Computational design of drainage systems for vascularized scaffolds

Abstract

This computational study analyzes how to design a drainage system for porous scaffolds so that the scaffolds can be vascularized and perfused without collapse of the vessel lumens. We postulate that vascular transmural pressure—the difference between lumenal and interstitial pressures—must exceed a threshold value to avoid collapse. Model geometries consisted of hexagonal arrays of open channels in an isotropic scaffold, in which a small subset of channels was selected for drainage. Fluid flow through the vessels and drainage channel, across the vascular wall, and through the scaffold were governed by Navier-Stokes equations, Starling’s Law of Filtration, and Darcy’s Law, respectively. We found that each drainage channel could maintain a threshold transmural pressure only in nearby vessels, with a radius-of-action dependent on vascular geometry and the hydraulic properties of the vascular wall and scaffold. We illustrate how these results can be applied to microvascular tissue engineering, and suggest that scaffolds be designed with both perfusion and drainage in mind.

Vascular Development and Morphogenesis in Biomaterials

“…Moreover, when the drain-to-vessel distance was held constant while the scaffold permeability was varied, the stabilizing effect of drainage was stronger in scaffolds of greater porosity (20 mg/mL vs. 30 mg/mL fibrin; Figure 6.4b). These results are all consistent with numerical models of the pressure distribution across the endothelium and in the scaffold (Figure 6.4c), and suggest that a large transmural pressure can be obtained by minimizing the hydraulic resistance from the vessel wall to low-pressure drainage (Truslow et al 2009).…”

“…This resistance lies in series with the resistance across the vessel wall; thus, in scaffolds of higher resistance, the pressure gradients in the scaffold are higher, the pressure differences across the vessel wall (i.e., P TM ) are lower, and the vessel is less stable (Truslow et al 2009). Indeed, we have experimentally found in fibrin gels of various densities that vascular stability is anticorrelated with scaffold permeability K (Figure 6.2b) (Wong et al 2013).…”

Carbon nanotube interaction with extracellular matrix proteins producing scaffolds for tissue engineering

“…This complex environment has not yet been achieved, but efforts are being made for such an organic model that could be produced satisfactorily. 42 The synthetic scaffold should act to promote the optimization of growth and cell development in injured tissue. It must be implanted, seeded with cells, directly into the affected area of tissue to be regenerated, 43 or seeded with cells and cultured in vitro with the intention of forming the new tissue prior to implantation.…”

Perfusion systems that minimize vascular volume fraction in engineered tissues

“…Thus, the same optima should apply to models in which oncotically active solutes are present in the perfusate, the endothelial hydraulic conductivity is spatially heterogeneous ͑e.g., due to a flowdependent vascular phenotype 31 ͒, or the scaffold is passively drained. 20 Other optimization functions ͑e.g., oxygen extraction efficiency͒ are certainly valid, and the choice of function will depend on the external constraints imposed on the engineered tissue. We expect lower vascular volume fractions to generally correlate with greater extraction efficiencies; thus, optimal designs based on this and possibly other functions may not differ substantially from those based on volume fractions.…”