The natural history of renal cell carcinoma with pulmonary metastases illuminated through mathematical modeling

• Published in: Mathematical biosciences 2019-03, Vol.309, p.118-130
• Main Authors: Hanin, Leonid, Jandrig, Burkhard, Pavlova, Lyudmila, Seidel, Karen
• Format: Article
• Language: English
• Subjects: Aged; Cancer; Carcinoma, Renal Cell - pathology; Clear cell-type renal cell carcinoma; Computed tomography; Data processing; Female; Humans; Kidney cancer; Kidney Neoplasms - pathology; Latency; Lung cancer; Lung Neoplasms - pathology; Lung Neoplasms - secondary; Lungs; Male; Mathematical models; Maximum likelihood; Metastases; Metastasis; Metastatic latency; Middle Aged; Models, Biological; Neoplasm Metastasis - pathology; Parameter estimation; Parameter identification; Patients; Poisson process; Primary tumor; Renal cell carcinoma; Surgery; Tumors
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2019.01.008

•Duration of metastatic latency was very small compared to the growth period.•Seeding of the first lung metastasis occurred before primary tumor reached detectable size, which implies that early cancer detection would not have prevented metastasis.•Primary tumor in situ may have slowed down metastatic growth; and.•Primary tumor contained a relatively fast growing subpopulation of metastasis-producing cells, which is consistent with the aggressive course of the disease in these patients. The goal of this study is to uncover some unobservable aspects of the individual-patient natural history of metastatic renal cell carcinoma (RCC) through mathematical modeling. We analyzed four clear cell RCC patients who at the time of primary tumor resection already had pulmonary metastases. Our description of the natural history of cancer in these patients was based on a parameterized version of a previously proposed very general mathematical model adjusted to these clinical cases. For each patient, identifiable model parameters were estimated by the method of maximum likelihood from the volumes of lung metastases computed from CT scans taken at or around the time of surgery. The model-based distribution of the volumes of lung metastases with likelihood maximizing parameters provided an excellent fit to the data for all patients analyzed. We found that, according to the model, the most likely scenario in all four patients had the following clinically important features: (1) duration of metastatic latency was very small compared to the growth period; (2) seeding of the first lung metastasis occurred before primary tumor reached detectable size, which implies that early cancer detection would not have prevented metastasis; (3) primary tumor contained a relatively fast growing subpopulation of metastasis-producing cells, which is consistent with the observed aggressive course of the disease; and (4) the volume of the primary tumor at the time of metastasis survey does not seem to be correlated with such characteristics of the metastatic burden as the number of detected lung metastases, their total volume, and the volume of the largest detected lung metastasis.