Cancer is one of the world's major health problems. After chemotherapy or surgery, some cancers, e.g., breast cancer and melanoma, by a still mysterious mechanism persist, apparently dormant, for years before distant metastases appear and tumors reactivate and grow. Latent tumor cells may survive by their microenvi- ronment partially excluding T-cells that would attack them. Transplant studies indicate that, rather than static quiescence, these cells and the immune system are in dynamic equilibrium and periodic bursts of cell division and elimination sometimes transform unobservable micrometastases that accumulate genetic, epigenetic and proteomic changes into macrometastases. Details and a complete mechanism are lacking. There is a paucity of experimental or theoretical models that recapitulate latency or its reactivation. One mouse breast cancer model exhibits short-term latency & recurrence. Mathematical cancer models typically describe single tumor growth and/or metastasis generation or the probability of several mutations, but not dor- mancy. We posit a new mathematical population model for the dynamics of a large ensemble (from one or many patients) of tumors of all sizes subject to mitosis, cell death (immunity, chemo or immunotherapy, necro- sis, etc.) and metastasis. Ensembles naturally incorporate response variations of similar tumors. Predictions are probabilistic, proportional to the expected tumor number of each size and time from any initial size distribu- tion. Smaller tumors often respond better to chemotherapy than larger ones, likely due to the latter's more ac- cumulated mutations; tumor-size-dependent parameters model this most simply. Our model finds a surprising interaction among these size-dependent processes in an ensemble that generates intriguing new unexpected qualitative behavior, e.g., diffusion in tumor size space that for the first time predicts dormancy & recurrence. This proposal intimately integrates this new mathematical model with the BALB/c murine breast cancer and the clear, stripeless zebrafish melanoma systems; both allow live non-invasive monitoring of tumor numbers and sizes vs time without animal sacrifice. Our model fits existing human hepatocellular carcinoma and im- mune-suppressed & competent fish melanoma histograms at many times extremely well with only 3 parame- ters. We plan new fish experiments to control/tune the level of immunity so as to access and test parameters predicted to yield dormancy & recurrence. We shall carry out detailed experiments on the mouse breast cancer system, which may exhibit dormancy & recurrence naturally, and use it to test our model. We shall also attempt to modulate its immunity to access and test parameters predicted to yield dormancy & recurrence. Since both these cancers show both ethnic and gender disparities, we shall use melanoma cell with snps that recapitulate ethnicity-specific genetics and segregate (fish) data by gender so as to see if parameters show ethnic and/or gender specificity; this would carry over to dormancy & recurrence. Time and funds permitting, we shall also begin to look at the effect of tumor shape on its parameters' tumor size dependences.
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