易普利姆玛治疗前后转移性黑色素瘤PET-CT图像的分形和多重分形分析
Fractal and multifractal analysis of PET-CT images of metastatic melanoma before and after treatment with ipilimumab
摘要：
已经使用分形和多重分形分析分析了患有转移性黑色素瘤的患者的具有F-18-氟脱氧葡萄糖（FDG）的PET/CT图像，以评估单克隆抗体伊匹单抗治疗对治疗结果的影响。我们的分析表明，描述示踪剂在体内分散的分形维数随着患者治疗结果条件的恶化而降低。在24例病例中，有20例的分形分析结果与病历的分形分析结果相匹配，而7例病例被认为是特殊病例，因为患者具有影响结果的非肿瘤相关的医疗状况或副作用。分形维数随着患者病情恶化（就疾病进展而言）而降低，这归因于示踪剂的分层定位，该示踪剂在受影响的病变中积累，并且不会均匀地扩散到整个身体。分形是恶性细胞在体内（循环系统、淋巴系统）繁殖所遵循的迁移模式的结果。多重分形谱的分析补充和支持分形分析的结果。在转移过程的动力学Monte Carlo建模中，少量恶性细胞在代表血液循环网络的分形介质中扩散。沿着它们的路径，恶性细胞以小的概率产生随机转移（集落），并且因此，形成与在PET/CT图像中观察到的类似的转移的分形空间分布。总之，我们提出，分形和多重分形分析在PET/CT图像的量化评价中具有潜在的应用，以监测疾病的演变以及对不同药物治疗的反应。
英文摘要：
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.
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