A New Mathematical Model for Tumor Growth, Reduction and Metastasis, Validation with Zebrafish Melanoma and Potential Implications for Dormancy and Recurrence

The genetic and environmental heterogeneity associated with tumors makes cancer treatment and recovery a difficult and unpredictable process. Patients with initially similar disease can experience vastly different outcomes including sustained recovery, refractory disease or, remarkably, recurrence years after treatment. Mathematical models informed with animal and human data provide tools for theoretical and clinical understanding of cancer progression and of the causes of highly variant disease outcomes. This work postulates a population balance model to describe how populations of a large ensemble of tumors of different sizes evolve in time. Each tumor can grow or reduce in size and metastasize. Gender-segregated, immune-competent and immune-suppressed translucent zebrafish (Casper variant) were inoculated with a transgenic melanoma cell line expressing human BRAF V600E and GFP and observed for tumor progression and metastasis. The model describes both these fish data sets, full histograms of population number vs size at multiple times for both immune states, and a human hepatocellular carcinoma data set also consisting of multiple time histograms very well with a minimum of cancer-specific parameters. The only zebrafish parameter to show strong gender-dependence was the host-dependent tumor reduction (immunity) parameter. This result significantly predicts that men should have far worse outcomes than females, yet similar metastasis rates, which are both indeed the case in human melanomas. Moreover the dynamic growth - reduction interplay, for certain relationships between these processes parameters in the model provides a potential mechanism for apparent cancer dormancy and recurrence. Although fish melanoma parameters are not in this range, the model guides future work to try to access it.