Use of fluorescently labeled erythrocytes and digital cross-correlation for the measurement of flow velocity in the cerebral microcirculation.
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Animals↗
Biomedical subjects
A G Hudetz
Publications and source records attributed to A G Hudetz.
Spontaneous flow oscillations in the cerebral cortex during acute changes in mean arterial pressure.
The purpose of this study was to characterize spontaneous oscillations of blood flow in the cerebral cortex of anesthetized rats under control conditions and after mean arterial pressure was altered by various means. Blood flow was monitored using a laser-Doppler flowmeter through the closed cranium. Spontaneous flow oscillations with amplitudes of 14-30% of the mean flow and frequencies of 4-11 cycles/min were recorded when arterial pressures were less than 90 mm Hg. Stepwise hemorrhagic hypotension and unilateral carotid occlusion increased the amplitude of oscillations. The amplitude of oscillations was negatively correlated with the level of mean arterial pressure after manipulation with norepinephrine or sodium nitroprusside. The oscillations were reversibly abolished during dilation of the cerebral circulation by elevating the inspired carbon dioxide content to 5%. The frequency of flow oscillations was very stable during all of the above maneuvers except during the infusion of norepinephrine, which increased the oscillation frequency slightly. The results suggest that flow oscillations are determined primarily by cerebral arterial pressure.
Animals↗
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.
Capillaries↗
A semi-empirical model of apparent blood viscosity as a function of vessel diameter and discharge hematocrit.
A semi-empirical model is developed to describe the dependence of apparent viscosity of blood on vessel diameter (2.7 to 500 microns) and vessel discharge hematocrit (5% to 60%). The blood flow is modeled as a cell-rich core and a cell-free marginal layer in the larger vessels and an axial-train in the smaller vessels. Laminar (Poiseuille) flow is assumed in all cases. An equation is derived in which apparent viscosity is a function of vessel diameter, core viscosity, and width of marginal layer. This is then complemented by empirical equations in which core viscosity varies exponentially with discharge hematocrit while the width of marginal layer varies linearly with discharge hematocrit. The model correlates well with several sets of experimental data and behaves according to the Fahraeus-Lindqvist effect. Predicted apparent viscosity tends to the expected finite value for large vessel diameters. Dependence of apparent viscosity on vessel diameter is realistically smooth in the whole diameter range.
Blood Vessels↗
Dependence of cerebral capillary hematocrit on red cell flow separation at bifurcations: a computer simulation study.
The influence of preferential red cell entry into microvascular branches with higher flow on microvessel hematocrit distribution was studied by mathematical modeling in a reconstructed cerebrocortical microvascular network. More heterogeneous hematocrit distribution was obtained at stronger cell partitioning. Small variations in the cell separation parameter resulted in significantly different hematocrit distributions. The significance of these findings in vivo should be further evaluated.
Animals↗
Computer simulation of cerebral microhemodynamics.
Microvascular network hemodynamics was simulated by computer in an anatomically reconstructed cerebral microvascular network. A video microscope system was used for three-dimensional mapping of the vessel network in the rat brain cortex. The complete topology, length and mean diameter of the microvessels were determined. The distribution of blood flow and red cell flux in the network was calculated based on vessel resistance estimated from geometrical data and a rheological model of blood. This model described apparent relative blood viscosity as a function of vessel diameter and local discharge hematocrit. The calculations predicted highly heterogeneous cell flux distribution at any feed hematocrit between 10 and 40 percent. The frequency distribution of microvessel hematocrit was bimodal and included values exceeding the feed hematocrit value. A probabilistic simulation of cell transit resulted in transit time distributions which agree with experimental findings. The most probable transit time and capillary path length and 4s and 300 microns, respectively.
Animals↗
Mathematical analysis of network topology in the cerebrocortical microvasculature.
The three-dimensional branching pattern of deep cerebrocortical capillary networks was reconstructed from histological sections. The distribution of blood flow in a mathematical model of the reconstructed network was calculated. The transit of red blood cells through the network was simulated by computer, and the total path length traveled by the cells was estimated. The results support both anatomical and hemodynamic heterogeneity of the cerebrocortical microvascular system.
Animals↗
The role of tissue acidosis in ischaemic tissue injury: the concept of the pH integral.
Cerebral cortical tissue pH was monitored with an extracellular glass electrode in 32 rats subjected to total global cerebral ischaemia produced by ligation of the basilar and carotid arteries with systemic hypotension for periods of 8 to 60 min. The totality of the ischaemia, and its duration were confirmed by monitoring with a brain tissue O2 electrode. Reperfusion was induced by hypertension and maintained thereafter to exclude delayed ischaemia during 3 h survival after which the rats were sacrificed by perfusion fixation. The severity of tissue pH change was varied by inducing hyperglycaemia in some of the rats. Quantitative counts were made of neurons demonstrating changes reflecting severe ischaemic injury within 500 microns of the electrode tip. For the criterion of an ischaemically injured neuron count greater than 20%, there appeared to be a threshold at about 30 min, and more than 0.8 units change in pH. For quantitative assessment of the ischaemic insult a more satisfactory index was found by combining both time and acidosis as the integral of the pH change during the period of ischaemia. This was found to have a strong correlation with the histologic changes. There was a less strong correlation between the acidosis during reperfusion and the histologic change. Comparing these results with those for 3 rats subjected to 215 min of ischaemia without reperfusion, it appears that most of the effect of acidosis in aggravating ischaemic injury takes place during the first hour of ischaemia with little further aggravation for longer periods.
Acidosis↗
Pressure distribution in the pial arterial system of rats based on morphometric data and mathematical models.
The objective of the present work was a theoretical evaluation of pial arterial pressures in normotensive rats and spontaneously hypertensive rats based on the geometry and topography of the pial arterial system as well as on various topological models of the vascular trees. Pial branches of the middle cerebral artery in the diameter range of 30-320 microns were selectively visualized by corrosion compound, and the diameter and length of vascular segments were measured. The vessels were classified into branching orders by the methods of Horsfield and Strahler. The steady-state pressure distribution in the pial arterial system was calculated assuming that the flow at the bifurcations was partitioned in proportion to a given power of the diameters of the daughter branches (diameter exponent). The maximum number of vascular segments along the longest branch varied between 16 and 33. The mean branching ratio was 4.14 +/- 0.23 (SD). The mean diameter of vessels classified into Strahler orders 1-5 were: 50 +/- 12, 71 +/- 19, 106 +/- 22, 168 +/- 22, and 191 +/- 7 microns, respectively. The calculated pressure drop in the pial trees of normotensive rats was approximately twice as large in proximal orders 3 and 4 than in distal orders 1 and 2. The mean pressure in arteries of order 1 ranged from 54.4 to 58.4 mm Hg in the normotensive rat (input pressure: 83 mm Hg), and from 77.2 to 89.0 mm Hg in the spontaneously hypertensive rat (input pressure: 110 mm Hg). The coefficient of variation of terminal pressures in vessels of order 1 increased linearly with the mean pressure drop in the system. The coefficient of variation in terminal pressure had a minimum as a function of the diameter exponent in case of each pial tree. At its minimum, it was higher in all spontaneously hypertensive rats (10.1-22.9%) than in any normotensive rats (6.0-8.5%). The corresponding diameter exponents were in most cases lower in the spontaneously hypertensive rat (1.3-2.5) than in the normotensive rat (2.5-3.0). Topologically consistent models of the pial arterial network predicted significantly less variation in intravascular pressures than was obtained by direct calculations. More idealized models suggested the dependence of coefficient of variation in terminal pressure on the total number of vascular segments contained by the tree. All models predicted the existence of the minimum of coefficient of variation in terminal pressure in function of the diameter exponent.(ABSTRACT TRUNCATED AT 400 WORDS)
Animals↗
Percolation and transit in microvascular networks.
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Animals↗
A semi-empirical nonlinear viscoelastic model of the arterial wall.
A mathematical model was developed for the characterization of quasistatic nonlinear viscoelastic behaviour of large arteries with activated smooth muscle. Arteries were considered to belong to the class of viscoelastic materials with fading memory and the first order term of the integral polynomial constitutive equations of Pipkin and Rogers satisfying the nonlinear superposition principle was modified to handle responses to increasing and decreasing loads independently. The two creep functions contained by the obtained one dimensional constitutive equation were determined experimentally from the series of creep and recovery tests of increasing amplitude performed on isolated canine iliac arteries following the activation of the vascular smooth muscle by normal dose of norepinephrine in vitro. Utilizing the constitutive equation of the arterial wall and the tabulated values of creep functions successive stress-strain hysteresis loops of various constant stress rates were simulated by digital computer. The computed hysteresis loops demonstrated the main characteristics, such as the weak and asymmetric rate-sensitivity of the experimentally observed hysteresis of arteries qualitatively well, thus allowing certain conclusions on the mechanism of quasistatic viscoelastic behaviour of vascular smooth muscle.
Animals↗
Changes in regional cerebrovascular resistance during partial cerebral ischemia in rats.
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Animals↗
A viscoelastic model of mechanically induced and spontaneous contractions of vascular smooth muscle.
A new viscoelastic model was developed for the mathematical characterisation of mechanically induced and intrinsic contractional responses of the vascular smooth muscle. To this end, the elastic and viscous analogue elements were supplemented with a new active element generating stress proportional to its momentary elongation. The four-element model consisting of an active element, a parallel viscous element and both series and parallel elastic elements predicted biphasic or damped oscillatory stress relaxation and creep responses which were similar to that found experimentally earlier. Above a certain exciting frequency the model exhibited dissipative and below energy producing behaviour, as indicated by the sign change of the hysteresis loop area. In the case of sinusoidal modulation of the stress generation parameter the model showed parametric resonance, which was regarded as a simulation of intrinsic oscillation of the smooth muscle.
Elasticity↗
Distribution of blood flow in partially closed cerebral capillary networks.
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Animals↗
Transient focal ischemia in subhuman primates. Neuronal injury as a function of local cerebral blood flow.
Unilateral, transient (30, 60, and 120 minutes (min)) middle-cerebral-artery (MCA) occlusion was induced via transorbital craniotomy in 11 waking subhuman primates. Local cerebral blood flow (LCBF) was calculated from hydrogen clearance curves obtained through the use of intracerebral platinum microelectrodes. Unilateral MCA occlusion decreased LCBF in the territory of the ipsilateral MCA. Within minutes of the arterial occlusion all monkeys developed contralateral neurologic deficits that began disappearing three hours (h) after reopening the MCA. Regional ischemia, followed by 24 h of reperfusion, produced varying degrees of tissue vacuolation which correlated (r = 0.60, p less than 0.01, n = 49) with the percent reduction in LCBF multiplied by the occlusion time. Neurons were classified according to the structural features of their perikaryon. A plot of neuron types versus percent vacuolation suggested that normal neurons become increasingly scalloped under increasingly severe ischemic conditions. The number of scalloped neurons decreased precipitously in areas of marked sponginess coincident with the appearance of irreversibly damaged neurons. Local tissue edema values exceeding 30% correlated with irreversible injury to all neurons in the same area. Regional cerebral ischemia of increasing severity was acompanied by increasing numbers of lethally injured neurons.
Animals↗
Biomechanical properties of normal and fibrosclerotic human cerebral arteries.
Quasi-static passive mechanical properties of histologically fibrosclerotic and normal groups of human anterior cerebral arteries (ACA) and internal carotid arteries (ICA) were studied in vivo. Cylindrical arterial segments were subjected to slow, cyclic inflation by air in the range of 5-250 mm Hg intraluminal pressure at axial isometry. To characterize mechanical properties, incremental elastic modulus, incremental distensibility and strain energy density were computed from the continuously recorded pressure-external diameter curves. Compared to normal arteries, at identical intraluminal pressures, the elastic modulus of fibrosclerotic arteries was found to be 34-45% lower in ACA and 40-56% lower in ICA, and the radius to wall thickness ratio was 25-30% smaller in ACA and 37-38% smaller in ICA. Distensibility of fibrosclerotic arteries was not smaller than that of the normal vessels. There were no significant differences in internal radius and in strain energy density between the fibrosclerotic and normal groups. Results of mathematical modelling suggests that the observed decrease in the elastic modulus of fibrosclerotic arteries was accompanied by different types of structural reorganization in the case of ACA and ICA. It is supposed that changes in mechanical properties of the passive wall elements have a compensatory character to restore some hemodynamically important properties of fibrosclerotic arteries, namely tangential stress, incremental distensibility or characteristic impedance.
Arteriosclerosis↗
Characterization of anisotropic elastic properties of the arteries by exponential and polynomial strain energy functions.
Three-dimensional quasi-static mechanical measurements were carried out on cylindrical segments of the dog carotid and iliac arteries for determination of the passive anisotropic elastic properties of the vessel wall. On the basis of passive characteristics of outer diameter vs. intraluminal pressure, and axial extending force vs. intraluminal pressure, picked up at various fixed initial vascular length values, the incremental Young moduli and poisson ratios of the vessel wall were calculated in the 0--33 kPa (0--250 mm Hg) pressure range. The strain energy function of the arteries was approximated by polynomial and exponential models. We found that an exponential energy function with 4-parameters gives more accurate results than the 7- or 12-parameter polynomial functions. According to the results the axial modulus reaches higher values than the tangential and radial moduli at a low tangential stretch level, while at high tangential stretch the tangential modulus is the highest in both carotid and iliac arteries. After elevation of the initial tangential stretch the increase in the tangential modulus is the most pronounced, while the values of radial and axial moduli increased less. A change in the initial axial stretch influences the axial and radial moduli to a similar extent, but has no substantial effect on the value of the tangential modulus. The values of corresponding poisson ratios depend in a similar way on the initial deformation state. The different behaviour of the two Poisson ratios characterizing the mechanical coupling between tangential and axial directions, indicates that the structural coupling between the two main directions is asymmetrical. It is assumed that this property of the passive vascular structure can be explained by the network arrangement of collagen fibres in the vessel wall.
Animals↗
The effect of smooth muscle activation on the mechanical properties of pig carotid arteries.
The contractile properties and the effect of contraction on the mechanical properties of noradrenaline (0.5 micrograms/ml) activated smooth muscle of cylindrical segments of porcine carotid arteries were studied in vitro under quasi-static pressure loading. Maximum tangential isometric stress developing in the vessel wall was 4.4 +/- 0.6 X 10(5) dyn/cm2. Incremental elastic modules of activated smooth muscle, calculated for total wall cross sectional area, was 4.6 +/- 2.7 X 10(6) dyn/cm2, whereas the value computed for estimated smooth muscle thickness was 9.8 +/- 14.8 X 10(6) dyn/cm2. During smooth muscle activation maximum increase of strain-energy density of the vessel wall was 6.8 +/- 1.2 X 10(4) dyn/cm2 under isometric conditions and 25 +/- 3% increase occurred under isobaric conditions. Isobaric diameter response was only 2--4% in the physiological pressure range (100--150 mmHg) while the incremental elastic modulus decreased by 40 +/- 3% and distensibility increased by 80 +/- 10% under isobaric conditions. Smooth muscle activation induced a 19 +/- 2% maximum decrease of characteristic impedance, and a rather a uniform 14--15% decrease in the impedance was observed in the 100--150 mmHg pressure range. The obtained results show that the control of distensibility and elastic modulus in smooth muscle is most efficient in the physiological pressure range under in vitro conditions. It is assumed that in vivo in addition to vascular diameter the most important controlled parameters are the distensibility and characteristic impedance of the large arteries.
Animals↗