title: Reconstruction of the natural history of metastatic cancer and assessment of the effects of surgery: Gompertzian growth of the primary tumor.
abstract: This work deals with retrospective reconstruction of the individual natural history of solid cancer and assessment of the effects of treatment on metastatic progression. This is achieved through a mathematical model of cancer progression accounting for the growth of the primary tumor, shedding of metastases, their dormancy and growth at secondary sites. To describe dynamics of the primary tumor, we used the Gompertz law, a parsimonious model of tumor growth accounting for its saturation. Parameters of the model were estimated from the age and volume of the primary tumor at surgery and volumes of detectable bone metastases collected from one breast cancer patient and one prostate cancer patient. This allowed us to estimate, for each patient, the ages at cancer onset and inception of all detected metastases, the expected metastasis latency time, parameters of the Gompertzian growth of the primary tumor, and the rates of growth of metastases before and after surgery. We found that for both patients: (1) onset of metastasis occurred when primary tumor was undetectable; (2) inception of all surveyed metastases except one occurred before surgery; and most importantly, (3) resection of the primary tumor led to a dramatic increase in the rate of growth of metastases. The model provides an excellent fit to the observed volumes of bone metastases in both patients. Our results agree well with those obtained previously based on exponential growth of the primary tumor, which serves as model validation. Our findings support the notion of metastatic dormancy and indirectly confirm the existence of stem-like cancer cells in breast and prostate tumors. We also explored the logistic law of primary tumor growth; however, it degenerated into the exponential law for both patients analyzed. The conclusions of this work are supported by a vast body of experimental, clinical and epidemiological knowledge accumulated over the last century.
authors.affiliation: Department of Mathematics, 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 Computer Science and Mathematics, Ariel University, Ariel 40700, Israel. Electronic address: svetlanabu@ariel.ac.il.
authors.forename: Svetlana
authors.initials: S
authors.lastname: Bunimovich-Mendrazitsky
mesh_terms: D017668:Age of Onset; D000369:Aged, 80 and over; D001859:Bone Neoplasms / Q000556:secondary*; D001943:Breast Neoplasms / Q000473:pathology* / Q000601:surgery; D018450:Disease Progression; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D014411:Neoplastic Stem Cells / Q000473:pathology; D011471:Prostatic Neoplasms / Q000473:pathology* / Q000601:surgery; D012189:Retrospective Studies
keywords: Cancer dormancy; Gompertz growth; Logistic growth; Metastatic latency; Stem-like cancer cell; Surgery-induced acceleration of metastasis