(790h) Predicting Cancer Progression using a Population Balance Model and Supporting Evidence from Zebrafish Melanoma Studies

Cancers are complicated diseases that in 2018, killed 600,000 people in the US. Reliable models for the progression of the disease save lives by guiding treatment and identifying risk factors. Of special interest is the perplexing phenomena of tumor dormancy and recurrence, where after treatment or surgery, patients remain disease-free for years or decades only to experience a sudden relapse of the same disease. We seek to explain this and other phenomena with a simple population balance model that describes how growth effects (e.g. mitosis), reduction effects (e.g. immunity or treatment) and metastases (inception of new tumors) determine disease progression.

In the model, these effects are represented as tumor-size-dependent rate parameters in a stochastic process. Treating cancer growth as an advection-diffusion transport process in tumor size space allows us to solve for the size distribution of tumors in a population of patients. Simulations using the model show that tumor size can change diffusively for long times after which the tumor begins to grow or shrink, indicating the model recapitulates the phenomena of dormancy and recurrence without any manipulation.

We used the zebrafish melanoma model to quickly acquire tumor growth data under various conditions including growth with and without the natural immunity and growth in different genders. The size-dependent parameter approach described experimental data well. We also saw statistically different immunity parameters between male and female fish, indicating how the model can be used to identify and elucidate population differences in disease progression. We further show through simulations backed by experimental data how changes in parameters affect the possibility of relapse using both parameters from animal and human cancers.

The model demonstrates a mechanism for tumor dormancy and recurrence that does not rely on any specific biological explanation such as the so called ‘angiogenic switch.’ Rather it shows that a series of small, incremental changes such as those due to a size-dependence can generate dormancy and recurrence. Recognizing that these phenomena could have no single biological cause mandates a radical shift in research methodology for this problem.