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Fractal and multifractal analysis of PET-CT images of metastatic melanoma before and after treatment with ipilimumab

PET/CT with F-18-Fluorodeoxyglucose (FDG) images of patients suffering from metastatic melanoma have been analysed using fractal and multifractal analysis to assess the impact of monoclonal antibody ipilimumab treatment with respect to therapy outcome. Our analysis shows that the fractal dimensions which describe the tracer dispersion in the body decrease consistently with the deterioration of the patient therapeutic outcome condition. In 20 out-of 24 cases the fractal analysis results match those of the medical records, while 7 cases are considered as special cases because the patients have non-tumour related medical conditions or side effects which affect the results. The decrease in the fractal dimensions with the deterioration of the patient conditions (in terms of disease progression) are attributed to the hierarchical localisation of the tracer which accumulates in the affected lesions and does not spread homogeneously throughout the body. Fractality emerges as a result of the migration patterns which the malignant cells follow for propagating within the body (circulatory system, lymphatic system). Analysis of the multifractal spectrum complements and supports the results of the fractal analysis. In the kinetic Monte Carlo modelling of the metastatic process a small number of malignant cells diffuse throughout a fractal medium representing the blood circulatory network. Along their way the malignant cells engender random metastases (colonies) with a small probability and, as a result, fractal spatial distributions of the metastases are formed similar to the ones observed in the PET/CT images. In conclusion, we propose that fractal and multifractal analysis has potential application in the quantification of the evaluation of PET/CT images to monitor the disease evolution as well as the response to different medical treatments.