(510b) Cancer Progression As a Transport Problem

Approximately 600,000 cancer deaths occurred in the United States in 2018 but scientists have estimated the prophylactic and clinical measures developed since 1990 have avert 300,000 deaths a year. Researchers have made headway, but the complexities of cancer are very far being unraveled. Accurate prognostic models for disease progression play an important role in improving patient outcomes, yet aspects of tumor progression, such as the phenomena of dormancy and recurrence remain mysterious and our work appears to be the first quantitative model of it. We propose a population balance model that uses size-dependent parameters representing tumor growth, reduction and metastasis to predict how the distribution of tumor sizes in a cohort of patients changes with time. Size-dependence is a reasonable proxy for effects due to tumor genomics, because larger tumors tend to have acquired more adaptive mutations, and can acquire better access to nutrient supply. Such dependence means tumor growth rate is proportional to tumor surface area, volume or some combination.

The model transforms into an advection-diffusion transport equation in tumor size space. Having a diffusive term and variable parameters means tumors can have low Péclet and high Péclet number regimes of growth in the same patient. Transitioning from a low Péclet regime, where tumor size changes slowly and fluctuates randomly, to a high Péclet regime, where tumors grow or shrink quickly, is reminiscent of dormancy and recurrence in cancer progression. This model thereby provides mechanistic insight into one way recurrence can occur in patients. An important feature of using a distribution rather than some other measure for disease progression is the ability to capture rare events in the tails of the distribution. In disease progression, these rare events (i.e. an especially large cancer or a recurrence after many years of being apparently cancer-free) have the largest impact on the patient.

We have analyzed how the interactions amongst parameters affects tumor progression. For example, an effect resembling dormancy and recurrence predominantly occurs when growth is only slightly more size-dependent than cell death due to, e.g., immunity or chemo or radiation therapy. This means a wider range of sizes are in the low Péclet regime. Additionally, the side-dependence of the metastasis parameter can drastically alter the shape of the distribution curve at small tumor sizes.

To validate the use of the model for realistic data, we developed a fitting procedure to obtain rate parameters from experimental and clinical data. We successfully obtained parameter for literature data for hepatocellular carcinoma as well as our own far more extensive experimental data using a zebrafish melanoma model that captures the effect of immunity (and gender) on cancer growth. In the case of the zebrafish model, growth is more size-dependent than immunity, implying tumors in these fish can diffuse from a low Péclet regime to a growth regime. Using only a few size-dependent parameters, the model matches experimental data and recapitulates complex behaviors such as dormancy and recurrence that researchers find in clinical data.