A coupled spatial-network model: A mathematical framework for applications in epidemiology

by Louis V. Kunz, Jesús J. Bosque, Mohammad Nikmaneshi, Ibrahim Chamseddine, Lance L. Munn, Jan Schuemann, Harald Paganetti, and Alejandro Bertolet

AMBER (Agent-based fraMework of radioBiological effects of Radiotherapy) simulates tumor growth, vasculature, and radiation response by combining agent-based modeling (ABM) with Monte Carlo (MC) methods. Using a hybrid approach and voxelated geometry it tracks tumor and microenvironmental changes over time, including oxygen levels and VEGF at a mesoscopic scale, allowing for facilitated comparison with MRI and CT. The inclusion of multifactorial biological determinants allows AMBER to represent tumor growth and response to radiotherapy in a relevant manner, with for example the appearance of a necrotic core. The modular implementation of the framework allows for easy extension and refinement to specific applications. 

Evolution of the distribution of alive and necrotic cells in a central slice of a tumor grown with AMBER, along with the evolution of the vasculature, from low density in purple to high density in yellow. Third row shows the micro vessel density, with well oxygenated voxels in blue and hypoxic/anoxic voxels in orange/red. Last row shows the explicit vasculature, with only healthy vasculature in the first column and new vessels growing due to angiogenesis in the next columns.