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Model analogues in the study of cephalic circulation
Comparative Biochemistry and Physiology Part A 125 (2000) 517 – 524
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Model analogues in the study of cephalic circulation Roger S. Seymour * Department of En6ironmental Biology, Uni6ersity of Adelaide, Adelaide, SA 5005, Australia Received 25 November 1999; received in revised form 11 February 2000; accepted 25 February 2000
Abstract Simple laboratory models are useful to demonstrate cardiovascular principles involving the effects of gravity on the distribution of blood flow to the heads of animals, especially tall ones like the giraffe. They show that negative pressures cannot occur in collapsible vessels of the head, unless they are protected from collapse by external structures such as the cranium and cervical vertebrae. Negative pressures in the cerebral-spinal fluid (CSF) can prevent cerebral circulation from collapsing, and the spinal veins of the venous plexus can return blood to the heart in essentially rigid vessels. However, cephalic vessels outside the cranium are collapsible, so require positive blood pressures to establish flow; CSF pressure and venous plexus flow are irrelevant in this regard. Pressures in collapsible vessels reflect pressures exerted by surrounding tissues, which may explain the observed pressure gradient in the giraffe jugular vein. Tissue pressure is distinct from interstitial fluid pressure which has little influence on pressure gradients across the walls of major vessels. © 2000 Elsevier Science Inc. All rights reserved. Keywords: Gravity; Hemodynamics; Cerebral-spinal fluid; Venous plexus; Jugular vein; Blood pressure; Tissue pressure; Interstitial fluid pressure; Posture; Giraffe
1. Introduction The elegant paradigms of Bernoulli, Hagen, and Poiseuille have helped physiologists understand the effects of gravity and viscous resistance on the circulation. Nevertheless, their mathematical models have led to problems of understanding flow dynamics in collapsible vessels in a gravitational field. A prime example concerns the controversy about vertical blood flow to the head of animals such as the giraffe. One proposal is that the arterial blood pressure at the heart must be high enough to support the column of arterial blood above it and to cause a positive perfusion pressure through the capillary beds of the head * Tel.: +61-8-83035596; fax: +61-8-83034364. E-mail address: [email protected] (R.S. Seymour)
(Avasthey, 1972; Seymour and Johansen, 1987; Seymour et al., 1993). It is further asserted that the heart increases the potential energy of the blood on its way to the head, and that all of the added energy is lost from the system by friction in collapsible vessels returning to the heart, none being returned to the system. Thus the conclusion is that the heart works against gravity and, in particular, that the greatly enlarged heart and high arterial blood pressure of the giraffe (Goetz and Keen, 1957; Hargens et al., 1987) are directly related to its long neck. The alternative opinion is that the circulatory system is a closed circuit in which the blood leaves the heart, moves through the body and returns to the heart at the same level, thus requiring no net energy to raise the blood against gravity (Hicks and Badeer, 1989, 1992). This view holds that a siphon-like mechanism exists in the neck of the giraffe, and the
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potential energy put into the blood on its way up the neck is at least partly gained from the energy lost during descent. Furthermore, it is proposed that the high arterial blood pressure in the giraffe is necessary to pump blood through a circulatory system that has an exceptionally high vascular resistance caused by unusually narrow blood vessels, particularly in the legs. Settling the controversy will require information on two levels. The first requirement is a clear understanding of theoretical principles of flow in ideal collapsible tubing in a gravitational field. The second is an appreciation of how actual characteristics of the circulatory system modify the theory. This study addresses the first level by using simple laboratory models to demonstrate patterns of fluid flow in tubing analogues of blood vessels. Such models have been used previously, with varying success (Holt, 1941; Duomarco and Rimini, 1954; Permutt and Riley, 1963; Seymour and Johansen, 1987; Badeer, 1988, 1997; Hicks and Badeer, 1989, 1992; Seymour et al., 1993). It is not the purpose here to review previous studies, but rather to present new models that address the main controversy and three new aspects related to blood flow in superior circuits, namely (a) the role of cerebral-spinal fluid pressure in distribution of flow inside and outside of the cranium, (b) the role of non-collapsible spinal veins of the venous plexus, and (c) the effect of tissue pressure on blood pressure within collapsible vessels. Collapsible blood vessels in situ are affected by structures around them. The principle of the siphon can be effective if the vessels are prevented from collapsing, either by enclosure within a rigid compartment or by attachment to structures that hold them open. For example, vessels inside the cranium can be protected from collapse, even at negative internal pressures, by a balancing negative pressure of the cerebral-spinal fluid that is transmitted through the cerebral tissue to the blood vessels (Rushmer et al., 1948). The spinal veins of the ‘venous plexus’, extending from the base of the cranium and intermingling among all of the vertebrae, are effectively non-collapsible (Batson, 1944; Epstein et al., 1970; Eckenhoff, 1971; Dilenge et al., 1975). It is conceivable that the jugular veins may also be protected from complete closure if they occur between taut muscles, fascia or cervical bones. Even small capillaries may be structurally prevented from collapse if embedded in tissue that is more rigid than the
vessels themselves — the ‘tunnel-in-gel’ concept (Fung, 1978). On the other hand, structures around blood vessels may press upon them and tend to close them, for example, adjacent organs (Duomarco and Rimini, 1954) or vascular smooth muscles (Nichol et al., 1951). This model study addresses the significance of these effects in circulatory loops above the heart.
2. Models and results All models were constructed with a centrifugal pump (Iwaki MD-10) that produced a pressure capable of supporting a static column of fluid (1.69 m) known as the ‘standing head’ (Fig. 1a). Although this was not a pulsatile pump like the heart, it well represented the condition in the arterial side of the circulation, where the pulsations of the heart are largely damped by elastic energy storage in the arterial walls (Windkessel effect), and positive arterial pressure is applied continuously. Two types of tubing were used in the circuit, either ‘rigid’ PVC or ‘collapsible’ dialysis tubing (circumference 48 mm). To simulate perfusion to the tissues inside the cranium, one length of dialysis tubing was threaded through a rigid acrylic tube filled with water that was connected to an open reservoir (Fig. 1a). This segment was a classical ‘Starling resistor’ in which the fluid flowing through the dialysis tubing was influenced by pressure of the surrounding fluid which could be changed by altering the level of the free water surface. For convenience, this segment was called the ‘brain’ and the fluids within it were the ‘blood’ and ‘cerebral-spinal fluid’ or ‘CSF’. A parallel segment, the ‘face’, consisted simply of a dialysis tube lying on a flat surface at the same level as the ‘brain’. The outflows of these joined, and descended either in dialysis tubing (‘jugular vein’) or rigid tubing (‘venous plexus’), 82 cm long (Fig. 2a). These opened above a reservoir so that flow rates could be measured by weighing water collected during 30 s intervals. Pressures were measured with water-filled manometers. Although the circuit was an ‘open system’ (Hicks and Badeer, 1992), there would be no difference in the model function if it were ‘closed’ by covering all free water surfaces with a flexible membrane that could not produce a transmural pressure difference.
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If the ‘brain’ and ‘face’ were below the standing head, then flow occurred through both (Fig. 1b). In this case, flow was measured separately in parallel dialysis tubes draining the ‘brain’ and ‘face’. The flows were not equal because of higher resistance in the connectors on the ‘brain’ segment. Lowering the ‘CSF’ reservoir created a negative pressure inside the ‘cranium’, causing the dialysis tubing inside to expand maximally and permit the maximum flow. However, when the ‘CSF’ pressure was increased to positive values, the tubing was compressed and flow diminished,
Fig. 1. Model of circulation to the head (a) and the effects of ‘cerebral-spinal fluid’ pressure on flow rates to the ‘face’ and ‘brain’ (b). The pump on the right is the ‘heart’ which is capable of producing a pressure sufficient to support a column of water to the level of the ‘standing head’, as illustrated by the pump on the left. In the real model, the ‘brain’ and ‘face’ are at the same level, but shown here on different levels for clarity. The level of ‘CSF’ fluid determines the ‘CSF’ pressure in the ‘brain’ compartment. Flow rates to the ‘face’ () and ‘brain’ ( ) depend on ‘CSF’ pressure. Each point is a mean from three measurements.
Fig. 2. Model demonstration of the effect of a rigid ‘venous plexus’ and a collapsible ‘jugular vein’ on flow to the head, both below (a) and above (c) the level of the standing head. Flow rates in the ‘venous plexus’ ( ) and ‘jugular vein’ () are related to the resistance in the ‘venous plexus’ (b).
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Fig. 3. Model demonstration of the effect of tissue pressure on blood pressures inside a vertical collapsible analogue of the jugular vein. The apparatus consists of a series of external cuffs that exert pressures on the descending tube (a). Tissue pressure is controlled by raising or lowering the external reservoir, blood pressure is measured with a U-tube inserted up the descending tube, and interstitial fluid pressure is atmospheric between the cuff and the tube. The pattern of blood pressure can be varied with height by changing the pattern of tissue pressure (b); the two are essentially equal (c). The points are means from triplicate measurements from four patterns of tissue pressure. The dashed line is isobaric and the solid line is a linear regression.
the difference in flow expanding the ‘face’ vessel. Detachment of the collapsible ‘jugular veins’ had virtually no effect on flow rates through either segment. If the ‘brain’ and ‘face’ were above the standing head level (not illustrated), there was no flow in the ‘face’, because the pressure was negative and the tube closed. There was also no flow in the ‘brain’, if the top of the ‘jugular vein’ was above the standing head. This was true regardless of ‘CSF’ pressure. All collapsible vessels outside of the ‘cranium’ and above the standing head closed completely, although the vessels in the ‘brain’ may have been held open by negative ‘CSF’ pressure. If the ‘brain’ and ‘face’ were below the standing head, and a rigid ‘venous plexus’ was added in parallel to the ‘jugular vein’, flow in the ‘brain’ always occurred, unless ‘CSF’ pressure was raised above the standing head (Fig. 2a). Flow through the ‘face’ depended on ‘venous plexus’ resistance, which was controlled with a variable clamp. At resistance below 0.12 cm H2O min/ml, pressure at the top of the ‘venous plexus’ was negative and some flow was diverted from the ‘face’ into it (Fig. 2b). At higher resistances, however, the pressure at the top became positive and part of the flow from the ‘brain’ was diverted into the ‘jugular vein’. If the ‘brain’ and ‘face’ were above the standing head, and a rigid ‘venous plexus’ was added, there was no flow through any vessel, because the artery closed above the standing head (Fig. 2c). If this segment was made rigid, however, flow occurred in the ‘brain’ only if the ‘CSF’ pressure was negative to the extent of the vertical distance of the ‘brain’ above the standing head (i.e. the open surface of the ‘CSF’ reservoir was below the standing head). Another model demonstrated the effect of tissue pressure on blood pressure gradients down the jugular vein (Fig. 3a). This was a pump, a rigid arterial tube and a collapsible descending tube, all of which were below the standing head, so that flow occurred. The collapsible vein was surrounded by six separate cuffs, each consisting of a rigid outer tube and a latex inner tube made from a condom. The latex was so loose that it was not stretched enough to cause a pressure on its own. Each cuff was independent of the descending dialysis tube, but was placed
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around it to exert a pressure that depended on the height of water in its external reservoir. The cuff was held away from the dialysis tube by a sheath of cloth that admitted air between its fibers. Thus the arrangement was analogous to a jugular vein—the pressure inside the dialysis tube was the ‘blood’ pressure, the mean pressure exerted by the cuff was the ‘tissue’ pressure, and the pressure of the air between the fibers of the cloth was the ‘interstitial fluid’ pressure. Mean ‘tissue’ pressure was measured as the difference in height of the middle of the cuff and the fluid level outside (Fig. 3a). ‘Blood’ pressure was measured with a U-shaped manometer inserted up the dialysis tubing to the middle of the cuff. The tip of the manometer had an opening in the side to minimise kinetic energy effects. The arrangement of cuffs was varied in four patterns of ‘tissue’ pressure, including two linear gradations from high at the top to low at the bottom and vice versa, and two patterns with highest pressures either at the ends or the middle of the tube. The top cuff was positioned away from the end of the dialysis tube to avoid restricting the flow at the juncture with the rigid tube (Fig. 3a). Three independent measurements of ‘blood’ pressure, ‘tissue’ pressure, and flow rate were averaged at each cuff and in each of the four cuff arrangements. It was possible to create linear ‘blood’ pressure gradients that increased or decreased with height (Fig. 3b), or any other pattern, simply by adjusting ‘tissue’ pressure appropriately. The mean flow rate was 1.386 l/min (SD= 0.003 l/min), and all individual measurements were within9 2% of the mean, regardless of the arrangement of cuff pressures. A paired t-test (2 tailed; P = 0.05; n=24) showed a slightly, but significantly, higher mean ‘blood’ pressure (Pb =11.2 cm H2O) than ‘tissue’ pressure (Pt =11.0 cm H2O), but the difference was less than 2%. A linear regression through the points gave the equation: Pb =1.05 Pt – 0.18 (Fig. 3c). The 95% confidence interval for the slope was 0.032, indicating that the slope was slightly greater than 1.0. The source of the small difference is unknown, but may have been due to kinetic effects of higher velocity water caused by higher tissue pressure.
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3. Discussion
3.1. The role of the CSF The models show clearly that negative pressures cannot occur in collapsible vessels of the head, unless they are protected from collapse by external structures. Vessels inside the cranium may be held open by negative CSF pressures, even if the brain is above the standing head. However, if either the arteries leading to the cranium or the veins leaving it are collapsible, then flow to the brain stops (Fig. 2c). In any case, the structures outside of the cranium (the ‘face’) completely collapse under negative pressures, and in real vascular beds, the arterioles may close even at low positive pressures (Nichol et al., 1951). Thus the pressures in the arteries of the head must be positive, regardless of CSF pressure. The heart must develop enough pressure to support the vertical blood column above it and provide additional positive pressure to cause perfusion of all cephalic vascular beds. Therefore, the work of the heart is directly influenced by the elevation of the head. This accounts for high arterial blood pressures and large heart size in the giraffe (Goetz and Keen, 1957; Hargens et al., 1987), and the tendency for arterial blood pressures to increase in longer terrestrial snakes (Seymour, 1987) and larger mammals (Seymour and Blaylock, unpublished). Pressures in the CSF are irrelevant in this regard, although they are very important in stabilizing cerebral perfusion during changes in posture or gravitational force (Rushmer et al., 1948).
3.2. The role of the 6enous plexus Much attention related to the siphon controversy has been directed at the state of the jugular veins, although it has been suggested that their characteristics are irrelevant if the microvessels of the head are collapsible (Seymour et al., 1993). The fact that a non-collapsible vein cannot cause perfusion in microvessels under negative pressure is demonstrated by the model involving the ‘venous plexus’ and cranium above the standing head (Fig. 2c). In this model, adding the rigid descending vessel does not establish flow in the ‘face’, and flow in the ‘brain’ in fact ceases, because pressure in unprotected arteries becomes negative. Cerebral flow under negative pressure would occur only if all arteries, microvessels and
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veins were protected from collapse, but there is no evidence that arteries in any animal are so protected. If the cranium is below the standing head, then flow ensues through both ‘brain’ and ‘face’ (Fig. 2a). The interesting question that arises is whether a rigid ‘venous plexus’ facilitates flow under these conditions. The answer depends on the resistance of the plexus. Adding a wide-bore rigid tube creates a siphon and augments flow through the ‘brain’, because the pressure at the top of the tube becomes negative. A narrow-bore tube, on the other hand, may not be able to accept all of the flow from the ‘brain’, so the pressure at its top becomes positive, the excess spills into the ‘jugular vein’ and total flow decreases (Fig. 3b). The situation in real animals is not clear. In humans, the venous plexus is capacious enough to accept practically all of the venous drainage of the brain after occlusion of the jugular veins (Batson, 1944). Radiographs of the circulation of upright primates show an engorged venous plexus and collapsed jugular veins (Epstein et al., 1970; Eckenhoff, 1971; Dilenge et al., 1975). In standing giraffes, however, flow in the jugular vein has been observed with ultrasonic imaging (R.W. Millard, pers. comm.), but the proportion of this flow derived from intra- and extra-cranial beds is not known.
3.3. Venous pressure and tissue pressure By definition, completely collapsible tubes can withstand no transmural pressure gradient. Although excised veins are extremely compliant and undergo large changes in cross-sectional area with very small transmural pressure gradients (Moreno et al., 1970), those surrounded by tissues are less compliant, because they are affected by ‘tissue pressure’. As in the case of negative CSF pressure in the cranium, pressures in surrounding tissues may be reflected in venous blood pressures (Rushmer et al., 1948). Similarly, pressures in the vena cavae are reflections of external pressures in the thoracic or abdominal cavities (Holt, 1941; Duomarco and Rimini, 1954; Avasthey, 1972). Such external pressures may change during activity, for example exercise, pulsations of the heart, breathing, postural changes, etc. (Fung, 1978). Direct pressure from surrounding muscles also affects venous blood pressure, the most striking example of which is the venous pumping action of leg
muscles (Rushmer, 1970). An artificial example involves the modification of radial artery pressures by sphygmomanometry cuffs. In this case, if arterial blood pressure is less than the pressure exerted by the cuff, then the vessel closes. Arterial systolic pressures must at least equal cuff pressure for blood to flow, which is, of course, the principle of the measurement. This is the situation in the model involving water cascading down a collapsible tube surrounded by a series of pressure cuffs (Fig. 3). It clearly demonstrates that internal fluid pressure is nearly equal to the pressure applied by the cuff. Two conclusions can be drawn from this model. First, any pattern of fluid pressure can be created by adjusting the cuff pressure appropriately. Therefore the pattern of blood pressure inside veins may faithfully represent the pattern of tissue pressure exerted on the vessels. Second, the cuff pressures have no influence on flow rate down the tube, unless the pressure is high enough to fully distend the tube all the way back to its connection with the rigid tube. This means that the pressures measured in descending collapsible veins may have no effect on flow rate through the head. Some patterns of venous blood pressure from the literature may be explained as effects of tissue pressure. The jugular vein in humans during 75° head-up tilting is positive (2.8 mmHg), even though the right atrium lower down is slightly negative (Katkov and Chestukhin, 1980). The jugular vein pressures in the giraffe are +14 mmHg near the top, decreasing linearly to about + 4 mmHg at the bottom (Hargens et al., 1987), a pattern difficult to explain (Pedley, 1987; Badeer, 1988). It is the reverse of that expected if the blood in the jugular were a supported fluid column in which the pressure increases toward the bottom, and it is not the atmospheric pressure expected in a vessel said to be collapsed (Goetz and Keen, 1957), or the negative pressure expected in a dumbbell-shaped vessel operating as a siphon (Hicks and Badeer, 1992). The present model provides the simple explanation that blood pressure in the jugular vein is influenced by external tissue pressures. Higher tissue pressure at the top of the giraffe’s neck may result from the animal’s tight skin (Hargens et al., 1987), which, according to the Law of Laplace, should exert a higher pressure where the neck is narrow near the head than it would lower down.
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In all cases of the cuff model, the air pressure around the descending dialysis tubing was atmospheric, analogous to the essential independence of blood pressure from interstitial fluid pressure. In evaluating transmural pressure difference, it is important to distinguish tissue pressure from interstitial fluid pressure. Tissue pressure is the pressure exerted by surrounding structures that are transmitted to the wall of a vessel, while interstitial fluid pressure results from molecular interactions between tissue gel and free interstitial fluid, modified by lymphatic pumping (Guyton et al., 1981). These pressures are not identical — tissue pressure is often positive, but interstitial fluid pressure is usually slightly negative (Leith, 1976; Guyton et al., 1981). Interstitial fluid does not appear to be significantly influenced by gravity, because the pressures in different parts of the body do not reflect expected gradients in a continuous fluid column. For example, interstitial fluid pressure in the giraffe is 6 mmHg in the foot and 1 mmHg in the neck, over 3 m higher (Hargens et al., 1987). The vertical distance in this case would produce a hydrostatic pressure difference of about 250 mmHg between the neck and feet, but the difference in interstitial fluid pressure is only 5 mmHg.
3.4. Usefulness of laboratory models Laboratory models have been used in attempts to support the view that fluid descending in a collapsible tube can facilitate flow to the head (Badeer, 1988; Hicks and Badeer, 1989, 1992), but these demonstrations were criticised (Seymour et al., 1993). One criticism concerned the nature of a ‘collapsible’ tube, which was explicitly defined as one which cannot sustain an internal pressure lower than the external pressure. Another pointed to the artefact created in the attachment of a collapsible tube onto a rigid one, where the collapsible one is held open (i.e., is not collapsible) for some distance from the point of attachment. These points were not considered by Badeer (1997) who recently recreated his former model (Badeer, 1988). The model consisted of an inverted, essentially rigid U-tube that drained water from a large container by siphoning it over the lip. Thus the outer arm of the tube was 5 cm lower than the surface of the water in the container, resulting in a flow of 8.5 ml/s. Without changing the position of the rigid U-tube, a verti-
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cal ‘Penrose’ drain tube was added to the end of the U-tube, resulting in an increase in flow to about 18 ml/s. The increase in flow was used to demonstrate the facilitating effect of the ‘collapsible’ drain. However, it becomes obvious that in adding the tube, the pressure at the original outlet of the U-tube must have decreased from zero (atmospheric) to approximately − 5.7 cm H2O, in order to achieve the increased flow through the rigid U-tube. Therefore, the ‘Penrose’ tube was held open for 5–6 cm below its attachment to the U-tube, and this increased the effect of the siphon. This is confirmed by further data which showed no consistent change in flow rate when tubes of 14, 28 and 42 cm length were used (Badeer, 1997). In these cases, the length of the supported segment at the top of the ‘Penrose’ tube was probably about the same, but the lengths of the collapsible segments were quite different. Holt (1941) showed that the length of a collapsible tube has little effect on flow rate through it. Flow dynamics through collapsible circuits are sometimes not intuitively obvious, which makes models useful tools for understanding the principles. The writer has found them valuable laboratory demonstrations for comparative physiology students when they are first exposed to principles of hemodynamics. Models have the advantages of being ethically neutral and inexpensive, yet they cause students to think, provide hands-on experience in experimental design and measurement, and create timely discussion, especially in view of the current controversy. In interpreting laboratory models, however, it is important to beware of artefacts and remember that vessels in animals are influenced by external structures.
Acknowledgements This study was supported by the Australian Research Council. I thank Amy Blaylock for technical help, Kevin Zippel for discussions concerning the venous plexus, and my students in the ‘fun with rubber’ laboratory.
References Avasthey, P., 1972. Venous pressure changes during orthostasis. Cardiovas. Res. 6, 657 – 663.
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Badeer, H.S., 1988. Haemodynamics of the jugular vein in the giraffe. Nature 332, 788–789. Badeer, H.S., 1997. Is the flow in the giraffe’s jugular vein a ‘free’ fall? Comp. Biochem. Physiol. 118A, 573–576. Batson, O.V., 1944. Anatomical problems concerned in the study of cerebral blood flow. Fed. Proc. 3, 139–144. Dilenge, D., Perey, B., Geraud, G., Nutik, S., 1975. Angiographic demonstration of the cervical vertebral venous plexus in man. J. Can. Assoc. Radiol. 26, 77–81. Duomarco, J.L., Rimini, R., 1954. Energy and hydraulic gradients along systemic veins. Am. J. Physiol. 178, 215–220. Eckenhoff, J.E., 1971. The vertebral venous plexus. Can. Anaesthesiol. Soc. J. 18, 487–495. Epstein, H.M., Linde, H.W., Crampton, A.R., Ciric, I.S., Eckenhoff, J.E., 1970. The vertebral venous plexus as a major cerebral venous outflow tract. Anesthesiol. 32, 332–337. Fung, Y.B., 1978. Mechanical properties of blood vessels. In: Johnson, P.C. (Ed.), Peripheral Circulation. Wiley, New York, pp. 45–79. Goetz, R.H., Keen, E.N., 1957. Some aspects of the cardiovascular system in the giraffe. Angiology 8, 542–564. Guyton, A.C., Barber, B.J., Moffatt, D.S., 1981. Theory of interstitial pressures. In: Hargens, A.R. (Ed.), Tissue Fluid Pressure and Composition. Williams and Wilkins, Baltimore, pp. 11–19. Hargens, A.R., Millard, R.W., Pettersson, K., Johansen, K., 1987. Gravitational haemodynamics and oedema prevention in the giraffe. Nature 329, 59– 60. Hicks, J.W., Badeer, H.S., 1989. Siphon mechanism in collapsible tubes: application to circulation of the giraffe head. Am. J. Physiol. 256, R567–R571.
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Hicks, J.W., Badeer, H.S., 1992. Gravity and the circulation: ‘open’ vs. ‘closed’ systems. Am. J. Physiol. 262, R725 – R732. Holt, J.P., 1941. The collapse factor in the measurement of venous pressure: the flow of fluid through collapsible tubes. Am. J. Physiol. 134, 292 – 299. Katkov, V.E., Chestukhin, V.V., 1980. Blood pressure and oxygenation in different cardiovascular compartments of a normal man during postural exposures. Aviat. Space, Environ. Med. 51, 1234 – 1242. Leith, D.E., 1976. Physiological waterfalls. Physiol. Teacher 5, 6 – 7. Moreno, A.H., Katz, A.I., Gold, L.D., Reddy, R.V., 1970. Mechanics of distension of dog veins and other very thin-walled tubular structures. Circ. Res. 27, 1069 – 1080. Nichol, J., Girling, F., Jerrard, W., Claxton, E.B., Burton, A.C., 1951. Fundamental instability of the small blood vessels and critical closing pressures in vascular beds. Am. J. Physiol. 164, 330 – 344. Pedley, T.J., 1987. How giraffes prevent oedema. Nature 329, 13 – 14. Permutt, S., Riley, R.L., 1963. Hemodynamics of collapsible vessels with tone: the vascular waterfall. J. Appl. Physiol. 18, 924 – 932. Rushmer, R.F., 1970. Cardiovascular Dynamics. Saunders, Philadelphia. Rushmer, R.F., Beckman, R.L., Lee, D., 1948. Protection of the cerebral circulation by the cerebrospinal fluid under the influence of radial acceleration. Am. J. Physiol. 151, 355 – 365. Seymour, R.S., 1987. Scaling of cardiovascular physiology in snakes. Am. Zool. 27, 97 – 109. Seymour, R.S., Hargens, A.R., Pedley, T.J., 1993. The heart works against gravity. Am. J. Physiol. 265, R715 – R720. Seymour, R.S., Johansen, K., 1987. Blood flow uphill and downhill: does a siphon facilitate circulation above the heart? Comp. Biochem. Physiol. 88A, 167 – 170.
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Model analogues in the study of cephalic circulation Roger S. Seymour * Department of En6ironmental Biology, Uni6ersity of Adelaide, Adelaide, SA 5005, Australia Received 25 November 1999; received in revised form 11 February 2000; accepted 25 February 2000
Abstract Simple laboratory models are useful to demonstrate cardiovascular principles involving the effects of gravity on the distribution of blood flow to the heads of animals, especially tall ones like the giraffe. They show that negative pressures cannot occur in collapsible vessels of the head, unless they are protected from collapse by external structures such as the cranium and cervical vertebrae. Negative pressures in the cerebral-spinal fluid (CSF) can prevent cerebral circulation from collapsing, and the spinal veins of the venous plexus can return blood to the heart in essentially rigid vessels. However, cephalic vessels outside the cranium are collapsible, so require positive blood pressures to establish flow; CSF pressure and venous plexus flow are irrelevant in this regard. Pressures in collapsible vessels reflect pressures exerted by surrounding tissues, which may explain the observed pressure gradient in the giraffe jugular vein. Tissue pressure is distinct from interstitial fluid pressure which has little influence on pressure gradients across the walls of major vessels. © 2000 Elsevier Science Inc. All rights reserved. Keywords: Gravity; Hemodynamics; Cerebral-spinal fluid; Venous plexus; Jugular vein; Blood pressure; Tissue pressure; Interstitial fluid pressure; Posture; Giraffe
1. Introduction The elegant paradigms of Bernoulli, Hagen, and Poiseuille have helped physiologists understand the effects of gravity and viscous resistance on the circulation. Nevertheless, their mathematical models have led to problems of understanding flow dynamics in collapsible vessels in a gravitational field. A prime example concerns the controversy about vertical blood flow to the head of animals such as the giraffe. One proposal is that the arterial blood pressure at the heart must be high enough to support the column of arterial blood above it and to cause a positive perfusion pressure through the capillary beds of the head * Tel.: +61-8-83035596; fax: +61-8-83034364. E-mail address: [email protected] (R.S. Seymour)
(Avasthey, 1972; Seymour and Johansen, 1987; Seymour et al., 1993). It is further asserted that the heart increases the potential energy of the blood on its way to the head, and that all of the added energy is lost from the system by friction in collapsible vessels returning to the heart, none being returned to the system. Thus the conclusion is that the heart works against gravity and, in particular, that the greatly enlarged heart and high arterial blood pressure of the giraffe (Goetz and Keen, 1957; Hargens et al., 1987) are directly related to its long neck. The alternative opinion is that the circulatory system is a closed circuit in which the blood leaves the heart, moves through the body and returns to the heart at the same level, thus requiring no net energy to raise the blood against gravity (Hicks and Badeer, 1989, 1992). This view holds that a siphon-like mechanism exists in the neck of the giraffe, and the
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potential energy put into the blood on its way up the neck is at least partly gained from the energy lost during descent. Furthermore, it is proposed that the high arterial blood pressure in the giraffe is necessary to pump blood through a circulatory system that has an exceptionally high vascular resistance caused by unusually narrow blood vessels, particularly in the legs. Settling the controversy will require information on two levels. The first requirement is a clear understanding of theoretical principles of flow in ideal collapsible tubing in a gravitational field. The second is an appreciation of how actual characteristics of the circulatory system modify the theory. This study addresses the first level by using simple laboratory models to demonstrate patterns of fluid flow in tubing analogues of blood vessels. Such models have been used previously, with varying success (Holt, 1941; Duomarco and Rimini, 1954; Permutt and Riley, 1963; Seymour and Johansen, 1987; Badeer, 1988, 1997; Hicks and Badeer, 1989, 1992; Seymour et al., 1993). It is not the purpose here to review previous studies, but rather to present new models that address the main controversy and three new aspects related to blood flow in superior circuits, namely (a) the role of cerebral-spinal fluid pressure in distribution of flow inside and outside of the cranium, (b) the role of non-collapsible spinal veins of the venous plexus, and (c) the effect of tissue pressure on blood pressure within collapsible vessels. Collapsible blood vessels in situ are affected by structures around them. The principle of the siphon can be effective if the vessels are prevented from collapsing, either by enclosure within a rigid compartment or by attachment to structures that hold them open. For example, vessels inside the cranium can be protected from collapse, even at negative internal pressures, by a balancing negative pressure of the cerebral-spinal fluid that is transmitted through the cerebral tissue to the blood vessels (Rushmer et al., 1948). The spinal veins of the ‘venous plexus’, extending from the base of the cranium and intermingling among all of the vertebrae, are effectively non-collapsible (Batson, 1944; Epstein et al., 1970; Eckenhoff, 1971; Dilenge et al., 1975). It is conceivable that the jugular veins may also be protected from complete closure if they occur between taut muscles, fascia or cervical bones. Even small capillaries may be structurally prevented from collapse if embedded in tissue that is more rigid than the
vessels themselves — the ‘tunnel-in-gel’ concept (Fung, 1978). On the other hand, structures around blood vessels may press upon them and tend to close them, for example, adjacent organs (Duomarco and Rimini, 1954) or vascular smooth muscles (Nichol et al., 1951). This model study addresses the significance of these effects in circulatory loops above the heart.
2. Models and results All models were constructed with a centrifugal pump (Iwaki MD-10) that produced a pressure capable of supporting a static column of fluid (1.69 m) known as the ‘standing head’ (Fig. 1a). Although this was not a pulsatile pump like the heart, it well represented the condition in the arterial side of the circulation, where the pulsations of the heart are largely damped by elastic energy storage in the arterial walls (Windkessel effect), and positive arterial pressure is applied continuously. Two types of tubing were used in the circuit, either ‘rigid’ PVC or ‘collapsible’ dialysis tubing (circumference 48 mm). To simulate perfusion to the tissues inside the cranium, one length of dialysis tubing was threaded through a rigid acrylic tube filled with water that was connected to an open reservoir (Fig. 1a). This segment was a classical ‘Starling resistor’ in which the fluid flowing through the dialysis tubing was influenced by pressure of the surrounding fluid which could be changed by altering the level of the free water surface. For convenience, this segment was called the ‘brain’ and the fluids within it were the ‘blood’ and ‘cerebral-spinal fluid’ or ‘CSF’. A parallel segment, the ‘face’, consisted simply of a dialysis tube lying on a flat surface at the same level as the ‘brain’. The outflows of these joined, and descended either in dialysis tubing (‘jugular vein’) or rigid tubing (‘venous plexus’), 82 cm long (Fig. 2a). These opened above a reservoir so that flow rates could be measured by weighing water collected during 30 s intervals. Pressures were measured with water-filled manometers. Although the circuit was an ‘open system’ (Hicks and Badeer, 1992), there would be no difference in the model function if it were ‘closed’ by covering all free water surfaces with a flexible membrane that could not produce a transmural pressure difference.
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If the ‘brain’ and ‘face’ were below the standing head, then flow occurred through both (Fig. 1b). In this case, flow was measured separately in parallel dialysis tubes draining the ‘brain’ and ‘face’. The flows were not equal because of higher resistance in the connectors on the ‘brain’ segment. Lowering the ‘CSF’ reservoir created a negative pressure inside the ‘cranium’, causing the dialysis tubing inside to expand maximally and permit the maximum flow. However, when the ‘CSF’ pressure was increased to positive values, the tubing was compressed and flow diminished,
Fig. 1. Model of circulation to the head (a) and the effects of ‘cerebral-spinal fluid’ pressure on flow rates to the ‘face’ and ‘brain’ (b). The pump on the right is the ‘heart’ which is capable of producing a pressure sufficient to support a column of water to the level of the ‘standing head’, as illustrated by the pump on the left. In the real model, the ‘brain’ and ‘face’ are at the same level, but shown here on different levels for clarity. The level of ‘CSF’ fluid determines the ‘CSF’ pressure in the ‘brain’ compartment. Flow rates to the ‘face’ () and ‘brain’ ( ) depend on ‘CSF’ pressure. Each point is a mean from three measurements.
Fig. 2. Model demonstration of the effect of a rigid ‘venous plexus’ and a collapsible ‘jugular vein’ on flow to the head, both below (a) and above (c) the level of the standing head. Flow rates in the ‘venous plexus’ ( ) and ‘jugular vein’ () are related to the resistance in the ‘venous plexus’ (b).
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Fig. 3. Model demonstration of the effect of tissue pressure on blood pressures inside a vertical collapsible analogue of the jugular vein. The apparatus consists of a series of external cuffs that exert pressures on the descending tube (a). Tissue pressure is controlled by raising or lowering the external reservoir, blood pressure is measured with a U-tube inserted up the descending tube, and interstitial fluid pressure is atmospheric between the cuff and the tube. The pattern of blood pressure can be varied with height by changing the pattern of tissue pressure (b); the two are essentially equal (c). The points are means from triplicate measurements from four patterns of tissue pressure. The dashed line is isobaric and the solid line is a linear regression.
the difference in flow expanding the ‘face’ vessel. Detachment of the collapsible ‘jugular veins’ had virtually no effect on flow rates through either segment. If the ‘brain’ and ‘face’ were above the standing head level (not illustrated), there was no flow in the ‘face’, because the pressure was negative and the tube closed. There was also no flow in the ‘brain’, if the top of the ‘jugular vein’ was above the standing head. This was true regardless of ‘CSF’ pressure. All collapsible vessels outside of the ‘cranium’ and above the standing head closed completely, although the vessels in the ‘brain’ may have been held open by negative ‘CSF’ pressure. If the ‘brain’ and ‘face’ were below the standing head, and a rigid ‘venous plexus’ was added in parallel to the ‘jugular vein’, flow in the ‘brain’ always occurred, unless ‘CSF’ pressure was raised above the standing head (Fig. 2a). Flow through the ‘face’ depended on ‘venous plexus’ resistance, which was controlled with a variable clamp. At resistance below 0.12 cm H2O min/ml, pressure at the top of the ‘venous plexus’ was negative and some flow was diverted from the ‘face’ into it (Fig. 2b). At higher resistances, however, the pressure at the top became positive and part of the flow from the ‘brain’ was diverted into the ‘jugular vein’. If the ‘brain’ and ‘face’ were above the standing head, and a rigid ‘venous plexus’ was added, there was no flow through any vessel, because the artery closed above the standing head (Fig. 2c). If this segment was made rigid, however, flow occurred in the ‘brain’ only if the ‘CSF’ pressure was negative to the extent of the vertical distance of the ‘brain’ above the standing head (i.e. the open surface of the ‘CSF’ reservoir was below the standing head). Another model demonstrated the effect of tissue pressure on blood pressure gradients down the jugular vein (Fig. 3a). This was a pump, a rigid arterial tube and a collapsible descending tube, all of which were below the standing head, so that flow occurred. The collapsible vein was surrounded by six separate cuffs, each consisting of a rigid outer tube and a latex inner tube made from a condom. The latex was so loose that it was not stretched enough to cause a pressure on its own. Each cuff was independent of the descending dialysis tube, but was placed
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around it to exert a pressure that depended on the height of water in its external reservoir. The cuff was held away from the dialysis tube by a sheath of cloth that admitted air between its fibers. Thus the arrangement was analogous to a jugular vein—the pressure inside the dialysis tube was the ‘blood’ pressure, the mean pressure exerted by the cuff was the ‘tissue’ pressure, and the pressure of the air between the fibers of the cloth was the ‘interstitial fluid’ pressure. Mean ‘tissue’ pressure was measured as the difference in height of the middle of the cuff and the fluid level outside (Fig. 3a). ‘Blood’ pressure was measured with a U-shaped manometer inserted up the dialysis tubing to the middle of the cuff. The tip of the manometer had an opening in the side to minimise kinetic energy effects. The arrangement of cuffs was varied in four patterns of ‘tissue’ pressure, including two linear gradations from high at the top to low at the bottom and vice versa, and two patterns with highest pressures either at the ends or the middle of the tube. The top cuff was positioned away from the end of the dialysis tube to avoid restricting the flow at the juncture with the rigid tube (Fig. 3a). Three independent measurements of ‘blood’ pressure, ‘tissue’ pressure, and flow rate were averaged at each cuff and in each of the four cuff arrangements. It was possible to create linear ‘blood’ pressure gradients that increased or decreased with height (Fig. 3b), or any other pattern, simply by adjusting ‘tissue’ pressure appropriately. The mean flow rate was 1.386 l/min (SD= 0.003 l/min), and all individual measurements were within9 2% of the mean, regardless of the arrangement of cuff pressures. A paired t-test (2 tailed; P = 0.05; n=24) showed a slightly, but significantly, higher mean ‘blood’ pressure (Pb =11.2 cm H2O) than ‘tissue’ pressure (Pt =11.0 cm H2O), but the difference was less than 2%. A linear regression through the points gave the equation: Pb =1.05 Pt – 0.18 (Fig. 3c). The 95% confidence interval for the slope was 0.032, indicating that the slope was slightly greater than 1.0. The source of the small difference is unknown, but may have been due to kinetic effects of higher velocity water caused by higher tissue pressure.
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3. Discussion
3.1. The role of the CSF The models show clearly that negative pressures cannot occur in collapsible vessels of the head, unless they are protected from collapse by external structures. Vessels inside the cranium may be held open by negative CSF pressures, even if the brain is above the standing head. However, if either the arteries leading to the cranium or the veins leaving it are collapsible, then flow to the brain stops (Fig. 2c). In any case, the structures outside of the cranium (the ‘face’) completely collapse under negative pressures, and in real vascular beds, the arterioles may close even at low positive pressures (Nichol et al., 1951). Thus the pressures in the arteries of the head must be positive, regardless of CSF pressure. The heart must develop enough pressure to support the vertical blood column above it and provide additional positive pressure to cause perfusion of all cephalic vascular beds. Therefore, the work of the heart is directly influenced by the elevation of the head. This accounts for high arterial blood pressures and large heart size in the giraffe (Goetz and Keen, 1957; Hargens et al., 1987), and the tendency for arterial blood pressures to increase in longer terrestrial snakes (Seymour, 1987) and larger mammals (Seymour and Blaylock, unpublished). Pressures in the CSF are irrelevant in this regard, although they are very important in stabilizing cerebral perfusion during changes in posture or gravitational force (Rushmer et al., 1948).
3.2. The role of the 6enous plexus Much attention related to the siphon controversy has been directed at the state of the jugular veins, although it has been suggested that their characteristics are irrelevant if the microvessels of the head are collapsible (Seymour et al., 1993). The fact that a non-collapsible vein cannot cause perfusion in microvessels under negative pressure is demonstrated by the model involving the ‘venous plexus’ and cranium above the standing head (Fig. 2c). In this model, adding the rigid descending vessel does not establish flow in the ‘face’, and flow in the ‘brain’ in fact ceases, because pressure in unprotected arteries becomes negative. Cerebral flow under negative pressure would occur only if all arteries, microvessels and
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veins were protected from collapse, but there is no evidence that arteries in any animal are so protected. If the cranium is below the standing head, then flow ensues through both ‘brain’ and ‘face’ (Fig. 2a). The interesting question that arises is whether a rigid ‘venous plexus’ facilitates flow under these conditions. The answer depends on the resistance of the plexus. Adding a wide-bore rigid tube creates a siphon and augments flow through the ‘brain’, because the pressure at the top of the tube becomes negative. A narrow-bore tube, on the other hand, may not be able to accept all of the flow from the ‘brain’, so the pressure at its top becomes positive, the excess spills into the ‘jugular vein’ and total flow decreases (Fig. 3b). The situation in real animals is not clear. In humans, the venous plexus is capacious enough to accept practically all of the venous drainage of the brain after occlusion of the jugular veins (Batson, 1944). Radiographs of the circulation of upright primates show an engorged venous plexus and collapsed jugular veins (Epstein et al., 1970; Eckenhoff, 1971; Dilenge et al., 1975). In standing giraffes, however, flow in the jugular vein has been observed with ultrasonic imaging (R.W. Millard, pers. comm.), but the proportion of this flow derived from intra- and extra-cranial beds is not known.
3.3. Venous pressure and tissue pressure By definition, completely collapsible tubes can withstand no transmural pressure gradient. Although excised veins are extremely compliant and undergo large changes in cross-sectional area with very small transmural pressure gradients (Moreno et al., 1970), those surrounded by tissues are less compliant, because they are affected by ‘tissue pressure’. As in the case of negative CSF pressure in the cranium, pressures in surrounding tissues may be reflected in venous blood pressures (Rushmer et al., 1948). Similarly, pressures in the vena cavae are reflections of external pressures in the thoracic or abdominal cavities (Holt, 1941; Duomarco and Rimini, 1954; Avasthey, 1972). Such external pressures may change during activity, for example exercise, pulsations of the heart, breathing, postural changes, etc. (Fung, 1978). Direct pressure from surrounding muscles also affects venous blood pressure, the most striking example of which is the venous pumping action of leg
muscles (Rushmer, 1970). An artificial example involves the modification of radial artery pressures by sphygmomanometry cuffs. In this case, if arterial blood pressure is less than the pressure exerted by the cuff, then the vessel closes. Arterial systolic pressures must at least equal cuff pressure for blood to flow, which is, of course, the principle of the measurement. This is the situation in the model involving water cascading down a collapsible tube surrounded by a series of pressure cuffs (Fig. 3). It clearly demonstrates that internal fluid pressure is nearly equal to the pressure applied by the cuff. Two conclusions can be drawn from this model. First, any pattern of fluid pressure can be created by adjusting the cuff pressure appropriately. Therefore the pattern of blood pressure inside veins may faithfully represent the pattern of tissue pressure exerted on the vessels. Second, the cuff pressures have no influence on flow rate down the tube, unless the pressure is high enough to fully distend the tube all the way back to its connection with the rigid tube. This means that the pressures measured in descending collapsible veins may have no effect on flow rate through the head. Some patterns of venous blood pressure from the literature may be explained as effects of tissue pressure. The jugular vein in humans during 75° head-up tilting is positive (2.8 mmHg), even though the right atrium lower down is slightly negative (Katkov and Chestukhin, 1980). The jugular vein pressures in the giraffe are +14 mmHg near the top, decreasing linearly to about + 4 mmHg at the bottom (Hargens et al., 1987), a pattern difficult to explain (Pedley, 1987; Badeer, 1988). It is the reverse of that expected if the blood in the jugular were a supported fluid column in which the pressure increases toward the bottom, and it is not the atmospheric pressure expected in a vessel said to be collapsed (Goetz and Keen, 1957), or the negative pressure expected in a dumbbell-shaped vessel operating as a siphon (Hicks and Badeer, 1992). The present model provides the simple explanation that blood pressure in the jugular vein is influenced by external tissue pressures. Higher tissue pressure at the top of the giraffe’s neck may result from the animal’s tight skin (Hargens et al., 1987), which, according to the Law of Laplace, should exert a higher pressure where the neck is narrow near the head than it would lower down.
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In all cases of the cuff model, the air pressure around the descending dialysis tubing was atmospheric, analogous to the essential independence of blood pressure from interstitial fluid pressure. In evaluating transmural pressure difference, it is important to distinguish tissue pressure from interstitial fluid pressure. Tissue pressure is the pressure exerted by surrounding structures that are transmitted to the wall of a vessel, while interstitial fluid pressure results from molecular interactions between tissue gel and free interstitial fluid, modified by lymphatic pumping (Guyton et al., 1981). These pressures are not identical — tissue pressure is often positive, but interstitial fluid pressure is usually slightly negative (Leith, 1976; Guyton et al., 1981). Interstitial fluid does not appear to be significantly influenced by gravity, because the pressures in different parts of the body do not reflect expected gradients in a continuous fluid column. For example, interstitial fluid pressure in the giraffe is 6 mmHg in the foot and 1 mmHg in the neck, over 3 m higher (Hargens et al., 1987). The vertical distance in this case would produce a hydrostatic pressure difference of about 250 mmHg between the neck and feet, but the difference in interstitial fluid pressure is only 5 mmHg.
3.4. Usefulness of laboratory models Laboratory models have been used in attempts to support the view that fluid descending in a collapsible tube can facilitate flow to the head (Badeer, 1988; Hicks and Badeer, 1989, 1992), but these demonstrations were criticised (Seymour et al., 1993). One criticism concerned the nature of a ‘collapsible’ tube, which was explicitly defined as one which cannot sustain an internal pressure lower than the external pressure. Another pointed to the artefact created in the attachment of a collapsible tube onto a rigid one, where the collapsible one is held open (i.e., is not collapsible) for some distance from the point of attachment. These points were not considered by Badeer (1997) who recently recreated his former model (Badeer, 1988). The model consisted of an inverted, essentially rigid U-tube that drained water from a large container by siphoning it over the lip. Thus the outer arm of the tube was 5 cm lower than the surface of the water in the container, resulting in a flow of 8.5 ml/s. Without changing the position of the rigid U-tube, a verti-
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cal ‘Penrose’ drain tube was added to the end of the U-tube, resulting in an increase in flow to about 18 ml/s. The increase in flow was used to demonstrate the facilitating effect of the ‘collapsible’ drain. However, it becomes obvious that in adding the tube, the pressure at the original outlet of the U-tube must have decreased from zero (atmospheric) to approximately − 5.7 cm H2O, in order to achieve the increased flow through the rigid U-tube. Therefore, the ‘Penrose’ tube was held open for 5–6 cm below its attachment to the U-tube, and this increased the effect of the siphon. This is confirmed by further data which showed no consistent change in flow rate when tubes of 14, 28 and 42 cm length were used (Badeer, 1997). In these cases, the length of the supported segment at the top of the ‘Penrose’ tube was probably about the same, but the lengths of the collapsible segments were quite different. Holt (1941) showed that the length of a collapsible tube has little effect on flow rate through it. Flow dynamics through collapsible circuits are sometimes not intuitively obvious, which makes models useful tools for understanding the principles. The writer has found them valuable laboratory demonstrations for comparative physiology students when they are first exposed to principles of hemodynamics. Models have the advantages of being ethically neutral and inexpensive, yet they cause students to think, provide hands-on experience in experimental design and measurement, and create timely discussion, especially in view of the current controversy. In interpreting laboratory models, however, it is important to beware of artefacts and remember that vessels in animals are influenced by external structures.
Acknowledgements This study was supported by the Australian Research Council. I thank Amy Blaylock for technical help, Kevin Zippel for discussions concerning the venous plexus, and my students in the ‘fun with rubber’ laboratory.
References Avasthey, P., 1972. Venous pressure changes during orthostasis. Cardiovas. Res. 6, 657 – 663.
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Badeer, H.S., 1988. Haemodynamics of the jugular vein in the giraffe. Nature 332, 788–789. Badeer, H.S., 1997. Is the flow in the giraffe’s jugular vein a ‘free’ fall? Comp. Biochem. Physiol. 118A, 573–576. Batson, O.V., 1944. Anatomical problems concerned in the study of cerebral blood flow. Fed. Proc. 3, 139–144. Dilenge, D., Perey, B., Geraud, G., Nutik, S., 1975. Angiographic demonstration of the cervical vertebral venous plexus in man. J. Can. Assoc. Radiol. 26, 77–81. Duomarco, J.L., Rimini, R., 1954. Energy and hydraulic gradients along systemic veins. Am. J. Physiol. 178, 215–220. Eckenhoff, J.E., 1971. The vertebral venous plexus. Can. Anaesthesiol. Soc. J. 18, 487–495. Epstein, H.M., Linde, H.W., Crampton, A.R., Ciric, I.S., Eckenhoff, J.E., 1970. The vertebral venous plexus as a major cerebral venous outflow tract. Anesthesiol. 32, 332–337. Fung, Y.B., 1978. Mechanical properties of blood vessels. In: Johnson, P.C. (Ed.), Peripheral Circulation. Wiley, New York, pp. 45–79. Goetz, R.H., Keen, E.N., 1957. Some aspects of the cardiovascular system in the giraffe. Angiology 8, 542–564. Guyton, A.C., Barber, B.J., Moffatt, D.S., 1981. Theory of interstitial pressures. In: Hargens, A.R. (Ed.), Tissue Fluid Pressure and Composition. Williams and Wilkins, Baltimore, pp. 11–19. Hargens, A.R., Millard, R.W., Pettersson, K., Johansen, K., 1987. Gravitational haemodynamics and oedema prevention in the giraffe. Nature 329, 59– 60. Hicks, J.W., Badeer, H.S., 1989. Siphon mechanism in collapsible tubes: application to circulation of the giraffe head. Am. J. Physiol. 256, R567–R571.
.
Hicks, J.W., Badeer, H.S., 1992. Gravity and the circulation: ‘open’ vs. ‘closed’ systems. Am. J. Physiol. 262, R725 – R732. Holt, J.P., 1941. The collapse factor in the measurement of venous pressure: the flow of fluid through collapsible tubes. Am. J. Physiol. 134, 292 – 299. Katkov, V.E., Chestukhin, V.V., 1980. Blood pressure and oxygenation in different cardiovascular compartments of a normal man during postural exposures. Aviat. Space, Environ. Med. 51, 1234 – 1242. Leith, D.E., 1976. Physiological waterfalls. Physiol. Teacher 5, 6 – 7. Moreno, A.H., Katz, A.I., Gold, L.D., Reddy, R.V., 1970. Mechanics of distension of dog veins and other very thin-walled tubular structures. Circ. Res. 27, 1069 – 1080. Nichol, J., Girling, F., Jerrard, W., Claxton, E.B., Burton, A.C., 1951. Fundamental instability of the small blood vessels and critical closing pressures in vascular beds. Am. J. Physiol. 164, 330 – 344. Pedley, T.J., 1987. How giraffes prevent oedema. Nature 329, 13 – 14. Permutt, S., Riley, R.L., 1963. Hemodynamics of collapsible vessels with tone: the vascular waterfall. J. Appl. Physiol. 18, 924 – 932. Rushmer, R.F., 1970. Cardiovascular Dynamics. Saunders, Philadelphia. Rushmer, R.F., Beckman, R.L., Lee, D., 1948. Protection of the cerebral circulation by the cerebrospinal fluid under the influence of radial acceleration. Am. J. Physiol. 151, 355 – 365. Seymour, R.S., 1987. Scaling of cardiovascular physiology in snakes. Am. Zool. 27, 97 – 109. Seymour, R.S., Hargens, A.R., Pedley, T.J., 1993. The heart works against gravity. Am. J. Physiol. 265, R715 – R720. Seymour, R.S., Johansen, K., 1987. Blood flow uphill and downhill: does a siphon facilitate circulation above the heart? Comp. Biochem. Physiol. 88A, 167 – 170.