A Hybrid Model for Three-Dimensional Simulations of Sprouting Angiogenesis

Abstract

Recent advances in cancer research have identified critical angiogenic signaling pathways and the influence of the extracellular matrix on endothelial cell migration. These findings provide us with insight into the process of angiogenesis that can facilitate the development of effective computational models of sprouting angiogenesis. In this work, we present the first three-dimensional model of sprouting angiogenesis that considers explicitly the effect of the extracellular matrix and of the soluble as well as matrix-bound growth factors on capillary growth. The computational model relies on a hybrid particle-mesh representation of the blood vessels and it introduces an implicit representation of the vasculature that can accommodate detailed descriptions of nutrient transport. Extensive parametric studies reveal the role of the extracellular matrix structure and the distribution of the different vascular endothelial growth factors isoforms on the dynamics and the morphology of the generated vascular networks.

Vascular remodelling of an arterio-venous blood vessel network during solid tumour growth

“…In particular the geometry and characteristics of the initial vasculature has to be taken into account, which is missing in almost all existing tumour growth models. Not only the morphology of the emerging tumour vasculature is completely different in vessel-in-growth models (Anderson and Chaplain, 1998;Zheng et al, 2004;Friboes et al, 2007;Wise et al, 2008;Milde et al, 2008) when compared with our results, also their blood flow characteristics and their determinants for blood-borne drug transport are completely different (McDougall et al, 2002;McDougall et al, 2006).…”

“…This describes certain processes on a coarser scale than ab-initio calculations (Friboes et al, 2007;Bauer et al, 2008;Wise et al, 2008, Milde et al, 2008. For instance rather than calculating the solid stress within the tumour explicitly and incorporating it, among other factors, into the vessel collapse probability we use the prediction of contiuum mechanical models for tumour growth (see e.g.…”

“…The subsequent migration, branching and anstomosis of angiogenic sprouts was recently modelled in a detailed way (Bauer et al, 2007;Milde et al, 2008), involving besides VEGF matrix metalloprotease (MMP) and the filamentous structure of the extracellular matrix (ECM). In our model tip cells migrate in the direction of a sufficiently large VEGF gradient (chemotaxis), otherwise randomly.…”

“…Such a rule is necessary when the initial vasculature is ubiquitous as in our model since otherwise the presence of VEGF generats tip-cells in an uncontrolled fashion. 2) Instead of modelling angiogenic sprout migration and branching involving matrix metalloproteasies and collagen fibers (Bauer et al, 2007;Milde et al, 2008) we used commonly accpeted stochastic rules (Anderson and Chaplain, 1998). The ubiquity of original vessels in our model diminishes the importance of the migration and banching process per se, since the intercapillary distances are rather short, which is different from models without initial vasculature.…”

A mechano-regulatory model for bone healing predictions under the influence of ultrasound

“…A similar method was also used in [23] for the determination of the acceleration of the tip cells. A rule-based model of sprouting angiogenesis has been also reported in [24] where the elongation and proliferation of stalk cells as well as the effect of Notch factor production are explicitly simulated.…”