Topological structure of rat mesenteric microvessel networks

Pulmonary vasculature development in congenital diaphragmatic hernia: a novel automated quantitative imaging analysis

PURPOSE

Impaired fetal lung vasculature determines the degree of pulmonary hypertension in the congenital diaphragmatic hernia (CDH). This study aims to demonstrate the morphometric measurements that differ in pulmonary vessels of fetuses with CDH.

METHODS

Nitrofen-induced CDH Sprague-Dawley rat fetuses were scanned with microcomputed tomography. The analysis of the pulmonary vascular tree was performed with artificial intelligence.

RESULTS

The number of segments in CDH was significantly lower than that in the control group on the left (U = 2.5, p = 0.004) and right (U = 0, p = 0.001) sides for order 1(O1), whereas there was a significant difference only on the right side for O2 and O3. The pooled element numbers in the control group obeyed Horton's law (R2 = 0.996 left and R2 = 0.811 right lungs), while the CDH group broke it. Connectivity matrices showed that the average number of elements of O1 springing from elements of O1 on the left side and the number of elements of O1 springing from elements of O3 on the right side were significantly lower in CDH samples.

CONCLUSION

According to these findings, CDH not only reduced the amount of small order elements, but also destroyed the fractal structure of the pulmonary arterial trees.

Fluid and protein exchange in microvascular networks: Importance of modelling heterogeneity in geometrical and biophysical properties

KEY POINTS

Microvascular network architecture defines coupling of fluid and protein exchange. Network arrangements markedly reduce capillary hydrostatic pressures and resting fluid movement at the same time as increasing the capacity for change The presence of vascular remodelling or angiogenesis puts constraints of network behaviour The sites of fluid and protein exchange can be segregated to different portions of the network Although there is a net filtration of fluid from a network of exchange vessels, there are specific areas where fluid moves into the circulation (reabsorption) and, when protein is moving into tissue, the amount is insufficient under basal conditions to result in changes in oncotic pressure.

ABSTRACT

Integration of functional results obtained across scales, from chemical signalling to the whole organism, is a daunting task requiring the marriage of experimental data with mathematical modelling. In the present study, a novel coupled computational fluid dynamics model is developed incorporating fluid and protein transport using measurements in an in vivo frog (Rana pipiens) mesenteric microvascular network. The influences of network architecture and exchange are explored systematically under the common assumptions of structurally and functionally identical microvessels (Homogeneous Scenario) or microvessels classified by position in flow (Class Uniform Scenario), which are compared with realistic microvascular network components (Heterogeneous Scenario). The model incorporates ten quantities that vary within a microvessel; pressure boundary conditions are calibrated against experimental measurements. The Homogeneous Scenario standard model showed that assuming a single 'typical' capillary hides the influence of vessels arranged into a network architecture, where capillary hydrostatic pressures (pT ) are reduced, resulting in both a nonuniform distribution of blood flow and reduced volume flow rate (Jf,T ). In the Class Uniform Scenario pT was further attenuated to produce a ∼60% reduction in Jf,T . Finally, the Heterogeneous Scenario, incorporating measures of individual vessel surface area, demonstrates additional lowering of pT from inlet values favouring a >70% reduction of Jf,T in the face of a ∼120% increase in protein movement into the tissues relative to the Homogeneous Scenario. Beyond the impacts of network architecture, an unanticipated finding was the influence of a blind-end microvessel on model convergence, indicating a profound influence of the largely unexplored dynamics of vascular remodelling on tissue perfusion.

An adaptive fractal model for sublingual microcirculation

The hemodynamic conditions and partial pressure of oxygen in microcirculation generally indicate the status of tissue perfusion, which provides essential information for the assessment and treatment of critical diseases such as sepsis. The human tongue is known to have abundant microcirculation and is an ideal window to observe the microcirculation. At present, the monitoring of sublingual microcirculation is mostly achieved using handheld vital microscopy (HVM). Microcirculation is organized and works as a network. However, HVM can obtain only limited view of few vessels and is not able to acquire information regarding the entire network. In this work, we proposed a method to construct a mathematical network model of sublingual microcirculation to solve the problems. The proposed method is based on fractal analysis to model and simulate the hemodynamic and functional activities of sublingual microcirculation. Specifically, the HVM technology is used to obtain the partial morphological and hemodynamic data of sublingual microcirculation, and fractal analysis is applied thereafter to establish the hemodynamic model of the network based on the data from few vessels. Further, the adaptive regulation mechanism of microcirculation is introduced to enhance the performance of the model. The model was validated by the experimental data and the results are consistent with the characteristics of microcirculation. The work demonstrates the potential of the proposed method in sublingual microcirculation research and for the further assessment of tissue perfusion.

Retinal Vascular Pathology in a Rat Model of Cerebral Small Vessel Disease

Introduction: The initial disease stages of hypertensive arteriopathy (HA) and cerebral amyloid angiopathy (CAA), the two main forms of sporadic human cerebral small vessel diseases (CSVD), are too subtle to be detectable on clinical routine imaging. Small vessel disease (SVD) is a systemic condition, affecting not only the brain, but also other organs. The retina appears as an ideal marker for the early detection of incipient CSVD. We therefore investigated the retinal microvasculature of the spontaneously hypertensive stroke-prone rat (SHRSP), an animal model of sporadic CSVD.

Materials and Methods: The brains and retinas of 26 male SHRSP (18–44 weeks) were examined histologically and immunohistochemically for the presence of HA phenomena (erythrocyte thrombi, small perivascular bleeds) and amyloid angiopathy (AA).

Results: CAA and AA in the retina showed a significant correlation with age (CAA: rho = 0.55, p = 0.005; AA: rho = 0.89, p < 0.001). The number of erythrocyte thrombi in the brain correlated with the severity of retinal erythrocyte thrombi (rho = 0.46, p = 0.023), while the occurrence of CAA correlated with the appearance of AA in the retina (rho = 0.51, p = 0.012). Retinal SVD markers predicted CSVD markers with good sensitivity.

Conclusions: These results indicate that SVD also occurs in the retinal microvasculature of SHRSP and the prediction of cerebral erythrocyte thrombi and CAA might be possible using retinal biomarkers. This underlines the important role of the investigation of the retina in the early diagnosis of CSVD.

NeuroPath2Path: Classification and elastic morphing between neuronal arbors using path-wise similarity

Neuron shape and connectivity affect function. Modern imaging methods have proven successful at extracting morphological information. One potential path to achieve analysis of this morphology is through graph theory. Encoding by graphs enables the use of high throughput informatic methods to extract and infer brain function. However, the application of graph-theoretic methods to neuronal morphology comes with certain challenges in term of complex subgraph matching and the difficulty in computing intermediate shapes in between two imaged temporal samples. Here we report a novel, efficacious graph-theoretic method that rises to the challenges. The morphology of a neuron, which consists of its overall size, global shape, local branch patterns, and cell-specific biophysical properties, can vary significantly with the cell's identity, location, as well as developmental and physiological state. Various algorithms have been developed to customize shape based statistical and graph related features for quantitative analysis of neuromorphology, followed by the classification of neuron cell types using the features. Unlike the classical feature extraction based methods from imaged or 3D reconstructed neurons, we propose a model based on the rooted path decomposition from the soma to the dendrites of a neuron and extract morphological features from each constituent path. We hypothesize that measuring the distance between two neurons can be realized by minimizing the cost of continuously morphing the set of all rooted paths of one neuron to another. To validate this claim, we first establish the correspondence of paths between two neurons using a modified Munkres algorithm. Next, an elastic deformation framework that employs the square root velocity function is established to perform the continuous morphing, which, as an added benefit, provides an effective visualization tool. We experimentally show the efficacy of NeuroPath2Path, NeuroP2P, over the state of the art.

Resonances in the response of fluidic networks inherent to the cooperation between elasticity and bifurcations

A global response function (GRF) of an elastic network is introduced as a generalization of the response function (RF) of a rigid network, relating the average flow along the network with the pressure difference at its extremes. The GRF can be used to explore the frequency behaviour of a fluid confined in a tree-like symmetric elastic network in which vessels bifurcate into identical vessels. We study such dynamic response for elastic vessel networks containing viscous fluids. We find that the bifurcation structure, inherent to tree-like networks, qualitatively changes the dynamic response of a single elastic vessel, and gives resonances at certain frequencies. This implies that the average flow throughout the network could be enhanced if the pulsatile forcing at the network's inlet were imposed at the resonant frequencies. The resonant behaviour comes from the cooperation between the bifurcation structure and the elasticity of the network, since the GRF has no resonances either for a single elastic vessel or for a rigid network. We have found that resonances shift to high frequencies as the system becomes more rigid. We have studied two different symmetric tree-like network morphologies and found that, while many features are independent of network morphology, particular details of the response are morphology dependent. Our results could have applications to some biophysical networks, for which the morphology could be approximated to a tree-like symmetric structure and a constant pressure at the outlet. The GRF for these networks is a characteristic of the system fluid-network, being independent of the dynamic flow (or pressure) at the network's inlet. It might therefore represent a good quantity to differentiate healthy vasculatures from those with a medical condition. Our results could also be experimentally relevant in the design of networks engraved in microdevices, since the limit of the rigid case is almost impossible to attain with the materials used in microfluidics and the condition of constant pressure at the outlet is often given by the atmospheric pressure.

Microvascular hemodynamics: System properties1

The hemodynamics of the microcirculation reflect system properties of the involved components. The blood itself is a complex suspension of water, small and large molecules and different cell types. Under most conditions, its rheologic properties are dominated by the different behaviour of fluid and cellular compartments. When perfused through small-bore tubes or vessels, the suspension exhibits specific emergent properties. The Fahraeus-effect and the Fahreaeus-Lindqvist-effect result from the interaction of cellular particles with each other and with the vessel wall. Additional phenomena occur in vascular networks due to the uneven distribution of blood cells and blood plasma at divergent microvascular bifurcations. In order to understand microvascular hemodynamics in vivo but also in artificial microfluidic geometries it is thus necessary to recognize the pertinent system properties on the level of the blood, the microvessels and the microvascular networks or perfused structures.

Scaling Laws of Flow Rate, Vessel Blood Volume, Lengths, and Transit Times With Number of Capillaries

The structure-function relation is one of the oldest hypotheses in biology and medicine; i.e., form serves function and function influences form. Here, we derive and validate form-function relations for volume, length, flow, and mean transit time in vascular trees and capillary numbers of various organs and species. We define a vessel segment as a "stem" and the vascular tree supplied by the stem as a "crown." We demonstrate form-function relations between the number of capillaries in a vascular network and the crown volume, crown length, and blood flow that perfuses the network. The scaling laws predict an exponential relationship between crown volume and the number of capillaries with the power, λ, of 4/3 < λ < 3/2. It is also shown that blood flow rate and vessel lengths are proportional to the number of capillaries in the entire stem-crown systems. The integration of the scaling laws then results in a relation between transit time and crown length and volume. The scaling laws are both intra-specific (i.e., within vasculatures of various organs, including heart, lung, mesentery, skeletal muscle and eye) and inter-specific (i.e., across various species, including rats, cats, rabbits, pigs, hamsters, and humans). This study is fundamental to understanding the physiological structure and function of vascular trees to transport blood, with significant implications for organ health and disease.

Microvascular hemodynamics in the chick chorioallantoic membrane

OBJECTIVE

The microvasculature of the CAM in the developing chick embryo is characterized by interdigitating arteriolar and venular trees, connected at multiple points along their lengths to a mesh-like capillary plexus. Theoretical modeling techniques were employed to investigate the resulting hemodynamic characteristics of the CAM.

METHODS

Based on previously obtained anatomical data, a model was developed in which the capillary plexus was treated as a porous medium. Supply of blood from arterioles and drainage into venules were represented by distributions of flow sources and sinks. Predicted flow velocities were compared with measurements in arterioles and venules obtained via video microscopy.

RESULTS

If it was assumed that blood flowed into and out of the capillary plexus only at the ends of terminal arterioles and venules, the predicted velocities increased with decreasing diameter in vessels below 50 μm in diameter, contrary to the observations. Distributing sources/sinks along arterioles/venules led to velocities consistent with the data.

CONCLUSIONS

These results imply that connections to the capillary plexus distributed along the arterioles and venules strongly affect the hemodynamic characteristics of the CAM. The theoretical model provides a basis for quantitative simulations of structural adaptation in CAM networks in response to hemodynamic stimuli.

Structure and hemodynamics of vascular networks in the chorioallantoic membrane of the chicken

The chick chorioallantoic membrane (CAM) is extensively used as an in vivo model. Here, structure and hemodynamics of CAM vessel trees were analyzed and compared with predictions of Murray's law. CAM microvascular networks of Hamburger-Hamilton stage 40 chick embryos were scanned by videomicroscopy. Three networks with ∼3,800, 580, and 480 segments were digitally reconstructed, neglecting the capillary mesh. Vessel diameters (D) and segment lengths were measured, and generation numbers and junctional exponents at bifurcations were derived. In selected vessels, flow velocities (v) and hematocrit were measured. Hemodynamic simulations, incorporating the branching of capillaries from preterminal vessels, were used to estimate v, volume flow, shear stress (τ), and pressure for all segments of the largest network. For individual arteriovenous flow pathways, terminal arterial and venous generation numbers are negatively correlated, leading to low variability of total topological and morphological pathway lengths. Arteriolar velocity is proportional to diameter (v∝D^1.03 measured, v∝D^0.93 modeling), giving nearly uniform τ levels (τ∝D^0.05). Venular trees exhibit slightly higher exponents (v∝D^1.3, τ∝D^0.38). Junctional exponents at divergent and convergent bifurcations were 2.05 ± 1.13 and 1.97 ± 0.95 (mean ± SD) in contrast to the value 3 predicted by Murray's law. In accordance with Murray's law, τ levels are (nearly) maintained in CAM arterial (venular) trees, suggesting vascular adaptation to shear stress. Arterial and venous trees show an interdigitating arrangement providing homogeneous flow pathway properties and have preterminal capillary branches. These properties may facilitate efficient oxygen exchange in the CAM during rapid embryonic growth.

Recovery of cell-free layer and wall shear stress profile symmetry downstream of an arteriolar bifurcation

Unequal RBC partitioning at arteriolar bifurcations contributes to dissimilar flow developments between daughter vessels in a bifurcation. Due to the importance of the cell-free layer (CFL) and the wall shear stress (WSS) to physiological processes such as vasoregulation and gas diffusion, we investigated the effects of a bifurcation disturbance on the development of the CFL width and WSS in bifurcation daughter branches. The analysis was performed on a two-dimensional (2-D) computational model of a transverse arteriole at three different flow rates corresponding to parent branch (PB) pseudoshear rates of 60, 170 and 470s(-1), while maintaining a 2-D hematocrit of about 55% in the PB. Flow symmetry was defined using the statistical similarity of the CFL and WSS distributions between the two walls of the vessel branch. In terms of the flow symmetry recovery, higher flow rates caused larger reductions in the flow symmetry indices in the MB and subsequently required longer vessel lengths for complete recovery. Lower tube hematocrits in the SB led to complete symmetry recovery for all flow rates despite the higher initial asymmetry in the SB than in the MB. Arteriolar bifurcations produce unavoidable local CFL asymmetry and the persistence of the asymmetry downstream may increase effective blood viscosity which is especially significant at higher physiological flow rates.

Growth, ageing and scaling laws of coronary arterial trees

Despite the well-known design principles of vascular systems, it is unclear whether the vascular arterial tree obeys some scaling constraints during normal growth and ageing in a given species. Based on the micro-computed tomography measurements of coronary arterial trees in mice at different ages (one week to more than eight months), we show a constant exponent of 3/4, but age-dependent scaling coefficients in a length-volume scaling law (Lc=K(length-volume) · Vc³/⁴; Lc is the crown length, Vc is the crown volume, K(length-volume) is the age-dependent scaling coefficient) during normal growth and ageing. The constant 3/4 exponent represents the self-similar fractal-like branching pattern (i.e. basic mechanism to regulate the development of vascular trees within a species), whereas the age-dependent scaling coefficients characterize the structural growth or resorption of vascular trees during normal growth or ageing, respectively. This study enhances the understanding of age-associated changes in vascular structure and function.

Constructal law of vascular trees for facilitation of flow

Diverse tree structures such as blood vessels, branches of a tree and river basins exist in nature. The constructal law states that the evolution of flow structures in nature has a tendency to facilitate flow. This study suggests a theoretical basis for evaluation of flow facilitation within vascular structure from the perspective of evolution. A novel evolution parameter (Ev) is proposed to quantify the flow capacity of vascular structures. Ev is defined as the ratio of the flow conductance of an evolving structure (configuration with imperfection) to the flow conductance of structure with least imperfection. Attaining higher Ev enables the structure to expedite flow circulation with less energy dissipation. For both Newtonian and non-Newtonian fluids, the evolution parameter was developed as a function of geometrical shape factors in laminar and turbulent fully developed flows. It was found that the non-Newtonian or Newtonian behavior of fluid as well as flow behavior such as laminar or turbulent behavior affects the evolution parameter. Using measured vascular morphometric data of various organs and species, the evolution parameter was calculated. The evolution parameter of the tree structures in biological systems was found to be in the range of 0.95 to 1. The conclusion is that various organs in various species have high capacity to facilitate flow within their respective vascular structures.

NAC changes the course of cerebral small vessel disease in SHRSP and reveals new insights for the meaning of stases - a randomized controlled study

Background

N-Acetylcystein (NAC) reduces the reperfusion injury and infarct size in experimental macroangiopathic stroke. Here we now investigate the impact of NAC on the development of the histopathology of microangiopathic cerebrovascular disease including initial intravasal erythrocyte accumulations, blood–brain-barrier (BBB)-disturbances, microbleeds and infarcts.

Methods

Spontaneously Hypertensive Stroke-Prone Rats (SHRSP) were treated with NAC (12 mg/kg body weight, daily oral application for three to 30 weeks) and compared to untreated SHRSP. In all rats the number of microbleeds, thromboses, infarcts and stases were quantified by HE-staining. Exemplary brains were stained against von Willebrand factor (vWF), IgG, Glutathione and GFAP.

Results

NAC animals exhibited significant more microbleeds, a greater number of vessels with BBB-disturbances, but also an elevation of Glutathione-levels in astrocytes surrounding small vessels. NAC-treatment reduced the numbers of thromboses, infarcts and arteriolar stases.

Conclusions

NAC reduces the frequency of thromboses and infarcts to the expense of an increase of small microbleeds in a rat model of microangiopathic cerebrovascular disease. We suppose that NAC acts via an at least partial inactivation of vWF resulting in an insufficient sealing of initial endothelial injury leading to more small microbleeds. By elevating Glutathione-levels NAC most likely exerts a radical scavenger function and protects small vessels against extended ruptures and subsequent infarcts. Finally, it reveals that stases are mainly caused by endothelial injuries and restricted thromboses.

The influence of network structure on the transport of blood in the human cerebral microvasculature

In this article, we explore how the structural properties of miniature networks influence the transport of blood through the human cerebral microvasculature. We propose four methods for generating such networks, and investigate both how the resulting network properties match available experimental data from the human cortex and how these properties affect the flow of blood through the networks. As the nature of such microvascular flow patterns is inherently random, we run multiple simulations. We find that the modified spanning tree method produces artificial networks having characteristics closest to those of the microvasculature in human brain, and also allows for high network flow passage per unit material cost, being statistically significantly better than three other methods considered here. Such results are potentially extremely valuable in interpreting experimental data acquired from humans and in improving our understanding of cerebral blood flow at this very small length scale. This could have a significant impact on improving clinical outcomes for vascular brain diseases, particularly vascular dementia, where localized flow patterns are very important.

The pathologic cascade of cerebrovascular lesions in SHRSP: is erythrocyte accumulation an early phase?

Cerebral small vessel disease (CSVD) is associated with vessel wall changes, microbleeds, blood-brain barrier (BBB) disturbances, and reduced cerebral blood flow (CBF). As spontaneously hypertensive stroke-prone rats (SHRSP) may be a valid model of some aspects of human CSVD, we aimed to identify whether those changes occur in definite temporal stages and whether there is an initial phenomenon beyond those common vascular alterations. Groups of 51 SHRSP were examined simultaneously by histologic (Hematoxylin-Eosin, IgG-Immunohistochemistry, vessel diameter measurement) and imaging methods (Magnetic Resonance Imaging, 201-Thallium-Diethyldithiocarbamate/99m-Technetium-HMPAO Single Photon Emission Computed Tomography conducted as pilot study) at different stages of age. Vascular pathology in SHRSP proceeds in definite stages, whereas an age-dependent accumulation of erythrocytes in capillaries and arterioles represents the homogeneous initial step of the disease. Erythrocyte accumulations are followed by BBB disturbances and microbleeds, both also increasing with age. Microthromboses, tissue infarctions with CBF reduction, and disturbed potassium uptake represent the final stage of vascular pathology in SHRSP. Erythrocyte accumulations--we parsimoniously interpreted as stases--without cerebral tissue damage represent the first step of vascular pathology in SHRSP. If that initial phenomenon could be identified in patients, these erythrocyte accumulations might be a promising target for implementing prophylactic and therapeutic strategies in human CSVD.

Intraspecific scaling laws of vascular trees

A fundamental physics-based derivation of intraspecific scaling laws of vascular trees has not been previously realized. Here, we provide such a theoretical derivation for the volume-diameter and flow-length scaling laws of intraspecific vascular trees. In conjunction with the minimum energy hypothesis, this formulation also results in diameter-length, flow-diameter and flow-volume scaling laws. The intraspecific scaling predicts the volume-diameter power relation with a theoretical exponent of 3, which is validated by the experimental measurements for the three major coronary arterial trees in swine (where a least-squares fit of these measurements has exponents of 2.96, 3 and 2.98 for the left anterior descending artery, left circumflex artery and right coronary artery trees, respectively). This scaling law as well as others agrees very well with the measured morphometric data of vascular trees in various other organs and species. This study is fundamental to the understanding of morphological and haemodynamic features in a biological vascular tree and has implications for vascular disease.

Consumption of bonito extract suppresses the decrease in cerebral blood flow in stroke-prone spontaneously hypertensive rats

The effect of consuming bonito extract (BE) on cerebral blood flow was evaluated in stroke-prone spontaneously hypertensive rats (SHRSP), a cerebrovascular disease model. BE dissolved in drinking water was given to 5-week-old male SHRSP for 7 weeks. Tap water was given to the control group. At the age of 12 weeks, blood flow and vascular diameter were measured in the middle cerebral artery. Both cerebral blood flow and cerebral vessel width were greater in the BE group than in the control group. Also, stroke occurred in 7 (with death in 2) of the 8 animals in the control group but in none of the 6 animals in the BE group. To clarify its mechanism, the expressions of nitrogen oxide synthase (NOS) and the superoxide dismutase activity (SOD) in the brain were evaluated. NOS mRNA expression and SOD activity in the cerebrum were higher in the BE group. These results suggest that the consumption of BE suppresses the decrease of cerebral blood flow and reduces the risk of stroke to maintain vasorelaxation through the production of nitrogen oxide and suppression of active oxygen generation.

Development of an image-based network model of retinal vasculature

The paper presents an image-based network model of retinal vasculature taking account of the 3D vascular distribution of the retina. Mouse retinas were prepared using flat-mount technique and vascular images were obtained using confocal microscopy. The vascular morphometric information obtained from confocal images was used for the model development. The network model developed directly represents the vascular geometry of all the large vessels of the arteriolar and venular trees and models the capillaries using uniformly distributed meshes. The vasculatures in different layers of the retina, namely the superficial, intermediate, and deep layer, were modeled separately in the network and were linked through connecting vessels. The branching data of the vasculatures was recorded using the method of connectivity matrix of network (the graph theory). Such an approach is able to take into account the detailed vasculature of individual retinas concerned. Using the network model developed, a circulation analysis based on Poiseuille's equation was carried out. The investigations produced predictions of spatial distribution of the pressure, flow, and wall shear stress in the entire retinal vasculature. The method developed can be used as a tool for continuous monitoring of the retinal circulation for clinical assessments as well as experimental studies.

Microvascular Rheology and Hemodynamics

The goal of elucidating the biophysical and physiological basis of pressure-flow relations in the microcirculation has been a recurring theme since the first observations of capillary blood flow in living tissues. At the birth of the Microcirculatory Society, seminal observations on the heterogeneous distribution of blood cells in the microvasculature and the rheological properties of blood in small bore tubes raised many questions on the viscous properties of blood flow in the microcirculation that captured the attention of the Society's membership. It is now recognized that blood viscosity in small bore tubes may fall dramatically as shear rates are increased, and increase (dramatically with elevations in hematocrit. These relationships are strongly affected by blood cell deformability and concentration, red cell aggregation, and white cell interactions with the red cells anti endothelium. Increasing strength of red cell aggregation may result in sequestration of clumps of red cells with either reductions or increases in microvascular hematocrit dependent upon network topography. During red cell aggregation, resistance to flow may thus decrease with hematocrit reduction or increase due to redistribution of red cells. Blood cell adhesion to the microvessel wall may initiate flow reductions, as, for example, in the case of red cell adhesion to the endothelium in sickle cell disease, or leukocyte adhesion in inflammation. The endothelial glycocalyx has been shown to result from a balance of the biosynthesis of new glycans, and the enzymatic or shear-dependent alterations in its composition. Flow-dependent reductions in the endothelial surface layer may thus affect the resistance to flow and/or the adhesion of red cells and/or leukocytes to the endothelium. Thus, future studies aimed at the molecular rheology of the endothelial surface layer may provide new insights into determinants of the resistance to flow.

The scaling of blood flow resistance: from a single vessel to the entire distal tree

Although the flow resistance of a single vessel segment is easy to compute, the equivalent resistance of a network of vessel segments or the entire vasculature of an organ is difficult to determine in an analytic form. Here, we propose what we believe is a novel resistance scaling law for a vascular tree (i.e., the resistance of a vessel segment scales with the equivalent resistance of the corresponding distal tree). The formulation can be written as (R(s)/R(c)) proportional, variant(L(s)/L(c)) (where R(s) and L(s) are the resistance and length of a vessel segment, respectively, and R(c) and L(c) are the equivalent resistance and total length of the corresponding distal tree, respectively), which was validated for the coronary vascular systems of the heart. The scaling law was also shown to apply to the vascular systems of the lung, mesentery, muscle, eye, and so on. The novel resistance scaling law, coupled with the 3/4-power scaling law for metabolic rates, can predict several structure-function relations of vascular trees, albeit with a different exponent. In particular, the self-similar nature of the scaling law may serve as a diagnostic tool with the help of noninvasive imaging modalities.

A scaling law of vascular volume

Vascular volume is of fundamental significance to the function of the cardiovascular system. An accurate prediction of blood volume in patients is physiologically and clinically significant. This study proposes what we believe is a novel volume scaling relation of the form: V(c)=K(v)D(s)(2/3)L(c), where V(c) and L(c) are cumulative vessel volume and length, respectively, in the tree, and D(s) is the diameter of the vessel segment. The scaling relation is validated in vascular trees of various organs including the heart, lung, mesentery, muscle, and eye of different species. Based on the minimum energy hypothesis and volume scaling relation, four structure-function scaling relations are predicted, including the diameter-length, volume-length, flow-diameter, and volume-diameter relations, with exponent values of 3/7, 1(2/7), 2(1/3), and 3, respectively. These four relations are validated in the various vascular trees, which further confirm the volume scaling relation. This scaling relation may serve as a control reference to estimate the blood volume in various organs and species. The deviation from the scaling relation may indicate hypovolemia or hypervolemia and aid diagnosis.

Geometric Characteristics of Arterial Network of Rat Pial Microcirculation

OBJECTIVE

The aim of the study was to assess the geometric characteristics of rat pial microcirculation and describe the vessel bifurcation patterns by 'connectivity matrix'.

METHODS

Male Wistar rats were used to visualize pial microcirculation by a fluorescent microscopy technique through an open cranial window, using fluorescein isothiocyanate bound to dextran (molecular weight 70 kDa). The arteriolar network was mapped by stop-frame images. Diameters and lengths of arterioles were measured with a computer-assisted method. Pial arterioles were classified according to a centripetal ordering scheme (Strahler method modified according to diameter) from the smallest order 1 to the largest order 5 arterioles in the preparation. A distinction between arteriolar segments and elements was used to express the series-parallel features of the pial arteriolar networks. A connectivity matrix was used to describe the connection of blood vessels from one order to another.

RESULTS

The arterioles were assigned 5 orders of branching by Strahler's ordering scheme, from order 1 (diameter: 16.0 +/- 2.5 microm) to order 5 (62 +/- 5.0 microm). Order 1 arterioles gave origin to capillaries, assigned order 0. The diameter, length and branching of the 5 arteriolar orders grew as a geometric sequence with the order number in accordance with Horton's law. The segments/elements ratio was the highest in order 4 and 3 arterioles, indicating the greatest asymmetry of ramifications. Finally, the branching vessels in the networks were described in details by the connectivity matrix. Fractal dimensions of arteriolar length and diameter were 1.75 and 1.78, respectively.

CONCLUSIONS

The geometric characteristics of rat pial microcirculation indicate that distribution of vessels is fractal. The connectivity matrix allowed us to describe the number of daughter vessels spreading from parent vessels. This ordering scheme may be useful to describe vessel function, according to diameter, length and branching.

Scaling laws of vascular trees: of form and function

The branching pattern and vascular geometry of biological tree structure are complex. Here we show that the design of all vascular trees for which there exist morphometric data in the literature (e.g., coronary, pulmonary; vessels of various skeletal muscles, mesentery, omentum, and conjunctiva) obeys a set of scaling laws that are based on the hypothesis that the cost of construction of the tree structure and operation of fluid conduction is minimized. The laws consist of scaling relationships between 1) length and vascular volume of the tree, 2) lumen diameter and blood flow rate in each branch, and 3) diameter and length of vessel branches. The exponent of the diameter-flow rate relation is not necessarily equal to 3.0 as required by Murray's law but depends on the ratio of metabolic to viscous power dissipation of the tree of interest. The major significance of the present analysis is to show that the design of various vascular trees of different organs and species can be deduced on the basis of the minimum energy hypothesis and conservation of energy under steady-state conditions. The present study reveals the similarity of nature's scaling laws that dictate the design of various vascular trees and the underlying physical and physiological principles.

A graph theory analysis of renal glomerular microvascular networks

A graph theory model and its invariants are used to compare previously published renal glomerular networks of six adult rats, one adult uremic rat, and one newborn rat. Invariants calculated include order, size, cycle rank, eccentricity, root distance, planarity, and vertex degree distribution. These invariants enabled the differentiation of six normal adult glomerular microvascular networks from that of the uremic glomerulus and from that of the normal newborn glomerulus. These invariants might then be used to differentiate between normal and pathological vascular networks. Also proposed are graph theory invariants that might be used to develop a quantitative model for angiogenesis.

Effect of chronic treatment with vitamin E on endothelial dysfunction in a type I in vivo diabetes mellitus model and in vitro

Diabetes mellitus often leads to generalized vasculopathy. Because of the pathophysiological role of free radicals we investigated the effects of vitamin E. Twenty-eight rats were rendered diabetic by streptozotocin injection and were fed either with a diet with low (10 mg/kg of chow), medium (75 mg/kg of chow) or high amounts of vitamin E (1300 mg/kg of chow). Nine age-matched nondiabetic rats receiving 75 mg of vitamin E/kg chow served as controls. After 7 months, mesenteric microcirculation was investigated. Smooth muscle contractile function was not altered in diabetic versus nondiabetic vessels. Endothelial function was significantly reduced in diabetics; relaxation upon 1 micro M acetylcholine was reduced by 50% in diabetics with a medium and high vitamin E diet. In vitamin E-deprived rats, a complete loss of endothelium-dependent relaxation was observed, and instead, acetylcholine elicited vasoconstriction. L-N(G)-Nitro-arginine-induced vasoconstriction was reduced in small arteries in diabetics, which was not prevented by vitamin E, but was aggravated by vitamin E deprivation. In a subchronic endothelial cell culture model, cells were cultivated with 5 or 20 mM D-glucose for an entire cell culture passage (4 days) with or without vitamin E (20 mg/l versus 0.01 mg/l). Hyperglycemia led to significant reduction in basal and ATP-stimulated nitric oxide (NO)-production. Hyperglycemia-induced reduction in basal NO-release was significantly prevented by vitamin E, whereas reduction in stimulated NO-release was not influenced. NADPH-diaphorase activity was reduced by 40% by hyperglycemia, which was completely prevented by vitamin E. We conclude that 1) vitamin E has a potential to prevent partially hyperglycemia-induced endothelial dysfunction, 2) under in vivo conditions vitamin E deficiency enhanced diabetic endothelial dysfunction dramatically, and 3) positive effects of vitamin E may be attenuated with a longer disease duration.

Heterogeneous perfusion is a consequence of uniform shear stress in optimized arterial tree models

Using optimized computer models of arterial trees we demonstrate that flow heterogeneity is a necessary consequence of a uniform shear stress distribution. Model trees are generated and optimized under different modes of boundary conditions. In one mode flow is delivered to the tissue as homogeneously as possible. Although this primary goal can be achieved, resulting shear stresses between blood and the vessel walls show very large spread. In a second mode, models are optimized under the condition of uniform shear stress in all segments which in turn renders flow distribution heterogeneous. Both homogeneous perfusion and uniform shear stress are desirable goals in real arterial trees but each of these goals can only be approached at the expense of the other. While the present paper refers only to optimized models, we assume that this dual relation between the heterogeneities in flow and shear stress may represent a more general principle of vascular systems.

Cerebral thrombosis and microcirculation of the rat during the oestrous cycle and after ovariectomy

1. The effects of oestrogen on thrombogenesis and the cerebral microcirculation of the female rat were studied during the oestrous cycle and after ovariectomy. 2. Serum levels of oestradiol (E2) and plasma concentrations of nitric oxide (NO) metabolites were significantly greater at pro-oestrus than at dioestrus. Blood vessel diameter, mean red cell velocity, wall shear rate and blood flow at pro-oestrus were significantly higher than at dioestrus. Thrombotic tendency, assessed using a He-Ne laser-induced thrombosis model, was significantly decreased at pro-oestrus compared with dioestrus. 3. The long-term deprivation of oestrogen by ovariectomy significantly depressed serum levels of E2 and plasma concentrations of NO metabolites. Thrombotic tendency was significantly increased 4 weeks after ovariectomy. Vessel diameter, mean red cell velocity, wall shear rate and blood flow in pial arterioles were significantly reduced after ovariectomy. 4. Exogenous administration of oestrogen (17 beta-oestradiol) after surgery reversed the increased thrombotic tendency mediated by ovariectomy. 5. These results strongly indicate that oestrogen mediates beneficial effects on the cerebral microcirculation and moderates cerebral thrombotic mechanisms in the female rat.

Effects of vitamin E and sesamin on hypertension and cerebral thrombogenesis in stroke-prone spontaneously hypertensive rats

The preventive effects of sesamin, a lignan from sesame oil, and vitamin E on hypertension and thrombosis were examined using stroke-prone spontaneously hypertensive rats (SHRSP). At 5 weeks of age the animals were separated into four groups: (i) a control group; (ii) a vitamin E group, which was given a 1,000 mg alpha-tocopherol/kg diet; (iii) a sesamin group, given a 1,000 mg sesamin/kg diet; and (iv) a vitamin E plus sesamin group, given a 1,000 mg alpha-tocopherol plus 1,000 mg sesamin/kg diet for 5 weeks from 5 to 10 weeks of age. Resting blood pressure was measured by the tail-cuff method once weekly. A closed cranial window was created and platelet-rich thrombi were induced in vivo using a helium-neon laser technique. The number of laser pulses required for formation of an occlusive thrombus was used as an index of thrombotic tendency. In control rats, systolic blood pressure and the amount of urinary 8-hydroxy-2'-deoxyguanosine (8-OHdG) became significantly elevated with age. However, the elevation in blood pressure and 8-OHdG were significantly suppressed in rats administrated vitamin E, sesamin, or vitamin E plus sesamin. At 10 weeks, the number of laser pulses required to induce an occlusive thrombus in arterioles of the control group was significantly lower than in the other groups (p<0.05). These results indicate that chronic ingestion of vitamin E and sesamin attenuated each of elevation in blood pressure, oxidative stress and thrombotic tendency, suggesting that these treatments might be beneficial in the prevention of hypertension and stroke.

Effects of erythrocyte aggregation and venous network geometry on red blood cell axial migration

Axial migration of red blood cells in small glass tubes can cause blood viscosity to be effectively independent of shear rate. However, this phase separation may not occur to the same degree in the venous network due to infusion of cells and aggregates at branch points. To investigate this hypothesis, we followed trajectories of fluorescently labeled red blood cells in the venular network of the rat spinotrapezius muscle at normal and reduced flow with and without red blood cell aggregation. Cells traveling near the wall of an unbranched venular segment migrated approximately 1% of the longitudinal path length without aggregation and migrated slightly more with aggregation. Venular segment length between branch points averaged three to five times the diameter. Cells in the main vessel were shifted centrally by up to 20% of diameter at branch points, reducing the migration rate of cells near the opposite wall to <1% even in the presence of aggregation. We conclude that formation of a cell-free marginal layer in the venular network is attenuated due to the time dependence of axial migration and the frequent branching of the network.

Late effects of ionizing radiation on the microvascular networks in normal tissue

Damage to the microvascular networks constitutes one of the most important components of ionizing radiation damage to normal tissue. Previously, we have reported the early (3, 7 and 30 days postirradiation) effects of ionizing radiation on the structure and function of normal tissue microvascular networks. Here we report on the late effects of ionizing radiation on the structural and functional changes in microvascular networks in locally irradiated (single 10-Gy dose) hamster cremaster muscles observed 60, 120 and 180 days postirradiation; age-matched animals were used as controls. As in the previous study, intravital microscopy was used to measure structural and functional parameters in complete microvascular networks in vivo. A factorial design was used to examine the effects of radiation status, time postirradiation, and network vessel type on the structure and function of microvascular networks. Our results indicate that the progression of radiation-induced microvascular damage continues during the late times but that there is partial recovery from radiation damage within 6 months postirradiation. Red blood cell flux, red blood cell velocity, and capillary blood flow in irradiated networks at 180 days postirradiation were significantly greater than control levels. As at the early times, all vessel types were not damaged equally by radiation at every time.

Effects of voluntary exercise and L-arginine on thrombogenesis and microcirculation in stroke-prone spontaneously hypertensive rats

1. The preventive effects of exercise and L-arginine intake on hypertension and thrombosis in stroke-prone spontaneously hypertensive rats (SHRSP) were studied. 2. Stroke-prone spontaneously hypertensive rats were divided into three groups: (i) the control, sedentary group; (ii) the exercise group, which was allowed to run voluntarily on running wheels; and (iii) the L-arginine intake group, which was given 2.25% L-arginine solution for 8 weeks from 4 to 12 weeks of age. In the control group, one rat died from stroke and symptoms of stroke were observed in the remaining animals. Similar symptoms were recorded in one rat of the exercise group, but not in the L-arginine group. 3. Blood pressure increased in the control group and this increase was suppressed significantly in the exercise and L-arginine groups. Thrombotic potential in cerebral vessels was the lowest at 4 weeks in all groups and was increased significantly at 12 weeks in the control group, but not in the exercise and L-arginine groups. Plasma concentrations of NO2/NO3 were lower in all animals at 12 weeks compared with those at 4 weeks. This reduction was significantly less marked in the L-arginine group. Cerebral arterioles in control rats at 12 weeks of age were significantly smaller in diameter than those at 4 weeks and these changes were less pronounced in the exercise and L-arginine groups. 4. The results provide clear evidence for the beneficial effects of L-arginine intake and voluntary exercise in mechanisms related to hypertension, thrombosis and stroke.

Different effects of the beta-adrenoceptor antagonists celiprolol and metoprolol on vascular structure and function in long-term type I diabetic rats

An intriguing problem of diabetes mellitus is the development of generalized angiopathy and concomitant hypertension. However, there is still a controversy whether beta-adrenoceptor antagonists can be used as antihypertensive agents in diabetes. Four groups of rats were investigated: nondiabetic controls, diabetes mellitus, diabetes + celiprolol (250 mg/kg body weight/day), diabetes + metoprolol (125 mg/kg body weight/day) after 6 months. Diabetes was induced by i.v. streptozotocin injection. We examined vascular structure and function histologically and by an in vitro microvideoangiometry of isolated perfused mesenterium. Additionally, we investigated the effects of hyperglycemia and celiprolol on NO release in cultivated aortic endothelial cells and the effect of celiprolol on transendothelial paracellular permeability. Diabetes resulted in endothelial dysfunction, characterized by a reduced response to acetylcholine and L-N(G)-nitro-arginine and an unchanged response to sodium nitroprusside (SNP). These effects were significantly antagonized by celiprolol but were not influenced by metoprolol treatment. This was supported by the finding of typical vascular changes associated with diabetes like media thickening, reduced cardiac capillary/muscle fiber ratio, and glomerulosclerosis, which were significantly reduced by celiprolol but not influenced by metoprolol treatment. Ketonuria improved after celiprolol treatment, whereas blood glucose, lipids, and body weight were not different between the diabetic groups. In cultured cells, celiprolol did not induce direct NO release but reversed the impairment of stimulated NO release caused by hyperglycemia. Furthermore, celiprolol reduced endothelial paracellular permeability. We conclude that celiprolol can exert antiangiopathic effects in diabetic rats and that both beta-adrenoceptor antagonists did not aggravate diabetic angiopathy and metabolic derangement.

Theoretical and experimental study of intermittent blood flows in microcirculation: application to the in-vivo determination of compliance

A new theoretical approach was used to study the nonlinear response of a microvascular segment subjected to a pressure step at one end. The method is suitable for both large and small deformations of the vessel wall in the case of an elastic response of the segment. It is shown that the use of this simulation permits an indirect determination of the compliance of the vessel. The procedure is applied in two cases of major interest: first the in-vivo study of the intermittent blood flow in the microcirculation, and second, the analysis of experiments using micropipettes. The resulting values of the compliance agree with other values found in the previous studies. The theoretical method is particularly adapted to nonlinear equations.

Effects of red blood cell hyperaggregation on the rat microcirculation blood flow

This study presents the effects of red blood cell (RBC) hyperaggregation on the blood flow and pressure in the rat mesentery and cremaster network. We exclusively studied in situ non-vasodilated organs, in order to maintain the physiological regulation mechanisms. Dextran 500 was injected at different concentrations to increase RBC aggregation. The aggregation rate was measured on very small blood samples with an erythroaggregameter (SEFAM) which evaluated the disaggregating shear stress (tau D) needed to break the RBC aggregates. Microscopic observations and laser Doppler velocimetry were used to quantify the flow rate. The plasmatic dextran concentration (C) increase had different correlated effects: for example, tau D increased from 3 dynes cm-2 (for the control sample) to 14 dynes cm-2 (for C = 75 microM L-1); the flow rate was reduced threefold and very large aggregates were observed in the venules; the arteriolar pressure increased while venular pressure decreased. In order to differentiate the effects of RBC hyperaggregation from those of plasma hyperviscosity (due to dextran 500) on microcirculatory blood flow, we injected an RBC antiaggregating drug (troxerutine) (50 or 100 mg kg-1 i.v.). The consequences were a high reduction for (tau D) (from 14 dynes cm(-2)-9 dynes cm-2), smaller aggregates and higher blood flow in the venules. No effect of troxerutine was observed on plasma viscosity (plasma control: 1.9 cP with or without troxerutine; plasma with dextran at C = 75 microM L-1: 2.45 cP with or without troxerutine). The results strongly suggest that RBC aggregation has a significant influence on blood flow rate in the microcirculatory network.

Longitudinal position matrix of the pig coronary vasculature and its hemodynamic implications

Hemodynamic analysis of coronary blood flow must be based on a statistically valid geometric model of the coronary vasculature. We have previously developed a diameter-defined Strahler model for the arterial and venous trees and a network model for the capillaries. A full set of data describing the geometric properties of the porcine coronary vasculature was given. The order number, diameter, length, connectivity matrix [m,n] (CM), and parallel-series features were measured for all orders of vessels of the right coronary artery (RCA), left anterior descending artery (LAD), left circumflex artery (LCX), and coronary venous system. The purpose of the present study is to present another feature of the branching pattern of the coronary vasculature: the longitudinal position matrix [m,n] (LPM), whose component in row m and column n is the fractional longitudinal position of the branch point on vessels of order n at which vessels of order m branch off (m < or = n). The LPM of the pig RCA, LAD and LCX arterial trees, as well as the coronary sinusal and thebesian venous trees, are presented. The hemodynamic implications of the LPM are illustrated by comparing two kinds of circuits: one, the CM + LPM model, simulates the mean data on the morphology (diameters, lengths, and numbers), CM, and LPM of vessels, whereas the other, the CM model, simulates the mean data on the morphology and CM without considering the LPM. We found that the LPM affects the hemodynamics of coronary blood flow especially with regard to the nonuniformity or dispersion of flow distribution.

Fosinopril improves regulation of vascular tone in mesenteric bed of diabetic rats

Because diabetes mellitus leads to vascular dysfunction, we examined the microvascular endothelial and smooth muscle function in long-term diabetes and a possible influence of fosinopril treatment (10 mg/kg). We investigated isolated perfused mesenteric beds of diabetic rats (4 groups: control, control + fosinopril, diabetes, diabetes + fosinopril; diabetes of 6-month duration, induced by streptozotocin, STC) were investigated using computer-assisted microvideoangiometry. Vascular diameter of four different vascular regions [classified as conductive (G1, 303 +/- 6.5 mu m and G2, 239 +/- 6.3 mu m) and resistance (G3, 192 +/- 4.5 mu m and G4, 124 +/- 2.6 mu m) vessel generations; resting conditions, control group] were increased in diabetes by approximately 20%. However, the endothelium-dependent relaxation in response to 1 mu M acetylcholine (ACh) was reduced from 38-44% to 20-25% (diabetes mellitus) with maximal impairment in G4 vessels. This could be significantly antagonized by fosinopril treatment. Similarly, vasodilation in response to 1 mu M glyceroltrinitrate (GTN) was reduced from 50-58 to 20-30%, but was partially prevented by fosinopril (32-38%), whereas potassium chloride (KCl)-induced vasoconstriction did not show differences between the groups. Inhibition of nitric oxide (NO) synthesis by 3 mu M L-NG-nitro arginine (L-NNA) resulted in a slight vasoconstriction of all vessels (12-25%), with maximum response in G3/G4. This was not altered by disease or treatment. We conclude that (a) long-term diabetes leads to endothelial and smooth muscle dysfunction with reduced capability of vasodilation and either an impairment of NO release or a reduced smooth muscle responsiveness to and (b) a predominant impairment of NO-dependent regulation in small resistance vessels, and (c) that fosinopril treatment can at least partially prevent this vascular dysfunction.

Branching patterns of human placental villous trees: perspectives of topological analysis

Topological analysis was applied to investigate the branching pattern of three specimens obtained from early human placenta (6, 9, and 16 weeks p.m.) reconstructed on the basis of semi-thin sections. Centripetal Horton-Strahler and centrifugal branching order nomenclature was used for topological description of the analysed tree-like structures. Bifurcation ratio and vertex ratio were determined for all three cases and were found to be relatively constant. It was shown that branching pattern is closely related to the model of random segment branching that implicates a high level of asymmetry and a small level of space limitation for branching. The significance of this approach for the analysis of development of the villous tree, for the analysis of mesenchymal villous heterogeneity, and for the estimation of physiological parameters for fetoplacental exchange is discussed. We suggest that topological analysis can lead to a new quantitative classification of branching patterns of the human placental villous trees in normal and pathologic pregnancies.

Celiprolol exerts microvascular dilatation by activation of ?2-adrenoceptors

In order to clarify the question whether the beta 1-selective adrenoceptor antagonist celiprolol possesses vasodilating properties, isolated vascular networks were perfused with increasing concentrations of celiprolol (in a cumulative manner) ranging from 10(-8) to 10(-4) mol/l. The study was carried out using the isolated mesenteric vascular bed of the guinea pig mesenterium coli. Vascular diameters of four different vascular regions [vessels classified as G1 (585 +/- 30 microns), G2 (403 +/- 25 microns), G3 (282 +/- 27 microns) and G4 (197 +/- 13 microns)] were assessed by means of microscopic videoangiometry. Perfusion with celiprolol resulted in concentration dependent vasodilation which was more pronounced in G3 and G4 vessels. In addition, cumulative concentration-response curves were determined from responses obtained in the presence of 10(-8), 10(-7), 10(-6) and 10(-4) mol/l ICI 118,551 (a highly selective adrenoceptor antagonist). In the presence of ICI 118,551 at concentrations greater than or equal to 10(-6) mol/l, no celiprolol response could be observed. Lower concentrations of ICI 118,551 shifted the celiprolol concentration-response curve to the right in a concentration-dependent manner. Therefore, it is concluded (a) that celiprolol has a vasodilating effect, (b) that this vasodilation is produced by stimulation of beta 2-adrenoceptors and (c) that the vasodilating effect is more pronounced in smaller than in larger vessels (G3, G4 vs G1, G2).

Redistribution of red blood cell flow in microcirculatory networks by hemodilution

The effect of isovolemic hemodilution on red blood cell flow distribution was studied in complete self-contained microvessel networks of the rat mesentery. Hematocrit, diameter, and length of all vessel segments as well as the topological structure were determined in control networks (systemic hematocrit, 0.54) and after hemodilution (systemic hematocrit, 0.30). Hemodilution was performed by exchanging blood with hydroxyethyl starch (MW 450,000; 6%) or homologous plasma. With hemodilution, the decrease of microvessel hematocrit exceeded that of systemic hematocrit. The average discharge hematocrit in capillaries was 79% of systemic hematocrit in the control group and 73% with hemodilution (p less than 0.001). The heterogeneity of capillary hematocrit within the network, expressed by the coefficient of variation, increased from 0.4 to 0.7. By using the morphological and topological data of four networks, the distribution of hematocrits was also calculated using a hydrodynamic flow model. The modeling results were found to be in close agreement with the experimental data. This indicates that the observed changes can be deduced from established rheological phenomena, most of all phase separation at arteriolar bifurcations. The changes in hematocrit distribution after hemodilution are accompanied by a redistribution of red blood cell flow within the network: relative to total red blood cell flow, red blood cell flow in the distal capillaries of the network increases by about 40% at the expense of the proximal capillaries that are close to the feeding arteriole and that exhibit the highest red blood cell flow under control conditions.(ABSTRACT TRUNCATED AT 250 WORDS)

Computer simulation of growth of anastomosing microvascular networks

Stochastic growth of polygonal microvascular networks was simulated on computer by dichotomous terminal branching and bridging (anastomosing with an existing segment). The model was applied to describe microvascular growth into a rectangular plane from the sides when vessels bifurcate in a probabilistic manner. The angle of bifurcation was drawn from a normal distribution, the mean of which was varied between 40 degrees and 80 degrees. The resulting networks contained an average of 88-104 nodes of which 30-38% were due to bridging. Number of nodes, number of branches, number of vascular polygons and a fractal dimension representing the density of nodes were calculated for each simulated network. Capillary density increased when mean angle of bifurcation was increased between 40 degrees and 80 degrees. Distributions of normalized vessel lengths and polygon shapes were compared with those of a mesenteric vascular network. The distributions were not found to be significantly different (p less than 0.05) for most values of the mean angle of bifurcation, matching best for the mean bifurcation angle of 50 degrees. Vascular polygons had an average shape between pentagonal and hexagonal for the mesenteric network as well as for all values of the mean bifurcation angle used in this study.

Blood flow in microvascular networks. Experiments and simulation

A theoretical model has been developed to simulate blood flow through large microcirculatory networks. The model takes into account the dependence of apparent viscosity of blood on vessel diameter and hematocrit (the Fahraeus-Lindqvist effect), the reduction of intravascular hematocrit relative to the inflow hematocrit of a vessel (the Fahraeus effect), and the disproportionate distribution of red blood cells and plasma at arteriolar bifurcations (phase separation). The model was used to simulate flow in three microvascular networks in the rat mesentery with 436,583, and 913 vessel segments, respectively, using experimental data (length, diameter, and topological organization) obtained from the same networks. Measurements of hematocrit and flow direction in all vessel segments of these networks tested the validity of model results. These tests demonstrate that the prediction of parameters for individual vessel segments in large networks exhibits a high degree of uncertainty; for example, the squared coefficient of correlation between predicted and measured hematocrit of single vessel segments ranges only between 0.15 and 0.33. In contrast, the simulation of integrated characteristics of the network hemodynamics, such as the mean segment hematocrit or the distribution of blood flow velocities, is very precise. In addition, the following conclusions were derived from the comparison of predicted and measured values: 1) The low capillary hematocrits found in mesenteric microcirculatory networks as well as their heterogeneity can be explained on the basis of the Fahraeus effect and phase-separation phenomena. 2) The apparent viscosity of blood in vessels of the investigated tissue with diameters less than 15 microns is substantially higher than expected compared with measurements in glass tubes with the same diameter.

Topological Link-Vertex Analysis of the growth of Purkinje cell dendritic trees in normal, reeler, and weaver mice

The growth of Purkinje cell dendritic trees in normal, reeler, and weaver mice has been defined by using Link-Vertex Analysis. Growth probably occurs in three phases in normal and cortically located reeler trees. Phase I, completed by 7 days postnatum (dpn), establishes a rudimentary tree of 100 segments by random terminal branching. Phase II lasts from 7 to 20 dpn when some 690 and 450 segments are generated in normal and cortical reeler trees respectively. Phase II is initiated by an inductive stimulus mediated by a finite number of parallel fibres. Thereafter, dendritic trees develop a similar topology in normal and cortical reeler Purkinje cells through random interactions between parallel fibres and dendritic growth cones. We have defined this process with the aid of computer simulation techniques. Interactions appear to be restricted to a narrow growth front occupied by the highest centrifugally ordered terminals behind which adhesions occur at a greatly reduced frequency. The cortical reeler tree thus has fewer segments than normal because fewer parallel fibres are available, but it is surprisingly normal in most other respects. Phase III is a period of remodelling and extends from 20 dpn into adulthood when high-ordered terminals are eroded and middle-ordered terminals are added, with no change in total segment number in both normal and cortical reeler trees. Weaver and deeply placed reeler Purkinje cell dendritic trees are not influenced by parallel fibres. Accordingly, their growth is arrested at the end of Phase I, when both types of mutant tree have generated 100 segments by unrestrained random terminal branching. In the absence of parallel fibres, Phase II is not induced and remodelling, characteristic of Phase III, does not occur.

Venulo-arteriolar communication and propagated response. A possible mechanism for local control of blood flow

The effect of microinjection of norepinephrine (10(-5) M) into precapillary microvessels of the rat mesentery was studied using intravital microscopy. Upon application, in 29 out of 40 cases (73%) flow ceased at the site of drug application, although in most cases the precapillary microvessels themselves did not show a diameter change due to a lack of smooth muscle cells as confirmed by transmission electron microscopy. In 17 out of the 29 cases with flow cessation (59%), an intimate contact between the venule draining the site of application and the supplying arteriole was found. Initial constriction was seen at the site where the venule crossed the arteriole. Constriction propagated both up- and downstream along the arteriole, and also across arteriolo-arteriolar arcades. Arteriolar constriction could be abolished by intentionally occluding the venule draining the norepinephrine solution. It is proposed that venuloarteriolar contacts and propagated vasomotor response may contribute to local blood flow regulation by providing a feedback loop between tissue capillaries and resistance arterioles. In three complete mesenteric microvessel networks, the arterioles (n = 34) supplying 273 out of 401 capillaries (68%) were in close proximity to venules draining these same capillaries. Each of these arterioles served, on average, 43 capillaries, showing a bimodal distribution with peaks at 4 to 16 and at 64 to 256 capillaries. On average, 62% of all capillaries drained by a given venule crossing an arteriole originated from this very arteriole, indicating a reasonably effective feedback.