title: A quantitative insight into metastatic relapse of breast cancer.
abstract: BACKGROUND
  Metastatic relapse is the principal source of breast cancer mortality. This work seeks to uncover unobservable, yet clinically important, aspects of post-surgery metastatic relapse of breast cancer and to quantify effects of surgery on metastatic progression.
  
  
  METHODS
  We classified metastases into three categories: (1) solitary cancer cells that were formed before or during surgery and either circulate in blood or are lodged at various secondary sites; (2) dormant or slowly growing avascular metastases; and (3) vascular secondary tumors. We developed a general mathematical model aimed at describing post-surgery dynamics of these three metastatic states. One parametric version of the model assumed that sojourn times of metastases in the three states are exponentially distributed while another was based on Erlang distribution. Model parameters were estimated from a sample of metastatic relapse or censoring times for 673 breast cancer patients treated with surgery.
  
  
  RESULTS
  We estimated the expected number of metastases at surgery and mean sojourn times for the three states and found that both are decreasing with state number. We also computed the probability that metastatic relapse resulted from a metastasis in a given state at surgery. The values of these attribution probabilities suggest that under the Erlang model all three states have a considerable effect on metastatic relapse while in the case of exponential model this is true for states 1 and 2 only.
  
  
  CONCLUSIONS
  (1) In some patients metastasis occurred before surgery; (2) our results confirm significance of metastatic dormancy; (3) according to the model surgery stimulates escape from dormancy, promotes angiogenesis and accelerates metastatic growth in a fraction of breast cancer patients. Taken summarily, these findings call into question the benefits of primary tumor resection for certain categories of breast cancer patients.
authors.affiliation: Department of Mathematics and Statistics, Idaho State University, 921 S. 8th Avenue, Stop 8085, Pocatello, ID 83209-8085, USA. Electronic address: hanin@isu.edu.
authors.forename: Leonid
authors.initials: L
authors.lastname: Hanin
authors.affiliation: Department of Applied Mathematics, St. Petersburg Polytechnical University, Polytechnicheskaya ul. 29, 195251 St. Petersburg, Russia.
authors.forename: Lyudmila
authors.initials: L
authors.lastname: Pavlova
mesh_terms: D001943:Breast Neoplasms / Q000473:pathology*; D018572:Disease-Free Survival; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008954:Models, Biological; D009362:Neoplasm Metastasis; D009364:Neoplasm Recurrence, Local / Q000473:pathology*; D011336:Probability; D015203:Reproducibility of Results
keywords: Attribution probability; Metastatic cascade; Metastatic dormancy; Surgery-induced acceleration of metastasis