ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

closed loop allowing the initiation of blood flow [1].
In order to ensure a correct development of the vasculature, the balance between stalk
and tip cell phenotypes must be tightly controlled. The process of tip cell selection
consists of two main steps. Firstly a gradient of vascular endothelial growth factor
(VEGF) is formed due to a hypoxic environment which causes the upregulation of
VEGF-expression and secretion. The VEGF-mediated activation of the VEGFR-2
receptors induces the upregulation of Dll4. Since the VEGF-levels are highest at the
leading tip, Dll4 is mostly expressed in tip cells. In the second step Dll4 activates the
Notch1-receptors on the neighboring cells, downregulating the expression of VEGFR-2
in the trailing stalk cells, making them less susceptible to VEGF. In this manner the
adequate amount of tip cells, required for a correct sprouting pattern, is established [1-
4].
Sprouting angiogenesis clearly involves multiple biological scales: the intracellular
scale where gene expression is altered so that different phenotypes (e.g. tip and stalk
cells) can arise, the cellular scale that involves proliferation and migration and the tissue
scale that encompasses the concentration fields of soluble and insoluble biochemical
factors. As these scales are highly coupled, multiscale models are needed to study the
mechanisms of sprouting angiogenesis. Currently, many computational models of
angiogenesis exist (for comprehensive reviews on mathematical models of angiogenesis
the reader is referred to [5-7]) but to the best of the authors’ knowledge, there is only
one model of sprouting angiogenesis with Dll4-Notch1 rigorously implemented [2].
However, its dynamics have not been simulated at the tissue level or in the context of
bone fracture healing. Furthermore, there is a lack of multiscale models of fracture
repair incorporating angiogenesis [8]. This study will couple the multiple biological
scales with the appropriate multiscale modeling techniques, thereby establishing a novel
platform to investigate sprouting angiogenesis during fracture healing.
3. MATERIALS AND METHODS
The MOSAIC model presented in this work integrates an intracellular module based on
the work of Bentley et al. [2] into the model of Peiffer et al. [9]. Fig. 1 gives a schematic
overview of the MOSAIC model which consists of (1) a tissue level describing the
various key processes of bone regeneration with continuous variables, (2) a cellular
level representing the developing vasculature with discrete endothelial cells and (3) the
intracellular level that defines the internal dynamics of every endothelial cell.
The discrete blood vessel network is implemented on a lattice. Every endothelial cell
has unique intracellular protein levels, which control the behavior of that specific cell.
The intracellular module is adapted from the agent-based model of Bentley et al. [2] and
consists of the following variables: the level of VEGFR-2 (V), Notch1 (N), Dll4 (D),
active VEGFR-2 (V’), active Notch1 (N’), effective active VEGFR-2 (V”), effective
active Notch1 (N”) and the amount of actin (A). The effective active levels (V” and N”)
represent the levels at the nucleus, influencing gene expression and include the time
delay of translocation to the nucleus. The amount of actin (A) refers to the polymerized
actin levels (F-actin) inside the cell. The intracellular dynamics will determine the
movement of the tip cell and whether sprouting and/or anastomosis will occur. As such,
the fundamental processes occurring at the micro-scale determine the evolution of the
vascular network.