Biomedical Engineering Reference
In-Depth Information
oxygen transport are then solved to yield a 3D map of oxygen level in the
computational domain.
Developing three-dimensional arterial tree based on sprouting angiogenesis
upon chemotaxis mediated by growth factors secreted by ischemic cells to match
the metabolic demand that can reorganize was modeled using morphometrical
optimality principles [
1374
]. The signaling is reduced to a single messenger
(VEGF). The iterative arterial tree generation that results from the balance between
growth and degeneration is carried out on a gradually growing simulation domain.
The geometry of the vasculature relies on node coordinates and connectivity. Each
vessel segment assumed to be a rigid, straight, cylindrical tube (of constant radius
R
and given length
L
) is represented by a single directed (streamwise pointing)
edge connecting 2 nodes. Vessel bending is defined by intermediary nodes (with
radius invariance). Branches are defined as paths between 2 bifurcation nodes.
Morphological constraints also prescribe the area ratio at bifurcations:
R
t
=
∑
R
b
(10.1)
(
p
∈
[
2
,
3
]
) as well as bifurcation angles:
R
t
+
R
i
−
R
j
cos
φ
i
=
.
(10.2)
2
R
t
R
i
The model relies on the mutual interplay of oxygen supply and released VEGF
amount with a given oxygen consumption rate function of the local oxygen
concentration, an arbitrary oxygen-dependent VEGF secretion rate function, and
given diffusivities (
04 m
2
/s). Reaction-transport
equations allow to approximate the perfusion and to compute VEGF concentration.
Capillary elongation or bifurcation is governed by a log-normal distribution of
branch aspect ratios. Sprouting occurs at downstream end nodes (symmetrical
bifurcations) and intermediary nodes (asymmetrical bifurcations), where the VEGF
concentration is maximal and exceeds a threshold; the direction is dictated by the
local VEGF gradient. Tree remodeling is ensured by pruning and rescaling.
Tumor growth characterized by its volume (
V
1
(
41 m
2
/s;
D
O
2
=
2
.
D
VEGF
=
1
.
) coupled to a developing tumor
vasculature described by its carrying capacity (
K
1
(
t
)
; tumor volume supported by
blood input at time
t
) was modeled as well as effects of anti-angiogenic therapy
with various drug administration modes [
1375
]. Hence, tumor vasculature growth
depends on the balance between tumor-derived stimulatory and inhibitory factors
(vessel loss function
t
)
) and exogenous drugs, in addition to natural loss (
N
).
Exogenous inhibitors of angiogenesis include cytostatic drugs that impede the
formation of new blood vessels and cytotoxic drugs that destroy existing blood
vessels (blood drug concentration
c
ψ
(
V
)
). Changes in blood vessel
density have delayed effects and this delay can affect therapy efficiency. The specific
growth rates of the tumor (
V
2
/
(
t
)
; drug effect
κ
c
(
t
)
K
1
) depend on the ratio
between the tumor volume and the carrying capacity of the vasculature (
V
V
1
) and vasculature (
K
2
/
/
K
),
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