Reply to the 'Comment on "Dynamics and rheology of vesicles under confined Poiseuille flow"' by G. Coupier and T. Podgorski, , 2024, , DOI: 10.1039/D3SM01679J.

In this answer, we provide our arguments in support of the possibility to observe the single file-organization of red blood cells in microvessels and the resulting unexpectedly weak increase of blood viscosity with increasing hematocrit, the physiological relevance of which was questioned in the comment. The key element is that the equivalent diameter in 3D for the maximal hematocrit corresponding to a single file of red blood cells is about 10 µm and not 20 µm, as in 2D. In addition, the viscosity contrast (ratio between the cell internal and external viscosities) value must be chosen in our 2D simulation in a such a way that the effective viscosity (a linear combination of the internal, external and membrane viscosities) be close to that of a real RBC.

Dynamics and rheology of vesicles under confined Poiseuille flow.

The rheological behavior and dynamics of a vesicle suspension, serving as a simplified model for red blood cells, are explored within a Poiseuille flow under the Stokes limit. Investigating vesicle response has led to the identification of novel solutions that complement previously documented forms like the parachute and slipper shapes. This study has brought to light the existence of alternative configurations, including a fully off-centered form and a multilobe structure.

Heterogeneous ATP patterns in microvascular networks.

ATP is not only an energy carrier but also serves as an important signalling molecule in many physiological processes. Abnormal ATP level in blood vessel is known to be related to several pathologies, such as inflammation, hypoxia and atherosclerosis. Using advanced numerical methods, we analysed ATP released by red blood cells (RBCs) and its degradation by endothelial cells (ECs) in a cat mesentery-inspired vascular network, accounting for RBC mutual interaction and interactions with vascular walls.

Mathematical modeling of intracellular calcium in presence of receptor: a homeostatic model for endothelial cell.

Calcium is a ubiquitous molecule and second messenger that regulates many cellular functions ranging from exocytosis to cell proliferation at different time scales. In the vasculature, a constant adenosine triphosphate (ATP) concentration is maintained because of ATP released by red blood cells (RBCs). These ATP molecules continuously react with purinergic receptors on the surface of endothelial cells (ECs).

Red blood cells under flow show maximal ATP release for specific hematocrit.

ATP release by red blood cells (RBCs) under shear stress (SS) plays a pivotal role in endothelial biochemical signaling cascades. The aim of this study is to investigate through numerical simulation how RBC spatiotemporal organization depends on flow and geometrical conditions to generate ATP patterns. Numerical simulations were conducted in a straight channel by considering both plasma and explicit presence of RBCs, their shape deformation and cell-cell interaction, and ATP release by RBCs.

Preliminary evaluation of a predictive controller for a rotary blood pump based on pulmonary oxygen gas exchange.

Physiological control of rotary blood pumps is becoming increasingly necessary for clinical use. In this study, the mean oxygen partial pressure in the upper airway was first quantitatively evaluated as a control objective for a rotary blood pump. A model-free predictive controller was designed based on this control objective.

Effects of membrane reference state on shape memory of a red blood cell.

By using a three-dimensional continuum model, we simulate the shape memory of a red blood cell after the remove of external forces. The purpose of this study is to illustrate the effect of membrane reference state on cell behavior during the recovery process. The reference state of an elastic element is the geometry with zero stress.

Effects on the pulmonary hemodynamics and gas exchange with a speed modulated right ventricular assist rotary blood pump: a numerical study.

Rotary blood pumps (RBPs) are the newest generation of ventricular assist devices. Although their continuous flow characteristics have been accepted widely, more and more research has focused on the pulsatile modulation of RBPs in an attempt to provide better perfusion. In this study, we investigated the effects of an axial RBP serving as the right ventricular assist device on pulmonary hemodynamics and gas exchange using a numerical method with a complete cardiovascular model along with airway mechanics and a gas exchange model.