Presenter: Adeyinka Lesi, Ph.D. (City College of New York)
Topic: A New Mathematical Model for the Dynamics of Large Tumor Populations and Applications to the Interpretation of Experimental Tumor Data
Though cancer progression is a complex interplay of many complicated biological processes such as genetic changes, chemical signals and metabolic considerations, our model examines how the dynamic interplay of just three processes can dictate disease progress. Our population balance model describes how the size distribution of a large ensemble of tumors evolve in time due to growth (mitosis), reduction (apoptosis or immunity) and metastasis, each with a size-dependent parameter. Mathematical analysis of the model’s parameter interactions leads to insights regarding the progression of metastatic cancer, including prediction of recurrence after long-term dormancy. We successfully tested the model against literature data on human hepatocellular carcinoma and then carried out extensive experiments on a zebrafish model of melanoma to validate the model. The experimental system consists of gender-segregated immune-competent and immune-suppressed translucent, stripeless zebrafish (casper variant) inoculated with a fluorescent GFP-expressing transgenic melanoma cell line (ZMEL). Obtaining parameters that optimally fit the data allowed the detection of differences between the immune status for each gender. Because the measured fish melanoma parameters are not in a range for which we predict dormancy and recurrence within fish lifetimes, this system cannot yet verify predictions on tumor recurrence. We complemented the above experiments with mathematical analysis, including both analytical and approximate solutions to the model for select parameters. We applied the theory of birth and death processes to estimate the probability and timing of recurrence. Furthermore, we have also developed a Markov chain simulation model to track the progression of discrete tumors. This formulation facilitates the study of tumor merging events by allowing individual tumors to be positioned in a virtual body. We used this model to investigate tumor merging in mouse lungs, which resolved the mismatch between the predicted number of lung metastasis and the observed number in mouse breast cancer experiments. Understanding the mechanisms and factors that influence the likelihood and timing of recurrence can strongly impact preferred treatments. Ultimately, the model may offer a flexible way to predict the progression of the cancer by using noninvasive imaging data to find model parameters.
