Quantification of Blood Flow and Topology in Developing Vascular Networks

Abstract

Since fluid dynamics plays a critical role in vascular remodeling, quantification of the hemodynamics is crucial to gain more insight into this complex process. Better understanding of vascular development can improve prediction of the process, and may eventually even be used to influence the vascular structure. In this study, a methodology to quantify hemodynamics and network structure of developing vascular networks is described. The hemodynamic parameters and topology are derived from detailed local blood flow velocities, obtained by in vivo micro-PIV measurements. The use of such detailed flow measurements is shown to be essential, as blood vessels with a similar diameter can have a large variation in flow rate. Measurements are performed in the yolk sacs of seven chicken embryos at two developmental stages between HH 13+ and 17+. A large range of flow velocities (1 µm/s to 1 mm/s) is measured in blood vessels with diameters in the range of 25–500 µm. The quality of the data sets is investigated by verifying the flow balances in the branching points. This shows that the quality of the data sets of the seven embryos is comparable for all stages observed, and the data is suitable for further analysis with known accuracy. When comparing two subsequently characterized networks of the same embryo, vascular remodeling is observed in all seven networks. However, the character of remodeling in the seven embryos differs and can be non-intuitive, which confirms the necessity of quantification. To illustrate the potential of the data, we present a preliminary quantitative study of key network topology parameters and we compare these with theoretical design rules.

Exploring the potential of blood flow network data

“…This continuous remodelling by flow is thought to be able to convert an initially unstructured network (or 'plexus') into an efficient branching network. This behaviour has been observed, for instance, in mouse embryos [16] and chicken embryos [13,14], both common model systems to study human cardiovascular development. The advantage of these model systems is that they are also accessible for mechanical or chemical intervention, so that deviations from normal development can be observed (e.g.…”

“…2) can facilitate the detection of vessel segments. A detailed example of this approach is given in Kloosterman et al [13]; here only the key points are summarised in the following paragraph.…”

“…An example of one of the capabilities of these modern approaches is shown in Fig. 2, based on data obtained by Kloosterman et al [13]. In their approach, which is based on in vivo microscopic particle image velocimetry [20], a sequence of images is first obtained using digital cameras that document the motion of tracers (here erythrocytes).…”

“…Two examples are given: (1) correction of flow data based on conservation of mass and (2) in vivo testing of haemorheological models. The chicken embryo data provided by Kloosterman et al [13] will be used throughout this study, but the approach can readily be applied to other data sets.…”

In vitro blood flow visualizations and cell-free layer (CFL) measurements in a microchannel network

“…However, it is important to point out that the effect of the angles on the CFL thickness requires further investigation by performing similar blood flow studies in both simple and complex networks but this time by only changing the angles in a meaningful way. An adequate alternative to study such effect is by using as reference a geometry that follows the Murray law [50][51][52].…”