$fractal dimension$

$fractal dimension$

Nonetheless, these simple quantifications of lung structure do not capture the complexity of the size and spatial distributions of the pathological features in COPD lungs. Indeed, the area and volume of emphysematous regions, the wall and lumen cross-sectional area (CSA) of airways, and the volume of smaller vessels have been measured and utilized as indexes of emphysema severity, airway remodeling, and reduced vascularity and shown to be associated with various outcomes of COPD ( Grydeland et al., 2010 Haruna et al., 2010 Matsuoka et al., 2010 Han et al., 2011). CT is accessible and less invasive and allows for a 3D separate evaluation of airway disease, emphysema, and vascular abnormality for the whole lungs ( Lynch and Al-Qaisi, 2013 Labaki et al., 2017). Alternatively, CT is commonly used to estimate the pathology of the lungs and extrapulmonary abnormalities. Even when histological samples are obtained from a biopsy specimen, these samples are usually small or affected by other diseases, such as malignancy, and cannot represent the heterogeneous structural changes in whole lungs. Histology is a gold standard for the morphological analysis of COPD lungs, but histology is too invasive to perform in live patients. A combination of these airway, lung parenchyma, and vessel lesions underlies the structural heterogeneity, which not only influences lung function but can be a driving factor for the disease progression in patients with COPD ( Mondoñedo et al., 2019). Furthermore, morphological alteration of vessels is also a pathological feature, and pulmonary hypertension is a common comorbidity in patients with COPD ( Matsuoka et al., 2010 Coste et al., 2019). For example, COPD patients with similar airflow limitation may have substantial near homogeneously-distributed emphysema without airway disease, moderate upper-dominant heterogeneously-distributed emphysema with moderate airway disease, or little emphysema with severe airway disease ( Schroeder et al., 2013 Lynch et al., 2015). Additionally, the heterogeneous spatial distribution of these two pathological changes in each patient complicates understanding of the structural basis of the disease.

$fractal dimension$

Emphysema and airway disease are two main pathological changes that contribute to airflow limitation, but their relative contributions to the disease differ among patients. Airflow limitation measured by spirometry is a key physiological feature and gold standard to diagnose COPD. 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.Ĭhronic obstructive pulmonary disease (COPD) is a major respiratory disease that imposes a high social health burden worldwide ( Adeloye et al., 2015). Simulations are also useful to understand the mechanism of disease progression. 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. 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. 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. This fractal property is governed by power-law functions characterized by the fractal dimension (FD). An object forms a fractal if it exhibits the property of self-similarity at different length scales of evaluations.

$fractal dimension$

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. 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.

2Department of Biomedical Engineering, Boston University, Boston, MA, United StatesĬhest CT is often used for localizing and quantitating pathologies associated with chronic obstructive pulmonary disease (COPD).

1Department of Respiratory Medicine, Graduate School of Medicine, Kyoto University, Kyoto, Japan.

Naoya Tanabe 1 * † Susumu Sato 1 † Béla Suki 2 Toyohiro Hirai 1

$fractal dimension$

Fractal dimension