Elasticity in Arteries

Robert E Shadwick. American Scientist. Volume 86, Issue 6. Nov/Dec 1998.

Many animals, from people to lobsters, rely on circulatory systems of fundamentally similar design. These systems consist of a pumping organ and a set of conduits that circulate the blood. In all cases, the pump is powered by cyclical contractions of linear motors, or muscle. Consequently, the flow of blood into the arterial tree is very pulsatile. During each cardiac cycle, the blood’s pressure and flow velocity rise and fall with these regular contractions.

Ideally, blood should flow steadily to and through the peripheral capillary beds. For one thing, when blood flows in pulses, much energy is spent accelerating and decelerating the blood. Therefore, smooth flow minimizes the hydraulic power requirements of the heart. All circulatory systems examined so far incorporate an exquisite mechanical solution to this challenge: elastic arteries.

The English clergyman and physician Stephen Hales first reported observing elasticity in arteries in 1733. Each time one of the heart’s ventricles contracted, Hales found, the aorta expanded enough to accommodate about two-thirds of the blood pumped in one stroke. Realizing that this blood must be expelled from the aorta between heartbeats, Hales proposed that the arteries must perform like an elastic reservoir, converting the heart’s pulsatile flow to steady flow in peripheral vessels. That is, the large arteries expand with blood each time the heart contracts, then recoil elastically to continue blood flow to the small peripheral vessels and capillary beds while the heart is refilling. The elastic compliance of the arterial system also prevents the arterial pressure from falling abruptly after the heart valves close.

As I shall show, physical principles must have guided the evolution of animal circulatory systems. If we examine the design and mechanics of these systems, some remarkable similarities emerge across a wide range of animals.

Elasticity

When it is deformed, an elastic solid recovers by developing a resisting force or tension. The energy stored elastically in the deformed state is recovered by elastic recoil. How do engineers measure the elastic capability of a material? They apply a range of tensile, or pulling, forces and measure how much the material deforms. These tests yield two measurements: stress, which is the pulling force divided by the cross-sectional area of the material, and strain, which is the change in length (deformation) divided by the original length of the material.

Some materials have linear elasticity. That is, when you plot stress versus strain, you get a straight line whose slope conveys the elastic stiffness, or modulus, of the material. Like most biological materials however, blood vessels exhibit nonlinear elasticity. Their elastic stiffness is not constant but increases with the magnitude of deformation.

Alan Burton, working at the University of Western Ontario, has demonstrated how nonlinear elasticity gives arteries the particular capability needed for a cylindrical vessel. Following Burton’s logic, the aorta can be contrasted with a cylindrical rubber balloon. When you blow into a balloon, a small expansion accompanies the initial rise in air pressure. If you keep blowing, the expansion becomes unstable, and a bulge appears abruptly. Continued inflation becomes easier because the pressure actually falls.

The balloon experiment demonstrates the Law of Laplace. If you multiply pressure, P, and the internal radius, R, of a pressurized cylinder, the product is the circumferential wall tension, T: T = PR. If you next plot T versus R for a cylindrical rubber balloon, the result is a sigmoid curve that has an initial steep region, a shoulder, then a region of decreasing slope and, finally, another steep part. At a given pressure, the equilibrium radius for the balloon is represented by an intersection of the T-R curve and the Laplace lines-a family of straight lines through the origin, each representing the Laplace relation at a different pressure. A balloon’s instability begins at the shoulder of the sigmoidal T-R curve, where the Laplace line becomes parallel to the tangent of the rubber curve. Beyond that point, a small increment in pressure results in a large jump in radius. In an artery, such a dilation could become an aneurysm.

Generally, however, this does not happen. An artery’s T-R curve has a continuously increasing slope because of the materials nonlinear elasticity. In addition, none of the Laplace lines is tangential to the T-R curve at normal pressures; there are no regions of instability and rapid inflation. There is, of course, a limit to the elastic stability of an artery and a pressure at which a Laplace line lies parallel to the steepest portion of the artery curve-a pressure that would result in a blowout. For the human aorta-the major artery leaving the left ventricle-Burton predicted a blowout pressure exceeding 1,000 millimeters of mercury or about 10 times the normal mean blood pressure of a healthy adult, which gives us a considerable degree of reassurance. Perhaps even more spectacular, Hales reported that the pressure needed to explode a dog’s carotid artery exceeded 5.7 atmospheres, or 4,300 millimeters of mercury!

Composite Characteristics

The nonlinear elasticity in arteries comes from the composite nature of the vessel wall. Composite structures, as human engineers have also discovered, can provide a wide range of mechanical properties, depending on the relative proportion, the spatial organization and the material properties of each component incorporated into a structure. An artery, like a garden hose, consists of both rubbery and stiff fibrous components.

The incorporation of extracellular elastic proteins :in arteries arose independently in the evolution of several animal phyla. The best known is elastin, which exists in nearly all vertebrates. This rubber-like protein forms highly extensible tissue with elastic stiffness comparable to that of a rubber band. The stiff material is collagen, which is also the main fibrous component of skin, tendons and ligaments. It is relatively inextensible and 1,000 times stiffer than elastin. Lampreys and invertebrates such as squids, octopuses, whelks, lobsters and crabs rely on elastin analogues, or proteins that have elastin-like properties but are chemically distinct. On the other hand, all nonvertebrates use collagen as the stiff element in their arteries.

In a perfectly elastic material, all the strain energy stored in deformation gets recovered by elastic recoil. Like other biological materials, however, blood vessels are not perfectly elastic, because some degree of viscous damping is always associated with each cycle of deformation. Such a phenomenon involves a combination of viscosity and elasticity, hence the term viscoelasticity.

The salient feature of viscoelasticity is that the elastic strain energy released during unloading is less than the strain energy that was applied during loading, with the difference being lost as heat. After a tennis ball is dropped each rebound is progressively smaller and repeated bounces cause the ball to warm. Likewise, the energy required to inflate an artery exceeds the energy returned as the artery deflates. In fact, most deflating arteries lose 15-20 percent of their potential strain energy. This means that most, but not all, of the strain energy is recovered elastically during each cycle of inflation and deflation. The lost strain energy helps to attenuate pressure pulses that propagate along arteries.

Arterial Experiments

Our current knowledge of artery-wall mechanics stems from pioneering experiments published in 1881 by Charles Roy. Without the aid of any electronic devices, he constructed a gravity-driven apparatus that inflated isolated segments of blood vessel from human beings and other mammals, measured instantaneous pressure and volume, and plotted the results on a rotating drum called a kymograph. He also tested strips of artery wall with an apparatus that plotted the force-length curves for the tissue as it was stretched. With these data, Roy determined an artery wall’s nonlinear elasticity and found that the distensibility of the human aorta decreases as a function of age. He also showed that arteries distend considerably at resting blood pressure, which means that the tensile stress is never zero. Finally, he showed that the aorta is most compliant in the normal range of blood pressure.

In other experiments, Roy investigated the thermoelastic properties of arterial tissues. He showed that an artery wall releases heat during extension, and that applying heat to a piece of artery that has been stretched by a suspended weight reduces the amount of stretch. In other words, heating makes an artery wall stiffer, so that an applied stress produces less strain. These properties appeared contrary to the known behavior of crystalline elastic solids, but Roy recognized that an artery wall had an elastic mechanism that was thermodynamically like that of caoutchouc, natural latex rubber, although the physics of this type of elastic material was not understood in Roy’s day. Modern research on synthetic rubber-like polymers, as well as on animal rubbers like elastin, has revealed that the elasticity of such polymer networks arises from changes in the entropy of the molecular chains. An imposed strain increases order in the molecular network, thereby decreasing its entropy. The elastic force arises from the tendency of the network to return to conformational states of higher entropy, or disorder, according to the laws of thermodynamics.

In the 1950s, Margot Roach and Alan Burton, both at the University of Western Ontario, selectively digested collagen or elastin from samples of human artery to demonstrate the mechanical roles of each. They found that elastin’s elasticity provides the initial stiffness of an artery wall, and fully tensed collagen supplies the higher stiffness at high strains. The stress-strain curve turns upward in the normal range of loading, revealing a transition between low and high stiffness. Roach and Burton proposed that during this transition, collagen fibers are straightened and mechanically recruited throughout a distending wall. The elastic force in an artery wall at normal physiological pressures and above, then, may depend on contributions from both elastin and collagen.

Roach and Burton also showed what may be happening when human arteries seem to “harden” with aging: There is a relative increase in collagen and a loss of the elastin-dominated phase, causing collagen loading to begin at lower strain levels.

In the 1960s, Derek Bergel, then a Ph.D. student in the laboratory of the renowned circulatory physiologist Donald McDonald at the University of London, undertook a very quantitative analysis of the mechanical properties of mammalian arteries. He characterized the nonlinear viscoelasticity of the artery wall in terms of the dynamic “incremental” elastic modulus, based on pressure-radius data for vessel segments subjected to sinusoidal pressure oscillations at different frequencies. This engineering approach quantified a vessel’s elastic stiffness as it changed with distension or pressure. Bergel showed that the incremental elastic modulus of an aorta increases sharply over the physiological pressure range. He also found that the elastic modulus, at mean blood pressure, increases along the arterial tree with greater distance from the heart. This longitudinal change is correlated with a decrease in the elastin:collagen ratio from about 2:1 in the aortic arch to about 1:2 in the abdominal aorta.

Beyond elasticity, the mechanical integrity of the arterial system depends on the connective-tissue components having high resistance to mechanical fatigue. This is not a trivial concern, because growth and replacement of collagen in adult mammals is very low and elastin turnover is virtually undetectable. So the “rubber bands” that keep our arteries safe from the stress applied relentlessly by our own blood pressure must literally last a lifetime. Since blood pressure and wall stress never decline to zero, an artery wall must withstand continuous tensile loading for very long times and an extremely large number of deformation cycles. For example, the elastin and collagen in the arterial tree of a person who lives 80 years, with an average of one heartbeat per second, will be subjected to more than 2.5 billion pressure pulses! Although fatigue tests on the order of 80 years are difficult to conduct, predictive studies by John Gosline and Margo Lillie at the University of British Columbia indicate that the fatigue lifetime of elastin, loaded at average working stress, exceeds 100 years. In other experiments that they conducted, arterial elastin showed no signs of mechanical fatigue after several million sinusoidal load cycles that mimicked natural levels of stress.

Evolutionary Elasticity

The suggestion that nonlinear elasticity is an evolutionary design requirement for any artery is supported by recent observations on a variety of lower vertebrates and some invertebrates. In species of reptiles, amphibians, teleost and elasmobranch fishes, lamprey, hagfish, nautilus, squid, cuttlefish, octopus, whelk, crab, lobster and horseshoe crab, the major arteries have nonlinear viscoelastic properties similar to those of the mammalian aorta. In general, low compliance gives way to a much-increased stiffness as inflation pressure increases over the physiological range. In all cases, the arteries are resilient and return at least 80 percent of the strain energy in each deformation cycle. These properties ensure that each vessel will act as an effective pulse-smoothing device.

In direct comparisons, plots of the aorta’s elastic modulus versus inflation pressure seem substantially different among various animal groups, but these differences all but vanish if pressures are normalized to the mean blood pressure of each species. Carol Gibbons and I first pointed this out in a comparative study of the arteries of lower vertebrates-lizard, snake and toad-that have relatively low blood pressures compared to a mammal, the rat. We concluded that the aortas of these species have the same functional behavior at their respective blood pressures and that differences in the composite structure of the artery wall must reflect mechanical adjustments to specific pressure ranges. When we add mechanical data for the aorta of fish and invertebrate species to our comparison, the pattern is maintained and the same conclusions hold. The elastic modulus of the aorta at the mean blood pressure for each animal-be it rat, shark, squid or lobster-is approximately 4 x 105 newtons per square meter.

Comparative Construction

Close examination of blood-vessel tissue shows that, in most cases, the elastic tissue is laid down in concentric layers, interspersed with collagen and circumferentially arranged smoothmuscle cells. In species as different as the nautilus, shark and rat, there is a striking similarity in the microscopic appearance of the aortic wall. In the major arteries of mammals, the bulk of the vessel wall is comprised of the tunica media, which contains the elastic layers, or lamellae. These are sandwiched between the inner tunica interna-a layer of endothelial cells and the underlying basal elastin layer-and the outer layer of predominantly collagen called the tunica adventitia. A distinction is often made between the large “elastic” and the smaller “muscular” arteries based on the relative abundance of elastin and smooth muscle. In terms of their mechanical properties, however, all of these vessels have qualitatively similar nonlinear elasticity.

In 1964, Harvey Wolinsky and Seymour Glagov, working at the University of Chicago, produced a detailed description of the three-dimensional architecture of the tunica media. They analyzed the microscopic structure of excised segments of rabbit aorta, which had been restored to their normal length and fixed under various distending pressures ranging from zero to 200 millimeters of mercury, which is about twice a rabbit’s normal mean blood pressure. This was an important innovation because the aorta expands by about 5060 percent when pressurized to the physiological range, so the orientation and degree of organization of the lamellar components change substantially as the wall distends and thins. This approach allowed the beginning of a clear picture of the arrangement of the fibrous and cellular components, which led to an explanation of how a load transfers from elastin to collagen with increasing pressure.

When unpressurized, the elastin lamellae take on a very wavy and disorganized appearance in longitudinal and transverse sections. With increasing pressure, they straighten progressively and the distances between them decrease. At 80 millimeters of mercury, which is the low end of the physiological pressure range, the lamellae are straight and give the appearance of regular concentric cylinders with uniform thickness and radial spacing. Within the interlamellar spaces, smooth muscle cells and collagen fibers become oriented in low-pitch helical paths around the circumference as the pressure rises. The circumferential straightening of elastin layers and the alignment of collagen fibers with distension under physiological pressures correlate with the increasing elastic modulus observed by mechanical testing. This probably represents the basis for transferring a load from compliant elastin to rigid collagen fibers. These studies stimulated the idea of a lamellar unit of structure or a muscle-elastin-collagen unit.

John Clark and Seymour Glagov of the University of Chicago recently refined this model based on scanning electron microscopy of the fracture surfaces of pressure-fixed aortas. They showed that the elastic tissue between concentric layers of circumferentially oriented smooth muscle cells actually consists of two layers of elastin fibers, each associated with adjacent muscle layers and containing interposed bundles of wavy collagen fibers. Although there are no apparent connections between fibers of elastin and collagen, both appear to be linked to the membranes of adjacent muscle cells, from which they are synthesized. Elaine Davis of McGill University showed that internal contractile filaments span the smooth-muscle cells obliquely, linking to the membrane-attachment sites of the adjacent elastin layers. This system of contractile-elastic units provides a mechanism for a direct line of tension transmission across the concentric elastic lamellae. Moreover, the high degree of structural organization suggests the artery wall is designed to uniformly distribute its tensile stresses.

The modular nature of the arterywall structure provides an explanation for how aortas of different-size mammals can have the same elastic properties: Larger mammals have larger arteries with proportionately more elastin layers. Wolinsky and Glagov showed this in a morphometric study of the lamellar unit in the thoracic aorta of adult mammals that ranged from 28gram mice to 200-kilogram pigs. Their data revealed that diameter and wall thickness increase in nearly constant proportion, so the ratio of wall thickness to radius is about 0.10, for all body sizes. The lamellar thickness also remains constant at about 0.015 millimeter. This means that the number of lamellar units increases in direct proportion to the radius and wall thickness. Given that the Laplace relation states that circumferential wall tension per unit length is the product of pressure and radius and that the mean blood pressure in mammals is the same (about 13,000 newtons per square meter) regardless of body size, the mean wall tension should increase in direct proportion to the radius and, thereby, to the number of lamellar units. Wolinsky and Glagov calculated that the tension per lamella for any aorta was always about 2 newtons per meter, despite the 26-fold increase in total tension in the artery wall from mouse to pig. Consequently, they concluded that the elastin-muscle-collagen lamella is the basic structural and functional unit of the aorta.

By analyzing lamellar structure in the aorta in reptiles and amphibians, Carol Gibbons and I found that, compared to a mammalian aorta, these vessels have a larger proportion of collagen, thinner elastin lamellae and a tension per lamella of only about 0.5 newtons per meter at mean blood pressure. This suggests that the lamellar unit of the aorta is structurally and mechanically different in the lower vertebrates than in mammals and that this is necessary in order to achieve the same elastic properties at the lower blood pressures found in these animals.

Based on the above description of the scaling of artery-wall structure, one might expect that growth of the aorta in each individual would result from adding new lamellar units, but this is not the case. A fixed number of lamellae in the aorta of each species is laid down very early in development. Pre- and postnatal growth involves addition of new elastin to existing layers, so that increases in wall thickness and diameter result from similar increases in each cylindrical lamella. Lowell Langille and his colleagues at the University of Toronto showed that the elastin lamellae in young animals contain very small holes that increase in size and number to facilitate the increases in lamellar diameter that accompany rapid arterial growth, without causing large stretching of the elastin. This process seems to be mediated by an endogenous enzyme that degrades elastin at the site of the holes, in concert with deposition of new elastin. This research group also found that stress can alter elastin’s lamellar thickness and diameter. For example, changes in the rate of blood flow cause positively correlated and dramatic changes in hole size and arterial diameter on a time scale of a few weeks.

Probing the Pressure Pulses

Modeling the dynamics of blood flow allows investigators to make further comparisons between animals. When Stephen Hales realized that each heart contraction led to arterial expansion, he compared the cardiac system to a fire engine’s air chamber, which smooths a pump’s pulsatile flow of water. In 1899, Otto Frank used this analogy-translated in German as the Windkessel model-in the first hydraulic analogue of the arterial tree. This model consists of two elements: an elastic chamber, the Windkessel, and a conduit that represents the arterial peripheral resistance. The Windkessel chamber distends with blood during a heart’s contraction and discharges blood through the resistance by elastic recoil while the heart refills.

The Windkessel model assumes that the pressure pulse is transmitted instantaneously throughout the system and that there is no interaction between successive pulses. For cold-blooded vertebrates and invertebrates, whose heart rates are relatively low, this is an appropriate model, as demonstrated by studies of fish and frogs by David Jones and others at the University of British Columbia, turtles by Warren Burggren at the University of East Anglia and octopuses and toads in my laboratory. In all of these animals, the transit time of the pressure pulse through the aorta is a very small fraction of the cardiac cycle, so each pulse and any of its reflections should be diminished before the next one begins.

In contrast, the Windkessel assumptions are invalid for the arterial systems of terrestrial mammals. With relatively high heart rates, the pulse transit time becomes a significant fraction of the heart period, so wave propagation and reflection effects dominate the composition of pressure and flow waves in the arterial tree. Partial wave reflections develop at points of increasing resistance-the major site being the bifurcation at the end of the abdominal aorta. The interaction of reflected waves with successive incident ones causes a marked increase in the pulse amplitude and the appearance of a secondary peak in the pressure waves as they travel away from the heart. Changes in the shape of the flow waves also form along the aorta for much the same reasons. Nevertheless, the striking differences in wave-propagation characteristics between mammals and cold-blooded animals arise from a combination of different body sizes and heart rates, not from fundamental differences in the elastic performance of the arteries.

A Mark of Marine Mammals

Marine mammals have a remarkable vascular specialization called the aortic bulb. This enlargement of the aortic arch, just outside the heart, can be as much as 3.5 times greater in diameter than the descending aorta to which it connects. The most likely explanation for this anatomical specialization is that it enlarges the elastic reservoir and increases the aorta’s ability to maintain blood flow during bradycardia, or slowing of the heart, during diving.

E. A. Rhode and his colleagues at of the Universities of Alaska studied the properties of the aortic bulb in seals. They made the astonishing calculation that the aortic blood volume of a 95kilogram harbor seal is equal to that of a 450-kilogram horse and that the volume of blood contained in the seal’s aortic bulb alone, at mean blood pressure, exceeds the total volume of the thoracic and abdominal aortas of a similar-sized person. In the case of large cetaceans, such as the fin whale, the aortic bulb represents virtually all of the elastic compliance of the entire arterial tree. John Gosline of the University of British Columbia and I studied the morphology and mechanical properties of fin-whale arteries and concluded that the aortic bulb actually functions as a Windkessel in these large mammals. Although the aortic bulb is greatly enlarged, it has essentially the same elastic modulus as the aorta of other mammals, but the remainder of the aorta is 30 times stiffer. This remarkably high stiffness is correlated with a high proportion of collagen relative to elastin and the presence of dense bands of intralamellar collagen that look like the parallel collagen fibers of tendons.

Our calculation of strains that would develop in fin whales if the pressure pulse was the same as in other mammals indicated that 96 percent of the volume added to the aorta by a heart contraction would reside in the aortic bulb alone. In these whales, the aorta’s ability to expand to take up a pulse of blood resides exclusively in the enlarged bulb adjacent to the heart. The remainder of the aorta functions as a stiff conduit. The abrupt decrease in diameter and increase in elastic stiffness at the distal end of the aortic bulb should result in an increase in pressurewave velocity by about a factor of three. These same feahires also cause the hydraulic resistance to increase markedly, thereby creating a major site of wave reflection quite close to the heart. Our estimates, based on extrapolating heart rate from scaling data for other mammals, predict heart rates in a 40,000kilogram fin whale to be on the order of 10-20 beats per minute, or about 0.17-0.33 hertz. That leads to a pressure-wave velocity of about 5 meters per second; the wavelength of the primary frequency contained in a heartbeat would be 15-30 meters, or about 20 times longer than the aortic bulb. Consequently, the time for a pressure pulse to traverse the aortic bulb is a small fraction of the heart period, so the conditions for Windkessel dynamics will be met in these large mammals.

Many aspects of elasticity in arteries remain unknown. For example, to what extent do the specializations in structure and elastic properties in a whale’s aorta represent an adaptation for diving as opposed to the consequence of extreme size? Future studies on vascular elasticity in smaller diving mammals, such as the Weddell seal, or large terrestrial mammals, such as elephants, might resolve this question. Likewise, investigators continue to study how artery-wall remodeling is coordinated with physiological demand. Despite these intriguing questions and the differences found among diverse animals, all arteries perform in surprisingly similar elastic ways as they endure the stretching that comes with the billions of beats in a lifetime.