Microcirculation and inflammation in a numerical simulation approach

Inflammation is the response of the organism to eradicate the agent of lesion or infection in order to achieve hemostasis. This response requires the migration of specific leukocyte populations from the blood circulation towards the inflamed area. Leukocyte recruitment constitutes a complex cellular process by which leukocytes are first recruited to the endothelial vascular wall of post-capillary venules across which they further extravasate into the interstitial tissue. Recruitment is mediated via cell-cell interactions between the leukocyte and the endothelium and occurs through a multi-step cascade: tethering, rolling, slow rolling, arrest, crawling, adhesion and transmigration. However, whether or not the leukocytes adhere to the endothelium depends not only on the chemical forces generated by adhesion molecules on leukocytes and endothelial cells, but also on the physical forces that act on those cells. It has been suggested that fluid shear stress resulting from blood flow also regulates leukocyte activity which makes the fluid dynamic environment of the circulation to be considered an important aspect for leukocyte recruitment and migration during the inflammatory response. Most of the studies on the inflammatory response and in particular on leukocyte recruitment are based on animal models and involve, among others, the quantification of inflammatory mediators and cellular players, and/or the analysis of the leukocyte-endothelial cell interactions by intravital microscopy. However, the contribution of hemodynamics for leukocyte recruitment has been seldom addressed in those studies. This is mostly due to the fact that the study of hemodynamics in in vivo animal models is not straightforward and moreover, that several hemodynamic parameters cannot be experimentally determined due to technical constraints. In this work, we reasoned that these limitations could be circumvented by the development and use of numerical simulations to describe leukocyte recruitment. Many of the processes, which take place in living organisms, can be expressed as mathematical equations. This applies to leukocyte recruitment, for which scarce numerical models existed before the beginning of this work. Importantly, these mathematical simulations were performed without considering simultaneously all the players in the process, namely the vessel, the blood flow and the leukocytes. Moreover, most of these studies were two dimensional, assumed blood as a Newtonian fluid with constant viscosity and did not take into account in vivo experimental data. Taken this, our major goal with this work was to understand the contribution of hemodynamics to leukocyte recruitment in inflammation. For such purpose, we aimed here at developing numerical simulations that more adequately reproduced this process. For such, we set up animal models of inflammation to obtain the experimental data required for the development of those numerical simulations. Finally, we used these models to investigate the role of hemodynamics in leukocyte recruitment in inflammation. First, we considered the simpler case of a numerical simulation that assumed leukocytes to be rigid spheres and blood, a non-Newtonian fluid. For such, we initially developed an animal model of inflammation in Wistar rats using a lipopolysaccharide (LPS) as an inflammatory agent. Blood samples were collected for determination of TNF-α levels to ensure the triggering of the inflammatory process. Importantly, the number of rolling and adherent leukocytes in post-capillary venules was monitored using an intravital microscopy approach. As expected, our results showed that there is an increase in TNF-α concentrations after 15 minutes of LPS administration and a significant increase in the number of rolling and adherent leukocytes. The recorded intravital microcopy images, along with other recorded parameters, were then used, in collaboration with a group of mathematicians, to develop a numerical model capable of describing leukocyte recruitment in the microcirculation. To evaluate the contribution of hemodynamics, the localized velocity fields and shear stresses on the surface of leukocytes and near the vessel wall contact points have been computed in two discrete situations, namely as a single leukocyte or when a cluster of them are recruited towards the vessel wall. In the first situation, our numerical results showed the presence of one region of maximum shear stress on the surface of the leuko- cyte close to the endothelial wall and of two regions of minimum shear stress on the op- posite side of the cell. The different areas of shear stress observed in the surface of the leukocyte may be important in directing it towards the endothelial wall during an inflammatory response. The identification of a region of maximum shear stress is consistent with the molecular mechanisms that govern leukocyte rolling because it may actually cor- respond to the area that supports the interaction with the endothelium. On the other hand, the relatively lower shear stress regions may correlate with leukocyte surface areas where binding to the endothelium is not occurring at the moment, thus enabling the roll- ing of the cell along the endothelium. It was also observed that the shear stress at the endothelium gets higher as a cluster of leukocytes moves in the main stream. This sug- gests that the presence of a cluster of leukocytes may potentiate leukocyte rolling, as the increase in the shear stress promoted by the recruited leukocytes may support the migra- tion and recruitment of additional cells. Despite closely simulating leukocyte recruitment, our initial numerical simulation consid- ered the simple case of leukocytes as rigid spheres. However, while circulating leukocytes maintain an approximately spherical shape, rolling leukocytes are known to deform. In order to account for the leukocyte deformability changes that occur during its recruit- ment in inflammation, we needed to assess the deformability profile of the leukocytes under flow and therefore, to “directly” observe them regardless of the other blood cells. For such, intravital microscopy was performed in the mouse cremaster of a transgenic mice strain (Lys-EGFP-ki) in which fluorescent neutrophils can be individually tracked. By using PAF as an inflammatory agent, the analysis of the leukocyte-endothelial cell interac- tions showed a continuous increase in the number of rolling and adherent neutrophils up to 4 hours after the introduction of the inflammatory stimuli, thus confirming the devel- opment of an inflammatory response. As the properties of the red blood cells modulate blood flow properties, erythrocyte deformability was also addressed in this model. A con- tinuous decrease of this parameter was observed throughout time. The decrease in the erythrocyte deformability will most probably lead to an increase in the blood viscosity and to the decrease of the blood flow velocity. These conditions should facilitate the mi- gration of leukocytes from the mainstream to the endothelial wall and promote leukocyte slow rolling and adhesion during the inflammatory response. Importantly, in the intravital microcopy images obtained with this latter model, we clearly observed the deformation of neutrophils along the endothelial wall during rolling, as well as the formation of tethers. As such, in these images, leukocyte trajectories were tracked and their velocities and diameters were measured and further applied to the numerical simulations. Using a recent validated mathematical model describing the coupled defor- mation-flow of an individual leukocyte and the respective experimental results, numerical simulations of the recruitment of an individual leukocyte and of two leukocytes under different velocities were performed, considering a constant blood viscosity. The mathe- matical models obtained showed that under conditions of increased velocity the cell movement is accelerated along the endothelial layer, favouring the dissociation of leuko- cyte-endothelium interactions at designated attraction points. These observations lead us to propose that, in order to attain an efficient inflammatory response, the blood flow ve- locity needs so as to decrease to facilitate slow rolling and subsequent adhesion. These results are corroborated by the decrease in the erythrocyte deformability observed in our animal model, which will ultimately have an impact on the blood flow velocity. Our results further showed that in the vicinity of an adherent leukocyte there is an early slight decel- eration of the rolling leukocyte when compared with the case of an individual leukocyte. As such, these observations strongly suggest that the presence of an adherent cell in the vicinity should decrease the velocity of another leukocyte that is being recruited, thus promoting its slow rolling, and contributing to its capture by the endothelial cells. Altogether, our experimental data and numerical simulations support our working hy- pothesis that the hemodynamic properties of the flow and of the cells in circulation should play an essential role in the margination and rolling of the leukocytes to the endo- thelial wall, which in turn will impact the success of the inflammatory response. In partic- ular, our results strongly suggest that changes in hemodynamic conditions, such as de- creased flow velocities and the increase of the shear stress, will contribute to target leu- kocytes to the endothelial wall. Given our results, we propose that any change in the he- modynamic properties will certainly influence the outcome of the inflammatory response. As such, the adherence of the leukocytes to the endothelium should depend not only on the relative magnitude of the chemical forces generated by the interaction of adhesion molecules between leukocytes and endothelial cells, but also on the physical forces that act on the leukocytes. In this respect, our results suggest that alterations in the blood flow, for example in the flow velocity, will occur during an inflammatory process, thus potentiating the recruitment of more leukocytes towards the inflamed area and contrib- uting to a successful inflammatory response. Overall, the numerical simulations allowed us to better understand the contribution of the hemodynamic properties of the flow to the progression of an inflammatory response and to deepen our knowledge on leukocyte recruitment in inflammation. Importantly, our work provided numerical tools that can be used for the subsequent study and modulation of the hemodynamic parameters involved in an inflammatory response. In particular, these numerical simulations will surely enable us, in the near future, to determine or es- timate a large set of parameters which are unlikely to be recoverable by in vivo experi- ments. Moreover, our methods will allow us to analyze how the parameters evolve over time. Altogether our results further reinforce the notion that the improvement and de- velopment of animal models and numerical tools will certainly provide the medical and biological community with useful tools to study leukocyte recruitment in inflammation. By closely reproducing the microcirculation and the inflammatory process, these tools will be critical for a better comprehension of the inflammatory process and of the mecha- nisms underlying a multitude of inflammatory pathological conditions

Flow of a blood analogue solution through microfabricated hyperbolic contractions

The flow of a blood analogue solution past a microfabricated hyperbolic contraction followed by an abrupt expansion was investigated experimentally. The shape of the contraction was designed in order to impose a nearly constant strain rate to the fluid along the centerline of the microgeometry. The flow patterns of the blood analogue solution and of a Newtonian reference fluid (deionized water), captured using streak line imaging, are quite distinct and illustrate the complex behavior of the blood analogue solution flowing through the microgeometry. The flow of the blood analogue solution shows elastic-driven effects with vortical structures emerging upstream of the contraction, which are absent in Newtonian fluid flow. In both cases the flow also develops instabilities downstream of the expansion but these are inertia driven. Therefore, for the blood analogue solution at high flow rates the competing effects of inertia and elasticity lead to complex flow patterns and unstable flow develops

A simplified particulate model for coarse-grained hemodynamics simulations

Human blood flow is a multi-scale problem: in first approximation, blood is a dense suspension of plasma and deformable red cells. Physiological vessel diameters range from about one to thousands of cell radii. Current computational models either involve a homogeneous fluid and cannot track particulate effects or describe a relatively small number of cells with high resolution, but are incapable to reach relevant time and length scales. Our approach is to simplify much further than existing particulate models. We combine well established methods from other areas of physics in order to find the essential ingredients for a minimalist description that still recovers hemorheology. These ingredients are a lattice Boltzmann method describing rigid particle suspensions to account for hydrodynamic long range interactions and---in order to describe the more complex short-range behavior of cells---anisotropic model potentials known from molecular dynamics simulations. Paying detailedness, we achieve an efficient and scalable implementation which is crucial for our ultimate goal: establishing a link between the collective behavior of millions of cells and the macroscopic properties of blood in realistic flow situations. In this paper we present our model and demonstrate its applicability to conditions typical for the microvasculature.Comment: 12 pages, 11 figure

A computational approach to arteriolar bifurcations: evaluation of factors influencing predicted wall shear stress

Recent studies of blood flow regulation at the microcirculatory level have linked the physical characteristics of the arteriolar bifurcations and the physiology of the flow through them to the autoregulatory mechanisms exhibited by the endothelial cell lining. Research in this area is decomposed to the following two components: understanding the biochemical activity that takes place at the cellular level as a result of flow-induced stimulation and characterizing the physical flow behavior causing the stimulation. The following study develops the currently accepted method of characterizing the physical flow behavior, in the form of wall shear stress, through computational analysis. The goal of this research was to improve the computational methodology used for arterial blood flow analysis to predict and characterize wall shear stress. In doing so, all factors introduced by the modeling techniques were analyzed for influence on predicted wall shear stress in order to prove the credibility of the methodology. This process also extended to a characterization of wall shear stress effects as a result of changing model geometry and the physical composition of the blood as a particle-laden fluid, which better represent the physical features of these microcirculatory vessels. The thoughts presented in this thesis corresponding to the development and proof of a revised approach for wall shear stress prediction in arteriolar bifurcations provide a consistent method for the development and evaluation of single factors of the realistic model as they relate to wall shear stress. The goal of this approach was to simplify the computational problem into its constituents and evaluate the wall shear stress influence of each on a singular basis

The effect of red blood cell deformability on microscale blood flows

The non-Newtonian nature of blood arises from the presence of suspended formed elements which are the red blood cells (RBCs), white blood cells (WBCs) and platelets. Red blood cells or erythrocytes are the predominant constituent elements of blood, hence their role on haemodynamics is of great importance. Their remarkable deformability enables their flow in microvessels and is vital to oxygen delivery to tissue. Different diseases, such as malaria, sickle cell anaemia, diabetes etc. affect the mechanical properties and mainly the deformability of RBCs leading to pathological conditions and disorders in the microcirculation. However, the exact role of RBC deformability in microvascular flows has not been established hitherto. In this study, the role of red blood cell deformability on microscale haemodynamics was examined by perfusing artificially hardened RBCs in straight and bifurcating microchannels mimicking the microvasculature. RBC microchannel flows were resolved using brightfield micro-PIV methods. Advanced image processing routines were implemented in MATLAB to simultaneously determine the velocity and haematocrit distributions for a range of flow rates and feed haematocrit conditions. At low feed haematocrits (5%) hardened RBCs were found to be more dispersed in the straight microchannel flows compared to healthy RBCs, consistent with reports of decreased migration of hardened cells. At high haematocrits (25%) hardened RBCs produced less blunted velocity profiles compared to healthy RBCs, implying a reduction in the shear thinning behaviour of the suspensions. However, the haematocrit profiles appeared to also be sharper indicating some complex interactions between hardened cells. These findings were supported by cell tracking experiments which produced similar cell distributions for fluorescent hardened RBCs in a hardened RBC suspension, in contrast to observed margination of the same cells when suspended in healthy RBCs suspensions. Experiments with higher aspect microchannels confirmed the same trends, indicating that the latter were not due to confinement. The extent of RBC aggregation – indicated by the bluntness of the velocity and haematocrit profiles as well as the standard deviation of the image intensity – was found to be decreased in flows of hardened RBCs, compared to healthy ones in the whole range of the measured flow rates. RBC flows showed a higher level of heterogeneity in the bifurcating microchannels with both haematocrit and velocity profiles downstream of the T-junction bifurcation, exhibiting skewness the extent of which depended on the flow ratio between branches and RBC properties. RBC aggregation appeared to affect the non-uniformity of the haematocrit and velocity distributions downstream the bifurcation to a larger extent than RBC hardening which showed smaller variations compared to healthy non-aggregated RBC suspensions. Finally, the parent branch flow rate affected the redistribution of RBCs downstream of the bifurcation producing less skewed distributions with increasing flow rate. The thesis elucidated the physics of RBCs flows with impaired deformability providing thus the fundamental knowledge that is required for the development of medical diagnostic tools able to capture and assess the severity of diseases associated with impaired RBC deformability

Computational Biorheology of Human Blood Flow in Health and Disease

Hematologic disorders arising from infectious diseases, hereditary factors and environmental influences can lead to, and can be influenced by, significant changes in the shape, mechanical and physical properties of red blood cells (RBCs), and the biorheology of blood flow. Hence, modeling of hematologic disorders should take into account the multiphase nature of blood flow, especially in arterioles and capillaries. We present here an overview of a general computational framework based on dissipative particle dynamics (DPD) which has broad applicability in cell biophysics with implications for diagnostics, therapeutics and drug efficacy assessments for a wide variety of human diseases. This computational approach, validated by independent experimental results, is capable of modeling the biorheology of whole blood and its individual components during blood flow so as to investigate cell mechanistic processes in health and disease. DPD is a Lagrangian method that can be derived from systematic coarse-graining of molecular dynamics but can scale efficiently up to arterioles and can also be used to model RBCs down to the spectrin level. We start from experimental measurements of a single RBC to extract the relevant biophysical parameters, using single-cell measurements involving such methods as optical tweezers, atomic force microscopy and micropipette aspiration, and cell-population experiments involving microfluidic devices. We then use these validated RBC models to predict the biorheological behavior of whole blood in healthy or pathological states, and compare the simulations with experimental results involving apparent viscosity and other relevant parameters. While the approach discussed here is sufficiently general to address a broad spectrum of hematologic disorders including certain types of cancer, this paper specifically deals with results obtained using this computational framework for blood flow in malaria and sickle cell anemia.National Institutes of Health (U.S.)Singapore-MIT Alliance for Research and Technology (SMART)United States. Dept. of Energy. Collaboratory on Mathematics for Mesoscopic Modeling of MaterialsUnited States. Dept. of Energy (INCITE Award

Dynamics of Elastic Capsules in constricted Microfluidic Channels

In this dissertation, we investigate computationally the transient dynamics of an elastic capsule in a square microchannel with two different types of constriction (i.e., a square or a rectangular constriction), and compare them with those owing to a droplet passing. The confinement and expansion dynamics of the fluid flow results in a rich deformation behavior for the capsule, from an elongated shape at the constriction entrance, to a flattened parachute shape at its exit. Larger capsules are shown to take more time to pass the constriction and cause higher additional pressure difference, owing to higher flow blocking. Our work highlights the effects of two different mechanisms for non-tank-treading transient capsule dynamics. The capsule deformation results from the combined effects of the surrounding and inner fluids normal stresses on the soft particles interface, and thus when the capsule viscosity increases, its transient deformation decreases, as for droplets. However, the capsule deformation is not able to create a strong enough inner circulation (owing to restrictions imposed by the material membrane), and thus the viscosity ratio does not affect much the capsule velocity and the additional pressure difference. In addition, the weak inner circulation results in a positive additional pressure difference even for low viscosity capsules, in direct contrast to low-viscosity droplets which create a negative. In addition, we focus on the hydrodynamic forces exerted on the constriction owing to the capsule passing by considering different capsule sizes, flow rates and viscosity ratios. As the capsule size increases, the forces increase owing to the higher flow blocking. The hydrodynamic forces on the constriction are only weakly affected by the viscosity ratio. For low-viscosity capsules, the additional hydrodynamic forces on the constriction are positive in direct contrast to low-viscosity droplets which create negative additional hydrodynamic forces on the constriction due to their strong inner circulation. Finally, we investigate the effects of the constriction type for the transient capsule dynamics. In the square constriction, the capsule is more deformed owing to the larger flow changes associated with the smaller cross-section area of this constriction. The higher flow blocking results in an increase of the capsule velocity, the additional pressure difference and the hydrodynamic forces exerted on the constriction owing to the capsule passing. Our findings suggest that the high cytoplasmatic viscosity, owing to the protein hemoglobin required for oxygen transport, does not affect adversely the motion of non-tank-trading erythrocytes in vascular capillaries