Metastases Growth Patterns in vivo—A Unique Test Case of a Metastatic Colorectal Cancer Patient

Gili Hochman, Einat Shacham-Shmueli, Tchia Heymann, Stephen Raskin, Svetlana Bunimovich-Mendrazitsky

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Colorectal cancer (CRC) is one of the most common causes of cancer-related mortality worldwide. Most cases of deaths result from metastases, assumed to be shed, in many cases, before disease detection. Providing reliable predictions of the metastases' growth pattern may help planning treatment. Available mathematical tumor growth models rely mainly on primary tumor data, and rarely relate to metastases growth. The aim of this work was to explore CRC lung metastases growth patterns. We used data of a metastatic CRC patient, for whom 10 lung metastases were measured while untreated by seven serial computed tomography (CT) scans, during almost 3 years. Three mathematical growth models—Exponential, logistic, and Gompertzian—were fitted to the actual measurements. Goodness of fit of each of the models to actual growth was estimated using different scores. Factors affecting growth pattern were explored: size, location, and primary tumor resection. Exponential growth model demonstrated good fit to data of all metastases. Logistic and Gompertzian growth models, in most cases, were overfitted and hence unreliable. Metastases inception time, calculated by backwards extrapolation of the fitted growth models, was 8–19 years before primary tumor diagnosis date. Three out of ten metastases demonstrated enhanced growth rate shortly after primary tumor resection. Our unique data provide evidence that exponential growth of CRC lung metastases is a legitimate approximation, and encourage focusing research on short-term effects of surgery on metastases growth rate. Significance: Providing reliable predictions of the metastases' growth pattern using mathematical models may help determining the optimal treatment plan that fits a given patient best and maximizes the probability of cure.

Original languageEnglish
Article number56
JournalFrontiers in Applied Mathematics and Statistics
StatePublished - 12 Nov 2019


  • exponential growth
  • gompertzian growth
  • logistic growth
  • lung metastases
  • mathematical growth models
  • primary tumor resection


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