Analysis of potassium ion diffusion from neurons to capillaries: Effects of astrocyte endfeet geometry.

Neurovascular coupling (NVC) refers to a local increase in cerebral blood flow in response to increased neuronal activity. Mechanisms of communication between neurons and blood vessels remain unclear. Astrocyte endfeet almost completely cover cerebral capillaries, suggesting that astrocytes play a role in NVC by releasing vasoactive substances near capillaries. An alternative hypothesis is that direct diffusion through the extracellular space of potassium ions (K+ ) released by neurons contributes to NVC. Here, the goal is to determine whether astrocyte endfeet present a barrier to K+ diffusion from neurons to capillaries. Two simplified 2D geometries of extracellular space, clefts between endfeet, and perivascular space are used: (i) a source 1 µm from a capillary; (ii) a neuron 15 µm from a capillary. K+ release is modelled as a step increase in [K+ ] at the outer boundary of the extracellular space. The time-dependent diffusion equation is solved numerically. In the first geometry, perivascular [K+ ] approaches its final value within 0.05 s. Decreasing endfeet cleft width or increasing perivascular space width slows the rise in [K+ ]. In the second geometry, the increase in perivascular [K+ ] occurs within 0.5 s and is insensitive to changes in cleft width or perivascular space width. Predicted levels of perivascular [K+ ] are sufficient to cause vasodilation, and the rise time is within the time for flow increase in NVC. These results suggest that direct diffusion of K+ through the extracellular space is a possible NVC signalling mechanism.

Estimation of shear stress heterogeneity along capillary segments in angiogenic rat mesenteric microvascular networks.

OBJECTIVE: Fluid shear stress is thought to be a regulator of endothelial cell behavior during angiogenesis. The link, however, requires an understanding of stress values at the capillary level in angiogenic microvascular networks. Critical questions remain. What are the stresses? Do capillaries experience similar stress magnitudes? Can variations explain vessel-specific behavior? The objective of this study was to estimate segment-specific shear stresses in angiogenic networks. METHODS: Images of angiogenic networks characterized by increased vascular density were obtained from rat mesenteric tissues stimulated by compound 48/80-induced mast cell degranulation. Vessels were identified by perfusion of a 40 kDa fixable dextran prior to harvesting and immunolabeling for PECAM. Using a network flow-based segment model with physiologically relevant parameters, stresses were computed per vessel for regions across multiple networks. RESULTS: Stresses ranged from 0.003 to 2328.1 dyne/cm2 and varied dramatically at the capillary level. For all regions, the maximum segmental shear stresses were for capillary segments. Stresses along proximal capillaries branching from arteriole inlets were increased compared to stresses along capillaries in more distal regions. CONCLUSIONS: The results highlight the variability of shear stresses along angiogenic capillaries and motivate new discussions on how endothelial cells may respond in vivo to segment-specific microenvironment during angiogenesis.

An autonomous mathematical model for the mammalian cell cycle.

A mathematical model for the mammalian cell cycle is developed as a system of 13 coupled nonlinear ordinary differential equations. The variables and interactions included in the model are based on detailed consideration of available experimental data. A novel feature of the model is inclusion of cycle tasks such as origin licensing and initiation, nuclear envelope breakdown and kinetochore attachment, and their interactions with controllers (molecular complexes involved in cycle control). Other key features are that the model is autonomous, except for a dependence on external growth factors; the variables are continuous in time, without instantaneous resets at phase boundaries; mechanisms to prevent rereplication are included; and cycle progression is independent of cell size. Eight variables represent cell cycle controllers: the Cyclin D1-Cdk4/6 complex, APCCdh1, SCFßTrCP, Cdc25A, MPF, NuMA, the securin-separase complex, and separase. Five variables represent task completion, with four for the status of origins and one for kinetochore attachment. The model predicts distinct behaviors corresponding to the main phases of the cell cycle, showing that the principal features of the mammalian cell cycle, including restriction point behavior, can be accounted for in a quantitative mechanistic way based on known interactions among cycle controllers and their coupling to tasks. The model is robust to parameter changes, in that cycling is maintained over at least a five-fold range of each parameter when varied individually. The model is suitable for exploring how extracellular factors affect cell cycle progression, including responses to metabolic conditions and to anti-cancer therapies.

Simulation of Angiogenesis in Three Dimensions: Development of the Retinal Circulation.

A theoretical model is used to describe the three-dimensional development of the retinal circulation in the human eye, which occurs after the initial spread of vasculature across the inner surface of the retina. In the model, random sprouting angiogenesis is driven by a growth factor that is produced in tissue at a rate dependent on oxygen level and diffuses to existing vessels. Vessel sprouts connect to form pathways for blood flow and undergo remodeling and pruning. These processes are controlled by known or hypothesized vascular responses to hemodynamic and biochemical stimuli, including conducted responses along vessel walls. The model shows regression of arterio-venous connections on the surface of the retina, allowing perfusion of the underlying tissue. A striking feature of the retinal circulation is the formation of two vascular plexuses located at the inner and outer surfaces of the inner nuclear layer within the retina. The model is used to test hypotheses regarding the formation of these structures. A mechanism based on local production and diffusion of growth factor is shown to be ineffective. However, sprout guidance by localized structures on the boundaries of the inner nuclear layer can account for plexus formation. The resulting networks have vascular density, perfusion and oxygen transport characteristics consistent with observed properties. The model shows how stochastic generation of vascular sprouts combined with a set of biologically based response mechanisms can lead to the generation of a specialized three-dimensional vascular structure with a high degree of organization.

Novel method for kinetic analysis applied to transport by the uniporter OCT2.

The kinetics of solute transport shed light on the roles these processes play in cellular physiology, and the absolute values of the kinetic parameters that quantitatively describe transport are increasingly used to model its impact on drug clearance. However, accurate assessment of transport kinetics is challenging. Although most carrier-mediated transport is adequately described by the Michaelis-Menten equation, its use presupposes that the rates of uptake used in the analysis of maximal rates of transport (Jmax) and half-saturation constants (Kt) reflect true unidirectional rates of influx from known concentrations of substrate. Most experimental protocols estimate the initial rate of transport from net substrate accumulation determined at a single time point (typically between 0.5 and 5 min) and assume it reflects unidirectional influx. However, this approach generally results in systematic underestimates of Jmax and overestimates of Kt; the former primarily due to the unaccounted impact of efflux of accumulated substrate, and the latter due to the influence of unstirred water layers. Here, we describe the bases of these time-dependent effects and introduce a computational model that analyzes the time course of net substrate uptake at several concentrations to calculate Jmax and Kt for unidirectional influx, taking into account the influence of unstirred water layers and mediated efflux. This method was then applied to calculate the kinetics of transport of 1-methyl-4-phenylpryridinium and metformin by renal organic cation transporter 2 as expressed in cultured Chinese hamster ovary cells.NEW & NOTEWORTHY Here, we describe a mathematical model that uses the time course of net substrate uptake into cells from several increasing concentrations to calculate unique kinetic parameters [maximal rates of transport (Jmax) and half-saturation constants (Kt)] of the process. The method is the first to take into consideration the common complicating factors of unstirred layers and carrier-mediated efflux in the experimental determination of transport kinetics.

Coalescent angiogenesis-evidence for a novel concept of vascular network maturation.

Angiogenesis describes the formation of new blood vessels from pre-existing vascular structures. While the most studied mode of angiogenesis is vascular sprouting, specific conditions or organs favor intussusception, i.e., the division or splitting of an existing vessel, as preferential mode of new vessel formation. In the present study, sustained (33-h) intravital microscopy of the vasculature in the chick chorioallantoic membrane (CAM) led to the hypothesis of a novel non-sprouting mode for vessel generation, which we termed "coalescent angiogenesis." In this process, preferential flow pathways evolve from isotropic capillary meshes enclosing tissue islands. These preferential flow pathways progressively enlarge by coalescence of capillaries and elimination of internal tissue pillars, in a process that is the reverse of intussusception. Concomitantly, less perfused segments regress. In this way, an initially mesh-like capillary network is remodeled into a tree structure, while conserving vascular wall components and maintaining blood flow. Coalescent angiogenesis, thus, describes the remodeling of an initial, hemodynamically inefficient mesh structure, into a hierarchical tree structure that provides efficient convective transport, allowing for the rapid expansion of the vasculature with maintained blood supply and function during development.

Spreading mechanics and differentiation of astrocytes during retinal development.

The retinal vasculature supplies oxygen to the inner layers of the retina, the light-sensitive tissue in the eye. During development, formation of the retinal vasculature depends on prior establishment of a mesh of astrocytes, a type of glial cell, which guide the growth of the vascular network. Astrocytes emerge from the optic nerve head and proliferate and spread, forming a mesh-like layer over the retinal surface. The initially formed cells are termed astrocyte precursor cells (APCs), which differentiate into immature perinatal astrocytes (IPAs) during the prenatal period. A continuum model is developed to describe the proliferation, differentiation, and migration these cells. Effects of oxygen and growth factor levels on proliferation and differentiation are included. Cell migration is driven by gradients in tension in the astrocyte mesh, which varies inversely with total density. The resulting governing equations have the form of a nonlinear diffusion-like equation. The model can account for the observed radial spread over time of the astrocyte disk. Experimental observations show that the APCs form a narrow rim around the edge of this disk, with IPAs in the interior. The model predicts this behavior if the mobility of the APCs is assumed to be higher than that of the IPAs under a given tension gradient. Thus, the model shows how tension-driven cell motions can account for separation of cell types in a cell layer spreading over a substrate.

Simulation of angiogenesis in three dimensions: Application to cerebral cortex.

The vasculature is a dynamic structure, growing and regressing in response to embryonic development, growth, changing physiological demands, wound healing, tumor growth and other stimuli. At the microvascular level, network geometry is not predetermined, but emerges as a result of biological responses of each vessel to the stimuli that it receives. These responses may be summarized as angiogenesis, remodeling and pruning. Previous theoretical simulations have shown how two-dimensional vascular patterns generated by these processes in the mesentery are consistent with experimental observations. During early development of the brain, a mesh-like network of vessels is formed on the surface of the cerebral cortex. This network then forms branches into the cortex, forming a three-dimensional network throughout its thickness. Here, a theoretical model is presented for this process, based on known or hypothesized vascular response mechanisms together with experimentally obtained information on the structure and hemodynamics of the mouse cerebral cortex. According to this model, essential components of the system include sensing of oxygen levels in the midrange of partial pressures and conducted responses in vessel walls that propagate information about metabolic needs of the tissue to upstream segments of the network. The model provides insights into the effects of deficits in vascular response mechanisms, and can be used to generate physiologically realistic microvascular network structures.

Distinct roles of red-blood-cell-derived and wall-derived mechanisms in metabolic regulation of blood flow.

OBJECTIVE: A theoretical model is used to analyze combinations of RBC-derived and wall-derived (RBC-independent) mechanisms for metabolic blood flow regulation, with regard to their oxygen transport properties. METHODS: Heterogeneous microvascular network structures are derived from observations in rat mesentery and hamster cremaster. The effectiveness of metabolic blood flow regulation using combinations of RBC-dependent and RBC-independent mechanisms is simulated in these networks under conditions of reduced oxygen delivery and increased oxygen demand. RESULTS: Metabolic regulation by a wall-derived mechanism results in higher predicted total blood flow rate and number of flowing vessels, and lower tissue hypoxic fraction, than regulation by combinations of RBC-derived and wall-derived signals. However, a combination of RBC-derived and wall-derived signals results in a higher predicted median tissue PO2 than either mechanism acting alone. CONCLUSIONS: Model results suggest complementary roles for RBC-derived and wall-derived mechanisms of metabolic flow regulation, with the wall-derived mechanism responsible for avoiding hypoxia, and the RBC-derived mechanism responsible for maintaining PO2 levels high enough for optimal tissue function.

Effects of impaired microvascular flow regulation on metabolism-perfusion matching and organ function.

Impaired tissue oxygen delivery is a major cause of organ damage and failure in critically ill patients, which can occur even when systemic parameters, including cardiac output and arterial hemoglobin saturation, are close to normal. This review addresses oxygen transport mechanisms at the microcirculatory scale, and how hypoxia may occur in spite of adequate convective oxygen supply. The structure of the microcirculation is intrinsically heterogeneous, with wide variations in vessel diameters and flow pathway lengths, and consequently also in blood flow rates and oxygen levels. The dynamic processes of structural adaptation and flow regulation continually adjust microvessel diameters to compensate for heterogeneity, redistributing flow according to metabolic needs to ensure adequate tissue oxygenation. A key role in flow regulation is played by conducted responses, which are generated and propagated by endothelial cells and signal upstream arterioles to dilate in response to local hypoxia. Several pathophysiological conditions can impair local flow regulation, causing hypoxia and tissue damage leading to organ failure. Therapeutic measures targeted to systemic parameters may not address or may even worsen tissue oxygenation at the microvascular level. Restoration of tissue oxygenation in critically ill patients may depend on restoration of endothelial cell function, including conducted responses.

Gap junctions regulate vessel diameter in chick chorioallantoic membrane vasculature by both tone-dependent and structural mechanisms.

OBJECTIVE: In this study, we examined the impact of gap junction blockade on chick chorioallantoic membrane microvessels. METHODS: Expression of Cx37, Cx40/42, and Cx43 in chick chorioallantoic membrane tissue was studied by PCR, Western blot, and confocal immunofluorescence microscopy. Vessel diameter changes occurring under gap junction blockade with carbenoxolone (175 µmol/L), palmitoleic acid (100 µmol/L), 43 GAP27 (1 mmol/L) were analyzed by intravital microscopy. To analyze vascular tone, chick chorioallantoic membrane vessels were exposed to a vasodilator cocktail consisting of acetylcholine (10 µmol/L), adenosine (100 µmol/L), papaverine (200 µmol/L), and sodium nitroprusside (10 µmol/L). RESULTS: In chick chorioallantoic membrane lysates, Western blot analysis revealed the expression of Cx40 and Cx43. Immunofluorescence in intact chick chorioallantoic membrane vasculature showed only Cx43, limited to arterial vessel walls. Upon gap junction blockade (3 hours) arterial and venous diameters decreased to 0.50 ± 0.03 and 0.36 ± 0.06 (carbenoxolone), 0.72 ± 0.08 and 0.63 ± 0.15 (palmitoleic acid) and 0.77 ± 0.004 and 0.58 ± 0.05 (GAP27), relative to initial values. Initially, diameter decrease was dominated by increasing vascular tone. After 6 hours, however, vessel tone was reduced, suggesting structural network remodeling. CONCLUSIONS: Our findings suggest a major role for connexins in mediating acute and chronic diameter changes in developing vascular networks.

Modelling the relationships between haemoglobin oxygen affinity and the oxygen cascade in humans.

KEY POINTS: Haemoglobin affinity is an integral concept in exercise physiology that impacts oxygen uptake, delivery and consumption. How chronic alterations in haemoglobin affinity impact physiology is unknown. Using human haemoglobin variants, we demonstrate that the affinity of haemoglobin for oxygen is highly correlated with haemoglobin concentration. Using the Fick equation, we model how altered haemoglobin affinity and the associated haemoglobin concentration influences oxygen consumption at rest and during exercise via alterations in cardiac output and mixed-venous PO2 . The combination of low oxygen affinity haemoglobin and reduced haemoglobin concentration seen in vivo may be unable to support oxygen uptake during moderate or heavy exercise. ABSTRACT: The physiological implications, with regard to exercise, of altered haemoglobin affinity for oxygen are not fully understood. Data from the Mayo Clinic Laboratories database of rare human haemoglobin variants reveal a strong inverse correlation (r = -0.82) between blood haemoglobin concentration and P50 , an index of oxygen affinity [Hb = -0.3135(P50 ) + 23.636]. In the present study, observed P50 values for high, normal and low oxygen-affinity haemoglobin variants (13, 26 and 39 mmHg) and corresponding haemoglobin concentrations (19.5, 15.5 and 11.4 g dL-1 respectively) are used to model oxygen consumption as a fraction of delivery at rest ( V̇O2  = 0.25 L min-1 , cardiac output = 5.70 L min-1 ) and during exercise ( V̇O2  = 2.75 L min-1 , cardiac output = 18.9 l min-1 ). With high-affinity haemoglobin, the model shows that normal levels of oxygen consumption can be achieved at rest and during exercise at the assumed cardiac output levels, with reduced oxygen extraction both at rest (16.8% high affinity vs. 21.7% normal) and during exercise (55.8% high affinity vs. 72.2% normal). With low-affinity haemoglobin, which predicts low haemoglobin concentration, oxygen consumption at rest can be sustained with the assumed cardiac output, with increased oxygen extraction (31.1% low affinity vs. 21.7% normal). However, exercise at 2.75 l min-1 cannot be achieved with the assumed cardiac output, even with 100% oxygen extraction. In conclusion, the model indicates chronic alterations in P50 associate directly with Hb concentration, highlighting that human Hb variants can serve as 'experiments of nature' to address fundamental hypotheses on oxygen transport and exercise.

Kinetic basis of metformin-MPP interactions with organic cation transporter OCT2.

Organic cation transporter 2 (OCT2) clears the blood of cationic drugs. Efforts to understand OCT2 selectivity as a means to predict the potential of new molecular entities (NMEs) to produce unwanted drug-drug interactions typically assess the influence of the NMEs on inhibition of transport. However, the identity of the substrate used to assess transport activity can influence the quantitative profile of inhibition. Metformin and 1-methyl-4-phenylpyridinium (MPP), in particular, display markedly different inhibitory profiles, with IC50 values for inhibition of MPP transport often being more than fivefold greater than IC50 values for the inhibition of metformin transport by the same compound, suggesting that interaction of metformin and MPP with OCT2 cannot be restricted to competition for a single binding site. Here, we determined the kinetic basis for the mutual inhibitory interaction of metformin and MPP with OCT2 expressed in Chinese hamster ovary cells. Although metformin did produce simple competitive inhibition of MPP transport, MPP was a mixed-type inhibitor of metformin transport, decreasing the maximum rate of mediated substrate transport and increasing the apparent Michaelis constant (Ktapp) for OCT2-mediated metformin transport. Furthermore, whereas the IC50 value for metformin's inhibition of MPP transport did not differ from the Ktapp value for metformin transport, the IC50 value for MPP's inhibition of metformin transport was less than its Ktapp value for transport. The simplest model to account for these observations required the influence of a distinct inhibitory site for MPP that, when occupied, decreases the translocation of substrate. These observations underscore the complexity of ligand interaction with OCT2 and argue for use of multiple substrates to obtain the needed kinetic assessment of NME interactions with OCT2.

Modeling the hematocrit distribution in microcirculatory networks: A quantitative evaluation of a phase separation model.

OBJECTIVE: Theoretical models are essential tools for studying microcirculatory function. Recently, the validity of a well-established phase separation model was questioned and it was claimed that it produces problematically low hematocrit predictions and lack of red cells in small diameter vessels. We conducted a quantitative evaluation of this phase separation model to establish common ground for future research. METHODS: Model predictions were validated against a comprehensive database with measurements from 4 mesenteric networks. A Bayesian data analysis framework was used to integrate measurements and network model simulations into a combined analysis and to model uncertainties related to network boundary conditions as well as phase separation model parameters. The model evaluation was conducted within a cross-validation scheme. RESULTS: Unlike the recently reported results, our analysis demonstrated good correspondence in global characteristics between measurements and predictions. In particular, predicted hematocrits for vessels with small diameters were consistent with measurements. Incorporating phase separation model parameter uncertainties further reduced the hematocrit validation error by 17% and led to the absence of red-cell-free segments. Corresponding model parameters are presented as alternatives to standard parameters. CONCLUSIONS: Consistent with earlier studies, our quantitative model evaluation supports the continued use of the established phase separation model.

Additive Damage Models for Cellular Pharmacodynamics of Radiation-Chemotherapy Combinations.

Many cancer patients receive combination treatments with radiation and chemotherapy. Available mathematical models for cellular pharmacodynamics have limited ability to represent observed in vitro responses to radiochemotherapy. Here, a family of additive damage models is proposed to describe cell kill resulting from radiochemotherapy with fixed schedule and variable doses. The pathways by which the agents produce cellular damage are assumed to converge in a single cell death process, so that survival depends on total damage, which can be represented as a sum of contributions from the various damage pathways. Heterogeneity in response across the cell population is ascribed to variations in the damage threshold for cell kill. The family of proposed models includes effects of one or two pathways of damage for each agent, saturation in drug responses, and cooperative or antagonistic interactions between agents. Models from this family with 4-7 unknown parameters are tested for their ability to fit 218 in vitro literature data sets for a range of drugs and cell lines. Overall, the additive damage models are found to outperform models based on the existing concept of independent cell kill, according to the corrected Akaike Information Criterion. The results are used to assess the importance of the various effects included in the models. These additive damage models have potential applications to the optimization of treatment and to the analysis and interpretation of in vitro screening data for new drug-radiation combinations.

The relative influence of hematocrit and red blood cell velocity on oxygen transport from capillaries to tissue.

OBJECTIVE: Oxygen transport to parenchymal cells occurs mainly at the microvascular level and depends on convective RBC flux, which is proportional in an individual capillary to the product of capillary hematocrit and RBC velocity. This study investigates the relative influence of these two factors on tissue PO2 . METHODS: A simple analytical model is used to quantify the respective influences of hematocrit, RBC velocity, and RBC flow on tissue oxygenation around capillaries. Predicted tissue PO2 levels are compared with a detailed computational model. RESULTS: Hematocrit is shown to have a larger influence on tissue PO2 than RBC velocity. The effect of RBC velocity increases with distance from the arterioles. Good agreement between analytical and numerical results is obtained, and the discrepancies are explained. Significant dependence of MTCs on RBC velocity at low hematocrit is demonstrated. CONCLUSIONS: For a given RBC flux in a capillary, the PO2 in the surrounding tissue increases with increasing hematocrit, as a consequence of decreasing IVR to diffusive oxygen transport from RBCs to tissue. These results contribute to understanding the effects of blood flow changes on oxygen transport, such as those that occur in functional hyperemia in the brain.

Model-based inference from microvascular measurements: Combining experimental measurements and model predictions using a Bayesian probabilistic approach.

OBJECTIVE: In vivo imaging of the microcirculation and network-oriented modeling have emerged as powerful means of studying microvascular function and understanding its physiological significance. Network-oriented modeling may provide the means of summarizing vast amounts of data produced by high-throughput imaging techniques in terms of key, physiological indices. To estimate such indices with sufficient certainty, however, network-oriented analysis must be robust to the inevitable presence of uncertainty due to measurement errors as well as model errors. METHODS: We propose the Bayesian probabilistic data analysis framework as a means of integrating experimental measurements and network model simulations into a combined and statistically coherent analysis. The framework naturally handles noisy measurements and provides posterior distributions of model parameters as well as physiological indices associated with uncertainty. RESULTS: We applied the analysis framework to experimental data from three rat mesentery networks and one mouse brain cortex network. We inferred distributions for more than 500 unknown pressure and hematocrit boundary conditions. Model predictions were consistent with previous analyses, and remained robust when measurements were omitted from model calibration. CONCLUSION: Our Bayesian probabilistic approach may be suitable for optimizing data acquisition and for analyzing and reporting large data sets acquired as part of microvascular imaging studies.

Dynamic remodeling of arteriolar collaterals after acute occlusion in chick chorioallantoic membrane.

OBJECTIVE: After arteriolar occlusion, collaterals enlarge and initially elevated WSS normalizes. While most previous studies focused on endpoints of such adaptive changes in larger collaterals, the present investigation aimed to continuously determine the relation between WSS and diameter in microvascular collaterals during adaptive reactions. METHODS: In Hamburger-Hamilton stage 40 CAMs, junction points between arteriolar segments were identified and the third upstream segment on one side was occluded. Intravital microscopy recordings were taken for 24 hours post-occlusion. Segment diameter and blood velocity were measured: WSS and capillary density were calculated. RESULTS: After occlusion, vascular diameters exhibited an immediate decrease, then increased with a time constant of 2.5 ± 0.8 hours and reached a plateau of up to 60% above baseline after about 7 hours. Vascular tone showed no significant change. WSS exhibited an immediate increase post-occlusion and linearly returned to baseline after about 12 hours. Local WSS change and diameter change rate showed similar patterns during the initial but not the later phase of post-occlusive adaptation. CONCLUSIONS: CAM collaterals undergo fast structural remodeling within 24 hours post-occlusion. This remodeling might be driven by local WSS and by other regulators within the vascular network.

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∝D1.03 measured, v∝D0.93 modeling), giving nearly uniform τ levels (τ∝D0.05). Venular trees exhibit slightly higher exponents (v∝D1.3, τ∝D0.38). 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.

Microvascular Plasticity: Angiogenesis in Health and Disease--Preface.

This Special Topic Issue is concerned with the mechanisms that determine the structure of microvascular networks. The vast number of vessels and the highly plastic character of the microcirculation give evidence that microvascular network structures emerge as a result of responses of individual vessels and cells to the local stimuli that they experience, through a combination of angiogenesis, remodeling and pruning. The articles in this issue of Microcirculation address a range of cellular and molecular mechanisms involved in these processes.