Department of Mathematics, Idaho State University, 921 S. 8th Avenue, Stop 8085, Pocatello, ID 83209, USA.
Cancers (Basel). 2011 Sep 20;3(3):3632-60. doi: 10.3390/cancers3033632.
This article brings mathematical modeling to bear on the reconstruction of the natural history of prostate cancer and assessment of the effects of treatment on metastatic progression. We present a comprehensive, entirely mechanistic mathematical model of cancer progression accounting for primary tumor latency, shedding of metastases, their dormancy and growth at secondary sites. Parameters of the model were estimated from the following data collected from 12 prostate cancer patients: (1) age and volume of the primary tumor at presentation; and (2) volumes of detectable bone metastases surveyed at a later time. This allowed us to estimate, for each patient, the age at cancer onset and inception of the first metastasis, the expected metastasis latency time and the rates of growth of the primary tumor and metastases before and after the start of treatment. We found that for all patients: (1) inception of the first metastasis occurred when the primary tumor was undetectable; (2) inception of all or most of the surveyed metastases occurred before the start of treatment; (3) the rate of metastasis shedding is essentially constant in time regardless of the size of the primary tumor and so it is only marginally affected by treatment; and most importantly, (4) surgery, chemotherapy and possibly radiation bring about a dramatic increase (by dozens or hundred times for most patients) in the average rate of growth of metastases. Our analysis supports the notion of metastasis dormancy and the existence of prostate cancer stem cells. The model is applicable to all metastatic solid cancers, and our conclusions agree well with the results of a similar analysis based on a simpler model applied to a case of metastatic breast cancer.
本文将数学建模应用于前列腺癌自然史的重建和治疗对转移进展影响的评估。我们提出了一个全面的、完全基于机制的癌症进展数学模型,该模型考虑了原发肿瘤潜伏期、转移瘤脱落、转移瘤休眠和继发部位生长等因素。该模型的参数是根据从 12 名前列腺癌患者中收集的数据进行估计的:(1)就诊时原发肿瘤的年龄和体积;(2)随后调查的可检测骨转移的体积。这使我们能够为每个患者估计癌症发病年龄和第一次转移的起始时间、预期转移潜伏期以及治疗开始前后原发肿瘤和转移瘤的生长速度。我们发现,对于所有患者:(1)第一次转移的起始时间发生在原发肿瘤不可检测时;(2)所有或大部分检测到的转移的起始时间发生在治疗开始之前;(3)转移脱落的速度在时间上基本保持不变,与原发肿瘤的大小无关,因此受治疗的影响很小;最重要的是,(4)手术、化疗和放疗可能会导致转移瘤平均生长速度急剧增加(对于大多数患者来说增加几十倍或几百倍)。我们的分析支持转移休眠和前列腺癌干细胞存在的观点。该模型适用于所有转移性实体瘤,我们的结论与基于简化模型应用于转移性乳腺癌病例的类似分析结果非常一致。