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

Abstract

Background: 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. Results: Thirty-one cases of patients suffering from metastatic melanoma have been scanned before and after two and after four cycles of treatment. For each patient, we calculated the fractal and multifractal dimensions using the box-counting method on the digitalised PET/CT images of all three studies to assess the therapeutic outcome. We modelled the spreading of malignant cells in the body via kinetic Monte Carlo simulations to address the dynamical evolution of the metastatic process and to predict the spatial distribution of malignant lesions. Our analysis shows that the fractal dimensions which describe the tracer dispersion in the body decrease consistently with the deterioration of the patient's therapeutic outcome condition. In 20 out of 24 cases, the fractal analysis results match those of the treatment outcome as defined by the oncologists, while 7 cases are considered as special cases because the patients had non-tumour-related findings 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) is 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 through 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.

New formulation of the Gompertz equation to describe the kinetics of untreated tumors

“…The theoretical and experimental results of this work confirm different findings reported previously in the literature, such as: 1) the fractal origin of GE 1 , GE 2 , GE 5 and GE 8 , as reported in [4, 15]; 2) the fractal property of tumors once reached n med /V med , a matter that agrees with [16, 17]; 3) the role of the fractal dimension for the understanding of TGK, as suggested by Sokolov [18] and Breki et al [19]; and 4) 1 < D f < 2, in agreement with [4, 20, 21] and the preferential growth along the largest diameter of the tumor, despite its ellipsoidal geometry [1, 3, 9, 11]. This fourth finding is in contradiction with 2 < D f < 3 reported by Breki et al [19] in patients with metastatic melanoma; 5) The condition 0 < u 2 < 1 for both types of tumors is consistent with the Steel equation [12]. If u 2 = 0, then the tumor growth fraction must be high so that its mean doubling time (TD) is short, in contrast to [10, 12].…”

Quantitative Dynamic 18F-FDG PET/CT in Survival Prediction of Metastatic Melanoma under PD-1 Inhibitors

“…The potential of fractal mathematics in oncological research and practice remains relatively unknown to most clinicians. Nevertheless, the hitherto rather limited but steadily growing literature in the field implies a possible contribution of the investigation of tumor heterogeneity, utilizing fractal principles on PET images, in tumor characterization and patient prognosis [ 48 , 49 , 50 , 51 ].…”

FDG PET/CT for assessing tumour response to immunotherapy

“…The apparently low specificity of these cut-off values, which conversely maintain high sensitivity, is attributable to the fact that response to immunotherapy depends on multiple factors. Imaging and metabolic data, analysed visually, semiquantitatively or with dedicated algorithms [ 36 ], are pieces of the “puzzle”. As a consequence, the metabolic characteristics of the tumour and its environment at baseline may be part of a larger panel of predictive factors of response to immunotherapy [ 37 ].…”