A three-dimensional model of the human airway tree. Lacunarity as a novel measure of cancer cells behavior. Lacunarity analysis: a general technique for the analysis of spatial patterns. An efficient implementation of the gliding box lacunarity algorithm. Multiple resolution texture analysis and classification. (eds) Fractal Geometry in Biological Systems: An Analytical Approach (CRC Press, 1996). Fractal methods and results in cellular morphology-dimensions, lacunarity and multifractals. Digital image analysis of self-similar cell profiles. Quantitating the subtleties of microglial morphology with fractal analysis. Neurons and fractals: how reliable and useful are calculations of fractal dimensions? J. Evaluating the fractal dimension of profiles. Fractal and multifractal analysis: a review. Fractal analysis of spatial and temporal variability. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Fractal analysis: methodologies for biomedical researchers. Chaos and fractals: New Frontiers of Science 2nd edn (Springer-Verlag, 2004). Change in lung tumor volume as a biomarker of treatment response: a critical review of the evidence. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.Īmerican Cancer Society. 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. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis.
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. 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.
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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. 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. Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions.