Hemodynamics for medical students.

The flow of blood through the cardiovascular system depends on basic principles of liquid flow in tubes elucidated by Bernoulli and Poiseuille. The elementary equations are described involving pressures related to velocity, acceleration/deceleration, gravity, and viscous resistance to flow (Bernoulli-Poiseuille equation). The roles of vascular diameter and number of branches are emphasized. In the closed vascular system, the importance of gravity is deemphasized, and the occurrence of turbulence in large vessels is pointed out.

Anatomical position of heart in snakes with vertical orientation: a new hypothesis.

It has been observed that climbing arboreal snakes have hearts closer to the head than nonclimbing terrestrial or aquatic snakes. The closeness to the head is said to minimize the work of the heart in pumping blood to the head. However, there is ample evidence that the gravitational pressure in the arteries going to the head is counterbalanced (neutralized) by the gravitational pressure of the blood in the veins going down to the heart. Hence, the heart does not do extra work so, another explanation must be sought. It is proposed that the position of the heart may be related to the filling pressure of the heart which is influenced by the compliance of the vessels above and below the heart. Some observations suggest that the caudal vessels in climbing snakes are less compliant than that of aquatic snakes. This tends to move the hydrostatic indifferent point closer to the head and provides an adequate filling pressure in climbing snakes in the vertical position.

Anatomical position of heart in snakes with vertical orientation: a new hypothesis.

It has been observed that climbing arboreal snakes have hearts closer to the head than nonclimbing terrestrial or aquatic snakes. The closeness to the head is said to minimize the work of the heart in pumping blood to the head. However, there is ample evidence that the gravitational pressure in the arteries going to the head is counterbalanced (neutralized) by the gravitational pressure of the blood in the veins going down to the heart. Hence, the heart does not do extra work so, another explanation must be sought. It is proposed that the position of the heart may be related to the filling pressure of the heart which is influenced by the compliance of the vessels above and below the heart. Some observations suggest that the caudal vessels in climbing snakes are less compliant than that of aquatic snakes. This tends to move the hydrostatic indifferent point closer to the head and provides an adequate filling pressure in climbing snakes in the vertical position.

Is the flow in the giraffe's jugular vein a "free" fall?

There is controversy as to whether or not the heart works against gravity in the arteries to the head in the upright position. One view is that the gravitational effects in the neck arteries are counterbalanced by the gravitational effects in the veins of the neck and the heart does not do extra pressure work. This concept has been challenged by others who claim that the heart works against gravity based on the notion that the jugular vein is collapsed and gravitational effects on jugular blood are inoperative, similar to the "free" fall of liquids. The present study supports the view that blood flow in the collapsible jugular vein of the giraffe is not a "free" fall and that the heart does not spend extra energy to raise the blood to the head.

Glomerular vascular resistance to blood flow: a brief review.

It is accepted that glomerular vascular resistance to blood flow is represented by a pressure drop of only a few mm Hg, but the hemodynamic basis for this concept is generally not well known. Our purpose is to review the evidence supporting the low resistance concept and to provide an explanation based on the fact that the glomerular network consists of 20-40 capillary loops placed 'in parallel' which markedly reduce the viscous resistance to flow (analogous to electrical circuits). A low pressure drop in the glomerular capillaries would be significant in filtration function.

Pitfalls in the assessment of vascular resistance.

Vascular resistance (R) to flow is calculated as the ratio of perfusion pressure between two points (P1-P2) to flow rate (Q). In high-pressure circuits (e.g., systemic), it is justifiable to use arterial pressure (P1) to represent perfusion pressure. It is not permissible to calculate resistance without measuring Q unless a comparison is being made in the resistance of different segments of a vascular bed; Q being constant, R: (P1-P2). In a low-pressure circuit (lower vertebrates, pulmonary) it is imperative to measure P2 to quantify the perfusion pressure. In closed circuits with a vertical orientation the effect of gravity on both the arterial and the venous pressures must be considered. In such circuits the perfusion pressure is due to viscous resistance only, excluding the gravitational pressure between the two points.

Gravity and the circulation: "open" vs. "closed" systems.

The elementary principles of liquid dynamics are described by the equations of Bernoulli and Poiseuille. Bernoulli's equation deals with nonviscous liquids under steady streamline flow. Pressures in such flows are related to gravity and/or acceleration. Changes in elevation affect the gravitational potential energy of the liquid and the velocity of flow determines the kinetic energy. The sum of these three factors represented in the Bernoulli equation remains constant, but the variables are interconvertible. In contrast, the Poiseuille equation describes the pressures related to viscous resistance only, and the energy of flow is dissipated as heat. A combination of the two equations describes the flow in tubes more realistically than either equation alone. In "open" systems gravity hinders uphill flow and causes downhill flow, in which the liquid acts as a falling body. In contrast, in "closed" systems, like the circulation, gravity does not hinder uphill flow nor does it cause downhill flow, because gravity acts equally on the ascending and descending limbs of the circuit. Furthermore, in closed systems, the liquid cannot "fall" by gravity from higher levels of gravitational potential to lower levels of potential. Flow, up or down, must be induced by some source of energy against the resistance of the circuit. In the case of the circulation, the pumping action of the heart supplies the needed energy gradients. Flow in collapsible tubes, like veins, obeys the same basic laws of liquid dynamics except that transmural pressures near zero or below zero reduce markedly the cross-sectional area of the tube, which increases the viscous resistance to flow.(ABSTRACT TRUNCATED AT 250 WORDS)

Hemodynamics of vascular 'waterfall': is the analogy justified?

The concept of 'vascular waterfall' has been used for collapsible vessels in different hemodynamic states which have little similarity to each other from a dynamic standpoint. Examples include (a) flow through large systemic veins entering the thorax, (b) flow through microvessels, such as pulmonary, cardiac, hepatic, cerebral, and (c) flow through the jugular vein of the giraffe. The dynamics of freely falling liquids (waterfall) as compared with flow through collapsible blood vessels (in vivo and in vitro) and in collapsible tubes are dissimilar in too many respects to justify analogy. The flow through collapsible tubes and blood vessels can be explained satisfactorily on the basis of elementary principles of fluid mechanics (Bernoulli-Poiseuille). Hence, the term waterfall as a metaphor is misleading and unjustified. We suggest that the use of the term be discontinued for describing vascular dynamics.

Siphon mechanism in collapsible tubes: application to circulation of the giraffe head.

Controversy exists over the principles involved in determining blood flow to the head of a giraffe, specifically over the role of gravity pressure (pgh) in the collapsible jugular vein in facilitating uphill flow in arteries. This study investigated the pressures within vertically oriented models containing both rigid and collapsible tubes. An inverted U tube was constructed (height = 103 cm) of thick rubber tubing in the ascending limb and collapsible dialysis tubing in the descending limb. Water flow was induced by a variable speed pump maintained at the reservoir level such that the descending limb was partially collapsed. Pressure measurements were made at various levels within the U tube by two methods: 1) with the transducer at same level as the tip of the water-filled catheter and 2) with the transducer at the reservoir level. During flow, the pressure at any point was nearly atmospheric along the length of the descending limb. Such methods of obtaining pressure indicated that the pressure gradient within the partially collapsed descending limb was the sum of viscous flow pressure (P1-P2 of Poiseuille) and gravitational pressure (pgh). To study the facilitatory effect of a siphon, the descending limb was compared with a horizontally placed limb (length = 100 cm), and the flow was kept constant. Calculations of hydraulic "work" (pressure x flow) indicated that with a partially collapsed descending limb, work of the pump was reduced by 15% compared with uphill flow to the elevated horizontal position. It is concluded that the siphon mechanism operates in a partially collapsed descending limb of a siphon loop.

Does gravitational pressure of blood hinder flow to the brain of the giraffe?

Vascular pressure consists of the sum of two pressures: (a) pressure developed by the pumping of the ventricles against the resistance of vessels, designated as viscous flow pressure, and (b) pressure caused by gravity, traditionally called hydrostatic, better described as gravitational pressure. In a conduit, both of these pressures must be overcome when a liquid is discharged to a higher level of gravitational potential energy. If a liquid is returned to its original level, gravity neither helps nor hinders flow because of the siphon effect. This circumstance prevails in the circulatory system. Hence, P1-P2 in the Poiseuille equation excludes gravitational pressure between those points. The long neck of the giraffe, therefore, poses no impediment to blood flow in the erect posture. The giraffe has a high aortic pressure. This is not for driving the blood to its head but is for minimizing the gravitational drop of intravascular pressure and collapse of the vessels. The cerebral circulation is protected by the cerebrospinal fluid which undergoes parallel changes in pressure with posture. Other vessels in the head are less protected by connective tissue, surrounding muscles and other structures. The high aortic pressure in the giraffe is probably caused by the high total peripheral resistance of the systemic circuit due to vascular adaptations related to the overall height of the animal.

Gravitational effects on the distribution of pulmonary blood flow: hemodynamic misconceptions.

In the upright individual the apex of the lung receives relatively little blood. This has often been explained by the low pulmonary arterial pressure which is said to be just sufficient to raise the blood to the apex. It is believed that pulmonary arterial pressure must overcome the pressure due to gravity. This misconception overlooks the fact that the siphon principle applies to the vascular system in which the gravitational pressure of venous blood counterbalances the gravitational pressure of blood in the arteries and vice versa. Accordingly, the perfusion or driving pressure (P1-P2) between arteries and veins at any horizontal level of the lung remains unchanged, irrespective of body position. Intravascular pressure at any point is the algebraic sum of dynamic pressure causing flow (cardiogenic) and the pressure of blood due to gravity which does not cause flow. In the upright position, since the dynamic pressure in the pulmonary circuit is low, the drop in gravitational pressure at the apex of the lung reduces significantly the intravascular and, consequently, the transmural pressure in these vessels. The pulmonary microvessels being highly compliant undergo collapse and increase their resistance to flow. The reduction in apical flow is, therefore, a consequence of increased vascular resistance and not a matter of raising the blood against gravity. Gravitational pressure of blood per se neither hinders upward flow nor favors downward flow.

Cardiac output and venous return as interdependent and independent variables.

Under steady states the heart pumps whatever it receives and receives whatever it pumps. In other words, cardiac output (CO) and venous return (VR) are equal and the distinction between the two seems unnecessary. However, under nonsteady states the two are temporarily unequal and the distinction becomes significant. VR varies directly with the difference in pressure between the end of systemic capillaries and the right ventricle during filling and inversely with the total resistance of the venous system. Thus, the energy for VR is derived from CO. In some transient states VR becomes an independent variable and CO dependent until a new steady state is reached (e.g., exercise, hemorrhage, fevers, hyperthyroidism, severe anemia, etc.). In other conditions the opposite is true (e.g., myocardial infarction, altered ventricular contractility, etc.). Explanation of changes in cardiac output in various perturbations of circulation are based on the identification of the independent variable (VR or CO) in a given physiologic or pathologic condition during the period that a nonsteady state exists.

Vascular hemodynamics: deep rooted misconceptions misnomers.

Erroneous concepts about vascular hemodynamics are widespread, notably as regards the effect of gravity on blood flow. Vascular pressure at any point is equal to the sum of two pressures of entirely different origins: (1) pressure caused by the pumping action of the heart ('cardiodynamic' pressure which is vital for circulation) and (2) pressure due to gravity acting on the blood ('gravitational' or hydrostatic pressure which plays no direct role in blood flow). Gravity neither helps nor hinders circulation because of the U tube or siphon principle. The gravitational energy of the column of blood in arteries is balanced exactly by the gravitational energy of the column in veins and vice versa. Thus, contrary to common belief, gravity does not hinder blood flow to the head in the upright position, nor does it hinder venous return from the dependent parts of the body. For this reason, in Poiseuille's equation, perfusion pressure should exclude gravitational pressure. Postural effects on circulation result from the distension vessels (particulary veins) subsequent to changes in gravitational pressure of blood.