Modeling Tumor Blood Vessel Dynamics - Mathematical Methods and Models in Biomedicine - page 114

improving the efficacy of subsequently administered chemotherapeutics (Fig. 1 e)
[ 18 , 37 , 60 , 72 ]. In theory, anti-angiogenic drugs would be used to improve vessel
network efficiency to increase the transport of subsequent drugs to cancer cells
[ 4 , 7 , 32 , 78 , 98 ]. In practice, though, the effects are unpredictable. Anti-VEGF ther-
apy can variably affect vessel diameters, permeabilities and network connectivity,
but it is difficult to determine whether the resulting networks have actually become
more efficient or whether the network improvements are transient or preserved
[ 43 , 88 , 97 ].
There are two main effects of anti angiogenic therapy that can lead to improved
network performance: structural changes to the network and decreased vascular
permeability. Structural and topological changes induced by anti-angiogenic therapy
(e.g., diameter changes, pruning redundant segments) may result in a network that
is more evenly distributed in the tissue. Such changes in topology may alter flow
patterns by changing the pressures and resistances within the network, thus forcing
flow into previously unperfused regions. A decrease in leakage of plasma can
cause similar changes in network pressure distribution, restoring normal perfusion
patterns. The ability of VEGF to modulate vascular permeability is well established,
but less is known about its involvement in structural changes in tumor vasculature.
At high levels, as in untreated tumors with significant hypoxia, VEGF causes
sprouting and vessel dilation, but at lower, normal levels, homeostasis is maintained.
We propose that anti-VEGF therapy brings the system into this normal regime of
VEGF concentrations, prevents sprouting and indiscriminate dilation, and enables
shear-based remodeling.
It is well known that endothelial cells sense shear stress and, through pathways
that include nitric oxide signaling, reorganize in the vessel wall to adjust local shear
to optimum levels [ 12 , 69 , 76 , 99 ]. By contracting or dilating individual segments,
overall flow patterns develop that distribute flow evenly through the network. It is
therefore possible that shear stress can serve as a driving force to remodel immature
tumor vessel networks, similar to that observed in wound healing and skeletal
muscle [ 33 , 35 , 36 , 71 ].

3 Models of Angiogenesis, Structural Adaptation,

and Normalization

Many mathematical models have been formulated and used to study blood vessel
development and function [ 14 , 15 , 27 , 41 , 45 , 56 , 67 , 73 , 86 ], drug delivery to tumor
tissue [ 5 , 8 - 10 , 63 ] or vessel normalization [ 18 , 40 , 53 , 72 , 81 ]. Unfortunately, there
is no single comprehensive, predictive mathematical framework for studying the
nonlinear relationships between vessel structure and function in real networks.
A number of elegant theoretical and experimental studies have addressed the
issues of tumor angiogenesis and structural adaptation of blood vessels. Lee et al.
modeled a growing tumor and a dynamically evolving blood vessel network,
reproducing inhomogeneous tumor-like capillary networks [ 55 ]. This model also