Blood Tracer Kinetics in the Arterial Tree

Evaluation of blood supply of different organs relies on labeling blood with a suitable tracer. The tracer kinetics is linear: Tracer concentration at an observation site is a linear response to an input somewhere upstream the arterial flow. The corresponding impulse response functions are currently treated empirically without incorporating the relation to the vascular morphology of an organ. In this work we address this relation for the first time. We demonstrate that the form of the response function in the entire arterial tree is reduced to that of individual vessel segments under approximation of good blood mixing at vessel bifurcations. The resulting expression simplifies significantly when the geometric scaling of the vascular tree is taken into account. This suggests a new way to access the vascular morphology in vivo using experimentally determined response functions. However, it is an ill-posed inverse problem as demonstrated by an example using measured arterial spin labeling in large brain arteries. We further analyze transport in individual vessel segments and demonstrate that experimentally accessible tracer concentration in vessel segments depends on the measurement principle. Explicit expressions for the response functions are obtained for the major middle part of the arterial tree in which the blood flow in individual vessel segments can be treated as laminar. When applied to the analysis of regional cerebral blood flow measurements for which the necessary arterial input is evaluated in the carotid arteries, present theory predicts about 20% underestimation, which is in agreement with recent experimental data.     

Relationship between chromaffin cells and blood vessels in the rat adrenal medulla: a transmission electron microscopic study combined with blood vessel reconstructions

The rat adrenal medulla architecture was examined using a combination of medullary blood vessel reconstructions and transmission electron microscopy. The peripheral radicles of the central vein and the medullary capillaries of the medullary arteries were thus precisely identified in the electron microscopic observations. The observations confirmed that the peripheral segments of the central vein were sinusoidal vessels with an attenuated and fenestrated endothelial wall. No ultrastructural differences were observed between segments lined by epinephrine-storing cells and those lined by norepinephrine-storing cells. The findings suggest that these peripheral segments of the adrenal central vein were sites of cortical hormonal effects on the adrenal medulla. The vessel structure does not support the hypothesis that medullary chromaffin-cell development is controlled by selective distribution of adrenal blood vessels.     

Haemodynamics-driven developmental pruning of brain vasculature in zebrafish

The brain blood vasculature consists of a highly ramified vessel network that is tailored to meet its physiological functions. How the brain vasculature is formed has long been fascinating biologists. Here we report that the developing vasculature in the zebrafish midbrain undergoes not only angiogenesis but also extensive vessel pruning, which is driven by changes in blood flow. This pruning process shapes the initial exuberant interconnected meshwork into a simplified architecture. Using in vivo long-term serial confocal imaging of the same zebrafish larvae during 1.5-7.5 d post-fertilization, we found that the early formed midbrain vasculature consisted of many vessel loops and higher order segments. Vessel pruning occurred preferentially at loop-forming segments via a process mainly involving lateral migration of endothelial cells (ECs) from pruned to unpruned segments rather than EC apoptosis, leading to gradual reduction in the vasculature complexity with development. Compared to unpruned ones, pruned segments exhibited a low and variable blood flow, which further decreased irreversibly prior to the onset of pruning. Local blockade of blood flow with micro-bead obstruction led to vessel pruning, whereas increasing blood flow by noradrenergic elevation of heartbeat impeded the pruning process. Furthermore, the occurrence of vessel pruning could be largely predicted by haemodynamics-based numerical simulation of vasculature refinement. Thus, changes of blood flow drive vessel pruning via lateral migration of ECs, leading to the simplification of the vasculature and possibly efficient routing of blood flow in the developing brain.     

Deformation-induced endothelin B receptor-mediated smooth muscle cell apoptosis is matrix-dependent

To maintain normal blood flow, pressure overload in both arteries and veins requires a structural adaptation of the vessel wall (remodelling) that involves smooth muscle cell (SMC) hypertrophy and/or hyperplasia. Due to its potent vasoconstrictor and growth-promoting effects, endothelin-1 (ET-1) is a likely candidate to initiate and/or promote remodelling in blood vessels exposed to a chronic increase in blood pressure. To test this hypothesis, isolated segments of the rabbit carotid artery and jugular vein were perfused at different levels of intraluminal pressure. In both types of segments, pressure overload (160 and 20 mmHg, respectively) resulted in an increase in endothelial prepro-ET-1 and SMC endothelin B receptor (ETB-R) expression. Moreover, in pressurised segments from the carotid artery an ETB-R antagonist-sensitive increase in SMC apoptosis in the media was observed, while in the vein medial SMC started to proliferate. Isolated SMC from these rabbit blood vessels as well as from the aorta and vena cava of the rat, when cultured on a collagen or laminin matrix, uniformly revealed an ETB-R-mediated increase in apoptosis upon exposure to mechanical deformation plus exogenous ET-1 (10 nmol/L). However, when grown on a fibronectin matrix, the cultured SMC did not respond with an increase in apoptosis under otherwise identical experimental conditions. These findings suggest that deformation-induced activation of the endothelin system in the vessel wall not only plays a crucial role in remodelling, but that the structural components of the vessel wall, in particular the cell-matrix interaction, determine how SMC respond phenotypically to these changes in gene expression.     

Modeling of angioadaptation: insights for vascular development

Vascular beds are generated by vasculogenesis and sprouting angiogenesis, and these processes have strong stochastic components. As a result, vascular patterns exhibit significant heterogeneity with respect to the topological arrangement of the individual vessel segments and the characteristics (length, number of segments) of different arterio-venous pathways. This structural heterogeneity tends to cause heterogeneous distributions of flow and oxygen availability in tissue. However, these quantities must be maintained within tolerable ranges to allow normal tissue function. This is achieved largely through adjustment of vascular flow resistance by control of vessel diameters. While short-term diameter control by changes in vascular tone in arterioles and small arteries plays an important role, in the long term an even more important role is played by structural adaptation (angioadaptation), occurring in response to metabolic and hemodynamic signals. The effectiveness, stability and robustness of this angioadaptation depend sensitively on the nature and strength of the vascular responses involved and their interactions with the network structure. Mathematical models are helpful in understanding these complex interactions, and can be used to simulate the consequences of failures in sensing or signal transmission mechanisms. For the tumor microcirculation, this strategy of combining experimental observations with theoretical models, has led to the hypothesis that dysfunctional information transport via vascular connexins is a major cause of the observed vascular pathology and increased heterogeneity in oxygen distribution.     

Effects of non-Newtonian blood and metabolic states of the blood and vessel wall on the optimum design of single vessels and the vascular bifurcation

Employing the optimality principle, we attempted to predict the effects of non-Newtonian blood and the metabolic states of individual vessel segments on the optimum vascular design. Our results implied that irrespective of the vessel caliber, the optimum flow rate of non-Newtonian blood through a cylindrical vessel is less than that of Newtonian blood by not more than some 12-13%, even though the non-Newtonian nature is within the pathologically-realistic highest range. Non-Newtonian blood does not exert the slightest degree of influence on the optimum geometry of the vascular bifurcation. In contrast, as the metabolic state of the vessel wall overwhelms that of the blood, the optimum flow through the cylindrical vessel becomes markedly increased: the optimum relative caliber of the branch of the bifurcation decreases and the optimum branching angle increases.     

Endothelial Cell Self-fusion during Vascular Pruning

During embryonic development, vascular networks remodel to meet the increasing demand of growing tissues for oxygen and nutrients. This is achieved by the pruning of redundant blood vessel segments, which then allows more efficient blood flow patterns. Because of the lack of an in vivo system suitable for high-resolution live imaging, the dynamics of the pruning process have not been described in detail. Here, we present the subintestinal vein (SIV) plexus of the zebrafish embryo as a novel model to study pruning at the cellular level. We show that blood vessel regression is a coordinated process of cell rearrangements involving lumen collapse and cell–cell contact resolution. Interestingly, the cellular rearrangements during pruning resemble endothelial cell behavior during vessel fusion in a reversed order. In pruning segments, endothelial cells first migrate toward opposing sides where they join the parental vascular branches, thus remodeling the multicellular segment into a unicellular connection. Often, the lumen is maintained throughout this process, and transient unicellular tubes form through cell self-fusion. In a second step, the unicellular connection is resolved unilaterally, and the pruning cell rejoins the opposing branch. Thus, we show for the first time that various cellular activities are coordinated to achieve blood vessel pruning and define two different morphogenetic pathways, which are selected by the flow environment.     

Dynamic Endothelial Cell Rearrangements Drive Developmental Vessel Regression

Patterning of functional blood vessel networks is achieved by pruning of superfluous connections. The cellular and molecular principles of vessel regression are poorly understood. Here we show that regression is mediated by dynamic and polarized migration of endothelial cells, representing anastomosis in reverse. Establishing and analyzing the first axial polarity map of all endothelial cells in a remodeling vascular network, we propose that balanced movement of cells maintains the primitive plexus under low shear conditions in a metastable dynamic state. We predict that flow-induced polarized migration of endothelial cells breaks symmetry and leads to stabilization of high flow/shear segments and regression of adjacent low flow/shear segments.     

Assessment of energy requirement for the retinal arterial network in normal and hypertensive subjects

The retinal arterial network structure can be altered by systemic diseases such as hypertension and diabetes. In order to compare the energy requirement for maintaining retinal blood flow and vessel wall metabolism between normal and hypertensive subjects, 3D hypothetical models of a representative retinal arterial bifurcation were constructed based on topological features derived from retinal images. Computational analysis of blood flow was performed, which accounted for the non-Newtonian rheological properties of blood and peripheral vessel resistance. The results suggested that the rate of energy required to maintain the blood flow and wall metabolism is much lower for normal subjects than for hypertensives, with the latter requiring 49.2% more energy for an entire retinal arteriolar tree. Among the several morphological factors, length-to-diameter ratio was found to have the most significant influence on the overall energy requirement.     

A new method for assessing arteriolar diameter and hemodynamic resistance using image analysis of vessel lumen

To characterize the nonuniform diameter response in a blood vessel after a given stimulus (e.g., arteriolar conducted response), frequent serial diameter measurements along the vessel length are required. We used an advanced image analysis algorithm (the "discrete dynamic contour") to develop a quick, reliable method for serial luminal diameter measurements along the arteriole visualized by intravital video microscopy. With the use of digitized images of the arteriole and computer graphics, the method required an operator to mark the image of the two inner edges of the arteriole at several places along the arteriolar length. The algorithm then "filled in" these marks to generate two continuous contours that "hugged" these edges. A computer routine used these contours to determine luminal diameters every 20 microm. Based on these diameters and on Poiseuille's law, the routine also estimated the hemodynamic resistance of the blood vessel. To demonstrate the usefulness of the method, we examined the character of spatial decay of KCl-induced conducted constriction along approximately 500-microm-long arteriolar segments and the KCl-induced increase in hemodynamic resistance computed for these segments. The decay was only modestly fitted by a simple exponential, and the computed increase in resistance (i.e., 5- to 70-fold) was only modestly predicted by resistance increase based on our mathematical model involving measurements at two arteriolar sites (Tyml K, Wang X, Lidington D, and Oullette Y. Am J Physiol Heart Circ Physiol 281: H1397-H1406, 2001). We conclude that our method provides quick, reliable serial diameter measurements. Because the change in hemodynamic resistance could serve as a sensitive index of conducted response, use of this index in studies of conducted response may lead to new mechanistic insights on the response.     

Microvascular surgical experimental thrombosis model: rationale and design

The rationale for the design of surgical models of microvascular thrombosis is discussed, and a new model, the arterial inversion graft (AIG), is described and evaluated in the New Zealand white rabbit. Femoral artery segments of predetermined length are excised, gently turned inside-out, and resutured into their native position. Blood flow is restored, and at varying time intervals, vessel patency is assessed through the direct "milking test." In this study, three groups of 20 arterial inversion grafts of 2, 5, and 10 mm in length are created and evaluated for patency at 1 hour and again at 7 days. The incidence of femoral artery occlusion in this model appears to be an increasing function of arterial inversion graft length both at 1 hour--30 percent (2 mm), 80 percent (5 mm), and 100 percent (10 mm)--and at 7 days--65 percent (2 mm), 90 percent (5 mm), and 100 percent (10 mm). This proportionality suggests the arterial inversion graft may be adjusted in length to provide an incidence of vessel occlusion best suited to the needs of any particular experiment.     

Blood flow regulation in the cerebral microvasculature with an arcadal network: a numerical simulation

Blood flow regulation in the cerebral microvasculature with an arcadal network was investigated using a numerical simulation. A mathematical model for blood flow in the arcadal network, based on in vivo data of cat cerebral microvasculature and flow velocity was developed. The network model consists of 45 vessel segments and 25 branching points. To simulate microvascular response to blood flow, non-reactive (solid), cerebral arteriole-like, or skeletal muscle arteriole-like responses to wall shear stress were taken into account. Numerical calculation was carried out in the flow condition where the inlet (arterial) pressure was changed from 60 to 120 mmHg. Flow-rate in each efferent vessel and the mean flow-rate over all efferent vessels were evaluated for assessment of blood supply to the local area of cerebral tissue. The simulation demonstrated the wall shear stress-induced vasodilation in the arcadal network worked to maintain the blood flow at a constant level with pressure variable in a wide range. It is suggested that an individual microvessel (segment) should join in the regulatory process of flow, interacting with other microvessels (cooperative regulation).     

The anatomy of the blood vascular system of the giant vestimentiferan tubeworm Riftia pachyptila (Siboglinidae,Annelida)

The giant dimensions of vestimentiferan Riftia pachyptila (Jones, 1981 ) are achieved thanks to the well‐developed vascular system. In the vestimentum, there is a complicated net of lacunae, including the brain blood supply and the ventral lacuna underlying the ciliary field. The trunk region has an extensive network of blood vessels feeding the gonads («rete mirabile»). The thick muscular lining of the mesenterial vessels in the trunk and the dorsal vessel in the opisthosome serves as an additional pump, pushing blood into numerous vessels in the segments. It was hypothesized that the blood envelope of the ventral blood vessel in the trunk provides the blood supply to the trophosome. The 3D reconstruction has revealed that there are two vascular systems of the tentacular crown of R. pachyptila . Blood runs into the tentacles via axial afferent vessels, as described earlier only for Riftia , and also via basal ones, as described for other vestimentiferans except Riftia . The basal ones are poorly developed, and the number of lamellar blood vessels is small, indicating a lack of demand for these within huge R. pachyptila . It appears that the presence of these vessels is the preserved ancestral state of Vestimentifera. In different portions of the dorsal vessel, the morphology of the intravasal body varies, depending on function.     

Centrifugal-order distributions in binary topological trees

Statistical properties of topological binary trees are studied on the basis of the distribution of segments in relation to centrifugal order. Special attention is paid to the mean of this distribution in a tree as it will be used as a measure of tree topology. It will be shown how the expectation of the mean centrifugal order depends both on the size of the tree and on the mode of growth in the context of modelling the growth of tree structures. Observed trees can be characterized by their mean orders and procedures are described to find the growth mode that optimally corresponds to these data. The variance structure of the mean-order measure appears to be a crucial factor in these fitting procedures. Examples indicate that mean-order analysis is an accurate alternative to partition analysis that is based on the partitioning of segments over sub-tree pairs at branching points.     

Microvascular blood viscosity in vivo and the endothelial surface layer

The apparent viscosity of blood in glass tubes declines with decreasing diameter (F?hraeus-Lindqvist effect) and exhibits a distinctive minimum at 6-7 microm. However, flow resistance in vivo in small vessels is substantially higher than predicted by in vitro viscosity data. The presence of a thick endothelial surface layer (ESL) has been proposed as the primary cause for this discrepancy. Here, a physical model is proposed for microvascular flow resistance as a function of vessel diameter and hematocrit in vivo; it combines in vitro blood viscosity with effects of a diameter-dependent ESL. The model was developed on the basis of flow distributions observed in three microvascular networks in the rat mesentery with 392, 546, and 383 vessel segments, for which vessel diameters, network architecture, flow velocity, and hematocrit were determined by intravital microscopy. A previously described hemodynamic simulation was used to predict the distributions of flow and hematocrit from the assumed model for effective blood viscosity. The dependence of ESL thickness on vessel diameter was estimated by minimizing deviations of predicted values for velocities, flow directions, and hematocrits from measured data. Optimal results were obtained with a layer thickness of approximately 0.8-1 microm for 10- to 40-microm-diameter vessels and declined strongly for smaller diameters, with an additional hematocrit-dependent impact on flow resistance exhibiting a maximum for approximately 10-microm-diameter vessels. These results show that flow resistance in vivo can be explained by in vitro blood viscosity and the presence of an ESL and indicate the rheologically effective thickness of the ESL in microvessels.     

Local selection rules that can determine specific pathways of DNA unknotting by type II DNA topoisomerases

We performed numerical simulations of DNA chains to understand how local geometry of juxtaposed segments in knotted DNA molecules can guide type II DNA topoisomerases to perform very efficient relaxation of DNA knots. We investigated how the various parameters defining the geometry of inter-segmental juxtapositions at sites of inter-segmental passage reactions mediated by type II DNA topoisomerases can affect the topological consequences of these reactions. We confirmed the hypothesis that by recognizing specific geometry of juxtaposed DNA segments in knotted DNA molecules, type II DNA topoisomerases can maintain the steady-state knotting level below the topological equilibrium. In addition, we revealed that a preference for a particular geometry of juxtaposed segments as sites of strand-passage reaction enables type II DNA topoisomerases to select the most efficient pathway of relaxation of complex DNA knots. The analysis of the best selection criteria for efficient relaxation of complex knots revealed that local structures in random configurations of a given knot type statistically behave as analogous local structures in ideal geometric configurations of the corresponding knot type.     

Blood velocity field numerical assessment using a GPL code in case of intravascular Doppler catheter affections: comparative analysis of different rheological models

In the use of intravascular Doppler catheters, one of the most common techniques to study the coronary arteries, the velocity field measured is partially affected by the presence of the catheter itself inside the blood vessel. It is therefore fundamental to quantify the nature of this disturbance. This paper treats a numerical investigation of the problem considering the hypothesis of blood as a Newtonian, Cassonian and Power Law fluid, comparing the results. The code used for numerical simulation is a General Public License Finite Element code denominated TOCHNOG. The results obtained, realistic within the terms explained in the text, provide an insight in the rheological characterisation of blood flow.     

Fibronectin Isoform Distribution in the Mouse I. The Alternatively Spliced EIIIB,EIIIA, and V Segments Show Widespread Codistribution in the Developing Mouse Embryo

Fibronectins (FNs) are extracellular matrix glycoproteins that are essential for embryonic development. In order to gain clues to possible developmental roles played by the particular isoforms of FN, we used indirect immunofluorescence microscopy to examine and compare the distributions of the alternatively spliced EIIIB, EIIIA, and V segments, as well as the total pool of FNs, in serial sections from mouse embryos. Antibodies to each of these segments produced staining patterns that colocalized during gastrulation (E7.5) and during early morphogenesis of somites and notochord (E9.5). During the period of continuing organogenesis in the latter half of gestation (E10.5 to E16.5), the antibodies generally continued to produce similar staining patterns localized to epithelial basement membranes, stromal connective tissues, blood vessel walls, and muscles. However, as development proceeded, there was a gradual decline in the intensity of staining for the spliced segments relative to the total pool of FN, with a particularly noticeable decline in staining for EIIIB and EIIIA segments in certain glandular organs, including the liver. A specific reduction in expression of these latter two segments was also evident in the uterus and placenta at early timepoints in gestation. However, the most dramatic difference in the expression of the spliced segments occurred in developing hyaline cartilage, which showed a selective reduction in staining for the EIIIA segment that was evident in the axial skeletal precursors by E12.5 and complete throughout the embryo by E15.5. Our findings suggest that the alternatively spliced EIIIB, EIIIA, and V segments are included in the FN that is required for the morphogenesis of “FN dependent” structures, including somites, notochord, and the vasculature. Conversely, these segments would appear to play divergent, and sometimes exclusive, biological roles in specific tissues such as liver, cartilage, and placenta.     

Computational study of pulsatile blood flow in prototype vessel geometries of coronary segments

The spatial and temporal distributions of wall shear stress (WSS) in prototype vessel geometries of coronary segments are investigated via numerical simulation, and the potential association with vascular disease and specifically atherosclerosis and plaque rupture is discussed. In particular, simulation results of WSS spatio-temporal distributions are presented for pulsatile, non-Newtonian blood flow conditions for: (a) curved pipes with different curvatures, and (b) bifurcating pipes with different branching angles and flow division. The effects of non-Newtonian flow on WSS (compared to Newtonian flow) are found to be small at Reynolds numbers representative of blood flow in coronary arteries. Specific preferential sites of average low WSS (and likely atherogenesis) were found at the outer regions of the bifurcating branches just after the bifurcation, and at the outer-entry and inner-exit flow regions of the curved vessel segment. The drop in WSS was more dramatic at the bifurcating vessel sites (less than 5% of the pre-bifurcation value). These sites were also near rapid gradients of WSS changes in space and time – a fact that increases the risk of rupture of plaque likely to develop at these sites. The time variation of the WSS spatial distributions was very rapid around the start and end of the systolic phase of the cardiac cycle, when strong fluctuations of intravascular pressure were also observed. These rapid and strong changes of WSS and pressure coincide temporally with the greatest flexion and mechanical stresses induced in the vessel wall by myocardial motion (ventricular contraction). The combination of these factors may increase the risk of plaque rupture and thrombus formation at these sites.