Fractal Analysis of Lung Structure in Chronic Obstructive Pulmonary Disease

Abstract

Chest CT is often used for localizing and quantitating pathologies associated with chronic obstructive pulmonary disease (COPD). While simple measurements of areas and volumes of emphysema and airway structure are common, these methods do not capture the structural complexity of the COPD lung. Since the concept of fractals has been successfully applied to evaluate complexity of the lung, this review is aimed at describing the fractal properties of airway disease, emphysema, and vascular abnormalities in COPD. An object forms a fractal if it exhibits the property of self-similarity at different length scales of evaluations. This fractal property is governed by power-law functions characterized by the fractal dimension (FD). Power-laws can also manifest in other statistical descriptors of structure such as the size distribution of emphysema clusters characterized by the power-law exponent D. Although D is not the same as FD of emphysematous clusters, it is a useful index to characterize the spatial pattern of disease progression and predict clinical outcomes in patients with COPD. The FD of the airway tree shape and the D of the size distribution of airway branches have been proposed indexes of structural assessment and clinical predictions. Simulations are also useful to understand the mechanism of disease progression. Therefore, the power-law and fractal analysis of the parenchyma and airways, especially when combined with computer simulations, could lead to a better understanding of the structural alterations during the progression of COPD and help identify subjects at a high risk of severe COPD.

Fractal analysis reveals functional unit of ventilation in the lung

“…In the present study, we assessed the fractal dimension of ventilation and tissue density in thin slices of the lung which result in 2D images. A 2D plane of a 3D process can accurately estimate the fractal properties of the spatial process as demonstrated by previous studies in the literature (Paumgartner et al 1981;Venegas & Galletti, 2000;Andersen et al 2012;Porzionato et al 2016;Tanabe et al 2020).…”

“…Beyond the challenge of direct measurement of gas concentrations within a complex bifurcating structure, the study of the inhomogeneity in lung ventilation is complicated by the fact that this inhomogeneity depends on the scale of resolution. Both the branching structure of pulmonary airways (West et al 1986;Haefeli-Bleuer & Weibel, 1988) and alveoli (Tanabe et al 2020) have been shown to have self-similar, fractal properties over a wide range of length scales. As a general rule, spatial inhomogeneity of a measured quantity q, representing an intrinsic characteristic in a self-similar fractal system, is a power law of the spatial length scale d, or resolution at which the measurement is performed, such that:…”

“…1986; Haefeli‐Bleuer & Weibel, 1988) and alveoli (Tanabe et al . 2020) have been shown to have self‐similar, fractal properties over a wide range of length scales. As a general rule, spatial inhomogeneity of a measured quantity q , representing an intrinsic characteristic in a self‐similar fractal system, is a power law of the spatial length scale d , or resolution at which the measurement is performed, such that: Where D f is fractal dimension, obtained from the slope of the log–log plot of q (inhomogeneity) as a function of length scale.…”

Computational Mesoscale Framework for Biological Clustering and Fractal Aggregation

“…They are important in physics [1, 2], chemistry [3, 4, 5], biology (i.e. multicellular organisms [6, 7], blood clotting [8], bronchi [9], nervous system morphogenesis [10] and tumor cells in cancer [11, 12]). Biological clustering is defined as the formation of higher-molecular-mass species as a result of the adhesion of smaller species.…”

Monofractal analysis of functional magnetic resonance imaging: An introductory review

“…Fractal analysis is a tool for quantifying various fractal features, one of which is self‐similarity, that is the presence of a self‐similar, repeating spatial or temporal structure that is observed at no dominant scale (hence is scale‐free or scale‐invariant; see Figure 1) (Eke et al, 2002). In recent decades, fractal analysis of physiological time series has revealed the fractal nature of multiple biophysical processes, predominantly in the cardiovascular (Captur et al, 2017), respiratory (Tanabe et al, 2020), and neurovascular (Lemmens et al, 2020) systems. While the scaling behavior of cardiac rhythms has arguably been the most widely investigated (Cecen & Erkal, 2009), the fractal properties of the brain have been increasingly recognized and are demonstrating great value in understanding brain function (Bullmore & Sporns, 2009).…”