No abstract

A detailed model of red blood cell (RBC) transport in a capillary network is an indispensable element of a comprehensive model for the supply of the human organism with oxygen and nutrients. In this paper, we introduce a two-phase model for the perfusion of a capillary network. This model accounts for the special role of RBCs, which have a strong influence on network dynamics. Analytical results and numerical simulations with a discrete model and a generic network topology indicate that there exists a local self-regulation mechanism for the flow rates and a global de-mixing process that leads to an inhomogeneous haematocrit distribution. Based on the results from the discrete model, we formulate an efficient algorithm suitable for computing the pressure and flow field as well as a continuous haematocrit distribution in large capillary networks at steady state.

A simple extension of the classic Görtler–Hämmerlin (1955) (GH) model, essential for three-dimensional linear instability analysis, is presented. The extended Görtler–Hämmerlin model classifies all three-dimensional disturbances in this flow by means of symmetric and antisymmetric polynomials of the chordwise coordinate. It results in one-dimensional linear eigenvalue problems, a temporal or spatial solution of which, presented herein, is demonstrated to recover results otherwise only accessible to the temporal or spatial partial-derivative eigenvalue problem (the former also solved here) or to spatial direct numerical simulation (DNS). From a numerical point of view, the significance of the extended GH model is that it delivers the three-dimensional linear instability characteristics of this flow, discovered by solution of the partial-derivative eigenvalue problem by Lin & Malik (1996a), at a negligible fraction of the computing effort required by either of the aforementioned alternative numerical methodologies. More significant, however, is the physical insight which the model offers into the stability of this technologically interesting flow. On the one hand, the dependence of three-dimensional linear disturbances on the chordwise spatial direction is unravelled analytically. On the other hand, numerical results obtained demonstrate that all linear three-dimensional instability modes possess the same (scaled) dependence on the wall-normal coordinate, that of the well-known GH mode. The latter result may explain why the three-dimensional linear modes have not been detected in past experiments; criteria for experimental identification of three-dimensional disturbances are discussed. Asymptotic analysis based on a multiple-scales method confirms the results of the extended GH model and provides an alternative algorithm for the recovery of three-dimensional linear instability characteristics, also based on solution of one-dimensional eigenvalue problems. Finally, the polynomial structure of individual three-dimensional extended GH eigenmodes is demonstrated using three-dimensional DNS, performed here under linear conditions.

Capillaries are the prime location for oxygen and nutrient exchange in all tissues. Despite their fundamental role, our knowledge of perfusion and flow regulation in cortical capillary beds is still limited. Here, we use in vivo measurements and blood flow simulations in anatomically accurate microvascular network to investigate the impact of red blood cells (RBCs) on microvascular flow. Based on these in vivo and in silico experiments, we show that the impact of RBCs leads to a bias toward equating the values of the outflow velocities at divergent capillary bifurcations, for which we coin the term “well-balanced bifurcations”. Our simulation results further reveal that hematocrit heterogeneity is directly caused by the RBC dynamics, i.e. by their unequal partitioning at bifurcations and their effect on vessel resistance. These results provide the first in vivo evidence of the impact of RBC dynamics on the flow field in the cortical microvasculature. By structural and functional analyses of our blood flow simulations we show that capillary diameter changes locally alter flow and RBC distribution. A dilation of 10% along a vessel length of 100 μm increases the flow on average by 21% in the dilated vessel downstream a well-balanced bifurcation. The number of RBCs rises on average by 27%. Importantly, RBC up-regulation proves to be more effective the more balanced the outflow velocities at the upstream bifurcation are. Taken together, we conclude that diameter changes at capillary level bear potential to locally change the flow field and the RBC distribution. Moreover, our results suggest that the balancing of outflow velocities contributes to the robustness of perfusion. Based on our in silico results, we anticipate that the bi-phasic nature of blood and small-scale regulations are essential for a well-adjusted oxygen and energy substrate supply.

Microvascular networks feature a complex topology with multiple bifurcating vessels. Nonuniform partitioning ( phase separation) of red blood cells (RBCs) occurs at diverging bifurcations, leading to a heterogeneous RBC distribution that ultimately affects the oxygen delivery to living tissues. Our understanding of the mechanisms governing RBC heterogeneity is still limited, especially in large networks where the RBC dynamics can be nonintuitive. In this study, our quantitative data for phase separation were obtained in a complex in vitro network with symmetric bifurcations and 176 microchannels. Our experiments showed that the hematocrit is heterogeneously distributed and confirmed the classical result that the branch with a higher blood fraction received an even higher RBC fraction (classical partitioning). An inversion of this classical phase separation (reverse partitioning) was observed in the case of a skewed hematocrit profile in the parent vessels of bifurcations. In agreement with a recent computational study [P. Balogh and P. Bagchi, Phys. Fluids 30,051902 (2018)], a correlation between the RBC reverse partitioning and the skewness of the hematocrit profile due to sequential converging and diverging bifurcations was reported. A flow threshold below which no RBCs enter a branch was identified. These results highlight the importance of considering the RBC flow history and the local RBC distribution to correctly describe the RBC phase separation in complex networks.

The non-uniform partitioning or phase separation of red blood cells (RBCs) at a diverging bifurcation of a microvascular network is responsible for RBC heterogeneity within the network. The mechanisms controlling RBC heterogeneity are not yet fully understood and there is a need to improve the basic understanding of the phase separation phenomenon. In this context, in vitro experiments can fill the gap between existing in vivo and in silico models as they provide better controllability than in vivo experiments without mathematical idealizations or simplifications inherent to in silico models. In this study, we fabricated simple models of symmetric/asymmetric microvascular networks; we provided quantitative data on the RBC velocity, line density and flux in the daughter branches. In general our results confirmed the tendency of RBCs to enter the daughter branch with higher flow rate (Zweifach-Fung effect); in some cases even inversion of the Zweifach-Fung effect was observed. We showed for the first time a reduction of the Zweifach-Fung effect with increasing flow rate. Moreover capillary dilation was shown to cause an increase of RBC line density and RBC residence time within the dilated capillary underlining the possible role of pericytes in regulating the oxygen supply.

ObjectiveTo evaluate the effect of time between the movements/steps, angle of body movements as well as the angular velocity of the maneuvers in an in vitro model of a semicircular canal (SCC) to improve the efficacy of the Sémont maneuver (SM) in benign paroxysmal positional vertigo.Materials and MethodsSémont maneuvers were performed on an in vitro SCC model. Otoconia trajectories were captured by a video camera. The effects of time between the movements, angles of motion (0°, 10°, 20°, and 30° below the horizontal line), different angular velocities (90, 135, 180°/s), and otoconia size (36 and 50 μm) on the final position of the otoconia in the SCC were tested.ResultsWithout extension of the movements beyond the horizontal, the in vitro experiments (with particles corresponding to 50 μm diameter) did not yield successful canalith repositioning. If the movements were extended by 20° beyond the horizontal position, SM were successful with resting times of at least 16 s. For larger extension angles, the required time decreased. However, for smaller particles (36 μm), the required time doubled. The angular maneuver velocity (tested between 90 and 180°/s) did not have a major impact on the final position of the otoconia.InterpretationThe two primary determinants for success of the SM are the time between the movements and the extension of the movements beyond the horizontal. The time between the movements should be at least 45 s. Angles of 20° or more below horizontal line (so-called Sémont+) should increase the success rate of SM.

It is recognised that high-flow nasal therapy can prevent desaturation during airway management. Studies in spontaneously breathing patients show an almost linear relationship between flow rate and positive airway pressure in the nasopharynx. Positive airway pressure has been suggested as one of the possible mechanisms explaining how high-flow nasal therapy works. However, data on pressures generated by high-flow nasal therapy in apnoeic adults under general anaesthesia are absent. This randomised controlled crossover trial investigated airway pressures generated by different flow rates during high-flow nasal therapy in anaesthetised and paralysed apnoeic patients, comparing pressures with closed and open mouths. Following induction of anaesthesia and neuromuscular blockade, a continuous jaw thrust was used to enable airway patency. Airway pressure was measured in the right main bronchus, the middle of the trachea and the pharynx, using a fibreoptically-placed catheter connected to a pressure transducer. Each measurement was randomised with respect to closed or open mouth and different flow rates. Twenty patients undergoing elective surgery were included (mean (SD) age 38 (18) years, BMI 25.0 (3.3) kg.m-2 , nine women, ASA physical status 1 (35%), 2 (55%), 3 (10%). While closed mouths and increasing flow rates demonstrated non-linear increases in pressure, the pressure increase was negligible with an open mouth. Airway pressures remained below 10 cmH 2 O even with closed mouths and flow rates up to 80 l.min À1 ; they were not influenced by catheter position. This study shows an increase in airway pressures with closed mouths that depends on flow rate. The generated pressure is negligible with an open mouth. These data question positive airway pressure as an important mechanism for maintenance of oxygenation during apnoea.