Abstract
Simple SummaryThe recruitment of new vasculature via angiogenesis is a critical component of tumor development, which fundamentally influences tumor growth and response to treatment. The characterization of tumor-induced angiogenesis via mathematical models could enable approaches to forecast tumor response and improve patient care. In this review, we discuss how time-resolved imaging data integrated with mathematical modeling can be used to systematically investigate angiogenesis from the cell to tissue scale and ultimately forecast response to therapy.Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2–3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.
Highlights
In the early stages of tumor growth, a small population of tumor cells is supported by existing tissue vasculature and the diffusion of nutrients through the extravascular space
Anderson et al developed a continuum model of tumor angiogenesis by considering the rate of change of endothelial cell density determined by the sum of the effects ofchemical
The microvasculature was initialized with micro-computed tomography (CT) imaging, the tumor oxygenation status was calibrated with positron emission tomography (PET) imaging data sensitive to hypoxia, and tumor growth was characterized by proliferation estimated from PET imaging data
Summary
In the early stages of tumor growth, a small population of tumor cells is supported by existing tissue vasculature and the diffusion of nutrients through the extravascular space. Therapeutic regimens need to be optimized while considering the structural and functional characteristics of an individual’s tumor-associated vasculature Achieving this goal requires a biophysical mathematical theory that accurately characterizes the relevant quantities of interest in the dynamic relationship between the tumor, vasculature, and therapy. There has been great interest in the modeling of tumor angiogenesis at the tissue scale [29,30,31] These efforts have often been motivated by the emerging availability of crucial vasculature properties in patient or animal data that previously could only be assessed through highly invasive means—such as angiogenesis and regression rates [32] (i.e., a time scale of formation and regression of tumor-induced vasculature), interstitial pressure, and blood pressure along vessels [33]. We identified reviews or landmark articles that provided the foundation for both the mathematical theory and experimental techniques
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