Modelling solute transport in the brain microcirculation: is it really well mixed inside the blood vessels?

Modelling regenerative angiogenesis in peripheral nerve injuries

“…The blood flow itself is solved using a pore-network model that considers the blood as a monophasic, non-Newtonian fluid with an apparent viscosity (Lorthois et al 2011). Regarding the intravascular transport of oxygen, we assimilate the vessels as one-dimensional elements and extend the effective advection-diffusion-reaction equation describing the cross-section average concentration derived by Berg et al (2020) for a generic nutrient to the case of oxygen. The coupling between this model and the cell-solute model is achieved by means of a membrane condition with an effective permeability to describe the local flux of oxygen going from the vessel to the hydrogel.…”

Solute dispersion in bifurcating networks

“…The vessel's length and radius are L and a, respectively. Following Fung & Tang (1975) and Berg et al (2020) among many others, we assume that solute concentration in a single vessel, C(x, r, t), satisfies an advection-diffusion equation,…”

“…Following Fung & Tang (1975) and Berg et al. (2020) among many others, we assume that solute concentration in a single vessel, , satisfies an advection–diffusion equation, where and are the axial and radial coordinates, respectively; is time; is the flow velocity given by the Poiseuille law; and is the coefficient of molecular diffusion. This equation is subject to initial and boundary conditions The last condition implies that vessel walls are impermeable to the solute.…”

Mixing in a sheared particulate suspension

“…Many situations in nature or in industries involve mixing a diffusive scalar in a sheared particulate suspension. The transport of oxygen or drugs by blood (Kabacaoglu, Quaife & Biros 2017;Kaoui 2018;Berg et al 2020), of nutrients inside the cell cytoplasm (Goldstein & van de Meent 2015), of adjuvants in concretes or of heat in some exchangers (Dbouk 2018;Yousefi et al 2020) provide a few examples illustrating the importance of this problem, which still lacks a fundamental description. So far, the enhanced transport properties of sheared suspensions have been described mostly at a macroscopic scale through an effective diffusion coefficient (Metzger, Rahli & Yin 2013;Souzy et al 2015;Thøgersen & Dabrowski 2017).…”

“…The transport of oxygen or drugs by blood (Kabacaoğlu, Quaife & Biros 2017; Kaoui 2018; Berg et al. 2020), of nutrients inside the cell cytoplasm (Goldstein & van de Meent 2015), of adjuvants in concretes or of heat in some exchangers (Dbouk 2018; Yousefi et al. 2020) provide a few examples illustrating the importance of this problem, which still lacks a fundamental description.…”