which could be used as a marker for gait adaptability, gait disorder, and fall risk among patients with movement disorders. This study is designed to systematically and comprehensively investigate two practical aspects of fractal analysis which significantly affect the outcome: the series length and the parameters used in the algorithm. The Hurst exponent, scaling exponent, and/or fractal dimension are computed from both simulated and experimental data using three fractal methods, namely detrended fluctuation analysis, box-counting dimension, and Higuchi's fractal dimension. The advantages and drawbacks of each method are discussed, in terms of biases and variability. The results demonstrate that a careful selection of fractal analysis methods and their parameters is required, which is dependent on the aim of study (either analyzing differences between experimental groups or estimating an accurate determination of fractal features). A set of guidelines for the selection of the fractal methods and the length of stride interval time series is provided, along with the optimal parameters for a robust implementation for each method.

The Goodness-of-fit of the Fractal Dimension as a Diagnostic Factor in Breast Cancer

A large number of studies have found that the fractal dimension increases with the progression towards pathological or more pathological states, but there are also studies that have demonstrated the opposite relationship. In this study, we calculate the nuclear box-counting fractal dimension of 109 malignant, 113 benign, and 80 normal isolated breast cells in order to investigate its possible diagnostic importance. We computed the fractal dimension and its goodness-of-fit (i.e., the r-squared value that describes how well the regression line fits the set of the measurements) for two different sets of box size lengths. The statistical analysis did not confirm an important diagnostic potential of the nuclear fractal dimension of isolated breast cells. However, the goodness-of-fit did display a diagnostic potential. The r-squared value may be able to serve as a complementary diagnostic parameter.

Fractal and stochastic geometry inference for breast cancer: a case study with random fractal models and Quermass-interaction process

Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper.