Realistic Microvascular Networks Research Articles

Cortical microvascular blood flow velocity mapping by combining dynamic light scattering optical coherence tomography and two-photon microscopy.

The accurate large-scale mapping of cerebral microvascular blood flow velocity is crucial for a better understanding of cerebral blood flow (CBF) regulation. Although optical imaging techniques enable both high-resolution microvascular angiography and fast absolute CBF velocity measurements in the mouse cortex, they usually require different imaging techniques with independent system configurations to maximize their performances. Consequently, it is still a challenge to accurately combine functional and morphological measurements to co-register CBF speed distribution from hundreds of microvessels with high-resolution microvascular angiograms. We propose a data acquisition and processing framework to co-register a large set of microvascular blood flow velocity measurements from dynamic light scattering optical coherence tomography (DLS-OCT) with the corresponding microvascular angiogram obtained using two-photon microscopy (2PM). We used DLS-OCT to first rapidly acquire a large set of microvascular velocities through a sealed cranial window in mice and then to acquire high-resolution microvascular angiograms using 2PM. The acquired data were processed in three steps: (i)2PM angiogram coregistration with the DLS-OCT angiogram, (ii)2PM angiogram segmentation and graphing, and (iii)mapping of the CBF velocities to the graph representation of the 2PM angiogram. We implemented the developed framework on the three datasets acquired from the mice cortices to facilitate the coregistration of the large sets of DLS-OCT flow velocity measurements with 2PM angiograms. We retrieved the distributions of red blood cell velocities in arterioles, venules, and capillaries as a function of the branching order from precapillary arterioles and postcapillary venules from more than 1000 microvascular segments. The proposed framework may serve as a useful tool for quantitative analysis of large microvascular datasets obtained by OCT and 2PM in studies involving normal brain functioning, progression of various diseases, and numerical modeling of the oxygen advection and diffusion in the realistic microvascular networks.

A computational study of red blood cell deformability effect on hemodynamic alteration in capillary vessel networks

Capillary blood vessels, the smallest vessels in the body, form an intricate network with constantly bifurcating, merging and winding vessels. Red blood cells (RBCs) must navigate through such complex microvascular networks in order to maintain tissue perfusion and oxygenation. Normal, healthy RBCs are extremely deformable and able to easily flow through narrow vessels. However, RBC deformability is reduced in many pathological conditions and during blood storage. The influence of reduced cell deformability on microvascular hemodynamics is not well established. Here we use a high-fidelity, 3D computational model of blood flow that retains exact geometric details of physiologically realistic microvascular networks, and deformation of every one of nearly a thousand RBCs flowing through the networks. We predict that reduced RBC deformability alters RBC trafficking with significant and heterogeneous changes in hematocrit. We quantify such changes along with RBC partitioning and lingering at vascular bifurcations, perfusion and vascular resistance, and wall shear stress. We elucidate the cellular-scale mechanisms that cause such changes. We show that such changes arise primarily due to the altered RBC dynamics at vascular bifurcations, as well as cross-stream migration. Less deformable cells tend to linger less at majority of bifurcations increasing the fraction of RBCs entering the higher flow branches. Changes in vascular resistance also seen to be heterogeneous and correlate with hematocrit changes. Furthermore, alteration in RBC dynamics is shown to cause localized changes in wall shear stress within vessels and near vascular bifurcations. Such heterogeneous and focal changes in hemodynamics may be the cause of morphological abnormalities in capillary vessel networks as observed in several diseases.

The severity of microstrokes depends on local vascular topology and baseline perfusion.

Cortical microinfarcts are linked to pathologies like cerebral amyloid angiopathy and dementia. Despite their relevance for disease progression, microinfarcts often remain undetected and the smallest scale of blood flow disturbance has not yet been identified. We employed blood flow simulations in realistic microvascular networks from the mouse cortex to quantify the impact of single-capillary occlusions. Our simulations reveal that the severity of a microstroke is strongly affected by the local vascular topology and the baseline flow rate in the occluded capillary. The largest changes in perfusion are observed in capillaries with two inflows and two outflows. This specific topological configuration only occurs with a frequency of 8%. The majority of capillaries have one inflow and one outflow and is likely designed to efficiently supply oxygen and nutrients. Taken together, microstrokes bear potential to induce a cascade of local disturbances in the surrounding tissue, which might accumulate and impair energy supply locally.

Predicting Vessel Diameter Changes to Up-Regulate Biphasic Blood Flow During Activation in Realistic Microvascular Networks.

A dense network of blood vessels distributes blood to different regions of the brain. To meet the temporarily and spatially varying energy demand resulting from changes in neuronal activity, the vasculature is able to locally up-regulate the blood supply. However, to which extent diameter changes of different vessel types contribute to the up-regulation, as well as the spatial and temporal characteristics of their changes, are currently unknown. Here, we present a new simulation method, which solves an inverse problem to calculate diameter changes of individual blood vessels needed to achieve predefined blood flow distributions in microvascular networks. This allows us to systematically compare the impact of different vessel types in various regulation scenarios. Moreover, the method offers the advantage that it handles the stochastic nature of blood flow originating from tracking the movement of individual red blood cells. Since the inverse problem is formulated for time-averaged pressures and flow rates, a deterministic approach for calculating the diameter changes is used, which allows us to apply the method for large realistic microvascular networks with high-dimensional parameter spaces. Our results obtained in both artificial and realistic microvascular networks reveal that diameter changes at the level of capillaries enable a very localized regulation of blood flow. In scenarios where only larger vessels, i.e., arterioles, are allowed to adapt, the flow increase cannot be confined to a specific activated region and flow changes spread into neighboring regions. Furthermore, relatively small dilations and constrictions of all vessel types can lead to substantial changes of capillary blood flow distributions. This suggests that small scale regulation is necessary to obtain a localized increase in blood flow.

Red Blood Cell‐resolved 3D Computational Modeling of Blood Flow in Physiologically Realistic Microvascular Networks

Microvascular networks represent geometrically complex architecture due to constantly bifurcating and merging vessels. Moreover, blood vessels are not necessarily straight, and often highly winding. Mathematical models of blood flow in such networks have treated these vessels as 1D straight segments neglecting the geometric complexity and details. These models also do not consider the deformation and flow of individual red blood cell, and instead use empirical relations to prescribe blood viscosity and red blood cell distribution at a vascular bifurcation. As such, these models cannot predict hemodynamic variations over short time and length scales. To overcome this limitation, we have recently developed a high‐fidelity 3D, first‐principle based, fluid‐‐structure interaction model of blood flow in physiologically realistic microvascular networks. The model retains the exact geometric details of the vasculature, e.g., 3D nature of the blood vessels and bifurcations, and vessel curvature. Deformation and flow of each individual red blood cell as they flow through the vessels are exactly modeled. The model is based on the minimal assumptions: it does not assume any empirical viscosity law or bifurcation law; rather, these laws are predicted by the model. The model provides microscale details of hemodynamic quantities that are not readily available in experiments, and cannot be predicted by the traditional 1D network models, such as wall shear stress gradient and time‐dependent red blood cell partitioning at bifurcations.Of particular interest is the role of red blood cell deformability on hematocrit distribution in the networks. Cell deformability is known to reduce in many diseases, such as sickle cell disease, malaria and diabetes. By using in vivo images of retinal microvasculature, we have performed simulation of network blood flow under varying cell deformability in such networks. The model shows that altered cell deformability significantly changes the cell distribution in the network, and subsequently the flow resistance in vessels. While some vessels show a significant increase in hematocrit, some show a significant decrease. Such a redistribution of hematocrit for diseased red blood cells may have a significant impact on tissue oxygen delivery. The simulation results are used to mechanistically explain the observed redistribution of hematocrit and vascular resistance.Support or Funding InformationFunded by NSF

Three-dimensional distribution of wall shear stress and its gradient in red cell-resolved computational modeling of blood flow in invivo-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.

High‐fidelity Modeling of Blood Flow in Physiologically Realistic Microvascular Networks

High-fidelity in silico modeling of blood flow in microvascular networks continues to be a challenge. Blood in small vessels behaves as a concentrated suspension of red blood cells (RBC), which are extremely deformable. Computational modeling must resolve the dynamics and deformation of individual RBC while simultaneously extending to a dense suspension. Most cellular-scale in silico models to date have considered blood flow in simple geometries, such as straight tubes or channels, which do not represent physiological conditions, since the architecture of vascular networks in vivo is characterized by bifurcating, merging, and winding vessels. Such geometrical differences result in significant deviations in hemodynamics between that achieved in a straight conduit versus a vascular network. We have recently developed a high-fidelity, multiscale, 3D computational model of flow of deformable RBCs in complex microvascular networks resembling in vivo-like architectures. The vascular networks are designed following in vivo images and data, and are comprised of bifurcating, merging, and tortuous vessels. Our model accurately resolves the large deformation and dynamics of each individual RBC, while simultaneously retaining complex geometric details of the vascular architecture. The model is versatile, and can consider networks irrespective of topological/geometrical complexities. Flow can be driven by either pressure or flow boundary conditions of physiological values. Cell distributions naturally develop in the networks from an initial random distribution, eventually resulting in a heterogeneous cell distribution as observed in vivo. Extreme deformation and a wide range of RBC shapes are observed that are in agreement with in vivo observations. Quantitative comparisons were made with in vivo data using hemodynamic quantities such as flow resistance, wall shear stress, cell-free layer, etc., and good agreement was observed. The model can also consider white blood cells and platelets, and receptor-mediated adhesion between vascular wall and cells. The model provides a full 3D quantification of hemodynamic quantities with unprecedented details that are not available in experimental measurements. For example, the model allows full 3D characterizations of the near-wall cell-free layer (CFL) and wall shear stress (WSS) and gradients (WSSG). It predicts that CFL becomes more asymmetric along vessel lengths with increasing vessel tortuosity. While WSS itself decreases from arterial to venous sides, the model predicts that WSS in presence of RBCs increases more than that without RBCs on the venous sides and at capillary bifurcations. This implies that the effect of RBCs on WSS is more enhanced at specific locations in a microvascular network. WSSG is also predicted to be much higher in presence of the RBCs, and increase at capillary bifurcations. The model is used further to study transport and deposition of nanoparticle drug carriers in the microvasculature. Results show that nanoparticle accumulation is highly nonuniform across the vasculature with the highest accumulation occurring in bifurcations and the lowest in venules. Support or Funding Information Supported by the National Science Foundation In silico model of flow of blood cells in a microvascular network. This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Direct Numerical Simulation of Cellular-Scale Blood Flow in 3D Microvascular Networks

We present, to our knowledge, the first direct numerical simulation of 3D cellular-scale blood flow in physiologically realistic microvascular networks. The vascular networks are designed following in vivo images and data, and are comprised of bifurcating, merging, and winding vessels. Our model resolves the large deformation and dynamics of each individual red blood cell flowing through the networks with high fidelity, while simultaneously retaining the highly complex geometric details of the vascular architecture. To our knowledge, our simulations predict several novel and unexpected phenomena. We show that heterogeneity in hemodynamic quantities, which is a hallmark of microvascular blood flow, appears both in space and time, and that the temporal heterogeneity is more severe than its spatial counterpart. The cells are observed to frequently jam at vascular bifurcations resulting in reductions in hematocrit and flow rate in the daughter and mother vessels. We find that red blood cell jamming at vascular bifurcations results in several orders-of-magnitude increase in hemodynamic resistance, and thus provides an additional mechanism of increased in vivo blood viscosity as compared to that determined in vitro. A striking result from our simulations is negative pressure-flow correlations observed in several vessels, implying a significant deviation from Poiseuille’s law. Furthermore, negative correlations between vascular resistance and hematocrit are observed in various vessels, also defying a major principle of particulate suspension flow. To our knowledge, these novel findings are absent in blood flow in straight tubes, and they underscore the importance of considering realistic physiological geometry and resolved cellular interactions in modeling microvascular hemodynamics.

Depth-dependent flow and pressure characteristics in cortical microvascular networks.

A better knowledge of the flow and pressure distribution in realistic microvascular networks is needed for improving our understanding of neurovascular coupling mechanisms and the related measurement techniques. Here, numerical simulations with discrete tracking of red blood cells (RBCs) are performed in three realistic microvascular networks from the mouse cerebral cortex. Our analysis is based on trajectories of individual RBCs and focuses on layer-specific flow phenomena until a cortical depth of 1 mm. The individual RBC trajectories reveal that in the capillary bed RBCs preferentially move in plane. Hence, the capillary flow field shows laminar patterns and a layer-specific analysis is valid. We demonstrate that for RBCs entering the capillary bed close to the cortical surface (< 400 μm) the largest pressure drop takes place in the capillaries (37%), while for deeper regions arterioles are responsible for 61% of the total pressure drop. Further flow characteristics, such as capillary transit time or RBC velocity, also vary significantly over cortical depth. Comparison of purely topological characteristics with flow-based ones shows that a combined interpretation of topology and flow is indispensable. Our results provide evidence that it is crucial to consider layer-specific differences for all investigations related to the flow and pressure distribution in the cortical vasculature. These findings support the hypothesis that for an efficient oxygen up-regulation at least two regulation mechanisms must be playing hand in hand, namely cerebral blood flow increase and microvascular flow homogenization. However, the contribution of both regulation mechanisms to oxygen up-regulation likely varies over depth.

A computational approach to modeling cellular-scale blood flow in complex geometry

We present a computational methodology for modeling cellular-scale blood flow in arbitrary and highly complex geometry. Our approach is based on immersed-boundary methods, which allow modeling flows in arbitrary geometry while resolving the large deformation and dynamics of every blood cell with high fidelity. The present methodology seamlessly integrates different modeling components dealing with stationary rigid boundaries of complex shape, moving rigid bodies, and highly deformable interfaces governed by nonlinear elasticity. Thus it enables us to simulate ‘whole’ blood suspensions flowing through physiologically realistic microvascular networks that are characterized by multiple bifurcating and merging vessels, as well as geometrically complex lab-on-chip devices. The focus of the present work is on the development of a versatile numerical technique that is able to consider deformable cells and rigid bodies flowing in three-dimensional arbitrarily complex geometries over a diverse range of scenarios. After describing the methodology, a series of validation studies are presented against analytical theory, experimental data, and previous numerical results. Then, the capability of the methodology is demonstrated by simulating flows of deformable blood cells and heterogeneous cell suspensions in both physiologically realistic microvascular networks and geometrically intricate microfluidic devices. It is shown that the methodology can predict several complex microhemodynamic phenomena observed in vascular networks and microfluidic devices. The present methodology is robust and versatile, and has the potential to scale up to very large microvascular networks at organ levels.