The arterial circulation of the heart

Blood flows into the aorta and its branches during left ventricular systole. Most of the arterial walls in the body stretch during systole in accordance with their elastic properties (Roston, 1962a, b). During diastole, the rebound of the distended walls supplies an additional propulsive force pushing the blood forward. Since the metabolic exchange between most of the tissues in the body and their blood vessels is ordinarily the same throughout the cardiac cycle, it makes little difference whether or not the blood flow occurs during systole or diastole. The circulation in the coronary arteries behaves in a quite different way. Because the muscle fibers of the heart contract during systole and relax during diastole, different conditions for blood flow and metabolic exchange exist during the phases of the cardiac cycle. As a result, specification of whether blood flows in the coronary arteries during systole or diastole may be important. Such specification complicates the study of the coronary artery circulation. For example, because of the arterial elasticity, some of the blood which enters the coronary arteries during diastole comes in contact with the muscle fibers during systole. The present work contains a theoretical study of the coronary artery circulation.     

Circulation changes depending on manifestations in soft tissue tensioning in the leg lengthening process

Surgical intervention was found to intensify circulation in the limb and redistribute the blood flow. Leg lengthening led to arterial inflow limitation due to the magisterial artery strain. The changes were accompanied both by increase of functioning capillaries in number and increase of venous outflow dependence on blood inflow. The decreased after surgery oxygen tension in m. gastrocnemius did not change throughout distraction. The increase of functioning capillaries in number in resting contributed to maintenance of tissue oxygenation in the initial period of distraction, and in case of maximal tissue tensioning hydrostatic pressure increased in the capillaries due to arterial pressure rise. Restoration of the circulation parameters in the fixation period started with an increase of circulation volumetric rate in vessels with preservation of the rest mechanisms of the tissue oxygenation maintenance.     

The interdependent contributions of gravitational and structural features to perfusion distribution in a multiscale model of the pulmonary circulation

Recent experimental and imaging studies suggest that the influence of gravity on the measured distribution of blood flow in the lung is largely through deformation of the parenchymal tissue. To study the contribution of hydrostatic effects to regional perfusion in the presence of tissue deformation, we have developed an anatomically structured computational model of the pulmonary circulation (arteries, capillaries, veins), coupled to a continuum model of tissue deformation, and including scale-appropriate fluid dynamics for blood flow in each vessel type. The model demonstrates that both structural and the multiple effects of gravity on the pulmonary circulation make a distinct contribution to the distribution of blood. It shows that postural differences in perfusion gradients can be explained by the combined effect of tissue deformation and extra-acinar blood vessel resistance to flow in the dependent tissue. However, gravitational perfusion gradients persist when the effect of tissue deformation is eliminated, highlighting the importance of the hydrostatic effects of gravity on blood distribution in the pulmonary circulation. Coupling of large- and small-scale models reveals variation in microcirculatory driving pressures within isogravitational planes due to extra-acinar vessel resistance. Variation in driving pressures is due to heterogeneous large-vessel resistance as a consequence of geometric asymmetry in the vascular trees and is amplified by the complex balance of pressures, distension, and flow at the microcirculatory level.     

The role of the surrounding tissue in the propagation of waves through the arterial system.

A theoretical analysis of the flow in arteries is presented, taking into consideration the role played by the surrounding tissues in determining the speed of propagatoion and the damping of the blood pressure pulse. This study was undertaken (a) to exhibit a method of computing the flow properties with a more nearly accurate model, (b) to see if the displacement on the skin would be related to the arterial wall displacement, and hence to pressure, velocity and flow rate of blood in the artery, and if it is likely to be measurable. It was found that the pressure of the 'viscous' part in the surrounding tissue increases the pulse velocity and the damping of the wave over the values found by other models which considered only thick-walled elastic tubes with no surrounding tissue. This study also shows that measurements on the skin can provide information about changes in arterial circulation due to diseases such as: edema, arteriosclerosis and others where the Young's modulus for either the arterial wall or the surrounding tissues is altered.     

The time course of capillary exchange

The equations governing the time course of the exchange of substances between the blood in the capillaries and the extracellular space are solved for the case of substances which do not penetrate the cells. The equations given relate the time course of the exchange process to the various tissue and circulation parameters such as the specific capillary wall area, the pore area, the inter-capillary distance, the size of the extra-vascular, extra-cellular space, the diffusion coefficient in this space, and the velocity of blood in the capillaries. Some experimental work on capillary exchange is discussed in relation to the theory and estimates are made of the relative importance of the various tissue and circulation parameters in the exchange of substances in different tissues.     

Current views on oxygen transport from blood to tissues]

During the recent 25-30 years, sophisticated experiments and mathematical simulation significantly changed the generally accepted theory of oxygen transport in tissue, which was based on two major postulates, namely: 1) Blood flows in capillaries continuously at uniform velocity, 2) Gas circulation between blood and tissue takes place exclusively in capillaries. As was shown by modern research techniques, blood flow in microvessels has irregular sharp velocity fluctuations in very short time intervals (seconds). In addition, mean velocity of blood flow in microvessels of the same caliber and the same micro-region of tissue may differ several times. Therefore, efficiency of microcirculation reactions may be assessed exclusively witH mean blood velocity in capillaries of the whole micro-region, and with complicated changes of the histogram of mean velocity distribution in capillaries. It was shown that arteriolas and venulas of inactive muscles and brain account for 30 to 50% of gas circulation between blood and tissue. This resulted in fundamental change of the previous postulates in the area of tissue gas circulation physiology, and, in effect, in replacement of oxygen transport paradigm created by A. Krog. This study is an attempt to present a new modern concept of oxygen transport in tissue, to show its research significance, and possible applications.     

Inert gas clearance from tissue by co-currently and counter-currently arranged microvessels

To elucidate the clearance of dissolved inert gas from tissues, we have developed numerical models of gas transport in a cylindrical block of tissue supplied by one or two capillaries. With two capillaries, attention is given to the effects of co-current and counter-current flow on tissue gas clearance. Clearance by counter-current flow is compared with clearance by a single capillary or by two co-currently arranged capillaries. Effects of the blood velocity, solubility, and diffusivity of the gas in the tissue are investigated using parameters with physiological values. It is found that under the conditions investigated, almost identical clearances are achieved by a single capillary as by a co-current pair when the total flow per tissue volume in each unit is the same (i.e., flow velocity in the single capillary is twice that in each co-current vessel). For both co-current and counter-current arrangements, approximate linear relations exist between the tissue gas clearance rate and tissue blood perfusion rate. However, the counter-current arrangement of capillaries results in less-efficient clearance of the inert gas from tissues. Furthermore, this difference in efficiency increases at higher blood flow rates. At a given blood flow, the simple conduction-capacitance model, which has been used to estimate tissue blood perfusion rate from inert gas clearance, underestimates gas clearance rates predicted by the numerical models for single vessel or for two vessels with co-current flow. This difference is accounted for in discussion, which also considers the choice of parameters and possible effects of microvascular architecture on the interpretation of tissue inert gas clearance.     

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.     

Functional Organization of the Teleost Gill

The circulation of the gills has been studied in the perch, trout and eel combining the conventional histological methods and casting techniques. The existence of two blood pathways in each gill arch was confirmed. 1 — An arterio-arterial pathway assuming the respiratory function. It includes the afferent branchial artery and in each primary lamella the afferent primary artery, the secondary lamellae capillaries and the primary and branchial efferent arteries. 2 — An arterio-venous pathway arising from both the branchial artery, in the gill arch, and the primary arteries in each primary lamella. This pathway includes the central venous sinus of the primary lamella, several small veins and is finally connected with the branchial veins. 3 — The lack of connections between afferent primary arteries and cvs in the trout and the perch makes impossible a direct blood flow from the afferent to the efferent artery (shunt). In the eel connections between cvs and both afferent and efferent arteries do not mean that a shunt is operating according to the pressure gradient.     

A continuum model for pressure-flow relationship in human pulmonary circulation

A continuum model was introduced to analyze the pressure-flow relationship for steady flow in human pulmonary circulation. The continuum approach was based on the principles of continuum mechanics in conjunction with detailed measurement of vascular geometry, vascular elasticity and blood rheology. The pulmonary arteries and veins were considered as elastic tubes and the "fifth-power law" was used to describe the pressure-flow relationship. For pulmonary capillaries, the "sheet-flow" theory was employed and the pressure-flow relationship was represented by the "fourth-power law". In this paper, the pressure-flow relationship for the whole pulmonary circulation and the longitudinal pressure distribution along the streamlines were studied. Our computed data showed general agreement with the experimental data for the normal subjects and the patients with mitral stenosis and chronic bronchitis in the literature. In conclusion, our continuum model can be used to predict the changes of steady flow in human pulmonary circulation.     

Influence of lung volume and left atrial pressure on reverse pulmonary venous blood flow

Infarction of the lung is uncommon even when both the pulmonary and the bronchial blood supplies are interrupted. We studied the possibility that a tidal reverse pulmonary venous flow is driven by the alternating distension and compression of alveolar and extra-alveolar vessels with the lung volume changes of breathing and also that a pulsatile reverse flow is caused by left atrial pressure transients. We infused SF6, a relatively insoluble inert gas, into the left atrium of anesthetized goats in which we had interrupted the left pulmonary artery and the bronchial circulation. SF6 was measured in the left lung exhalate as a reflection of the reverse pulmonary venous flow. No SF6 was exhaled when the pulmonary veins were occluded. SF6 was exhaled in increasing amounts as left atrial pressure, tidal volume, and ventilatory rates rose during mechanical ventilation. SF6 was not excreted when we increased left atrial pressure transients by causing mitral insufficiency in the absence of lung volume changes (continuous flow ventilation). Markers injected into the left atrial blood reached the alveolar capillaries. We conclude that reverse pulmonary venous flow is driven by tidal ventilation but not by left atrial pressure transients. It reaches the alveoli and could nourish the alveolar tissues when there is no inflow of arterial blood.     

How well mixed is inert gas in tissues?

The washout of inert gas from tissues typically follows multiexponential curves rather than monoexponential curves as would be expected from homogeneous, well-mixed compartment. This implies that the ratio for the square root of the variance of the distribution of transit times to the mean (relative dispersion) must be greater than 1. Among the possible explanations offered for multiexponential curves are heterogeneous capillary flow, uneven capillary spacing, and countercurrent exchange in small veins and arteries. By means of computer simulations of the random walk of gas molecules across capillary beds with parameters of skeletal muscle, we find that heterogeneity involving adjacent capillaries does not suffice to give a relative dispersion greater than one. Neither heterogeneous flow, nor variations in spacing, nor countercurrent exchange between capillaries can account for the multiexponential character of experimental tissue washout curves or the large relative dispersions that have been measured. Simple diffusion calculations are used to show that many gas molecules can wander up to several millimeters away from their entry point during an average transit through a tissue bed. Analytical calculations indicate that an inert gas molecule in an arterial vessel will usually make its first vascular exit from a vessel larger than 20 micron and will wander in and out of tissue and microvessels many times before finally returning to the central circulation. The final exit from tissue will nearly always be into a vessel larger than 20 micron. We propose the hypothesis that the multiexponential character of skeletal muscle tissue inert gas washout curves must be almost entirely due to heterogeneity between tissue regions separated by 3 mm or more, or to countercurrent exchanges in vessels larger than 20 micron diam.     

Waveform dependence of pulsatile flow in a stenosed channel

Bloodflow in arteries often shows a rich variety of vortical flows, which are dominated by the complex geometry of blood vessels, the dynamic pulsation of blood flow, and the complicated boundary conditions. With a two-dimensional model of unsteady flow in a stenosed channel, the pulsatile influence on such vortical fluid dynamics has been numerically studied in terms of waveform dependence on physiological pulsation. Results are presented for unsteady flows downstream of the stenosed portion with variation in the wavefiorms of systole and diastole. Overall, a train of propagating vortex waves is observed for all the cases, but it shows great sensitivity to the waveforms. The generation and development of the vortex waves may be linked to the presence of an adverse pressure gradient within a specific interval between two points of inflection of the systolic waveform. The adverse pressure gradient consists of a global pressure gradient that is found to be closely related to the dynamnics of' the pulsation, and a local pressure gradient, which is obsented to be dominated by the nonlinear vortex dynamics.     

Tissue-growth-based synthetic tree generation and perfusion simulation

Biological tissues receive oxygen and nutrients from blood vessels by developing an indispensable supply and demand relationship with the blood vessels. We implemented a synthetic tree generation algorithm by considering the interactions between the tissues and blood vessels. We first segment major arteries using medical image data and synthetic trees are generated originating from these segmented arteries. They grow into extensive networks of small vessels to fill the supplied tissues and satisfy the metabolic demand of them. Further, the algorithm is optimized to be executed in parallel without affecting the generated tree volumes. The generated vascular trees are used to simulate blood perfusion in the tissues by performing multiscale blood flow simulations. One-dimensional blood flow equations were used to solve for blood flow and pressure in the generated vascular trees and Darcy flow equations were solved for blood perfusion in the tissues using a porous model assumption. Both equations are coupled at terminal segments explicitly. The proposed methods were applied to idealized models with different tree resolutions and metabolic demands for validation. The methods demonstrated that realistic synthetic trees were generated with significantly less computational expense compared to that of a constrained constructive optimization method. The methods were then applied to cerebrovascular arteries supplying a human brain and coronary arteries supplying the left and right ventricles to demonstrate the capabilities of the proposed methods. The proposed methods can be utilized to quantify tissue perfusion and predict areas prone to ischemia in patient-specific geometries.

     

The venous circulation

Some aspects of the circulation through the veins remain unexplained. The pressure gradient which ordinarily exists across a large vein, for example, is much greater than that necessary to maintain the same flow through a rigid tube of identical diameter (Brecher, 1956; Starling and Evans, 1962). During inspiration, blood flow through the thoracic portion of the inferior vena cava increases markedly, while that through the distal abdominal portion does not change. Furthermore, an active source of pressure drop in the chest is necessary to maintain venous flow. For the open chest the pressure drop occurs mainly during ventricular contraction, while in the closed chest it is produced chiefly by inspiration. The present study indicates that the high distensibility of the veins accounts in significant degree for the behavior characteristic of the venous circulation.     

Morphology of central compartment and vasculature of the gills of Lepidosiren paradoxa (Fitzinger)

The four paired gill arches of the South American lungfish Lepidosiren paradoxa contain single branchial arteries directly connecting dorsal and ventral arteries. In gill arches 3 and 4 the branchial arteries also supply looped arlerioles and capillaries to much-reduced gill filaments. Regulation of blood between these routes is thought to be by alteration of vascular resistance. Within the filaments, extensive subepithelial capillary networks and numerous small pumps connect lymphatic vessels in the central connective tissue compartment with venules which, in turn, drain to paired branchial veins.
The features of the endothelium of many of the filament blood vessels suggest extensive transporting, haematolytic and granulopoeitic functions. Large numbers of macrophages pack the connective tissue. Many contain extensive quantities of haemosiderin.     

Microvascularization of the spleen in larval and adult Xenopus laevis: Histomorphology and scanning electron microscopy of vascular corrosion casts

Microvascular anatomy and histomorphology of larval and adult spleens of the Clawed Toad, Xenopus laevis were studied by light microscopy of paraplast embedded serial tissue sections and scanning electron microscopy (SEM) of vascular corrosion casts (VCCs). Histology showed i) that white and red pulp are present at the onset of metamorphic climax (stage 57) and ii) that splenic vessels penetrated deeply into the splenic parenchyma at the height of metamorphic climax (stage 64). Scanning electron microscopy of VCCs demonstrated gross arterial supply and venous drainage, splenic microvascular patterns as well as the structure of the interstitial (extravasal) spaces representing the “open circulation routes.” These spaces identified themselves as interconnected resin masses of two distinct forms, namely “broccoli‐shaped” forms and highly interconnected small resin structures. Arterial and venous trees were clearly identified, as were transitions from capillaries to interstitial spaces and from interstitial spaces to pulp venules. Venous sinuses were not diagnosed (nonsinusal spleen). The splenic circulation in Xenopus laevis is “open.” It is hypothesized that red blood cells circulate via splenic artery, central arteries, penicillar arteries, and red pulp capillaries primarily via “broccoli‐shaped” interstitial spaces, pulp venules and veins into subcapsular veins to splenic veins while lymphocytes circulate also via the interstitial spaces represented by the highly interconnected small resin structures in vascular corrosion casts. In physiological terms, the former most likely represent the fast route for blood circulation, while the latter represent the slow route. J. Morphol. 277:1559–1569, 2016. © 2016 Wiley Periodicals, Inc.     

In vivo Observations on a Specialized Microvasculature,the Primary and Secondary Vessels in Fishes

Microscopical observations have been made on the blood circulation of intact, unanaesthetized specimens of the transparent glass catfish. Along the segmental arteries of the trunk, groups of short, curled vessels of capillary dimensions (termed inter-arterial anastomoses) branch off and reunite to form large so-called secondary arteries running parallel to the main (primary) arteries. Secondary arteries give rise to capillaries in the median ventral fin membrane. Secondary capilaries are drained via separate secondary veins. When blood passes from primary to secondary arteries via the inter-arterial anastomoses a pronounced plasma skimming is observed. Hence, blood perfusing the secondary capillaries of the fin membrane contains very few red blood cells.     

A histochemical study of the innervation of cerebral blood vessels in the snake

Summary Dual innervation of snake cerebral blood vessels by adrenergic and cholinergic fibres was demonstrated with the use of histochemical methods. Although the nerve plexuses are somewhat less dense, the essential features of innervation of the blood vessels are similar to those of mammals with the exception that the adrenergic plexuses are more prominent than the cholinergic plexuses. The major arteries of the cerebral carotid system have a rich nerve supply. However, the innervation is less rich in the basilar and poor in the spinal (vertebral) arteries. Although the arteries supplying the right side of head are poorly developed, three pairs of arteries, cerebral carotids, ophthalmics and spinals, supply the snake brain. The carotids and ophthalmics are densely innervated and are accompanied by thick nerve bundles, suggesting that the nerves preferentially enter the skull along those arteries. Some parenchymal arterioles are also dually innervated. Connection between the brain parenchyma and intracerebral capillaries via both cholinergic and adrenergic fibres was observed. In addition cholinergic nerve fibres, connecting capillaries and the intramedullary nerve fibre bundles, were noticed. Capillary blood flow may be influenced by both adrenergic and cholinergic central neurons. The walls of capillaries also exhibit heavy acetylcholinesterase activity. This may indicate an important role for the capillary in the regulation of intracerebral blood flow.