The wall-stress footprint of blood cells flowing in microvessels

A cell-and-plasma numerical model reveals hemodynamic stress and flow adaptation in zebrafish microvessels after morphological alteration

The development of a functional cardiovascular system ensures a sustainable oxygen, nutrient and hormone delivery system for successful embryonic development and homeostasis in adulthood. While early vessels are formed by biochemical signaling and genetic programming, the onset of blood flow provides mechanical cues that participate in vascular remodeling of the embryonic vascular system. The zebrafish is a prolific animal model for studying the quantitative relationship between blood flow and vascular morphogenesis due to a combination of favorable factors including blood flow visualization in optically transparent larvae. In this study, we have developed a cell-and-plasma blood transport model using computational fluid dynamics (CFD) to understand how red blood cell (RBC) partitioning affect lumen wall shear stress (WSS) and blood pressure in zebrafish trunk blood vascular networks with altered rheology and morphology. By performing live imaging of embryos with reduced hematocrit, we discovered that cardiac output and caudal artery flow rates were maintained. These adaptation trends were recapitulated in our CFD models, which showed reduction in network WSS via viscosity reduction in the caudal artery/vein and via pressure gradient weakening in the intersegmental vessels (ISVs). Embryos with experimentally reduced lumen diameter showed reduced cardiac output and caudal artery flow rate. Factoring in this trend into our CFD models, simulations highlighted that lumen diameter reduction increased vessel WSS but this increase was mitigated by flow reduction due to the adaptive network pressure gradient weakening. Additionally, hypothetical network CFD models with different vessel lumen diameter distribution characteristics indicated the significance of axial variation in lumen diameter and cross-sectional shape for establishing physiological WSS gradients along ISVs. In summary, our work demonstrates how both experiment-driven and hypothetical CFD modeling can be employed for the study of blood flow physiology during vascular remodeling.

Marginated aberrant red blood cells induce pathologic vascular stress fluctuations in a computational model of hematologic disorders

Red blood cell (RBC) disorders such as sickle cell disease affect billions worldwide. While much attention focuses on altered properties of aberrant RBCs and corresponding hemodynamic changes, RBC disorders are also associated with vascular dysfunction, whose origin remains unclear and which provoke severe consequences including stroke. Little research has explored whether biophysical alterations of RBCs affect vascular function. We use a detailed computational model of blood that enables characterization of cell distributions and vascular stresses in blood disorders and compare simulation results with experimental observations. Aberrant RBCs, with their smaller size and higher stiffness, concentrate near vessel walls (marginate) because of contrasts in physical properties relative to normal cells. In a curved channel exemplifying the geometric complexity of the microcirculation, these cells distribute heterogeneously, indicating the importance of geometry. Marginated cells generate large transient stress fluctuations on vessel walls, indicating a mechanism for the observed vascular inflammation.

Angiogenic Microvascular Wall Shear Stress Patterns Revealed Through Three-dimensional Red Blood Cell Resolved Modeling

The wall shear stress (WSS) exerted by blood flowing through microvascular capillaries is an established driver of new blood vessel growth, or angiogenesis. Such adaptations are central to many physiological processes in both health and disease, yet three-dimensional (3D) WSS characteristics in real angiogenic microvascular networks are largely unknown. This marks a major knowledge gap because angiogenesis, naturally, is a 3D process. To advance current understanding, we model 3D red blood cells (RBCs) flowing through rat angiogenic microvascular networks using state-of-the-art simulation. The high-resolution fluid dynamics reveal 3D WSS patterns occurring at sub-endothelial cell (EC) scales that derive from distinct angiogenic morphologies, including microvascular loops and vessel tortuosity. We identify the existence of WSS hot and cold spots caused by angiogenic surface shapes and RBCs, and notably enhancement of low WSS regions by RBCs. Spatiotemporal characteristics further reveal how fluctuations follow timescales of RBC "footprints." Altogether, this work provides a new conceptual framework for understanding how shear stress might regulate EC dynamics in vivo.

The counterbalance of endothelial glycocalyx and high wall shear stress to low-density lipoprotein concentration polarization in mouse ear skin arterioles

BACKGROUND AND AIMS

Atherosclerosis preferentially occurs at regions in arterial branching, curvature, and stenosis, which may be explained by the geometric predilection of low-density lipoprotein (LDL) concentration polarization that has been investigated in major arteries in previous studies. Whether this also happens in arterioles remains unknown.

METHODS

Herein, a radially non-uniform distribution of LDL particles and a heterogeneous endothelial glycocalyx layer in the mouse ear arterioles, as shown by fluorescein isothiocyanate labeled wheat germ agglutinin (WGA-FITC), were successfully observed by a non-invasive two-photon laser-scanning microscopy (TPLSM) technique. The stagnant film theory was applied as the fitting function to evaluate LDL concentration polarization in arterioles.

RESULTS

The concentration polarization rate (CPR, the ratio of the number of polarized cases to that of total cases) in the inner walls of curved and branched arterioles was 22% and 31% higher than the outer counterparts, respectively. Results from the binary logistic regression and multiple linear regression analysis showed that endothelial glycocalyx thickness increases CPR and the thickness of the concentration polarization layer (CPL). Flow field computation indicates no obvious disturbances or vortex in modeled arterioles with different geometries and the mean wall shear stress is about 7.7-9.0 Pa.

CONCLUSIONS

These findings suggest a geometric predilection of LDL concentration polarization in arterioles for the first time, and the existence of an endothelial glycocalyx, acting together with a relatively high wall shear stress in arterioles, may explain to some extent why atherosclerosis rarely occurs in these regions.

Dynamic Stimulations with Bioengineered Extracellular Matrix-Mimicking Hydrogels for Mechano Cell Reprogramming and Therapy

Cells interact with their surrounding environment through a combination of static and dynamic mechanical signals that vary over stimulus types, intensity, space, and time. Compared to static mechanical signals such as stiffness, porosity, and topography, the current understanding on the effects of dynamic mechanical stimulations on cells remains limited, attributing to a lack of access to devices, the complexity of experimental set-up, and data interpretation. Yet, in the pursuit of emerging translational applications (e.g., cell manufacturing for clinical treatment), it is crucial to understand how cells respond to a variety of dynamic forces that are omnipresent in vivo so that they can be exploited to enhance manufacturing and therapeutic outcomes. With a rising appreciation of the extracellular matrix (ECM) as a key regulator of biofunctions, researchers have bioengineered a suite of ECM-mimicking hydrogels, which can be fine-tuned with spatiotemporal mechanical cues to model complex static and dynamic mechanical profiles. This review first discusses how mechanical stimuli may impact different cellular components and the various mechanobiology pathways involved. Then, how hydrogels can be designed to incorporate static and dynamic mechanical parameters to influence cell behaviors are described. The Scopus database is also used to analyze the relative strength in evidence, ranging from strong to weak, based on number of published literatures, associated citations, and treatment significance. Additionally, the impacts of static and dynamic mechanical stimulations on clinically relevant cell types including mesenchymal stem cells, fibroblasts, and immune cells, are evaluated. The aim is to draw attention to the paucity of studies on the effects of dynamic mechanical stimuli on cells, as well as to highlight the potential of using a cocktail of various types and intensities of mechanical stimulations to influence cell fates (similar to the concept of biochemical cocktail to direct cell fate). It is envisioned that this progress report will inspire more exciting translational development of mechanoresponsive hydrogels for biomedical applications.

Numerical simulation of flow characteristics in a permeable liver sinusoid with leukocytes

Double-layered channels of sinusoid lumen and Disse space separated by fenestrated liver sinusoidal endothelial cells (LSECs) endow the unique mechanical environment of the liver sinusoid network, which further guarantees its biological function. It is also known that this mechanical environment changes dramatically under liver fibrosis and cirrhosis, including the reduced plasma penetration and metabolite exchange between the two flow channels and the reduced Disse space deformability. The squeezing of leukocytes through narrow sinusoid lumen also affects the mechanical environment of liver sinusoid. To date, the detailed flow-field profile of liver sinusoid is still far from clear due to experimental limitations. It also remains elusive whether and how the varied physical properties of the pathological liver sinusoid regulate the fluid flow characteristics. Here a numerical model based on the immersed boundary method was established, and the effects of Disse space and leukocyte elasticities, endothelium permeability, and sinusoidal stenosis degree on fluid flow as well as leukocyte trafficking were specified upon a mimic liver sinusoid structure. Results showed that endothelium permeability dominantly controlled the plasma penetration velocity across the endothelium, whereas leukocyte squeezing promoted local penetration and significantly regulated wall shear stress on hepatocytes, which was strongly related to the Disse space and leukocyte deformability. Permeability and elasticity cooperatively regulated the process of leukocytes trafficking through the liver sinusoid, especially for stiffer leukocytes. This study will offer new insights into deeper understanding of the elaborate mechanical features of liver sinusoid and corresponding biological function.

Mechanical control of tissue shape: Cell-extrinsic and -intrinsic mechanisms join forces to regulate morphogenesis

During vertebrate development, cells must proliferate, move, and differentiate to form complex shapes. Elucidating the mechanisms underlying the molecular and cellular processes involved in tissue morphogenesis is essential to understanding developmental programmes. Mechanical stimuli act as a major contributor of morphogenetic processes and impact on cell behaviours to regulate tissue shape and size. Specifically, cell extrinsic physical forces are translated into biochemical signals within cells, through the process of mechanotransduction, activating multiple mechanosensitive pathways and defining cell behaviours. Physical forces generated by tissue mechanics and the extracellular matrix are crucial to orchestrate tissue patterning and cell fate specification. At the cell scale, the actomyosin network generates the cellular tension behind the tissue mechanics involved in building tissue. Thus, understanding the role of physical forces during morphogenetic processes requires the consideration of the contribution of cell intrinsic and cell extrinsic influences. The recent development of multidisciplinary approaches, as well as major advances in genetics, microscopy, and force-probing tools, have been key to push this field forward. With this review, we aim to discuss recent work on how tissue shape can be controlled by mechanical forces by focusing specifically on vertebrate organogenesis. We consider the influences of mechanical forces by discussing the cell-intrinsic forces (such as cell tension and proliferation) and cell-extrinsic forces (such as substrate stiffness and flow forces). We review recently described processes supporting the role of intratissue force generation and propagation in the context of shape emergence. Lastly, we discuss the emerging role of tissue-scale changes in tissue material properties, extrinsic forces, and shear stress on shape establishment.

Continuum microhaemodynamics modelling using inverse rheology

Modelling blood flow in microvascular networks is challenging due to the complex nature of haemorheology. Zero- and one-dimensional approaches cannot reproduce local haemodynamics, and models that consider individual red blood cells (RBCs) are prohibitively computationally expensive. Continuum approaches could provide an efficient solution, but dependence on a large parameter space and scarcity of experimental data for validation has limited their application. We describe a method to assimilate experimental RBC velocity and concentration data into a continuum numerical modelling framework. Imaging data of RBCs were acquired in a sequentially bifurcating microchannel for various flow conditions. RBC concentration distributions were evaluated and mapped into computational fluid dynamics simulations with rheology prescribed by the Quemada model. Predicted velocities were compared to particle image velocimetry data. A subset of cases was used for parameter optimisation, and the resulting model was applied to a wider data set to evaluate model efficacy. The pre-optimised model reduced errors in predicted velocity by 60% compared to assuming a Newtonian fluid, and optimisation further reduced errors by 40%. Asymmetry of RBC velocity and concentration profiles was demonstrated to play a critical role. Excluding asymmetry in the RBC concentration doubled the error, but excluding spatial distributions of shear rate had little effect. This study demonstrates that a continuum model with optimised rheological parameters can reproduce measured velocity if RBC concentration distributions are known a priori. Developing this approach for RBC transport with more network configurations has the potential to provide an efficient approach for modelling network-scale haemodynamics.

Haemodynamic dependence of mechano-genetic evolution of the cardiovascular system in Japanese medaka

The progression of cardiac gene expression-wall shear stress (WSS) interplay is critical to identifying developmental defects during cardiovascular morphogenesis. However, mechano-genetics from the embryonic to larval stages are poorly understood in vertebrates. We quantified peak WSS in the heart and tail vessels of Japanese medaka from 3 days post fertilization (dpf) to 14 dpf using in vivo micro-particle image velocimetry flow measurements, and in parallel analysed the expression of five cardiac genes (fgf8, hoxb6b, bmp4, nkx2.5, smyd1). Here, we report that WSS in the atrioventricular canal (AVC), ventricular outflow tract (OFT), and the caudal vessels in medaka peak with inflection points at 6 dpf and 10-11 dpf instead of a monotonic trend. Retrograde flows are captured at the AVC and OFT of the medaka heart for the first time. In addition, all genes were upregulated at 3 dpf and 7 dpf, indicating a possible correlation between the two, with the cardiac gene upregulation preceding WSS increase in order to facilitate cardiac wall remodelling.

Integration of substrate- and flow-derived stresses in endothelial cell mechanobiology

Endothelial cells (ECs) lining all blood vessels are subjected to large mechanical stresses that regulate their structure and function in health and disease. Here, we review EC responses to substrate-derived biophysical cues, namely topography, curvature, and stiffness, as well as to flow-derived stresses, notably shear stress, pressure, and tensile stresses. Because these mechanical cues in vivo are coupled and are exerted simultaneously on ECs, we also review the effects of multiple cues and describe burgeoning in vitro approaches for elucidating how ECs integrate and interpret various mechanical stimuli. We conclude by highlighting key open questions and upcoming challenges in the field of EC mechanobiology.

Association between erythrocyte dynamics and vessel remodelling in developmental vascular networks

Sprouting angiogenesis is an essential vascularization mechanism consisting of sprouting and remodelling. The remodelling phase is driven by rearrangements of endothelial cells (ECs) within the post-sprouting vascular plexus. Prior work has uncovered how ECs polarize and migrate in response to flow-induced wall shear stress (WSS). However, the question of how the presence of erythrocytes (widely known as red blood cells (RBCs)) and their impact on haemodynamics affect vascular remodelling remains unanswered. Here, we devise a computational framework to model cellular blood flow in developmental mouse retina. We demonstrate a previously unreported highly heterogeneous distribution of RBCs in primitive vasculature. Furthermore, we report a strong association between vessel regression and RBC hypoperfusion, and identify plasma skimming as the driving mechanism. Live imaging in a developmental zebrafish model confirms this association. Taken together, our results indicate that RBC dynamics are fundamental to establishing the regional WSS differences driving vascular remodelling via their ability to modulate effective viscosity.

Viscosity Estimation of a Suspension with Rigid Spheres in Circular Microchannels Using Particle Tracking Velocimetry

Suspension flows are ubiquitous in industry and nature. Therefore, it is important to understand the rheological properties of a suspension. The key to understanding the mechanism of suspension rheology is considering changes in its microstructure. It is difficult to evaluate the influence of change in the microstructure on the rheological properties affected by the macroscopic flow field for non-colloidal particles. In this study, we propose a new method to evaluate the changes in both the microstructure and rheological properties of a suspension using particle tracking velocimetry (PTV) and a power-law fluid model. Dilute suspension (0.38%) flows with fluorescent particles in a microchannel with a circular cross section were measured under low Reynolds number conditions (Re ≈ 10^-4). Furthermore, the distribution of suspended particles in the radial direction was obtained from the measured images. Based on the power-law index and dependence of relative viscosity on the shear rate, we observed that the non-Newtonian properties of the suspension showed shear-thinning. This method will be useful in revealing the relationship between microstructural changes in a suspension and its rheology.

Three-dimensional distribution of wall shear stress and its gradient in red cell-resolved computational modeling of blood flow in in vivo-like microvascular networks

Using a high-fidelity, 3D computational model of blood flow in microvascular networks, we provide the full 3D distribution of wall shear stress (WSS), and its gradient (WSSG), and quantify the influence of red blood cells (RBCs) on WSS and WSSG. The deformation and flow dynamics of the individual RBCs are accurately resolved in the model, while physiologically realistic microvascular networks comprised of multiple bifurcations, convergences, and tortuous vessels are considered. A strong heterogeneity in WSS and WSSG is predicted across the networks, with the highest WSS occurring in precapillary bifurcations and capillary vessels. 3D variations of WSS and WSSG are shown to occur due to both network morphology and the influence of RBCs. The RBCs increase the WSS by as much as three times compared to that when no RBCs are present, and the highest increase is observed in venules. WSSG also increases significantly, and high WSSGs occur over wider regions in the presence of RBCs. In most vessels, the circumferential component of WSSG is observed to be greater than the axial component in the presence of RBCs, while the opposite trend is observed when RBCs are not considered. These results underscore the important role of RBCs on WSS and WSSG that cannot be predicted by widely used 1D models of network blood flow. Furthermore, the subendothelium-scale variations of WSS and WSSG predicted by the present model have implications in terms of endothelial cell functions in the microvasculature.

Shear stress in the microvasculature: influence of red blood cell morphology and endothelial wall undulation

The effect of red blood cells and the undulation of the endothelium on the shear stress in the microvasculature is studied numerically using the lattice Boltzmann-immersed boundary method. The results demonstrate a significant effect of both the undulation of the endothelium and red blood cells on wall shear stress. Our results also reveal that morphological alterations of red blood cells, as occur in certain pathologies, can significantly affect the values of wall shear stress. The resulting fluctuations in wall shear stress greatly exceed the nominal values, emphasizing the importance of the particulate nature of blood as well as a more realistic description of vessel wall geometry in the study of hemodynamic forces. We find that within the channel widths investigated, which correspond to those found in the microvasculature, the inverse minimum distance normalized to the channel width between the red blood cell and the wall is predictive of the maximum wall shear stress observed in straight channels with a flowing red blood cell. We find that the maximum wall shear stress varies several factors more over a range of capillary numbers (dimensionless number relating strength of flow to membrane elasticity) and reduced areas (measure of deflation of the red blood cell) than the minimum wall shear stress. We see that waviness reduces variation in minimum and maximum shear stresses among different capillary and reduced areas.

Mechanotransduction Mechanisms in Mitral Valve Physiology and Disease Pathogenesis

The mitral valve exists in a mechanically demanding environment, with the stress of each cardiac cycle deforming and shearing the native fibroblasts and endothelial cells. Cells and their extracellular matrix exhibit a dynamic reciprocity in the growth and formation of tissue through mechanotransduction and continuously adapt to physical cues in their environment through gene, protein, and cytokine expression. Valve disease is the most common congenital heart defect with watchful waiting and valve replacement surgery the only treatment option. Mitral valve disease (MVD) has been linked to a variety of mechano-active genes ranging from extracellular components, mechanotransductive elements, and cytoplasmic and nuclear transcription factors. Specialized cell receptors, such as adherens junctions, cadherins, integrins, primary cilia, ion channels, caveolae, and the glycocalyx, convert mechanical cues into biochemical responses via a complex of mechanoresponsive elements, shared signaling modalities, and integrated frameworks. Understanding mechanosensing and transduction in mitral valve-specific cells may allow us to discover unique signal transduction pathways between cells and their environment, leading to cell or tissue specific mechanically targeted therapeutics for MVD.

Anisotropic shear stress patterns predict the orientation of convergent tissue movements in the embryonic heart

Myocardial contractility and blood flow provide essential mechanical cues for the morphogenesis of the heart. In general, endothelial cells change their migratory behavior in response to shear stress patterns, according to flow directionality. Here, we assessed the impact of shear stress patterns and flow directionality on the behavior of endocardial cells, the specialized endothelial cells of the heart. At the early stages of zebrafish heart valve formation, we show that endocardial cells are converging to the valve-forming area and that this behavior depends upon mechanical forces. Quantitative live imaging and mathematical modeling allow us to correlate this tissue convergence with the underlying flow forces. We predict that tissue convergence is associated with the direction of the mean wall shear stress and of the gradient of harmonic phase-averaged shear stresses, which surprisingly do not match the overall direction of the flow. This contrasts with the usual role of flow directionality in vascular development and suggests that the full spatial and temporal complexity of the wall shear stress should be taken into account when studying endothelial cell responses to flow in vivo.

Summary: Blood flow modeling shows that dynamic shear stress patterns, rather than mean flow direction, predict the stereotypical behavior of endocardial cells during the early steps of heart valve formation.

Theory and algorithms to compute Helfrich bending forces: a review

Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.

Transcriptome reveals the overexpression of a kallikrein gene cluster (KLK1/3/7/8/12) in the Tibetans with high altitude-associated polycythemia

High altitude-associated polycythemia (HAPC) is a very common disease. However, it the disease is still unmanageable and the related molecular mechanisms remain largely unclear. In the present study, we aimed to explore the molecular mechanisms responsible for the development of HAPC using transcriptome analysis. Transcriptome analysis was conducted in 3 pairs of gastric mucosa tissues from patients with HAPC and healthy residents at a similar altitude. Endoscopy and histopathological analyses were used to examine the injury to gastric tissues. Molecular remodeling was performed for the interaction between different KLK members and cholesterol. HAPC was found to lead to morphological changes and pathological damage to the gastric mucosa of patients. A total of 10,304 differentially expressed genes (DEGs) were identified. Among these genes, 4,941 DEGs were upregulated, while 5,363 DEGs were downregulated in the patients with HAPC (fold change ≥2, P<0.01 and FDR <0.01). In particular, the kallikrein gene cluster (KLK1/3/7/8/12) was upregulated >17-fold. All the members had high-score binding cholesterol, particularly for the polymers of KLK7. The kallikrein gene cluster (KLK1/3/7/8/12) is on chromosome 19q13.3-13.4. The elevated levels of KLK1, KLK3, KLK7, KLK8 and KLK12 may be closely associated with the hypertension, inflammation, obesity and other gastric injuries associated with polycythemia. The interaction of KLKs and cholesterol maybe play an important role in the development of hypertension. The findings of the present study revealed that HAPC induces gastric injury by upregulating the kallikrein gene cluster (KLK1/3/7/8/12), which can bind cholesterol and result in kallikrein hypertension. These findings provide some basic information for understanding the molecular mechanisms responsible for HAPC and HAPC-related diseases.

Computational fluid dynamics assisted characterization of parafoveal hemodynamics in normal and diabetic eyes using adaptive optics scanning laser ophthalmoscopy

Diabetic retinopathy (DR) is the leading cause of visual loss in working-age adults worldwide. Previous studies have found hemodynamic changes in the diabetic eyes, which precede clinically evident pathological alterations of the retinal microvasculature. There is a pressing need for new methods to allow greater understanding of these early hemodynamic changes that occur in DR. In this study, we propose a noninvasive method for the assessment of hemodynamics around the fovea (a region of the eye of paramount importance for vision). The proposed methodology combines adaptive optics scanning laser ophthalmoscopy and computational fluid dynamics modeling. We compare results obtained with this technique with in vivo measurements of blood flow based on blood cell aggregation tracking. Our results suggest that parafoveal hemodynamics, such as capillary velocity, wall shear stress, and capillary perfusion pressure can be noninvasively and reliably characterized with this method in both healthy and diabetic retinopathy patients.

Flow of Red Blood Cells in Stenosed Microvessels

A computational study is presented on the flow of deformable red blood cells in stenosed microvessels. It is observed that the Fahraeus-Lindqvist effect is significantly enhanced due to the presence of a stenosis. The apparent viscosity of blood is observed to increase by several folds when compared to non-stenosed vessels. An asymmetric distribution of the red blood cells, caused by geometric focusing in stenosed vessels, is observed to play a major role in the enhancement. The asymmetry in cell distribution also results in an asymmetry in average velocity and wall shear stress along the length of the stenosis. The discrete motion of the cells causes large time-dependent fluctuations in flow properties. The root-mean-square of flow rate fluctuations could be an order of magnitude higher than that in non-stenosed vessels. Several folds increase in Eulerian velocity fluctuation is also observed in the vicinity of the stenosis. Surprisingly, a transient flow reversal is observed upstream a stenosis but not downstream. The asymmetry and fluctuations in flow quantities and the flow reversal would not occur in absence of the cells. It is concluded that the flow physics and its physiological consequences are significantly different in micro- versus macrovascular stenosis.

Flow structures and red blood cell dynamics in arteriole of dilated or constricted cross section

Vessel with 'circular' or 'star-shaped' cross sections are studied, representing respectively dilated or constricted cases where endothelial cells smoothly line or bulge into the lumen. Computational haemodynamics simulations are carried out on idealised periodic arteriole-sized vessels, with red blood cell 'tube' hematocrit value=24%. A further simulation of a single red blood cell serves for comparison purposes. The bulk motion of the red blood cells reproduces well-known effects, including the presence of a cell-free layer and the apparent shear-thinning non-Newtonian rheology. The velocity flow field is analysed in a Lagrangian reference frame, relative to any given red blood cell, hence removing the bulk coaxial motion and highlighting instead the complex secondary flow patterns. An aggregate formation becomes apparent, continuously rearranging and dynamic, brought about by the inter-cellular fluid mechanics interactions and the deformability properties of the cells. The secondary flow field induces a vacillating radial migration of the red blood cells. At different radial locations, the red blood cells express different residence times, orientation and shape. The shear stresses exerted by the flow on the vessel wall are influenced by the motion of red blood cells, despite the presence of the cell-free layer. Spatial (and temporal) variations of wall shear stress patters are observed, especially for the 'circular' vessel. The 'star-shaped' vessel bears considerable stress at the protruding endothelial cell crests, where the stress vectors are coaxially aligned. The bulging endothelial cells hence regularise the transmission of stresses on the vessel wall.

Hemodynamics driven cardiac valve morphogenesis

Mechanical forces are instrumental to cardiovascular development and physiology. The heart beats approximately 2.6 billion times in a human lifetime and heart valves ensure that these contractions result in an efficient, unidirectional flow of the blood. Composed of endocardial cells (EdCs) and extracellular matrix (ECM), cardiac valves are among the most mechanically challenged structures of the body both during and after their development. Understanding how hemodynamic forces modulate cardiovascular function and morphogenesis is key to unraveling the relationship between normal and pathological cardiovascular development and physiology. Most valve diseases have their origins in embryogenesis, either as signs of abnormal developmental processes or the aberrant re-expression of fetal gene programs normally quiescent in adulthood. Here we review recent discoveries in the mechanobiology of cardiac valve development and introduce the latest technologies being developed in the zebrafish, including live cell imaging and optical technologies, as well as modeling approaches that are currently transforming this field. This article is part of a Special Issue entitled: Cardiomyocyte Biology: Integration of Developmental and Environmental Cues in the Heart edited by Marcus Schaub and Hughes Abriel.

Live imaging and modeling for shear stress quantification in the embryonic zebrafish heart

Hemodynamic shear stress is sensed by the endocardial cells composing the inner cell layer of the heart, and plays a major role in cardiac morphogenesis. Yet, the underlying hemodynamics and the associated mechanical stimuli experienced by endocardial cells remains poorly understood. Progress in the field has been hampered by the need for high temporal resolution imaging allowing the flow profiles generated in the beating heart to be resolved. To fill this gap, we propose a method to analyze the wall dynamics, the flow field, and the wall shear stress of the developing zebrafish heart. This method combines live confocal imaging and computational fluid dynamics to overcome difficulties related to live imaging of blood flow in the developing heart. To provide an example of the applicability of the method, we discuss the hemodynamic frequency content sensed by endocardial cells at the onset of valve formation, and how the fundamental frequency of the wall shear stress represents a unique mechanical cue to endocardial, heart-valve precursors.

Multi-scale biological and physical modelling of the tumour micro-environment

Paced by advances in high performance computing, and algorithms for multi-physics and multi-scale simulation, a number of groups have recently established numerical models of flowing blood systems, where cell-scale interactions are explicitly resolved. To be biologically representative, these models account for some or all of: (1) fluid dynamics of the carrier flow, (2) structural dynamics of the cells and vessel walls, (3) interaction and transport biochemistry, and, (4) methods for scaling to physiologically representative numbers of cells. In this article, our interest is the modelling of the tumour micro-environment. We review the broader area of cell-scale resolving blood flow modelling, while focusing on the particular interactions of tumour cells and white blood cells, known to play an important role in metastasis.

Temporal and spatial variations of wall shear stress in the entrance region of microvessels

Using a simplified two-dimensional divider-channel setup, we simulate the development process of red blood cell (RBC) flows in the entrance region of microvessels to study the wall shear stress (WSS) behaviors. Significant temporal and spatial variation in WSS is noticed. The maximum WSS magnitude and the strongest variation are observed at the channel inlet due to the close cell-wall contact. From the channel inlet, both the mean WSS and variation magnitude decrease, with a abrupt drop in the close vicinity near the inlet and then a slow relaxation over a relatively long distance; and a relative stable state with approximately constant mean and variation is established when the flow is well developed. The correlations between the WSS variation features and the cell free layer (CFL) structure are explored, and the effects of several hemodynamic parameters on the WSS variation are examined. In spite of the model limitations, the qualitative information revealed in this study could be useful for better understanding relevant processes and phenomena in the microcirculation.

Blood flow mechanics in cardiovascular development

Hemodynamic forces are fundamental to development. Indeed, much of cardiovascular morphogenesis reflects a two-way interaction between mechanical forces and the gene network activated in endothelial cells via mechanotransduction feedback loops. As these interactions are becoming better understood in different model organisms, it is possible to identify common mechanogenetic rules, which are strikingly conserved and shared in many tissues and species. Here, we discuss recent findings showing how hemodynamic forces potentially modulate cardiovascular development as well as the underlying fluid and tissue mechanics, with special attention given to the flow characteristics that are unique to the small scales of embryos.