Modeling Tumor Blood Vessel Dynamics - Mathematical Methods and Models in Biomedicine - page 116

networks to address questions of heterogeneous perfusion and transport in relatively
large volumes of tumor tissue.

5 Modeling Vascular Adaptation During Anti-angiogenic

Therapy

Although many of the previous models of vascular remodeling are useful for
integrating physiological information, they generally make simplifying, yet crip-
pling, assumptions about vasculature, blood flow, and the boundary conditions.
To overcome these limitations and form a better understanding of this complex
physiology, we have developed a mathematical model that simulates blood flow in
complex vascular networks, incorporating the necessary components for simulating
vascular dynamics and function during anti-VEGF therapy. These components
include:

1. Lattice-Boltzmann calculations of the full flow field within the vasculature and
within the tissue
2. Diffusion and convection of soluble species such as oxygen or drugs within
vessels and the tissue domain
3. Distinct and spatially-resolved vessel hydraulic conductivities and permeabilities
for each species
4. Upstream signaling to control inlet vessel tone
5. Erythrocyte particles advecting in the flow and delivering oxygen with real
oxygen release kinetics
6. Hypoxia-driven VEGF production and vascular remodeling driven by VEGF
level and shear stress

The model decouples vascular leakiness and network structural changes,
allowing determination of how each influences flow patterns and oxygen and
drug delivery during anti-angiogenic therapy. An understanding of how hydraulic
conductivity and network architecture act independently “or in synergy” to enhance
delivery of chemotherapeutics will allow rational use of existing drugs, or the design
of new ones, to improve chemotherapy.
To develop our mechanistic model of structural adaptation, we use a
lattice-Boltzmann model (LBM), which solves flow and transport of blood
[ 20 , 61 , 81 , 83 , 84 ], oxygen, drugs and growth factors in the tissue. Being fully local,
LBM offers a distinct advantage over traditional CFD when dealing with complex
boundary conditions and highly irregular geometry within the computational
domain. Further, coding an LBM solver is rather simple, and the algorithm is
essentially the same in either two or three dimensions. In addition, the LBM
approach is imminently adaptable to parallel and distributed implementations.
Having its roots in kinetic theory, LBM also offers the advantage of studying the
continuum macroscopic properties of a system from its microscopic phenomena.