Cross-Sectional Shape of Collapsible Tubes

In order to quantify the collapse phenomenon in veins, this paper presents a mathematical analysis of the cross-sectional shape of a flexible tube as its internal pressure varies. Quantitative results are presented in terms of the physical parameters of the tube, such as wall thickness and Young's modulus. It is assumed that the tube is thin walled, that no stretching occurs, that the cross-sectional shape is elliptical when the transmural pressure is zero, and that the longitudinal prestress is zero. The equations were solved on a digital computer which displayed the cross-sectional shapes on an oscilloscope, which were then photographed. A selection of these photographs is presented. Curves are shown which give the cross-sectional area and compliance as functions of transmural pressure. Other curves are shown which are useful for interpolation, and for use in the experimental determination of the physical parameters which may otherwise be difficult or impossible to measure accurately.     

Age-related changes in chest geometry during cardiopulmonary resuscitation

We studied alterations of chest geometry during conventional cardiopulmonary resuscitation in anesthetized immature swine. Pulsatile force was applied to the sternum in increments to determine the effects of increasing compression on chest geometry and intrathoracic vascular pressures. In 2-wk- and 1-mo-old piglets, permanent changes in chest shape developed due to incomplete recoil of the chest along the anteroposterior axis, and large intrathoracic vascular pressures were generated. In 3-mo-old animals, permanent chest deformity did not develop, and large intrathoracic vascular pressures were not produced. We propose a theoretical model of the chest as an elliptic cylinder. Pulsatile displacement along the minor axis of an ellipse produces a greater decrease in cross-sectional area than displacement of a circular cross section. As thoracic cross section became less circular due to deformity, greater changes in thoracic volume, and hence pressure, were produced. With extreme deformity at high force, pulsatile displacement became limited, diminishing pressure generation. We conclude that changes in chest geometry are important in producing intrathoracic intravascular pressure during conventional cardiopulmonary resuscitation in piglets.     

Blood vessel buckling within soft surrounding tissue generates tortuosity

The stability of blood vessel under lumen pressure load is essential to the maintenance of normal arterial function. Previous mechanical models showed that blood vessels may buckle into a half sine wave but arteries and veins in vivo often demonstrate tortuous paths with multiple waves. The objective of this study was to analyze the buckling of blood vessels under lumen pressure with surrounding tissue support. Blood vessels were modeled as elastic cylindrical vessels within an elastic substrate. Buckling equations were established to determine the critical pressure and the wavelength. These equations and simulation results demonstrated that blood vessels do take higher order mode shapes when buckling inside an elastic substrate while they take the basal mode shape without the substrate. The wave number increases i.e. blood vessels take a higher mode shape, as the stiffness of the substrate increases. These results suggest that mechanical buckling is a possible mechanism for the development of tortuous blood vessels. The current model provides a powerful tool for further studying the tortuosity of arteries and veins.     

Effect of respiratory gases on compliance of intrapulmonary arteries and veins

A method was developed that permitted changes in the pressure-volume characteristics of large intrapulmonary vessels occurring with changes in the composition of alveolar gas to be studied in excised lungs. The capillary bed was emptied by keeping intravascular pressure well below alveolar pressure, and the relationship between changes in the volume of the pulmonary arteries or veins with changes in transpulmonary pressure was measured. The volume of the arteries and veins always decreased with a decrease in transpulmonary pressure, but when the alveoli contained carbon dioxide, the decrease in vascular volume was less, for the same decrease in transpulmonary pressure, than when the alveoli contained oxygen or nitrogen without carbon dioxide. This change with carbon dioxide was probably due to a decrease in the compliance of the larger intrapulmonary arteries and veins. Since there was no pathway for carbon dioxide to enter these vessels except by diffusion from the alveoli, it is concluded that carbon dioxide can act directly on the intrapulmonary arteries and veins to reduce their compliance, but it is not known whether this effect has physiological significance. No effect on the large pulmonary vessels was found with variations in alveolar concentrations of oxygen. blood vesselsblood volumecarbon dioxidediffusionlungspulmonary circulation     

Structure and Stress-Strain Relationship of Soft Tissues

The mechanical properties of a soft tissue are related to itsstructure. Weshall illustrate this by the properties of thearteries and the lung. Viscoelasticity, strain rate effects,pseudo-elasticity, and constitutive equations ar discussed.The mecahnical properties of an organ is, however, not onlybased onthe tissues of the organ, but also on its geometry andrelationship to the neighboring organs. A typical example isthe blood vessel. The capillary blood vessels of the mesenteryare "rigid"; those in the bat's wing are "distensible"; whereasthe capillaries of the lung are "sheet" like: rigid in one plane,and compliant in another. The stress-strain relationship ofthe systemic arteries is highly nonlinear, stiffening exponentiallywith increasing strains; yet that of the pulmonary arteriesin the lung is linear. The systemic veins are easily collapsible;yet the pulmonary veins in the lung are not: they remain patentwhen the blood pressure falls below the alveolargas pressure.The explanation of these differences lies in the varied interactionsbetween the blood vessels and the surrounding tissues in differentorgans. The implications of these differences on blood circulationare pointed out. Therole of ultrastructure is discussed.     

Cross-sectional area of flexible tubes

Kresch (1977) presented the results of calculations which determined the cross-sectional shapes assumed by flexible, elastic tubes for varying transmural pressures. Extensions of these results are presented here in the form of graphs of the cross-sectional area as a function of the transmural pressure. Since the circumferential arc length, theX-axis intercept and theY-axis intercept were necessarily computed, and are of interest, graphs of these are also presented. Each graph is a composite of several curves. Each curve in the graph shows the behavior of the parameter as a function of the relative pressure (P) for a specific value ofR, a parameter related to the wall thickness. The curves are shown for both positive and negative values ofP. The most negative value ofP shown is the point where the walls touch and the most positive value shown is the point where the equations fail to converge. The cross sections were assumed to be elliptical when the transmural pressure was zero. Graphs for three of these initial shapes are shown: nearly circular, major-to-minor axis ratio equal to 2, and an intermediate case. For the nearly circular case, the curves divide into two regimes: one where stretching clearly predominates and another where bending clearly predominates. For the more eccentric initial cross-sections, the distinction between the two regimes cannot be made in this simple manner.     

Diameter and flow velocity changes in small pulmonary vessels due to microembolization

The pulmonary vascular bed was embolized with glass beads in small doses that induced no significant changes in pulmonary arterial pressure in anesthetized cats. We analyzed changes in internal diameter (ID), flow velocity, and volume flow of embolized and nonembolized arteries simultaneously with ID changes of small veins. In embolized arteries, with 180-, 300-, and 500-microns beads, ID constricted maximally in just proximal portions of the plug by 22, 23, and 17%, respectively, but with 840-microns beads, no ID constriction occurred. With 50-microns beads, the maximum ID constriction occurred in arteries of 200-300 microns but not in those of 100-200 microns. The constriction decreased in the upstream larger arteries and disappeared in those greater than 800 microns ID. In the nonembolized arteries no ID change occurred. Veins constricted slightly compared with arteries. By heparin pretreatment, ID constriction was slightly attenuated in arteries and was almost abolished in veins, whereas it was not affected with hexamethonium bromide. At a branching site, volume flow to an embolized artery decreased because of a decrease in ID and flow velocity, whereas volume flow to a nonembolized artery increased because of an increase in flow velocity. We concluded that pulmonary microembolization induced a vasoconstriction chiefly in small pulmonary arteries upstream to the plug. After embolization, blood flow was locally redistributed from an embolized to a nonembolized artery at a branching site. Arterial vasoconstriction may be mediated chiefly by local mechanical factors.     

Adrenoceptor function in the bovine pulmonary circulation

The bovine pulmonary vascular response to alpha- and beta-agonists was studied using an awake intact calf model. Pulmonary arterial pressure, pulmonary arterial wedge pressure, left atrial pressure, systemic arterial pressure, and cardiac output were measured in response to 3 min infusions of isoproterenol (beta-agonist; 0.12, 0.24, 0.48, 0.9, and 1.8 micrograms X kg-1 X min-1) and phenylephrine (alpha-agonist, 0.15, 0.30, 0.60, 1.15, and 2.30 micrograms X kg-1 X min-1). Phenylephrine caused an increase in vascular resistance in the pulmonary arterial and venous compartments. The slope of the resistance in response to phenylephrine was greater in the pulmonary arterial than pulmonary venous circulation. Isoproterenol resulted in a dose-dependent decrease in vascular resistance in the pulmonary arteries and veins. The vascular resistance was decreased to the same level in the pulmonary arteries and veins although the arteries showed a greater percent change. In addition, isoproterenol infusion resulted in a transient decrease in arterial pH and increase in values for packed cell volume and haemoglobin.     

Adrenergic innervation of the large arteries and veins of the semiarboreal rat snake Elaphe obsoleta

Fluorescence histochemistry was used to study the adrenergic innervation of the large arteries and veins at six points along the body of the semiarboreal rat snake Elaphe obsoleta. Apart from the vessels adjacent to the heart, there was a marked contrast in the density of adrenergic innervation of anterior and posterior systemic arteries and veins. The anterior arteries and veins have little adrenergic innervation in contrast to the extremely dense innervation of the arteries and veins posterior to the heart. The innervation pattern is consistent with known physiological adjustments to gravity and suggests a mechanism for regulating dependent blood flow via sympathetic nerves. In comparison to the posterior systemic arteries, parallel segments of pulmonary artery taken from the same body position of Elaphe contained a much sparser innervation by adrenergic nerves. The sparser innervation can be correlated with less gravitational disturbance in the pulmonary artery, which is relatively short in this and in other arboreal snakes.     

What does inductance plethysmography really measure?

Inasmuch as it has been claimed that inductance plethysmography can measure cross-sectional area changes, we tested this assumption. We present experimental and computed relationships between self-inductance (L) of coils and areas (A) included inside for a coil with a well-defined side wavy pattern (triangular or sinusoidal) and for a real belt (Respitrace) placed on elliptical or rectangular configurations. The results are applied to the physiological field using measurements obtained from a computed tomography experiment. We demonstrate that the L-A relationships vary not only with shape or ellipticity of the cross section but also with the wavy pattern shape. This last parameter is critical because it is difficult to actually control. When the coil wavy pattern remains steady, there are some physiological situations where inductance plethysmography can more accurately estimate area changes: when the configuration shape is constant, the correspondence between delta L and delta A is almost linear with a shape-dependent sensitivity; when the configuration is nearly circular (ellipticity in the range 0.8-1), the relative error in delta A estimation is less than 5%.     

Measurements of mouse pulmonary artery biomechanics

BACKGROUND: Robust techniques for characterizing the biomechanical properties of mouse pulmonary arteries will permit exciting gene-level hypotheses regarding pulmonary vascular disease to be tested in genetically engineered animals. In this paper, we present the first measurements of the biomechanical properties of mouse pulmonary arteries. METHOD OF APPROACH: In an isolated vessel perfusion system, transmural pressure, internal diameter and wall thickness were measured during inflation and deflation of mouse pulmonary arteries over low (5-40 mmHg) and high (10-120 mmHg) pressure ranges representing physiological pressures in the pulmonary and systemic circulations, respectively. RESULTS: During inflation, circumferential stress versus strain showed the nonlinear "J"-shape typical of arteries. Hudetz's incremental elastic modulus ranged from 27 +/- 13 kPa (n = 7) during low-pressure inflation to 2,700 +/- 1,700 kPa (n = 9) during high-pressure inflation. The low and high-pressure testing protocols yielded quantitatively indistinguishable stress-strain and modulus-strain results. Histology performed to assess the state of the tissue after mechanical testing showed intact medial and adventitial architecture with some loss of endothelium, suggesting that smooth muscle cell contractile strength could also be measured with these techniques. CONCLUSIONS: The measurement techniques described demonstrate the feasibility of quantifying mouse pulmonary artery biomechanical properties. Stress-strain behavior and incremental modulus values are presented for normal, healthy arteries over a wide pressure range. These techniques will be useful for investigations into biomechanical abnormalities in pulmonary vascular disease.     

Micropuncture pressure in small arteries or veins of perfused rabbit lungs

Until now, direct micropuncture measurements of vascular pressure in lung have been limited to small vessels less than 100 microns on the pleural surface. On the other hand, direct pressure measurements using small catheters (less than 1-mm OD) in pulmonary vessels have been limited to those greater than 1.2 mm. We measured pressure in intermediate-sized microvessels (300-700 microns) using the micropuncture method in isolated perfused rabbit lungs. These microvessels are located 2 or 3 mm beneath the pleura. We exposed them by microsurgery and punctured the relatively thick-walled vessels with specially configured micropipettes. We exposed one pulmonary microvessel in each rabbit lung by microsurgery on the left middle lobe. In 15 rabbit lungs we measured pressure in a total of six small arteries (275- to 470-microns diam) and nine small veins (300- to 700-microns diam) under high zone 3 conditions, near the zone 2/3 boundary. We found approximately 35% of the total pulmonary vascular pressure drop in arteries greater than 275-microns diam and 7% in veins greater than 300-microns diam. In veins greater than 500-microns diam, there was no measurable pressure drop. After the measurements, we froze the lung and confirmed that there was no detectable interstitial or alveolar edema in the cross sections of the punctured site. Our data are compatible with those of other investigators who have used isolated perfused rabbit lungs under similar experimental conditions.     

Pressure and flow in the systemic arterial system

The dynamic characteristics of the proximal arterial system are studied by solving the nonlinear momentum and mass conservation equations for pressure and flow. The equations are solved for a model systemic arterial system that includes the aorta, common iliacs, and the internal and external iliac arteries. The model includes geometric and elastic taper of the aorta, nonlinearly elastic arteries, side flows, and a complex distal impedance. The model pressure wave shape, inlet and outlet impedance, wave travel, and apparent wave velocity compare favorably with the values measured on humans. Calculations indicate that: (i) reflections are the major factor determining the shape and distal amplification of the pressure wave in the arterial tree; (ii) although important in attenuating the proximal transmission of reflecting waves, geometric taper is not the major cause of the distal pressure wave amplification; (iii) the dicrotic wave is a result of peripheral reflection and is not due to the sudden change in flow at the end of systole; (iv) the elastic taper and nonlinearity of the wall elasticity are of minor significance in determining the flow and pressure profiles; and (v) in spite of numerous nonlinearities, the system behaves in a somewhat linear fashion for the lower frequency components.     

Structural and functional characteristics of the special regulatory devices in the peripheral pulmonary circulation in rabbits

The present study intended to describe in detail the several blood vessels harboring special regulatory devices in rabbit’s pulmonary tissue using light and electron microscopy and immuno-histochemistry. Numerous throttle arteries were recorded within the adventitia of the segmental and sub-segmental bronchi and within pulmonary pleura. These arteries showed characteristic narrow or obliterated lumens and some of them bear longitudinal muscular intimal bolsters. For the first time, TEM revealed some structural modifications of the vascular endothelial cells of these arteries indicating that they become more activated to perform some additional functions. Arteriovenous anastomoses (AVAs) including direct shunt vessels and glomus organs were also recognized. Direct arteriovenous shunts appeared as small connecting devices communicating between small arteries and small veins while glomus organs consisted of the tortuous glomus vessels and the related afferent and efferent vessels. Several arteries and veins showing unique unusual structural characteristics were also described. For the first time, serotonin (5-HT) was strongly expressed in the vascular endothelium and muscle fibers of throttle arteries, in glomus cells of the glomus vessels, and in vascular endothelium of some veins and venules of special structure. The exact role of 5-HT is still unknown and further investigations are required to determine the types and distribution of 5-HT receptors present in these vascular devices. We concluded that these special vascular devices can play a critical role in controlling blood flow and pressure in the peripheral pulmonary circulation; however, the exact physiological mechanisms by which they work or are controlled remain unknown providing a ripe area for further investigation.     

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.     

The cardiac muscle in the pulmonary vein of the rat: A morphological and electrophysiological study

The pulmonary veins of albino Wistar rats were studied by means of light and electron microscopy. The media of larger veins consists of cardiac muscle fibers which extend until the vessels attain about 100 μ in diameter. This coat consists of external longitudinal fibers and internal circular fibers. The vasa vasorum are well developed and the capillaries show pseudofenestrations. The numerous adrenergic and cholinergic nerve endings do not form typical motor end-plates as seen in skeletal muscles. The ultrastructure of these media muscle fibers is similar to that of rat hearts. The smooth muscle layer of larger pulmonary veins is not continuous as it is in smaller veins where it forms cushions. Comparisons of albino rats and other rodents reveal striking differences. Action potential shape and propagation velocity (0.5–1.2 m/s) along the myocardial coat of the pulmonary vein were similar to those observed in the left atrium and so was their sensitivity to locally applied acetylcholine. The physiological direction of propagation in rat pulmonary veins is toward the lung. This finding lends support to the hypothesis of a rhythmic, valve-like action of the striated musculature of the pulmonary venous wall during the systole and a possible role in the capacitance of the pulmonary circulation.     

Postnatal changes in pulmonary vein responses to endothelin-1 in the normal and chronically hypoxic lung

The response of pulmonary arteries to endothelin-1 (ET-1) changes with age in normal pigs and is abnormal in pulmonary hypertension. The purpose of this study was to determine if the same is true of the pulmonary veins. We studied the wall structure and functional response to ET-1 in pulmonary veins from normal pigs from fetal life to adulthood and from pigs subjected to chronic hypobaric hypoxia either from birth for 3 days or from 3 to 6 days of age. In isolated normal veins, the contractile response decreased by 40% between late fetal life and 14 days of age with a concomitant twofold increase in endothelium-dependent relaxant response. The ET(A) antagonist BQ-123 reduced the contractile response significantly more in newborn than older animals, whereas the ET-B antagonist BQ-788 had no effect in fetal animals and maximally increased contraction at 14 days of age. Hypoxic exposure significantly increased pulmonary vein smooth muscle area and contractile response to ET-1. The relaxation response was impaired following hypoxic exposure from birth but not from 3 to 6 days of age. The ET(A) antagonist BQ-123 decreased contractile and increased dilator responses significantly more than in age-matched controls. Thus pulmonary veins show age-related changes similar to those seen in the pulmonary arteries with a decrease in ET(A)-mediated contractile and increase in ET-B-mediated relaxant response with age. Contractile response was also increased in hypoxia as in the arteries. This study suggests that pulmonary veins are involved in postnatal adaptation and the pathogenesis of pulmonary hypertension.     

Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation

A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen et al. (Ann Biomed Eng 28:1281–1299, 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of ‘large’ arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the ‘smaller’ arteries and veins of radii \(\ge \) 50  \(\upmu \) m. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment for circulatory diseases within the lung.     

Dynamics of changes in pulmonary catecholamine content and lipid fatty acid composition in traumatic shock

The content of noradrenaline in the lungs, pulmonary arteries and veins was found to be reduced at definite stages of traumatic shock. At the same time the level of oleic acids was decreased in pulmonary lipid fractions. The content of adrenaline rose in the pulmonary arteries and veins, and it was high in the blood collected from the right atrium as compared to the blood from the carotid artery. It is assumed that the changes in the content of fatty acids are linked with those occurring in lung catecholamine metabolism.     

Comparison of the effects of prostaglandins F1alpha, F2alpha, F1beta, and F2beta on the canine pulmonary vascular bed.

The effects of four F series prostaglandins on the pulmonary vascular bed were compared under conditions of controlled pulmonary blood flow in the intact spontaneously breathing dog. PGF1alpha and PGF2alpha increased lobar arterial pressure whereas PGF1beta and PGF2beta had little if any effect when infused into the lobar artery. The increase in lobar arterial pressure in response to PGF1alpha and PGF2alpha was associated with a significant increase in lobar venous pressure but no change in left atrial pressure. These data indicate that PGF1alpha and PGF2alpha increase pulmonary vascular resistance by constricting lobar veins and vessels upstream to small veins, presumed to be small arteries. It is concluded that in the pulmonary vascular bed the configuration of the hydroxyl group at carbon 9 is an important determinant of pressor activity.