Hochman Gili, Shacham-Shmueli Einat, Raskin Stephen P, Rosenbaum Sara, Bunimovich-Mendrazitsky Svetlana
Department of Mathematics, Ariel University, Ariel, Israel.
Sheba Medical Center, Tel Hashome, Israel.
Front Physiol. 2020 Dec 17;11:533101. doi: 10.3389/fphys.2020.533101. eCollection 2020.
Most cases of deaths from colorectal cancer (CRC) result from metastases, which are often still undetectable at disease detection time. Even so, in many cases, shedding is assumed to have taken place before that time. The dynamics of metastasis formation and growth are not well-established. This work aims to explore CRC lung metastasis growth rate and dynamics. We analyzed a test case of a metastatic CRC patient with four lung metastases, with data of four serial computed tomography (CT) scans measuring metastasis sizes while untreated. We fitted three mathematical growth models-exponential, logistic, and Gompertzian-to the CT measurements. For each metastasis, a best-fitted model was determined, tumor doubling time (TDT) was assessed, and metastasis inception time was extrapolated. Three of the metastases showed exponential growth, while the fourth showed logistic restraint of the growth. TDT was around 93 days. Predicted metastasis inception time was at least 4-5 years before the primary tumor diagnosis date, though they did not reach detectable sizes until at least 1 year after primary tumor resection. Our results support the exponential growth approximation for most of the metastases, at least for the clinically observed time period. Our analysis shows that metastases can be initiated before the primary tumor is detectable and implies that surgeries accelerate metastasis growth.
大多数结直肠癌(CRC)死亡病例是由转移导致的,而这些转移灶在疾病检测时往往仍无法被检测到。即便如此,在许多情况下,人们认为转移在那个时间点之前就已经发生了。转移形成和生长的动态过程尚未完全明确。这项工作旨在探索结直肠癌肺转移的生长速率和动态过程。我们分析了一名患有四处肺转移灶的转移性结直肠癌患者的病例,利用四次连续计算机断层扫描(CT)的数据来测量未接受治疗时转移灶的大小。我们将三种数学生长模型——指数模型、逻辑模型和冈珀茨模型——应用于CT测量数据。对于每个转移灶,确定最佳拟合模型,评估肿瘤倍增时间(TDT),并外推转移灶起始时间。其中三个转移灶呈现指数生长,而第四个则显示出生长的逻辑抑制。TDT约为93天。预测的转移灶起始时间至少在原发性肿瘤诊断日期前4 - 5年,不过直到原发性肿瘤切除后至少1年它们才达到可检测的大小。我们的结果支持了大多数转移灶的指数生长近似,至少在临床观察期内是如此。我们的分析表明,转移灶可以在原发性肿瘤可检测到之前就开始形成,这意味着手术会加速转移灶的生长。