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

Abstract

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)

Standing up to the challenge of standing: a siphon does not support cerebral blood flow in humans

“…2). The results thereby provide an experimental confirmation of studies in which the gravitational influence on cerebral blood flow has been modeled (8,14) although an alternative model is provided as well (6).…”

“…The only work that is needed to move the fluid is that required to overcome viscous friction (14). For maintaining cerebral blood flow in the upright position, Hicks and Badeer (6) argue that in a closed system like the circulation, gravity acts on all of the system, indicating that a siphon does support cerebral blood flow. In the upright position, the major outflow pathway from the brain is shifted from the internal jugular veins to posterior veins (16), suggesting an increase in resistance.…”

“…With a siphon supporting cerebral blood flow, its MAP of ϳ260 mmHg, which is more than twofold that of humans, is considered to be necessary to overcome the viscous resistance of blood (6). With respect to cerebral outflow of the giraffe, it has been concluded that a siphon is not established (5).…”

Cerebral Hemodynamics After Short- and Long-Term Reduction in Blood Pressure in Mild and Moderate Hypertension

“…During HUT, hydrostatic effects of gravity on cerebral perfusion pressure under steady-state conditions were not considered, because gravitational potential energy of blood is likely to be conserved in a closed circulatory system. 13 The magnitude of beat-to-beat changes in mean BP and CBF velocity was quantified by power spectral analysis. Transfer function and coherence function between these variables was calculated to assess dynamic cerebral autoregulation as described previously ( Figure 1).…”

Independent effects of heart–head distance and caudal blood pooling on blood pressure regulation in aquatic and terrestrial snakes

“…The principle of the siphon is thought to make blood flow to the head independent of the height of the vascular loop. This notion is derived from the idea that the heart does not work against gravity in the circulatory system but works only against viscous resistance (Hicks and Badeer, 1992), although the idea and its experimental evidence have been shown to be seriously flawed (Pedley et al, 1996;Seymour et al, 1993). Nevertheless, Badeer proposes that the hearts of arboreal snakes are closer to the head because they can fill better in this location when the animal is tilted headup (Badeer, 1998).…”