论文标题

使用细胞自动机评估熵和分形维度作为肿瘤生长和治疗反应的生物标志物

Evaluation of Entropy and Fractal Dimension as Biomarkers for Tumor Growth and Treatment Response using Cellular Automata

论文作者

Legaria-Peña, Juan Uriel, Sánchez-Morales, Félix, Cortés-Poza, Yuriria

论文摘要

基于细胞的模型为模拟具有适应性,弹性质量的复杂系统(例如癌症)提供了有用的方法。他们对单个细胞相互作用的关注使它们成为研究癌症疗法影响的特别合适的策略,癌症疗法通常旨在破坏单细胞动态。在这项工作中,我们还建议它们是研究癌症成像生物标志物(IBM)时间演变的可行方法。我们提出了一种用于肿瘤生长的细胞自动机模型和三种不同的疗法:化学疗法,放疗和免疫疗法,遵循文献中记录的完善的建模程序。该模型产生了一系列肿瘤图像,从中获得了两个生物标志物的时间序列:熵和分形维度。我们的模型表明,在癌细胞传播开始时,分形维度更快,而熵对不同疗法方式对肿瘤诱导的变化的反应更大。这些观察结果表明,所提出的生物标志物的预测值可能随着时间而变化。因此,重要的是要评估它们在癌症的不同阶段和不同成像方式的使用。从结果中得出的另一个观察结果是,当应用治疗以沿着自动机区域的散射方式攻击癌细胞时,这两个生物标志物都会缓慢变化,在治疗结束时留下了多个独立的细胞簇。因此,模拟生物标志物时间序列的变化模式可以反映给定癌症干预的空间作用的基本品质。

Cell-based models provide a helpful approach for simulating complex systems that exhibit adaptive, resilient qualities, such as cancer. Their focus on individual cell interactions makes them a particularly appropriate strategy to study the effects of cancer therapies, which often are designed to disrupt single-cell dynamics. In this work, we also propose them as viable methods for studying the time evolution of cancer imaging biomarkers (IBM). We propose a cellular automata model for tumor growth and three different therapies: chemotherapy, radiotherapy, and immunotherapy, following well-established modeling procedures documented in the literature. The model generates a sequence of tumor images, from which time series of two biomarkers: entropy and fractal dimension, is obtained. Our model shows that the fractal dimension increased faster at the onset of cancer cell dissemination, while entropy was more responsive to changes induced in the tumor by the different therapy modalities. These observations suggest that the predictive value of the proposed biomarkers could vary considerably with time. Thus, it is important to assess their use at different stages of cancer and for different imaging modalities. Another observation derived from the results was that both biomarkers varied slowly when the applied therapy attacked cancer cells in a scattered fashion along the automatons' area, leaving multiple independent clusters of cells at the end of the treatment. Thus, patterns of change of simulated biomarkers time series could reflect on essential qualities of the spatial action of a given cancer intervention.

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