Dynamics of vascular branching morphogenesis: The effect of blood and tissue flow

Abstract

Vascularization of embryonic organs or tumors starts from a primitive lattice of capillaries. Upon perfusion, this lattice is remodeled into branched arteries and veins. Adaptation to mechanical forces is implied to play a major role in arterial patterning. However, numerical simulations of vessel adaptation to haemodynamics has so far failed to predict any realistic vascular pattern. We present in this article a theoretical modeling of vascular development in the yolk sac based on three features of vascular morphogenesis: the disconnection of side branches from main branches, the reconnection of dangling sprouts ͑"dead ends"͒, and the plastic extension of interstitial tissue, which we have observed in vascular morphogenesis. We show that the effect of Poiseuille flow in the vessels can be modeled by aggregation of random walkers. Solid tissue expansion can be modeled by a Poiseuille ͑parabolic͒ deformation, hence by deformation under hits of random walkers. Incorporation of these features, which are of a mechanical nature, leads to realistic modeling of vessels, with important biological consequences. The model also predicts the outcome of simple mechanical actions, such as clamping of vessels or deformation of tissue by the presence of obstacles. This study offers an explanation for flow-driven control of vascular branching morphogenesis.

Simulation study of brain blood flow regulation by intra-cortical arterioles in an anatomically accurate large human vascular network. Part II: Flow variations induced by global or localized modifications of arteriolar diameters

“…In this context, it may also prove useful to perform numerical studies on structures generated in silico to reproduce the main known morphometric and topological characteristics of the human intra-cortical networks (Cassot et al, 2006;Lauwers et al, 2008;Cassot et al, 2010;Lorthois and Cassot, 2010). Such studies could either use ad hoc algorithms to reproduce the fractal properties of arteriolar and venular trees (Schreiner et al, 2005;Bui et al, 2009) or be based on morphogenesis models (Nguyen et al, 2006;Lorthois and Cassot, 2010).…”

Fractal analysis of vascular networks: Insights from morphogenesis

“…after heart removal, capillary plexi fail to remodel, although continuing to grow for several days (le Noble et al, 2004). Furthermore, manipulation of blood flow, for example by ligation of an artery, dramatically affects the final vascular pattern (Nguyen et al, 2006;le Noble et al, 2004).…”

“…To our knowledge, only few models (Honda and Yoshizato, 1997;Gödde and Kurz, 2001;Fleury andSchwartz, 1999, 2000;Nguyen et al, 2006) account for this fundamental feature. However, Honda and Yoshizato (1997) do not reproduce the interdigitation of arterial and venous arborescences, whereas Gödde and Kurz (2001), while producing interdigitating vascular patterns, begin with an initial stochastic capillary growth phase which ends ''as soon as supplying and draining vessel structures approach each other''.…”

“…The aim of the present paper is to clarify both the spatial organization and scales of healthy vascular structures and the potential of fractal analysis in this context by a careful mathematical analysis of the significance of fractal dimension estimation in biological vascular patterns. Our hypothesis is that, aside from methodological problems (see Hamburger et al, 1996;Halley et al, 2004;Russ, 1994), the lack of consensus on the fractal nature of healthy vascular structures is rooted in their morphogenesis, which proceeds in two successive steps, as described in a series of theoretical papers (Fleury andSchwartz, 1999, 2000;Nguyen et al, 2006). Indeed, according to these authors, vascular networks form via progressive penetration of arterial and venous arborescences into a previously formed capillary mesh, by means of a Laplacian growth mechanism of hemodynamical origin, suggesting that mature vascular structure should be the union of quasi-fractal trees and of a homogeneous capillary mesh.…”

“…However, we believe that their interpretation of the data is incorrect. Indeed, relying on a series of theoretical papers about vascular morphogenesis (Fleury andSchwartz, 1999, 2000;Nguyen et al, 2006), we will construct simple examples demonstrating that the usual multiscale tools can lead to counter-intuitive results when the structures under study are not true fractals. For that purpose, the main features of vascular morphogenesis are first introduced.…”