Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Unraveling the occurrence of fracture non-unions with a multiscale bioregulatory model
Aurélie Carlier, Nick van Gastel, Geert Carmeliet, Hans Van Oosterwyck, Liesbet Geris

Last modified: 2014-06-09



The healing of a bone fracture strongly depends on the development of a new blood vessel network

(angiogenesis) in the fracture zone. In a previous study, a multiscale model of sprouting angiogenesis

during fracture healing, including Dll4-Notch1 signalling to determine tip cell selection (MOSAIC [1]),

was extended with a rigorous description of the influence of oxygen on several cellular processes.

Currently, we are using this mathematical model as a tool for a more in depth investigation of the

influence of oxygen in critical size defects and possible therapies thereof.

Results and Discussion

The oxygen model correctly simulated the

formation of a non-union in critical size

defects and was used to study the underlying

mechanisms. In the central region of the

fracture callus, we found that all cells die due

to severe hypoxia, leading to bone healing

arrest. This finding prompted us to explore

the influence of the vasculature from the host

environment on the fracture healing outcome.

Experimental evidence has previously shown

that blood vessels originating in the overlying

muscle contribute to the revascularization of

the fracture callus [2]. Interestingly, the

oxygen model predicts a considerably

improved healing outcome in the case of full

muscle contribution and an intermediate

result if the fracture callus is only partially

supplied with blood vessels from the host

environment (Fig 1).

Figure 1: (A) The geometrical domain

considers one-fourth of the real fracture callus

geometry of a critical size defect (assuming

symmetry); 1 periosteal callus; 2 intercortical

callus; 3 endosteal callus; 4 cortical bone ends.

(B) Predicted spatiotemporal evolution of the

active vasculature and bone matrix density (x

0.1 g/ml) in a critical size defect with different

contributions of the overlying muscle to the

vascularization of the fracture callus. Red dots

at day zero represent endothelial cells from the

host environment.

Motivated by these results, we investigated whether the injection of either mesenchymal stem cells

(MSCs), osteochondrogenic growth factors or the combination thereof in an impaired environment, i.e.

without muscle contribution, must be delayed in order to allow a (partial) restoration of the vasculature

and be more effective (Fig 2). We found that the injection of only growth factors at either post fracture

day (PFD) 7, 14, 28, 42 or 56 does not improve the bone formation since oxygen tensions still become

critically low in the central callus area due to delayed revascularization. The injection of MSCs is more

beneficial at PFD 42 or 56 since the vasculature in the interfragmentary gap is already partially restored,

sustaining the viability of the injected cells. Similar conclusions can be drawn for the combination

product, except that the combination yields better results at PFD 56 than the injection of cells alone (Fig


Figure 2: Predicted amount of bone formed at PFD

90 as a function of the PFD at which the treatment,

consisting of a single injection of cells, growth factors

or a combination thereof, was initiated.


This work clearly indicates the importance of angiogenesis in tissue engineering. Future work will focus

on the in silico design of efficient vascularization strategies for tissue engineering constructs, including

angiogenic growth factor delivery and in vitro prevascularization or a combination thereof.


1. Carlier A., et al. PLoS Comput Biol, 8(10), 2012. 2. Harry L., et al. Plast Reconstr Surg, 124, 2009


Aurélie Carlier is a PhD fellow of the Research Foundation Flanders (FWO-Vlaanderen).

Short abstract

In this study we hypothesized that the spatiotemporal distribution of oxygen tension, influenced by

amongst others cellular consumption as well as the timely revascularization of the callus is an important

determinant of the occurrence of fracture non-unions. Therefore, we performed a thorough sensitivity

analysis on a previously established multiscale bioregulatory model of fracture healing in order to unravel

the non-intuitive oxygen dynamics. In a next step this knowledge was used to design potential treatment



The main objective of this study was to use a multiscale model of fracture healing to explore the

underlying mechanisms of the occurrence of fracture non-unions and design potential treatment strategies



Multiscale – bone fracture healing – hybrid – model