Emergent cell-free layer asymmetry and biased haematocrit partition in a biomimetic vascular network of successive bifurcations

Abstract

We describe, characterise and explain emerging heterogeneity of red bolood cell partitioning within a network substantially deviating from empirical predictions.

Continuum microhaemodynamics modelling using inverse rheology

“…However, not only the average haematocrit, but also the distribution of RBCs within the side branch is changed, with haematocrit skewed towards higher values at the inner wall of the daughter branch (that closest to the bifurcation point). Although not widely addressed, this phenomenon can be seen in previous studies in vivo (Pries et al 1989;Manjunatha and Singh 2002;Ye et al 2016), in vitro (Sherwood et al 2014b;Shen et al 2016) and in silico (Balogh and Bagchi 2017;Lykov et al 2015;Ye et al 2016;Zhou et al 2021). Even on vessel scales where the continuum assumption breaks down ( ≈ 20 μm (Cokelet 1999)), the time-averaged haematocrit distribution follows these characteristics, as demonstrated elegantly in a numerical study of a capillary network (Balogh and Bagchi 2018).…”

“…Experimental studies of haematocrit distributions have predominantly been carried out in long straight capillary tubes in vitro (Alonso et al 1995;Pries et al 1992) or selected regions of microvascular networks in vivo (Kim et al 2007;Yalcin et al 2011), where a large distance between bifurcations allows for a 'cell-free' or 'celldepleted' layer to develop at the walls (CFL or CDL, respectively). In practice, even where a CFL has had sufficient distance to form, it will be disrupted at the next bifurcation and will take many vessel diameters to recover (Ye et al 2016), with high likelihood of another bifurcation occurring before this happens, dependent on the particular microvascular network of interest (Bishop et al 2001;Luo et al 2017;Zhou et al 2021). Notably, even in 1969 Merrill noted: 'It is surprising that in the literature so much emphasis has been placed on annular layers of clear plasma at the wall of the living vessel in spite of the cinematographic proof that under normal conditions no such layer exists' (Merrill 1969).…”

“…Such modelling approaches are increasing in elegance and efficiency, but are fundamentally restricted by the large number of RBCs, even at microvessel scales. A vessel section such as investigated in this study would contain 7000 RBC at a given moment in time, with a turnover rate of 1 s. As a result, even with supercomputing, finite RBC modelling is limited by computational expense and hence typically applied to simulation in two dimensions (Ye et al 2016), at vessel scales below ≈ 30 μm in three dimensions (Balogh and Bagchi 2017;Freund and Vermot 2014;Lykov et al 2015) or at low haematocrits (Zhou et al 2021). For larger vessels, finite RBC approaches have predominantly been used to model long, straight vessel sections using periodic boundary conditions for efficiency (Lei et al 2013).…”

A few upstream bifurcations drive the spatial distribution of red blood cells in model microfluidic networks

“…12 and 17 and recently confirmed in ref. 16 and 18-20. In the case of a bifurcation with daughter branches of equal diameter, this may result in the RBC enrichment of the low flow branch 12,[16][17][18][19][20] and lead to a situation that is qualitatively similar to the case with daughter branches of unequal diameters, where the low-flow branch preferentially receives blood from the enriched central region. 12,21 Predicting the distribution of RBCs in interconnected networks, even the simplest ones, has thus proven highly challenging.…”

Association between erythrocyte dynamics and vessel remodelling in developmental vascular networks

“…However, recent computational studies in microscale vessels have demonstrated that RBCs leave transient WSS luminal footprints and therefore could non-trivially modify the local WSS differences driving vascular remodelling [23][24][25]. This effect of RBCs is closely related to their crucial role in the formation of cell-free layer and the regulation of effective viscosity as well as flow field in microvascular blood flow [26][27][28][29][30][31][32].…”