A micro-scale simulation of red blood cell passage through symmetric and asymmetric bifurcated vessels

Photoplethysmography for Assessing Microcirculation in Hypertensive Patients After Taking Antihypertensive Drugs: A Review

High blood pressure (BP) is a common disease and is associated with many chronic diseases. Measuring BP is essential for the treatment and management of many diseases, and therefore there is a growing need for a non-invasive, sleeveless and continuous BP monitoring device. With the development of technology, pulse waveform analysis using photoplethysmography (PPG) has become more feasible for evaluating BP. This study aimed to evaluate the changes of vascular elasticity and blood volume over time by using the characteristic parameters extracted by PPG. We reviewed the latest progress and literature on the observation of capillary network characteristics in hypertensive and non-hypertensive patients by PPG, the influence of different drugs on microcirculation characteristics in hypertensive patients with PPG, and further explored the key relationship between microcirculation and hypertension. We found that the PPG waveform produced by the fingertips of hypertensive patients is very different from that of healthy people, and the PPG waveform changes significantly during diastolic period after antihypertensive treatment. With the rapid development of medical technology, people can get more intuitive microcirculation image data, which provides beneficial help for the comprehensive understanding of hypertension.

Simulation of a tumor cell flowing through a symmetric bifurcated microvessel

Microvessel bifurcations serve as the major sites of tumor cell adhesion and further extravasation. In this study, the movement, deformation, and adhesion of a circulating tumor cell flowing in a symmetric microvessel with diverging and converging bifurcations were simulated by dissipative particle dynamics combined with a spring-based network model. Effects of the initial position of the CTC, externally-applied acceleration and the presence of RBCs on the motion of the CTC were investigated. The results demonstrated that the CTC released at the centerline of the parent vessel would attach to the vessel wall when arriving at the apex of diverging bifurcation and slide into the daughter branch determined by its centroid deflection and finally form firm adhesion at relatively lower flow rates. As the external acceleration increases, the increasing shear force enlarges the contact area for the adherent CTC on the one hand and reduces the residence time on the other hand. With the presence of RBCs in the bloodstream, the collision between the adherent tumor cell at the diverging bifurcation and flowing RBCs promotes the firm adhesion of CTC at lower flow rates.

Comparative study of photoplethysmographic waveforms with application of antihypertensive medication in hypertensive patients

BACKGROUND

Multiple studies have been published using a pulse oximeter's photoplethysmographic (PPG) capability to detect tissue perfusion. However, the origin of the PPG signal is still debatable.

AIM

A comparative study was performed of PPG waveforms in hypertensive patients before and after treatment with antihypertensive medication. The aim of this study was to observe the changes of PPG waveforms before and after lowering blood pressure in hypertensive patients and then to detect the relationship between blood pressure and PPG waveforms.

METHODS

The PPG waveforms of 60 patients with hypertension were collected. After administration of the antihypertensive medication nitroglycerin, PPG waveforms were collected again. The changes of the T3 (time3): This phase occurred between Marker 3 and Marker 4 (this phase occurs mid-diastolic) angle, before and after the antihypertensive medication treatment, were compared. The statistical analyses of two related groups were performed using the Paired t-test.

RESULTS

The blood perfusion waveforms of hypertensive patients before and after antihypertensive medication administration were differently indicated with the tilt angle T3. The slope angle of the T3 phase waveform increased significantly when the blood pressure dropped to normal (-41.9 ± 16.2° vs. -25.6 ± 21.9°, p < .0001), and the tilt angle of some patients was similar to that of adults with normal blood pressure.

CONCLUSION

In patients with hypertension, the tilt angle of the PPG waveform in the T3 phase increased significantly after administration of the antihypertensive medication nitroglycerin. It is worth to conduct deeper research about the relationship between hypertension and the blood perfusion of microcirculation in the diastolic period.

Shape transformations of red blood cells in the capillary and their possible connections to oxygen transportation

In this work, a series of numerical simulations have been performed to obtain the steady shapes of red blood cells under a shear force field in the capillary. Two possible classes of steady shapes, the axisymmetric parachute and the non-axisymmetric parachute, are found. If we assume that oxygen diffusion across the red cell membrane is mediated by membrane curvature, it is found that the non-axisymmetric parachute will be more favorable due to its special shape which enables it to have a larger portion of membrane patch capable of releasing oxygen to tissues.

Modeling Red Blood Cell Viscosity Contrast Using Inner Soft Particle Suspension

The inner viscosity of a biological red blood cell is about five times larger than the viscosity of the blood plasma. In this work, we use dissipative particles to enable the proper viscosity contrast in a mesh-based red blood cell model. Each soft particle represents a coarse-grained virtual cluster of hemoglobin proteins contained in the cytosol of the red blood cell. The particle interactions are governed by conservative and dissipative forces. The conservative forces have purely repulsive character, whereas the dissipative forces depend on the relative velocity between the particles. We design two computational experiments that mimic the classical viscometers. With these experiments we study the effects of particle suspension parameters on the inner cell viscosity and provide parameter sets that result in the correct viscosity contrast. The results are validated with both static and dynamic biological experiment, showing an improvement in the accuracy of the original model without major increase in computational complexity.

Numerical simulation of spatiotemporal red blood cell aggregation under sinusoidal pulsatile flow

Previous studies on red blood cell (RBC) aggregation have elucidated the inverse relationship between shear rate and RBC aggregation under Poiseuille flow. However, the local parabolic rouleaux pattern in the arterial flow observed in ultrasonic imaging cannot be explained by shear rate alone. A quantitative approach is required to analyze the spatiotemporal variation in arterial pulsatile flow and the resulting RBC aggregation. In this work, a 2D RBC model was used to simulate RBC motion driven by interactional and hydrodynamic forces based on the depletion theory of the RBC mechanism. We focused on the interaction between the spatial distribution of shear rate and the dynamic motion of RBC aggregation under sinusoidal pulsatile flow. We introduced two components of shear rate, namely, the radial and axial shear rates, to understand the effect of sinusoidal pulsatile flow on RBC aggregation. The simulation results demonstrated that specific ranges of the axial shear rate and its ratio with radial shear rate strongly affected local RBC aggregation and parabolic rouleaux formation. These findings are important, as they indicate that the spatiotemporal variation in shear rate has a crucial role in the aggregate formation and local parabolic rouleaux under pulsatile flow.

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

Blood is a vital soft matter, and its normal circulation in the human body relies on the distribution of red blood cells (RBCs) at successive bifurcations. Understanding how RBCs are partitioned at bifurcations is key for the optimisation of microfluidic devices as well as for devising novel strategies for diagnosis and treatment of blood-related diseases. We report the dynamics of RBC suspensions flowing through a biomimetic vascular network incorporating three generations of microchannels and two classical types of bifurcations at the arteriole level. Our microfluidic experiments with dilute and semidilute RBC suspensions demonstrate the emergence of excessive heterogeneity of RBC concentration in downstream generations upon altering the network's outflow rates. Through parallel simulations using the immersed-boundary-lattice-Boltzmann method, we reveal that the heterogeneity is attributed to upstream perturbations in the cell-free layer (CFL) and lack of its recovery between consecutive bifurcations owing to suppressed hydrodynamic lift under reduced flow conditions. In the dilute/semidilute regime, this perturbation dominates over the effect of local fractional flow at the bifurcation and can lead to inherently unfavourable child branches that are deprived of RBCs even for equal flow split. Our work highlights the importance of CFL asymmetry cascading down a vascular network, which leads to biased phase separation that deviates from established empirical predictions.

PyOIF: Computational tool for modelling of multi-cell flows in complex geometries

A user ready, well documented software package PyOIF contains an implementation of a robust validated computational model for cell flow modelling. The software is capable of simulating processes involving biological cells immersed in a fluid. The examples of such processes are flows in microfluidic channels with numerous applications such as cell sorting, rare cell isolation or flow fractionation. Besides the typical usage of such computational model in the design process of microfluidic devices, PyOIF has been used in the computer-aided discovery involving mechanical properties of cell membranes. With this software, single cell, many cell, as well as dense cell suspensions can be simulated. Many cell simulations include cell-cell interactions and analyse their effect on the cells. PyOIF can be used to test the influence of mechanical properties of the membrane in flows and in membrane-membrane interactions. Dense suspensions may be used to study the effect of cell volume fraction on macroscopic phenomena such as cell-free layer, apparent suspension viscosity or cell degradation. The PyOIF module is based on the official ESPResSo distribution with few modifications and is available under the terms of the GNU General Public Licence. PyOIF is based on Python objects representing the cells and on the C++ computational core for fluid and interaction dynamics. The source code is freely available at GitHub repository, runs natively under Linux and MacOS and can be used in Windows Subsystem for Linux. The communication among PyOIF users and developers is maintained using active mailing lists. This work provides a basic background to the underlying computational models and to the implementation of interactions within this framework. We provide the prospective PyOIF users with a practical example of simulation script with reference to our publicly available User Guide.

Sanal Flow Choking: A Paradigm Shift in Computational Fluid Dynamics Code Verification and Diagnosing Detonation and Hemorrhage in Real-World Fluid-Flow Systems

The discovery of Sanal flow choking is a scientific breakthrough and a paradigm shift in the diagnostics of the detonation/hemorrhage in real-world fluid flow systems. The closed-form analytical models capable of predicting the boundary-layer blockage factor for both 2D and 3D cases at the Sanal flow choking for adiabatic and diabatic fluid flow conditions are critically reviewed here. The beauty and novelty of these models stem from the veracity that at the Sanal flow choking condition for diabatic flows all the conservation laws of nature are satisfied at a unique location, which allows for computational fluid dynamics (CFD) code verification. At the Sanal flow choking condition both the thermal choking and the wall-friction-induced flow choking occur at a single sonic fluid throat location. The blockage factor predicted at the Sanal flow choking condition can be taken as an infallible data for various in silico model verification, validation, and calibration. The 3D blockage factor at the Sanal flow choking is found to be 45.12% lower than the 2D case of a wall-bounded diabatic fluid flow system with air as the working fluid. The physical insight of Sanal flow choking presented in this review article sheds light on finding solutions, through in silico experiments in base flow and nanoflows, for numerous unresolved problems carried forward over the centuries in physical, chemical, and biological sciences for humankind.

In vitro investigations of red blood cell phase separation in a complex microchannel network

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.

Antimargination of Microparticles and Platelets in the Vicinity of Branching Vessels

We investigate the margination of microparticles/platelets in blood flow through complex geometries typical for in vivo vessel networks: a vessel confluence and a bifurcation. Using three-dimensional lattice Boltzmann simulations, we confirm that behind the confluence of two vessels, a cell-free layer devoid of red blood cells develops in the channel center. Despite its small size of roughly 1 μm, this central cell-free layer persists for up to 100 μm after the confluence. Most importantly, we show from simulations that this layer also contains a significant amount of microparticles/platelets and validate this result by in vivo microscopy in mouse venules. At bifurcations, however, a similar effect does not appear, and margination is largely unaffected by the geometry. This antimargination toward the vessel center after a confluence may explain earlier in vivo observations, which found that platelet concentrations near the vessel wall are seen to be much higher on the arteriolar side (containing bifurcations) than on the venular side (containing confluences) of the vascular system.

Cell trapping in Y-junction microchannels: A numerical study of the bifurcation angle effect in inertial microfluidics

The majority of microfluidic technologies for cell sorting and isolation involve bifurcating (e.g., Y- or T-shaped junction) microchannels to trap the cells of a specific type. However, the microfluidic trapping efficiency remains low, independently of whether the cells are separated by a passive or an active sorting method. Using a custom computational algorithm, we studied the migration of separated deformable cells in a Y-junction microchannel, with a bifurcation angle ranging from 30° to 180°. Single or two cells of initially spherical shape were considered under flow conditions corresponding to inertial microfluidics. Through the numerical simulation, we identified the effects of cell size, cytoplasmic viscoelasticity, cortical tension, flow rate, and bifurcation angle on the critical separation distance for cell trapping. The results of this study show that the trapping and isolation of blood cells, and circulating tumor cells in a Y-junction microchannel was most efficient and least dependent on the flow rate at the bifurcation angle of 120°. At this angle, the trapping efficiency for white blood cells and circulating tumor cells increased, respectively, by 46% and 43%, in comparison with the trapping efficiency at 60°. The efficiency to isolate invasive tumor cells from noninvasive ones increased by 32%. This numerical study provides important design criteria to optimize microfluidic technology for deformability-based cell sorting and isolation.

Red blood cell distribution in a microvascular network with successive bifurcations

Nonproportional RBC distribution is an important characteristic in microvascular networks, which can result in heterogeneity of oxygen supply that may cause ischemic death in severe cases. In this paper, we perform three-dimensional numerical simulations of a large number of RBCs in a microvascular network, by using a hybrid method of smoothed dissipative particle dynamic and immersed boundary method. The distribution of multiple RBCs in a T-bifurcation is first simulated as a validation study, and a reasonable agreement is observed both qualitatively and quantitatively on the RBC flux between our results and the previously published numerical and empirical results. Next, the distribution of a large number of RBCs in a microvascular network is investigated, including the effects of cell deformability, aggregation and tube hematocrit. The simulation results indicate that decreased deformability and increased aggregation strength have a similar effect on the RBC distribution: the large RBC flux becomes larger, but the small becomes smaller. A high hematocrit also causes a similar phenomenon that the RBCs are more apt to flow into a high RBC-flux branch, because they are arranged compactly into a rouleaux and difficultly broken up at a high hematocrit. These results imply that lower cell deformability, stronger aggregation or higher tube hematocrit would be conducive to the phase separation of hematocrit and plasma skimming processes in microcirculation.

In vitro analysis of blood flow in a microvascular network with realistic geometry

In vitro blood flow was measured in a polydimethysiloxane micro channel to reflect the complex geometry of a microvascular network. Flow rates were determined from the velocities of tracer particles moving along the center line of the flow channel, and the flow rates of two working fluids were then compared: water and blood. In some bifurcating channels, the measured flow rate showed that the effects of bifurcation in the apparent viscosity depend on the hematocrit, such that the flow rate in the daughter channel with the higher (lower) flow rate was lower (higher) for blood than for water. The measured flow rates in other bifurcating channels reflected effects from the surrounding flow channels acting as bypasses, which tended to balance out the effects of bifurcation.

Extended photoacoustic transport model for characterization of red blood cell morphology in microchannel flow

The dynamic response behavior of red blood cells holds the key to understanding red blood cell related diseases. In this regard, an understanding of the physiological functions of erythrocytes is significant before focusing on red blood cell aggregation in the microcirculatory system. In this work, we present a theoretical model for a photoacoustic signal that occurs when deformed red blood cells pass through a microfluidic channel. Using a Green's function approach, the photoacoustic pressure wave is obtained analytically by solving a combined Navier-Stokes and photoacoustic equation system. The photoacoustic wave expression includes determinant parameters for the cell deformability such as plasma viscosity, density, and red blood cell aggregation, as well as involving laser parameters such as beamwidth, pulse duration, and repetition rate. The effects of aggregation on blood rheology are also investigated. The results presented by this study show good agreements with the experimental ones in the literature. The comprehensive analytical solution of the extended photoacoustic transport model including a modified Morse type potential function sheds light on the dynamics of aggregate formation and demonstrates that the profile of a photoacoustic pressure wave has the potential for detecting and characterizing red blood cell aggregation.

Investigation of red blood cell mechanical properties using AFM indentation and coarse-grained particle method

Background

Red blood cells (RBCs) deform significantly and repeatedly when passing through narrow capillaries and delivering dioxygen throughout the body. Deformability of RBCs is a key characteristic, largely governed by the mechanical properties of the cell membrane. This study investigated RBC mechanical properties using atomic force microscopy (AFM) with the aim to develop a coarse-grained particle method model to study for the first time RBC indentation in both 2D and 3D. This new model has the potential to be applied to further investigate the local deformability of RBCs, with accurate control over adhesion, probe geometry and position of applied force.

Results

The model considers the linear stretch capacity of the cytoskeleton, bending resistance and areal incompressibility of the bilayer, and volumetric incompressibility of the internal fluid. The model’s performance was validated against force–deformation experiments performed on RBCs under spherical AFM indentation. The model was then used to investigate the mechanisms which absorbed energy through the indentation stroke, and the impact of varying stiffness coefficients on the measured deformability. This study found the membrane’s bending stiffness was most influential in controlling RBC physical behaviour for indentations of up to 200 nm.

Conclusions

As the bilayer provides bending resistance, this infers that structural changes within the bilayer are responsible for the deformability changes experienced by deteriorating RBCs. The numerical model presented here established a foundation for future investigations into changes within the membrane that cause differences in stiffness between healthy and deteriorating RBCs, which have already been measured experimentally with AFM.

Electronic supplementary material

The online version of this article (10.1186/s12938-017-0429-5) contains supplementary material, which is available to authorized users.

Molecular Sensors of Blood Flow in Endothelial Cells

Mechanical stress from blood flow has a significant effect on endothelial physiology, with a key role in initiating vasoregulatory signals. Disturbances in blood flow, such as in regions of disease-associated stenosis, arterial branch points, and sharp turns, can induce proatherogenic phenotypes in endothelial cells. The disruption of vascular homeostasis as a result of endothelial dysfunction may contribute to early and late stages of atherosclerosis, the underlying cause of coronary artery disease. In-depth knowledge of the mechanobiology of endothelial cells is essential to identifying mechanosensory complexes involved in the pathogenesis of atherosclerosis. In this review, we describe different blood flow patterns and summarize current knowledge on mechanosensory molecules regulating endothelial vasoregulatory functions, with clinical implications. Such information may help in the search for novel therapeutic approaches.

Partitioning of red blood cell aggregates in bifurcating microscale flows

Microvascular flows are often considered to be free of red blood cell aggregates, however, recent studies have demonstrated that aggregates are present throughout the microvasculature, affecting cell distribution and blood perfusion. This work reports on the spatial distribution of red blood cell aggregates in a T-shaped bifurcation on the scale of a large microvessel. Non-aggregating and aggregating human red blood cell suspensions were studied for a range of flow splits in the daughter branches of the bifurcation. Aggregate sizes were determined using image processing. The mean aggregate size was marginally increased in the daughter branches for a range of flow rates, mainly due to the lower shear conditions and the close cell and aggregate proximity therein. A counterintuitive decrease in the mean aggregate size was apparent in the lower flow rate branches. This was attributed to the existence of regions depleted by aggregates of certain sizes in the parent branch, and to the change in the exact flow split location in the T-junction with flow ratio. The findings of the present investigation may have significant implications for microvascular flows and may help explain why the effects of physiological RBC aggregation are not deleterious in terms of in vivo vascular resistance.

A Two-Dimensional Numerical Investigation of Transport of Malaria-Infected Red Blood Cells in Stenotic Microchannels

The malaria-infected red blood cells experience a significant decrease in cell deformability and increase in cell membrane adhesion. Blood hemodynamics in microvessels is significantly affected by the alteration of the mechanical property as well as the aggregation of parasitized red blood cells. In this study, we aim to numerically study the connection between cell-level mechanobiological properties of human red blood cells and related malaria disease state by investigating the transport of multiple red blood cell aggregates passing through microchannels with symmetric stenosis. Effects of stenosis magnitude, aggregation strength, and cell deformability on cell rheology and flow characteristics were studied by a two-dimensional model using the fictitious domain-immersed boundary method. The results indicated that the motion and dissociation of red blood cell aggregates were influenced by these factors and the flow resistance increases with the increase of aggregating strength and cell stiffness. Further, the roughness of the velocity profile was enhanced by cell aggregation, which considerably affected the blood flow characteristics. The study may assist us in understanding cellular-level mechanisms in disease development.

Red blood cell phase separation in symmetric and asymmetric microchannel networks: effect of capillary dilation and inflow velocity

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.

Microdevice for plasma separation from whole human blood using bio-physical and geometrical effects

In this research work, we present a simple and efficient passive microfluidic device for plasma separation from pure blood. The microdevice has been fabricated using conventional photolithography technique on a single layer of polydimethylsiloxane, and has been extensively tested on whole blood and enhanced (upto 62%) hematocrit levels of human blood. The microdevice employs elevated dimensions of about 100 μm; such elevated dimensions ensure clog-free operation of the microdevice and is relatively easy to fabricate. We show that our microdevice achieves almost 100% separation efficiency on undiluted blood in the flow rate range of 0.3 to 0.5 ml/min. Detailed biological characterization of the plasma obtained from the microdevice is carried out by testing: proteins by ultra-violet spectrophotometric method, hCG (human chorionic gonadotropin) hormone, and conducting random blood glucose test. Additionally, flow cytometry study has also been carried on the separated plasma. These tests attest to the high quality of plasma recovered. The microdevice developed in this work is an outcome of extensive experimental research on understanding the flow behavior and separation phenomenon of blood in microchannels. The microdevice is compact, economical and effective, and is particularly suited in continuous flow operations.