title: Lung cancer-a fractal viewpoint.
abstract: Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.
authors.affiliation: Section of Hematology/Oncology, University of Chicago, 5841 South Maryland Avenue, MC 2115 Chicago, IL 60637, USA.
authors.forename: Frances E
authors.initials: FE
authors.lastname: Lennon
authors.affiliation: Department of Cell and Molecular Biology, Feinberg School of Medicine, Northwestern University, 303 East Chicago Avenue, Chicago, IL 60611, USA.
authors.forename: Gianguido C
authors.initials: GC
authors.lastname: Cianci
authors.affiliation: Department of Pathology, University of Chicago, 5841 South Maryland Avenue, MC 2115 Chicago, IL 60637, USA.
authors.forename: Nicole A
authors.initials: NA
authors.lastname: Cipriani
authors.affiliation: NorthShore University Health System, 2650 Ridge Avenue, Evanston, IL 60201, USA.
authors.forename: Thomas A
authors.initials: TA
authors.lastname: Hensing
authors.affiliation: Department of Radiology, University of Chicago, 5841 South Maryland Avenue, MC 2115 Chicago, IL 60637, USA.
authors.forename: Hannah J
authors.initials: HJ
authors.lastname: Zhang
authors.affiliation: Department of Radiology, University of Chicago, 5841 South Maryland Avenue, MC 2115 Chicago, IL 60637, USA.
authors.forename: Chin-Tu
authors.initials: CT
authors.lastname: Chen
authors.affiliation: Department of Medicine, University of Chicago, 5841 South Maryland Avenue, MC 2115 Chicago, IL 60637, USA.
authors.forename: Septimiu D
authors.initials: SD
authors.lastname: Murgu
authors.affiliation: Section of Hematology/Oncology, University of Chicago, 5841 South Maryland Avenue, MC 2115 Chicago, IL 60637, USA.
authors.forename: Everett E
authors.initials: EE
authors.lastname: Vokes
authors.affiliation: Department of Radiology, University of Chicago, 5841 South Maryland Avenue, MC 2115 Chicago, IL 60637, USA.
authors.forename: Michael W
authors.initials: MW
authors.lastname: Vannier
authors.affiliation: Section of Hematology/Oncology, University of Chicago, 5841 South Maryland Avenue, MC 2115 Chicago, IL 60637, USA.
authors.forename: Ravi
authors.initials: R
authors.lastname: Salgia
mesh_terms: D017709:Fractals; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008175:Lung Neoplasms / Q000473:pathology*; D008954:Models, Biological