Study of human cerebral blood flow by corrosion casts of the carotid system

20 corrosion casts of human anterior cerebral arteries and middle cerebral arteries were analyzed. In 588 vessel sections in between 2 bifurcations, the relation of vessel length and vessel diameter was investigated. Measurements were taken starting from the arterial trunk down to vessels with a diameter of 0.4 mm. The mean values of the lengths show that both the anterior cerebral artery and the middle cerebral artery can be grouped into 5 diameter ranges with significant different lengths. With decreasing diameter there are short vessels in the groups 1, 3 and 5 and long vessels in the groups 2 and 4. However, the long branches in the groups 2 and 4 of the middle cerebral artery are longer and thinner than in the anterior cerebral artery. Due to the higher pressure loss in thin and long vessels, blood pressure drop occurs earlier in the branches of the middle cerebral artery than in those of the anterior cerebral artery.     

Blood flow in the capillary bed

From arteries to veins, the blood has to go through the ‘capillary’ blood vessels. These blood vessels are so small that often their diameter is smaller than that of the red blood cells. Intimate interactions occur, therefore, between the blood cells and the blood vessels.

A general survey of recent works on capillary blood flow is given in this article. Some details are presented for two problems: the problem of deformation of the flexible red blood cells, their motion in the capillary blood vessels, and the pressure drop due to the red cell blood vessel interaction; and the problem of the flow of plasma ‘bolus’ between neighboring red cells.

The solution supplies many details about the microcirculation phenomenon. Taken together, a method is offered for the calculation of pressure drop in the capillary as a function of various physical parameters: the red cell volume per unit blood volume, (hematocrit), the ratio of the cell diameter to the blood vessel diameter, the ratio of the length of the blood vessel to its length, the volume of individual red cells, and a parameter relating the cell membrane elasticity, plasma viscosity and the cell velocity.     

A hemodynamic model representation of the dog lung

The published morphometric data from human, cat, and dog lungs suggest that the power-law relationships between the numbers (Na and Nv) and diameters (Da and Dv) of arteries and veins and between the lengths (La and Lv) and diameters of the arteries and veins could be used as scaling rules for assigning dimensions and numbers to the intrapulmonary vessels of the arterial and venous trees of the dog lung. These rules, along with the dimensions of the extrapulmonary arteries and capillary sheet and the distensibility coefficients of the vessels obtained from the literature, were used to construct a steady-state hemodynamic model of the dog lung vascular bed. The model can be characterized approximately by 15 orders of arteries with Na approximately 2.07 Da-2.58 and 13 orders of veins with Nv approximately 2.53 Dv-2.61. For the intrapulmonary vessels (orders 1-12), La approximately 4.85 Da1.01, and Lv approximately 6.02 Da1.07. The average ratio of the numbers of vessels in consecutive orders is approximately 3.2 for the arteries and veins. These arterial and venous trees are connected by the capillary sheet with an undistended thickness of approximately 3.5 microns and an area of 33 m2. The average distensibility (% increase in diameter over the undistended diameter/Torr increase in transmural pressure) for the model arteries and veins is approximately 2.4%/Torr, and the distensibility of the capillary sheet (% increase in thickness over the undistended thickness/Torr increase in transmural pressure) is approximately 3.6%/Torr. The calculated arterial-capillary-venous volumes and compliances of the model agree well with experimental estimates of these variables in dogs. In addition, the model appears consistent with certain aspects of the pressure-flow relationships measured in dog lungs. The model appears to be a useful summary of some of the available data on pulmonary morphometry and vessel properties. It is anticipated that the model will provide the basis for dynamic modeling of the dog lung in the future.     

Pressure and flow in the umbilical cord

A fluid dynamic study of blood flow within the umbilical vessels of the human maternal-fetal circulatory system is considered. It is found that the umbilical coiling index (UCI) is unable to distinguish between cords of significantly varying pressure and flow characteristics, which are typically determined by the vessel curvature, torsion and length. Larger scale geometric non-uniformities superposed over the inherent coiling, including cords exhibiting width and/or local UCI variations as well as loose true knots, typically produce a small effect on the total pressure drop. Crucially, this implies that a helical geometry of mean coiling may be used to determine the steady vessel pressure drop through a more complex cord. The presence of vessel constriction, however, drastically increases the steady pressure drop and alters the flow profile. For pulsatile-flow within the arteries, the steady pressure approximates the time-averaged value with high accuracy over a wide range of cords. Furthermore, the relative peak systolic pressure measured over the period is virtually constant and approximately 25% below the equivalent straight-pipe value for a large range of non-straight vessels. Interestingly, this suggests that the presence of vessel helicity dampens extreme pressures within the arterial cycle and may provide another possible evolutionary benefit to the coiled structure of the cord.     

Distensibility of small arteries of the dog lung.

To obtain in situ measurements of the distensibility of small (100- to 1,000-microns-diam) pulmonary arterial vessels of the dog lung, X-ray angiograms were obtained from isolated lung lobes with the vascular pressure adjusted to various levels. The in situ diameter-pressure relationships were compared with the diameter-pressure relationships for small arteries that were dissected free from the lungs and cannulated with small glass pipettes for the measurement of diameter and transmural pressure. The diameter-vascular or diameter-transmural pressure curves from both in situ and cannulated vessels were sufficiently linear in the pressure range studied (0-30 Torr) that they could be characterized by linear regression to obtain estimates of D0, the diameter at zero vascular pressure, and beta, the change in diameter (micron) per Torr change in pressure. The vessel distensibility coefficient (alpha) was defined as alpha = beta/D0. The mean values of alpha were approximately 2.0 +/- 0.8%/Torr (SD) for the in situ vessels and 1.7 +/- 0.6%/Torr for the cannulated vessels, with no statistically significant difference between the two methods. The influence of vasoconstriction elicited by serotonin was evaluated in the in situ vessels. Serotonin-induced vasoconstriction caused a decrease in D0 and little change in alpha.     

Effects of arterial wall stress on vasomotion

Smooth muscle and endothelial cells in the arterial wall are exposed to mechanical stress. Indeed blood flow induces intraluminal pressure variations and shear stress. An increase in pressure may induce a vessel contraction, a phenomenon known as the myogenic response. Many muscular vessels present vasomotion, i.e., rhythmic diameter oscillations caused by synchronous cytosolic calcium oscillations of the smooth muscle cells. Vasomotion has been shown to be modulated by pressure changes. To get a better understanding of the effect of stress and in particular pressure on vasomotion, we propose a model of a blood vessel describing the calcium dynamics in a coupled population of smooth muscle cells and endothelial cells and the consequent vessel diameter variations. We show that a rise in pressure increases the calcium concentration. This may either induce or abolish vasomotion, or increase its frequency depending on the initial conditions. In our model the myogenic response is less pronounced for large arteries than for small arteries and occurs at higher values of pressure if the wall thickness is increased. Our results are in agreement with experimental observations concerning a broad range of vessels.     

Biomechanical properties of decellularized porcine common carotid arteries

To analyze the effects of decellularization on the biomechanical properties of porcine common carotid arteries, decellularization was performed by a detergent-enzymatic procedure that preserves extracellular matrix scaffold. Internal diameter, external diameter, and wall thickness were measured by optical microscopy on neighboring histological sections before and after decellularization. Rupture tests were conducted. Inner diameter and wall thickness were measured by echo tracking during pressure inflation from 10 to 145 mmHg. Distensibility and incremental elastic modulus were computed. At 10 mmHg, mean diameter of decellularized arteries was 5.38 mm, substantially higher than controls (4.1 mm), whereas decellularized and control arteries reached the same internal diameter (6.7 mm) at 145 mmHg. Wall thickness decreased 16% for decellularized and 32% for normal arteries after pressure was increased from 10 to 145 mmHg. Decellularized arteries withstood pressure >2,200 mmHg before rupture. At 145 mmHg, decellularization reduced compliance by 66% and increased incremental elastic modulus by 54%. Removal of cellular elements from media led to changes in arterial dimensions. Collagen fibers engaged more rapidly during inflation, yielding a stiffer vessel. Distensibility was therefore significantly lower (by a factor of 3) in decellularized than in normal vessels: reduced in the physiological range of pressures. In conclusion, decellularization yields vessels that can withstand high inflation pressures with, however, markedly different geometrical and biomechanical properties. This may mean that the potential use of a decellularized artery as a scaffold for the creation of xenografts may be compromised because of geometrical and compliance mismatch.     

As human pial arteries (internal diameter 200-1000 microm) get smaller, their wall thickness and capacity to develop tension relative to their diameter increase.

Pial arteries play a key role in the regulation of human cerebral blood flow. However, many of the features and mechanisms that regulate the tone and diameters of these vessels cannot be studied in situ. One approach is to study in vitro segments of arteries obtained during neurosurgical procedures. The ratios of arterial media thickness to lumen diameter and of the capacity to develop wall force to lumen diameter have important functional consequences and are known to change in disease. Experiments were carried out on pial arteries from normotensive humans to determine the way in which these parameters vary with vessel size. Vessel dimensions--media thickness and lumen diameter were derived from fixed sections using quantitative morphometry. Wall force was measured using a resistance artery myograph. The ratio of media thickness to lumen diameter and of maximum tension developed to lumen diameter both increased as vessel diameter decreased. These ratios do not change over the age range of 15-75 years. These findings show that although in vivo intralumenal pressure falls as human pial arteries become smaller, their media thickness and capacity to develop tone increase.     

Quantitative study of intimal longitudinal smooth muscle in human small mesenteric arteries

The present paper examines the results of quantitative assessment of intimal longitudinal smooth muscle (ILSM) in small arteries from normal mesentery in man. 212 vessels from 24 patients who underwent colectomy for colorectal carcinoma were studied. The mean amount of ILSM in these vessels was found to be 1.42% (range 0.00-8.90%) of external vessel diameter. A statistically significant (p = 0.018) positive correlation was demonstrated between the mean amount of ILSM in vessels from any individual patient and the level of diastolic blood pressure. It is concluded that increased intravascular tension is one factor which influences the development of ILSM in human small mesenteric arteries.     

Readdressing the issue of thermally significant blood vessels using a countercurrent vessel network

A physiologically realistic arterio-venous countercurrent vessel network model consisting of ten branching vessel generations, where the diameter of each generation of vessels is smaller than the previous ones, has been created and used to determine the thermal significance of different vessel generations by investigating their ability to exchange thermal energy with the tissue. The temperature distribution in the 3D network (8178 vessels; diameters from 10 to 1000 microm) is obtained by solving the conduction equation in the tissue and the convective energy equation with a specified Nusselt number in the vessels. The sensitivity of the exchange of energy between the vessels and the tissue to changes in the network parameters is studied for two cases; a high temperature thermal therapy case when tissue is heated by a uniformly distributed source term and the network cools the tissue, and a hypothermia related case, when tissue is cooled from the surface and the blood heats the tissue. Results show that first, the relative roles of vessels of different diameters are strongly determined by the inlet temperatures to those vessels (e.g., as affected by changing mass flow rates), and the surrounding tissue temperature, but not by their diameter. Second, changes in the following do not significantly affect the heat transfer rates between tissue and vessels; (a) the ratio of arterial to venous vessel diameter, (b) the diameter reduction coefficient (the ratio of diameters of successive vessel generations), and (c) the Nusselt number. Third, both arteries and veins play significant roles in the exchange of energy between tissue and vessels, with arteries playing a more significant role. These results suggest that the determination of which diameter vessels are thermally important should be performed on a case-by-case, problem dependent basis. And, that in the development of site-specific vessel network models, reasonable predictions of the relative roles of different vessel diameters can be obtained by using any physiologically realistic values of Nusselt number and the diameter reduction coefficient.     

Pulmonary arterial dilation by inhaled NO: arterial diameter, NO concentration relationship.

The objective of this study was to determine the nitric oxide (NO) concentration and vessel diameter dependence of the pulmonary arterial dilation induced by inhaled NO. Isolated dog lung lobes were situated between a microfocal X-ray source and X-ray detector and perfused with either blood or plasma. Boluses of radiopaque contrast medium were injected into the lobar artery under control conditions, when the pulmonary arteries were constricted by infusion of serotonin and when the serotonin infusion was accompanied by inhalation of from 30 to 960 parts/million NO. Arterial diameter measurements were obtained from X-ray images of vessels having control diameters in the 300- to 3,400-microm range. Serotonin constricted the vessels throughout the size range studied, with an average decrease in diameter of approximately 20%. The fractional reversal of the serotonin-induced constriction by inhaled NO was directly proportional to inhaled NO concentration, inversely proportional to vessel size, and greater with plasma than with blood perfusion in vessels as large as 3 mm in diameter. The latter indicates that intravascular hemoglobin affected the bronchoalveolar-to-arterial luminal NO concentration gradient in fairly large pulmonary arteries. The data provide information regarding pulmonary arterial smooth muscle accessibility to intrapulmonary gas that should be useful as part of the database for modeling the communication between intrapulmonary gas and pulmonary arterial smooth muscle cells in future studies.     

Estimated flow resistance increase in a spiral human coronary artery segment

Coronary flow estimates were made for a spiral coronary artery segment (identified from a post-mortem replica casting) by using a modified Dean number based on the approximate coil radius of curvature, as suggested earlier. The estimates were found to correlate experimental pressure drop data for helical coiled tubes. Over a physiological range of mean Reynolds numbers from 100 to 400 for blood flow through main coronary arteries, estimates of the flow resistance increase relative to a straight lumen segment ranged from about 20 to 80 percent, and were of similar magnitude to those found in a flow study in a sinuous coronary vessel segment with no spiral.     

Analysis of the passive mechanical properties of rat carotid arteries

The passive mechanical properties of rat carotid arteries were studied in vitro. Using a tensile testing machine and a piston pump, intact segments of carotid arteries were subjected to large deformations both in the longitudinal and circumferential directions. Internal pressure, external diameter, length and longitudinal force were measured during the experiment and compared with the in vivo dimensions of the segments prior to excision. The anisotropic mechanical properties of the vessel wall material were analyzed using incremental elastic moduli and incremental Poisson's ratios. The results suggest that there is a characteristic deformation pattern common to all vessels investigated which is highly correlated with the conditions of loading that occur in vivo. That is, under average physiological deformation of the vessel, the longitudinal force is nearly independent of internal pressure. In this range of loading the circumferential incremental elastic modulus is nearly independent of longitudinal strain. However, the longitudinal and radial incremental elastic moduli vary significantly with deformation in this direction. The values of the moduli in all three directions increase with raising internal pressure. The weak coupling between circumferential and longitudinal direction in the wall material of carotid arteries is shown by the small value of the corresponding incremental Poisson's ratios.     

Vascular smooth muscle cell stress as a determinant of cerebral artery myogenic tone

Although the level of myogenic tone (MT) varies considerably from vessel to vessel, the regulatory mechanisms through which the actual diameter set point is determined are not known. We hypothesized that a unifying principle may be the equalization of active force at the contractile filament level, which would be reflected in a normalization of wall stress or, more specifically, media stress. Branched segments of rat cerebral arteries ranging from <50 microm to >200 microm in diameter were cannulated and held at 60 mmHg with the objectives of: 1) evaluating the relationship between arterial diameter and the extent of myogenic tone, 2) determining whether differences in MT correlate with changes in cytosolic calcium ([Ca(2+)](i)), and 3) testing the hypothesis that a normalization of wall or media stress occurs during the process of tone development. The level of MT increased significantly as vessel size decreased. At 60 mmHg, vascular smooth muscle [Ca(2+)](i) concentrations were similar in all vessels studied (averaging 230 +/- 9.2 nM) and not correlated with vessel size or the extent of tone. Wall tension increased with increasing arterial size, but wall stress and media stress were similar in large versus small arteries. Media stress, in particular, was quite uniform in all vessels studied. Both morphological and calcium data support the concept of equalization of media stress (and, hence, vascular smooth muscle cell stress and force) as an underlying mechanism in determining the level of tone present in any particular vessel. The equalization of active (vascular smooth muscle cell) stress may thus explain differences in MT observed in the different-sized vessels constituting the arterial network and provide a link between arterial structure and function, in both short- and long-term (hypertension) pressure adaptation.     

Do lianas really have wide vessels? Vessel diameter–stem length scaling in non-self-supporting plants

Lianas and other climbing plants are known for their extraordinarily wide vessels. Wide vessels are thought to contribute to the extreme hydraulic efficiency of lianas and to play a part in their ability to dominate many tropical habitats, and even their globally increasing abundance with anthropic disturbance. However, recent hydraulic optimality models suggest that the average vessel diameter of plants generally is the result of tip-to-base vessel widening reflecting the effects of selection buffering conductive path length-imposed hydraulic resistance. These models state that mean vessel diameter should be predicted by stem length, by implication even in lianas. We explore vessel–stem relations with 1409 samples from 424 species in 159 families of both self- and non-self-supporting plants. We show that, far from being exceptional in their vessel diameter, lianas have average natural (not hydraulically weighted) vessel diameters that are indistinguishable for a given stem length from those in self-supporting plants. Lianas do, however, have wider variance in vessel diameter. They have a small number of vessels that are wider than those in self-supporting plants of similar stem lengths, and also narrower vessels. This slightly greater variance is sufficient to make hydraulically weighted vessel diameters in lianas higher than those of self-supporting counterparts of similar stem lengths. Moreover, lianas have significantly more vessels per unit of wood transection than self-supporting plants do. This subtle combination of slightly higher vessel diameter variance and higher vessel density for a given stem length is likely what makes lianas hydraulically distinctive, rather than their having vessels that are truly exceptionally wide.     

Diameter-dependent axial prestretch of porcine coronary arteries and veins

The pressure-diameter relation (PDR) and the wall strain of coronary blood vessels have important implications for coronary blood flow and arthrosclerosis, respectively. Previous studies have shown that these mechanical quantities are significantly affected by the axial stretch of the vessels. The objective of this study was to measure the physiological axial stretch in the coronary vasculature; i.e., from left anterior descending (LAD) artery tree to coronary sinus vein and to determine its effect on the PDR and hence wall stiffness. Silicone elastomer was perfused through the LAD artery and coronary sinus trees to cast the vessels at the physiologic pressure. The results show that the physiological axial stretch exists for orders 4 to 11 (> 24 μm in diameter) arteries and orders -4 to -12 (>38 μm in diameter) veins but vanishes for the smaller vessels. Statistically, the axial stretch is higher for larger vessels and is higher for arteries than veins. The axial stretch λ(z) shows a linear variation with the order number (n) as: λ(z) = 0.062n + 0.75 (R(2) = 0.99) for artery and λ(z) = -0.029n + 0.89 (R(2) = 0.99) for vein. The mechanical analysis shows that the axial stretch significantly affects the PDR of the larger vessels. The circumferential stretch/strain was found to be significantly higher for the epicardial arteries (orders 9-11), which are free of myocardium constraint, than the intramyocardial arteries (orders 4-8). These findings have fundamental implications for coronary blood vessel mechanics.     

Investigation of the structure of human coronary vasculature

Some results of a morphometric study of the parameters of coronary arteries are presented. The parameters that characterize the structure of the arterial vasculature as an optimal branching system have been calculated. Statistically reliable correlations between the diameter of the bigger of two daughter vessels in a bifurcation with the diameter of the parent vessel as well as between the diameter of the smaller daughter vessel and the asymmetry coefficient have been obtained. Differences in the structural parameters of the two types of coronary arteries that provide blood delivery and distribution have been revealed. The relationships between the lengths and diameters of the arteries of different subsystems have been obtained. It is shown that asymmetrical branching is characteristic of the coronary vasculature, and self-similar asymmetric tree-like systems may be used for its modeling.     

Biaxial anisotropy of dog carotid artery: estimation of circumferential elastic modulus

Experiments were performed to study biaxial anisotropy in relaxed canine carotid arteries subjected to a wide range of longitudinal lengths and transmural pressures. In order to encompass the range of vessel lengths which occurs in situ, 120 carotid arteries were studied at 20%, 40%, 60% and 80% extension relative to retracted vessel length. These studies were performed in systematically randomized order. At each length, the vessels were pressurized in steps up to 200 mmHg transmural pressure, or until the traction force fell to zero. Results showed that longitudinal extension markedly increased the longitudinal elastic modulus, but had only a slight effect on the circumferential modulus. At physiological pressures, the vessels were nearly isotropic at about 70% longitudinal extension, but were anisotropic at shorter lengths. Estimates of the anisotropic circumferential modulus by a number of simplified methods revealed that use of a 'pressure-elastic modulus' (Ep) underestimated the anisotropic modulus by 80%, but was extremely consistent. Therefore when suitably corrected, Ep could be used to reliably estimate the anisotropic modulus of carotid arteries over a wide range of pressures and vessel lengths.     

Arterial adaptations to altered blood flow

Arterial remodeling in response to altered blood flow is believed to be critical to vascular adaptations to developmental, physiological, pathological, and therapeutically induced changes in blood flow. To assess this remodeling, we used left-to-right carotid anastomosis to increase blood flow in the right common carotid arteries of adult rabbits by 60%. After 2 months, these vessels exhibited no compensatory enlargement. In contrast, the same procedure performed in 5- to 6-week-old weanling rabbits resulted in accelerated growth of the vessels: diameters exceeded those of control arteries by 19% after 2 months. Common carotid arteries in adult rabbits remodeled to produce a diameter reduced by 23% when blood flow was reduced by 63% by external carotid ligation. This adaptation restored shear stress exerted on the vessel wall to control levels. The reduced diameter was not reversed when the vessels were maximally dilated with nitroprusside, adenosine, and forskolin; however, normal diameters were restored within 1 week when normal blood flows were reestablished. Thus, the adult arteries did not respond to increased blood flow produced by the anastomosis, but this procedure did reverse adaptations to decreased flow. In contrast, immature arteries were responsive to this increase in blood flow, even in the absence of prior flow modulation.     

Vessel tortuousity and reduced vascularization in the fetoplacental arterial tree after maternal exposure to polycyclic aromatic hydrocarbons

Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous environmental pollutants and the main toxicants found in cigarettes. Women are often exposed to PAHs before pregnancy, typically via prepregnancy smoking. To determine how prepregnancy exposure affects the fetoplacental vasculature of the placenta, we exposed female mice to PAHs before conception, perfused the fetoplacental arterial trees with X-ray contrast agent, and imaged the vasculature ex vivo by microcomputed tomography (micro-CT) at embryonic day 15.5. Automated vascular segmentation and flow calculations revealed that in control trees, <40 chorionic plate vessels (diameter>180 μm) gave rise to ～1,300 intraplacental arteries (50-180 μm), predicting an arterial vascular resistance of 0.37±0.04 mmHg·s·μl(-1). PAH exposure increased vessel curvature of chorionic plate vessels and significantly increased the tortuousity ratio of the tree. Intraplacental arteries were reduced by 17%, primarily due to a 27% decrease in the number of arteriole-sized (50-100 μm) vessels. There were no changes in the number of chorionic vessels, the depth or span of the tree, the diameter scaling coefficient, or the segment length-to-diameter ratio. PAH exposure resulted in a tree with a similar size and dichotomous branching structure, but one that was comparatively sparse so that arterial vascular resistance was increased by 30%. Assuming the same pressure gradient, blood flow would be 19% lower. Low flow may contribute to the 23% reduction observed in fetal weight. New insights into the specific effects of PAH exposure on a developing arterial tree were achieved using micro-CT imaging and automated vascular segmentation analysis.