Towards integration of time-resolved confocal microscopy of a 3D in vitro microfluidic platform with a hybrid multiscale model of tumor angiogenesis

The goal of this study is to calibrate a multiscale model of tumor angiogenesis with time-resolved data to allow for systematic testing of mathematical predictions of vascular sprouting. The multi-scale model consists of an agent-based description of tumor and endothelial cell dynamics coupled to a continuum model of vascular endothelial growth factor concentration. First, we calibrate ordinary differential equation models to time-resolved protein concentration data to estimate the rates of secretion and consumption of vascular endothelial growth factor by endothelial and tumor cells, respectively. These parameters are then input into the multiscale tumor angiogenesis model, and the remaining model parameters are then calibrated to time resolved confocal microscopy images obtained within a 3D vascularized microfluidic platform. The microfluidic platform mimics a functional blood vessel with a surrounding collagen matrix seeded with inflammatory breast cancer cells, which induce tumor angiogenesis. Once the multi-scale model is fully parameterized, we forecast the spatiotemporal distribution of vascular sprouts at future time points and directly compare the predictions to experimentally measured data. We assess the ability of our model to globally recapitulate angiogenic vasculature density, resulting in an average relative calibration error of 17.7% ± 6.3% and an average prediction error of 20.2% ± 4% and 21.7% ± 3.6% using one and four calibrated parameters, respectively. We then assess the model’s ability to predict local vessel morphology (individualized vessel structure as opposed to global vascular density), initialized with the first time point and calibrated with two intermediate time points. In this study, we have rigorously calibrated a mechanism-based, multiscale, mathematical model of angiogenic sprouting to multimodal experimental data to make specific, testable predictions.Author summary: The integration of experimentally obtained data to complex mathematical models, specifically in relation to tumor angiogenesis, is a rich field that is of great interest to the community. This integration, typically through calibrating model parameters that govern the mathematical model, is paramount to making specific, testable predictions of the system under investigation. In this work, we have used several forms of quantitative experimental data to inform a complex mathematical model to predict tumor angiogenesis. We do this through a multi-step calibration method by separating individual processes described in the model and utilizing data to inform key model parameters involved in that process. At the final step in our calibration method, we use longitudinal studies of tumor sprouting in our 3D microfluidic platform to fully parameterize our multiscale model of tumor angiogenesis. We utilize early time points to inform model parameters and then test our models ability to predict both local vascular features and vascular summary statistics at later time points. We have shown, with uncertainty, the prediction ability of our model and have shown we can reliably predict in vitro experiments of tumor-induced angiogenesis.