Assessing tumor treatment modalities using an allometric model

Allometric growth models apply universal growth laws to predict growth of organisms and structures from very small to very large and have accurately modeled avascular tumor growth. These models have been extended by coupling the allometric growth law to a reaction-diffusion equation for nutrient transport to model necrotic core formation [A. L. Garner, Y. Y. Lau, T. L. Jackson, M. D. Uhler, D. W. Jordan, and R. M. Gilgenbach, J. Appl. Phys. 98, 124701 (2005).] and incorporated vascularization by applying energy arguments to incorporate vascularization [A. B. Herman, V. M. Savage, G. B. West, PLoS ONE 6, e22973 (2011).]. Recent developments of artificial, 3D tumor in vitro models that can incorporate vasculature provide a future means to assess chemical, physical, and combined treatments [R. Michna, M. Gadde, A. Ozkan, M. DeWitt, and M. Rylander, Biotech. Bioeng., https://doi.org/10.1002/bit.26778] for eventual clinical use. In this study, we modify the allometric growth model to assess the implications of dosage profiles on tumor growth. For a constant dosage, we observe that a subthreshold treatment reduces the steady-state tumor size while a suprathreshold amount destroys the tumor. The therapeutic implications of these results and future experiments will be discussed.