Analysis of all possible combinations of four measurements determining true propagation in arteries

All possible combinations of four measurements of blood pressure, blood flow and vascular diameter are examined by transmission-line theory. It is found that only nine measurement combinations can give the attenuation coefficient γ, reflection coefficient R and characteristic impedance Z₀ simultaneously. At least one pressure measurement must be included. Their general expressions with arbitrary measuring locations are presented, together with some simplified forms which cover all the previous methods. A greater choice of method is thereby made available for use in practice. The results show that, regardless of the measurement locations, all combinations can be solved in the order γ first, R second and Z₀ last.     

Energy dissipation and pulse wave attenuation in the canine carotid artery

This paper presents methods for calculating, for a segment of artery in vivo, (1) viscous and viscoelastic energy dissipation as a function of time, and (2) the viscous and viscoelastic components of the frequency-dependent attenuation coefficient. The calculations require measurement of arterial diameter and of intra-arterial pressure and flow-rate at two sites along the vessel. Viscous energy dissipation is calculated from the radius-dependent velocity shear in the lumen given by linear theory from the pressure measurements. The attenuation coefficient for a given harmonic of heart rate is calculated as half the sum of the viscous and viscoelastic components at that frequency of the energy dissipated per unit length by forwardtravelling waves, divided by the forward-wave flow work input to the segment at that frequency. Measurements in canine carotid arteries indicate that wall viscoelasticity contributes relatively little to energy dissipation per cardiac cycle and pulse wave attenuation.     

Possible sources of discrepancy between sphygmomanometer cuff pressure and blood pressure quantified in a collapsible-tube analogue.

This paper examines the assumption that the audible events detected as Korotkov sounds in sphygmomanometry occur when blood pressure equals arm-cuff pressure. Several effects that contribute to discrepancy between these pressures are quantified using an idealised arm-and-cuff system consisting of a thick-walled collapsible tube subject to external compression along a central part of its length. The effects studied are (1) transverse pressure difference, resulting from tissues sustaining a part of the external compression through (a) circumferential bending stiffness and (b) longitudinal curvature of the tensed localised neck at the site of initial collapse, (2) longitudinal pressure difference between upstream pressure and pressure at the collapse point due to both (a) viscous and (b) inertial pressure drop. These effects are found to compensate partially for each other; the pressure within the vessel at the collapse point is less than the cuff pressure, but is also less than the blood pressure at the upstream end of the cuff. All four of the contributing terms increase proportionally to the flow-rate raised to a power greater than one, except the viscous pressure drop. Owing to a progressive shortening of the collapsed neck as flow-rate increases, the viscous term is almost independent of the flow-rate. The overall discrepancy displays less flow-rate dependency and is smaller than some of the terms which contribute to it. This means that considerable accuracy is needed if measurements of the effects are to be used to correct the raw data on cuff pressure at the time of Korotkov sound emission so as to obtain an improved estimate of the blood pressure.     

Experimental measurements of the temperature variation along artery-vein pairs from 200 to 1000 microns diameter in rat hind limb

Theoretical studies have indicated that a significant fraction of all blood-tissue heat transfer occurs in artery-vein pairs whose arterial diameter varies between 200 and 1000 microns. In this study, we have developed a new in vivo technique in which it is possible to make the first direct measurements of the countercurrent thermal equilibration that occurs along thermally significant vessels of this size. Fine wire thermocouples were attached by superglue to the femoral arteries and veins and their subsequent branches in rats and the axial temperature variation in each vessel was measured under different physiological conditions. Unlike the blood vessels < 200 microns in diameter, where the blood rapidly equilibrates with the surrounding tissue, we found that the thermal equilibration length of blood vessels between 200 microns and 1000 microns in diameter is longer than or at least equivalent to the vessel length. It is shown that the axial arterial temperature decays from 44% to 76% of the total core-skin temperature difference along blood vessels of this size, and this decay depends strongly on the local blood perfusion rate and the vascular geometry. Our experimental measurements also showed that the SAV venous blood recaptured up to 41% of the total heat released from its countercurrent artery under normal conditions. The contribution of countercurrent heat exchange is significantly reduced in these larger thermally significant vessels for hyperemic conditions as predicted by previous theoretical analyses. Results from this study, when combined with previous analyses of vessel pairs less than 200 microns diameter, enable one estimate the arterial supply temperature and the correction coefficient in the modified perfusion source term developed by the authors.     

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.     

Simulation of a chain of collapsible contracting lymphangions with progressive valve closure

The aim of this investigation was to achieve the first step toward a comprehensive model of the lymphatic system. A numerical model has been constructed of a lymphatic vessel, consisting of a short series chain of contractile segments (lymphangions) and of intersegmental valves. The changing diameter of a segment governs the difference between the flows through inlet and outlet valves and is itself governed by a balance between transmural pressure and passive and active wall properties. The compliance of segments is maximal at intermediate diameters and decreases when the segments are subject to greatly positive or negative transmural pressure. Fluid flow is the result of time-varying active contraction causing diameter to reduce and is limited by segmental viscous and valvular resistance. The valves effect a smooth transition from low forward-flow resistance to high backflow resistance. Contraction occurs sequentially in successive lymphangions in the forward-flow direction. The behavior of chains of one to five lymphangions was investigated by means of pump function curves, with variation of valve opening parameters, maximum contractility, lymphangion size gradation, number of lymphangions, and phase delay between adjacent lymphangion contractions. The model was reasonably robust numerically, with mean flow-rate generally reducing as adverse pressure was increased. Sequential contraction was found to be much more efficient than synchronized contraction. At the highest adverse pressures, pumping failed by one of two mechanisms, depending on parameter settings: either mean leakback flow exceeded forward pumping or contraction failed to open the lymphangion outlet valve. Maximum pressure and maximum flow-rate were both sensitive to the contractile state; maximum pressure was also determined by the number of lymphangions in series. Maximum flow-rate was highly sensitive to the transmural pressure experienced by the most upstream lymphangions, suggesting that many feeding lymphatics would be needed to supply one downstream lymphangion chain pumping at optimal transmural pressure.     

Structure-function relationships in the pulmonary arterial tree

Knowledge of the relationship between structure and function ofthe normal pulmonary arterial tree is necessary for understanding normal pulmonary hemodynamics and the functional consequences of thevascular remodeling that accompanies pulmonary vascular diseases. In aneffort to provide a means for relating the measurable vascular geometryand vessel mechanics data to the mean pressure-flow relationship andlongitudinal pressure profile, we present a mathematical model of thepulmonary arterial tree. The model is based on the observation that thenormal pulmonary arterial tree is a bifurcating tree in which theparent-to-daughter diameter ratios at a bifurcation and vesseldistensibility are independent of vessel diameter, and although theactual arterial tree is quite heterogeneous, the diameter of eachroute, through which the blood flows, tapers from the arterial inlet toessentially the same terminal arteriolar diameter. In the model theaverage route is represented as a tapered tube through which the bloodflow decreases with distance from the inlet because of the diversion offlow at the many bifurcations along the route. The taper and flowdiversion are expressed in terms of morphometric parameters obtainedusing various methods for summarizing morphometric data. To help putthe model parameter values in perspective, we applied one such methodto morphometric data obtained from perfused dog lungs. Modelsimulations demonstrate the sensitivity of model pressure-flowrelationships to variations in the morphometric parameters. Comparisonsof simulations with experimental data also raise questions as to the"hemodynamically" appropriate ways to summarize morphometric data.     

Microvessel diameter estimation: error bias correction of serial measurements

The assessment of vessel patency can be substantially improved by serial microvessel diameter measurements taken successively along an extensive length of the vessel. It is possible to avoid making the a priori assumptions about the existence or location of local constriction sites implicit in single diameter measurements. The problem then becomes one of making sense of tens or hundreds of measurements for each vessel. Equivalent diameter is defined here as as the diameter of a uniform circular cylinder of the same length as the original vessel, and having the same total resistance. Direct computation of the equivalent diameter, without taking measurement errors into account, leads to an underestimation of the true equivalent diameter even if the individual diameter measurements were not biased. We have developed a method for effectively eliminating this bias. It has been applied to serial microvessel diameter measurements of the guinea pig cochlea, automatically measured using an image analysis system. In this report, the results were developed for diameter estimates with an approximate gaussian distribution; however the method is readily extended to other error distributions. Convergence of the bias compensation was rapid. Use of the new method is advisable with as few as three diameter estimates per vessel.     

Determination of oxygen saturation and hematocrit of flowing human blood using two different spectrally resolving sensors.

The blood parameters oxygen saturation and hematocrit were determined by two different spectral sensors using reflectance spectra from 550 to 900 nm and partial transmission spectra centered at 660 nm. The spectra were analyzed by the method of partial least squares. One sensor consists of a miniature integrating sphere, while the other was fiber-guided. The results show that the geometry of the sensors and different blood flows do not influence the spectral analysis significantly. Independent of the sensor geometry, both hematocrit and oxygen saturation could be determined with an absolute predicted root mean square error of less than 3%. Furthermore, the analysis showed that hematocrit prediction requires eight wavelength regions and oxygen saturation prediction requires four wavelength regions using reflectance spectroscopy. This implies that if the measurement is restricted to reflectance, a spectrometer is indispensable for determining both blood parameters. Hematocrit determination could be improved using reflectance measurements in combination with transmission.     

Pulse Wave Velocity Testing in the Baltimore Longitudinal Study of Aging

Carotid-femoral pulse wave velocity is considered the gold standard for measurements of central arterial stiffness obtained through noninvasive methods¹. Subjects are placed in the supine position and allowed to rest quietly for at least 10 min prior to the start of the exam. The proper cuff size is selected and a blood pressure is obtained using an oscillometric device. Once a resting blood pressure has been obtained, pressure waveforms are acquired from the right femoral and right common carotid arteries. The system then automatically calculates the pulse transit time between these two sites (using the carotid artery as a surrogate for the descending aorta). Body surface measurements are used to determine the distance traveled by the pulse wave between the two sampling sites. This distance is then divided by the pulse transit time resulting in the pulse wave velocity. The measurements are performed in triplicate and the average is used for analysis.     

Numerical study to evaluate the effect of a surface-based sensor on arterial tonometry

Abstract

Arterial tonometry is a widely used non-invasive blood pressure measurement method. In contrast to the cuff-based method, it is possible to obtain a continuous pressure profile with respect to systolic and diastolic pressures using this method. However, due to a requirement of arterial tonometry—that a sensor needs to be placed directly above a blood vessel—placement error is inevitable if the measurement device is only capable of measuring local regions. This study assumed that the plate sensor is flexible, thus reducing the placement error. We investigated the pressure distribution along the wrist surface rather than the local region through the contact simulation between the flexible plate sensor and the wrist. As a result, we concluded that there is a unique pressure distribution for any specific wrist, regardless of the length and position of the plate, and that it is possible to measure the blood pressure using the response at the wrist surface to the pressure inside the radial artery.     

Method of studying the reactions of single vessels in situ

A new method of continuous measurement of vascular resistance has been proposed for studying the reactivity of single blood vessels. According to the method, blood flows through the artery, then through a rigid tube, serving as a reference resistance, and a flow control system and then returns back to the animal. The parameter of interest is pressure drop along the artery to reference resistance ratio. The method permits the study of practically intact vessels with diameters to 0.3 mm. Changes in blood viscosity have but a slight effect on the results of the measurement.     

Criteria for set point estimation in the volume clamp method of blood pressure measurement.

When blood pressure is measured in the finger using the volume clamp method the value at which the vascular volume is clamped is of crucial importance. Since the discovery of the method, several criteria of finding a correct set point have been elaborated: 1. The volume oscillations reach their maximum amplitude at cuff pressure equalling mean blood pressure. 2. The form of the diastolic portion of volume pulsations changes if the cuff pressure moves around the mean blood pressure. 3. The set point can be positioned at one third of the arterial volume. 4. The dynamic vascular compliance (DVC) may be continuously measured as the instantaneous amplitude of vascular volume oscillations is elicited by a relatively small and rapid vibration of the cuff pressure. The shape of the DVC pulse characteristically depends on the transmural pressure (TP): at negative TP (cuff pressure exceeding the blood pressure) it shows a distinct positive systolic peak, at positive TP the polarity of the DVC pulse is reversed. In contrast to the first three ways to find the set point, the last one may operate even in closed-loop performance, i.e. during the blood pressure measurement.     

Flow-induced control of arterial lumen

Blood flow velocity is a factor that affects the diameter of arteries. In order to investigate the flow-induced arterial dilatation, the outer diameter of the femoral, common carotid or renal arteries of anaesthetized cats was measured during perfusion of these arteries with blood or plasma-substituting solutions under conditions of stabilized perfusion pressure. It has been shown that, whatever the perfusate, blood or a substituent, an increase in flow makes the artery to dilate. Consequently, the flow-induced dilatation is not due to any blood-borne humoral factor. As an increase in the solution's viscosity causes dilatation even at constant flow-rate and pressure in the artery, the effect is to be ascribed to the ability of the vascular wall to perceive shear stress. As far as removal of endothelium eliminates the dilatation evoked by increasing flow or fluid viscosity, it may be concluded that the flow-induced dilatation is due to the sensitivity to shear stress of the endothelium.     

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.     

A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network

To quantitatively assess the arteriovenous distribution of hemodynamic parameters throughout the microvascular network of the human retina, we constructed a retinal microcirculatory model consisting of a dichotomous symmetric branching system. This system is characterized by a diameter exponent of 2.85, instead of 3 as dictated by Murray’s law, except for the capillary networks. The value of 2.85 was the sum of a fractal dimension (1.70) and a branch exponent (1.15) of the retinal vasculature. Following the feeding artery (central retinal artery), each bifurcation was recursively developed at a distance of an individual branch length [L(r) = 7.4r ^1.15] by a centrifugal scheme. The venular tree was formed in the same way. Using this model, we evaluated hemodynamic parameters, including blood pressure, blood flow, blood velocity, shear rate, and shear stress, within the retinal microcirculatory network as a function of vessel diameter. The arteriovenous distributions of blood pressure and velocity in the simulation were consistent with in vivo measurements in the human retina and other vascular beds of small animals. We therefore conclude that the current theoretical model was useful for quantifying hemodynamics as a function of vessel diameter within the retinal microvascular network.     

Flow and pressure distributions in vascular networks consisting of distensible vessels

We examine the influence of vessel distensibility on the fraction of the total network flow passing through each vessel of a model vascular network. An exact computational methodology is developed yielding an analytic proof. For a class of structurally heterogeneous asymmetric vascular networks, if all the individual vessels share a common distensibility relation when the total network flow is changed, this methodology proves that each vessel will continue to receive the same fraction of the total network flow. This constant flow partitioning occurs despite a redistribution of pressures, which may result in a decrease in the diameter of one and an increase in the diameter of the other of two vessels having a common diameter at a common pressure. This theoretical observation, taken along with published experimental observations on pulmonary vessel distensibilities, suggests that vessel diameter-independent distensibility in the pulmonary vasculature may be an evolutionary adaptation for preserving the spatial distribution of pulmonary blood flow in the face of large variations in cardiac output.     

Optimizing cell-anatomical chronologies of Scots pine by stepwise increasing the number of radial tracheid rows included—Case study based on three Scandinavian sites

Cell-anatomical studies are a fast growing branch of dendrochronology, since they promise additional environmental proxy information with high temporal resolution. It is unclear, however, how many radial files of tracheids have to be considered to establish reliable wood anatomical time series for conifer species. Here, we investigate this question for four common cell-anatomical variables (cell-wall thickness, lumen area, lumen diameter and cell diameter) in Scots pine using examples from three Scandinavian sites. Cell-anatomical time series averaged from six measurement paths can reach the 90% confidence level of ten measurement paths at all sites. While lumen area generally required the most measurement paths in other cell-anatomical variables, cell-wall thickness required the least measurement paths.     

Design and evaluation of a device for measurement of interface pressure

An electropneumatic device has been designed to measure the interface pressure profile under compression bandages. The device uses commercially available pneumatic sensors (Talley Group Ltd, SJ235/3) and measures interface pressure at up to eight sites simultaneously along the lower limb, with an accuracy of ± 3 mmHg. Measurements can be made in one of two modes: continuously at a rate of up to three samples per second with the results output to a suitable display device, or single measurements of interface pressure can be made and displayed on a digital display incorporated in the device. This enables the monitoring and recording of interface pressure under compression bandages during either ambulation or passive recumbency. The electropneumatic system is described together with its following characteristics: the hysteresis of the Talley pneumatic sensors, the accuracy of pressure measurement and the maximum achievable sample rate. Dynamic measurements in a single normal volunteer are shown.     

Evaluation of a new tail-cuff method for blood pressure measurements in rats with special reference to the effects of ambient temperature

We evaluated a recently developed tail-cuff apparatus for the indirect blood pressure measurement in rats with special reference to the effects of ambient temperature. For this purpose, we designed two preparations 1) an intact preparation to determine the effect of ambient temperature on blood pressure measurements and 2) an anesthetized and catheterized preparation for comparison of the values of blood pressure obtained by the indirect and by the direct method. This apparatus also required enough pulse volume oscillations to measure the accurate value of blood pressure. Sufficient pulse volume oscillations were obtained within 20 min at 30 and 40 degrees C. At 40 degrees C, the values of blood pressure, pulse rate and rectal temperature were significantly higher than those at 30 degrees C. Correlation between blood pressure and rectal temperature was significant, and blood pressure increased with rectal temperature dependently. The values of the indirect measurement were close to the values measured directly, and these correlations were highly significant. Thus, we showed the effects of temperature for indirect blood pressure measurement. This tail-cuff apparatus could measure the accurate value of indirect blood pressure without thermal stress at 30 degrees C.