Modeling Tumor Blood Vessel Dynamics - Mathematical Methods and Models in Biomedicine - page 112

improve the efficacy of subsequently administered chemotherapeutics [ 34 , 38 ,
62 , 92 , 96 ]. The predominant effects of anti-VEGF therapies are decreased vessel
leakiness (hydraulic conductivity), decreased vessel diameters and pruning of the
unstable vessel network [ 42 , 88 , 97 ](Fig. 1 ). It is thought that each of these effects
can influence perfusion of the vessel network, inducing flow in regions that were
previously sluggish or stagnant. Unfortunately, changes induced by anti-VEGF
therapies are transient and overlapping in time, and a rational, generalized strategy
for using normalization in combination with chemotherapeutics remains elusive.
This is in part due to the nonlinearity in the system and the inability to distinguish
the effects of decreased vessel leakiness from those due to network structural
changes.
In many physiological systems, angiogenic blood vessels respond to blood
forces, reorganizing locally to optimize the network globally [ 1 , 33 , 35 , 36 , 71 ].
Undergoing structural adaptation, some segments dilate while others contract;
excessive contraction can even lead to complete regression of some vessel segments.
A stable configuration is eventually reached and then supported and fortified
by perivascular cells. In contrast, tumor blood vessels are chronically immature,
probably due to the high levels of VEGF and other growth factors in the mi-
croenvironment. Interestingly, many anti-VEGF, therapies can cause maturation and
stabilization of tumor blood vessels through a process resembling flow-based adap-
tive remodeling (Fig. 1 b). Because it so closely resembles flow-based adaptation,
it is possible that the central mechanism underlying tumor vessel normalization is
the same: blood shear forces drive the structural remodeling. But how the blood
forces, VEGF and other signals are integrated by the endothelium is not known.
An appropriate mathematical model, which incorporates the necessary elements for
predicting the convection and diffusion of nutrients and drugs throughout tumor
vessels and tissues, as well as the adaptive remodeling of the network topology, is
needed to dissect the critical determinants of vessel normalization and to predict
how it might be used most effectively in combination with cytotoxic drugs.

2 Anti-angiogenic Therapies and Tumor Vessel

Normalization

Because tumor expansion depends on nutrients delivered by blood vessels, Folkman
proposed that preventing new vasculature would effectively control the progression
of solid tumors [ 74 ]. And because VEGF is a major growth factor that supports
the growth of new vasculature, it has been the target of many recent therapies
[ 24 - 26 , 39 ].
Unfortunately, the original goal of anti-angiogenic therapies to starve tumors
by targeting their blood supply has been difficult to achieve. In most clinical
studies, these therapies have had inconsistent effects on tumor physiology, with
no long-term inhibition of tumor growth [ 48 , 49 ]. Nevertheless, drugs that block
angiogenic growth factors such as VEGF often have dramatic effects on the structure
and function of the vascular network, normalizing the tumor blood vessels and