Estimating Dose Painting Effects in Radiotherapy: A Mathematical Model

Tumor heterogeneity is widely considered to be a determinant factor in tumor progression and in particular in its recurrence after therapy. Unfortunately, current medical techniques are unable to deduce clinically relevant information about tumor heterogeneity by means of non-invasive methods. As a consequence, when radiotherapy is used as a treatment of choice, radiation dosimetries are prescribed under the assumption that the malignancy targeted is of a homogeneous nature. In this work we discuss the effects of different radiation dose distributions on heterogeneous tumors by means of an individual cell-based model. To that end, a case is considered where two tumor cell phenotypes are present, which we assume to strongly differ in their respective cell cycle duration and radiosensitivity properties. We show herein that, as a result of such differences, the spatial distribution of the corresponding phenotypes, whence the resulting tumor heterogeneity can be predicted as growth proceeds. In particular, we show that if we start from a situation where a majority of ordinary cancer cells (CCs) and a minority of cancer stem cells (CSCs) are randomly distributed, and we assume that the length of CSC cycle is significantly longer than that of CCs, then CSCs become concentrated at an inner region as tumor grows. As a consequence we obtain that if CSCs are assumed to be more resistant to radiation than CCs, heterogeneous dosimetries can be selected to enhance tumor control by boosting radiation in the region occupied by the more radioresistant tumor cell phenotype. It is also shown that, when compared with homogeneous dose distributions as those being currently delivered in clinical practice, such heterogeneous radiation dosimetries fare always better than their homogeneous counterparts. Finally, limitations to our assumptions and their resulting clinical implications will be discussed.

肿瘤异质性（tumor heterogeneity）被广泛认为是肿瘤进展，尤其是治疗后复发的决定性因素。遗憾的是，当前医学技术尚无法通过非侵入性手段获取具有临床价值的肿瘤异质性相关信息。因此，当放射治疗作为首选治疗方案时，放射剂量分布的制定均以靶恶性病灶具有均一性为假设前提。本研究通过基于单细胞的模型（individual cell-based model），探讨了不同放射剂量分布对异质性肿瘤的影响。为此，我们设定了存在两种肿瘤细胞表型的研究场景，假定二者在细胞周期时长与放射敏感性特性上存在显著差异。本文研究表明，正是由于这些差异，对应表型的空间分布会随肿瘤生长发生变化，进而可随肿瘤增殖进程预测肿瘤异质性的发展。具体而言，若初始状态下多数普通癌细胞（CCs）与少数癌症干细胞（CSCs）呈随机分布，且假定癌症干细胞的细胞周期显著长于普通癌细胞，则随着肿瘤生长，癌症干细胞会逐渐聚集于肿瘤内部区域。由此可得，若假定癌症干细胞的放射抵抗性强于普通癌细胞，那么可通过针对高放射抵抗性肿瘤细胞表型占据区域提升放射剂量的异型放射剂量分布方案，增强肿瘤的局部控制效果。研究同时证实，相较于当前临床实践中常规采用的均一剂量分布方案，此类异型放射剂量分布的治疗效果始终更优。最后，本文将讨论本研究假设的局限性及其潜在的临床意义。