Department of Mathematics, Idaho State University, 921 S. 8th Avenue, Pocatello, ID 83209-8085, USA.
Math Biosci. 2010 Feb;223(2):133-41. doi: 10.1016/j.mbs.2009.11.006. Epub 2009 Nov 20.
A comprehensive mechanistic model of cancer natural history was utilized to obtain an explicit formula for the distribution of volumes of detectable metastases in a given secondary site at any time post-diagnosis. This model provided an excellent fit to the volumes of n=31, 20 and 15 bone metastases observed in three breast cancer patients 8 years, 5.5 years and 9 months after primary diagnosis, respectively. The model with optimal parameters allowed us to reconstruct the individual natural history of cancer for the first patient. This gave definitive answers, for the patient in question, to the following three questions of major importance in clinical oncology: (1) How early an event is metastatic dissemination of breast cancer? (2) How long is the metastasis latency time? and (3) Does extirpation of the primary breast tumor accelerate the growth of metastases? Specifically, according to the model applied to the first patient, (1) inception of the first metastasis occurred 29.5 years prior to the primary diagnosis; (2) the expected metastasis latency time was about 79.5 years; and (3) resection of the primary tumor was followed by a 32-fold increase in the rate of metastasis growth. The model and our conclusions were validated by the results for the two other patients.
利用一个全面的癌症自然史机制模型,获得了在给定的次级部位在诊断后任何时间检测到的转移体积的分布的明确公式。该模型与分别在原发性诊断后 8 年、5.5 年和 9 个月的 3 名乳腺癌患者的 n=31、20 和 15 个骨转移体积非常吻合。具有最佳参数的模型使我们能够重建第一个患者的个体癌症自然史。这为该患者提供了临床肿瘤学中三个重要问题的明确答案:(1)乳腺癌的转移扩散有多早?(2)转移潜伏期有多长?(3)切除原发性乳腺肿瘤是否会加速转移的生长?具体而言,根据应用于第一个患者的模型,(1)第一个转移的发生时间是在原发性诊断前 29.5 年;(2)预期的转移潜伏期约为 79.5 年;(3)切除原发性肿瘤后,转移的生长速度增加了 32 倍。模型和我们的结论通过另外两名患者的结果得到了验证。