LaPlace's Law The larger the vessel radius, the larger the wall tension required to withstand a given internal fluid pressure. For a given vessel radius and internal pressure, a spherical vessel will have half the wall tension of a cylindrical vessel.Why does the wall tension increase with radius?Alveoli of the Lungs The oxygen exchange in the lungs takes place across the membranes of small balloon-like structures called alveoli attached to the branches of the bronchial passages. These alveoli inflate and deflate with inhalation and exhalation. The behavior of the alveoli is largely dictated by LaPlace's law and surface tension. It takes some effort to breathe in because these tiny balloons must be inflated, but the elastic recoil of the tiny balloons assists us in the process of exhalation. If the elastic recoil of the alveoli is compromised, as in the case of emphysema, then it is difficult to exhale forcibly.
The difficulty of inspiration during the baby's first breath is great because all the balloons must be inflated from a collapsed state. Inflation of alveoli
Respiratory System
Inflating the Alveoli Inflating the alveoli in the process of respiration requires an excess pressure inside the alveoli relative to their surroundings. This is actually accomplished by making the pressure in the thoracic cavity negative with respect to atmospheric pressure. The amount of net pressure required for inflation is dictated by the surface tension and radii of the tiny balloon-like alveoli. During inhalation the radii of the alveoli increase from about 0.05 mm to 0.1 mm . The normal mucous tissue fluid surrounding the alveoli has a nominal surface tension of about 50 dynes/cm so the required net outward pressure is: The remarkable property of the surfactant which coats the alveoli is that it reduces the surface tension by a factor of about 15 so that the 1 mmHg pressure differential is sufficient to inflate the alveoli. Other factors affecting the remarkable efficiency of oxygen transport across the lung membranes is characterized in Fick's Law.
IndexLaPlace's law conceptsReferenceShier, et al.Ch 19
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Surfactant Role in Respiration One of the remarkable phenomena in the process of respiration is the role of the fluid coating the walls of the alveoli of the lungs. This fluid, called a surfactant, lowers the surface tension of the balloon-like alveoli by about a factor of 15 compared to the normal mucous tissue fluid in which they are immersed. There appears to be a nearly constant amount of this surfactant per alveolus, so that when the alveoli are deflated it is more concentrated on the surface. Since the surface-tension-lowering effect of the surfactant depends on this concentration, it diminishes the required pressure for inflation of the alveoli at their most critical phase. For a given surface tension, the pressure to inflate a smaller bubble is greater. It is the surfactant which makes possible the inflation of the alveoli with only about 1 mmHg of pressure excess over their surroundings. The baby's first breath depends upon this surfactant and is made more difficult in premature infants by the incomplete formation of the surfactant.
IndexLaPlace's law conceptsReferenceShier, et al.Ch 19
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Alveoli and Exhalation The alveoli of the lungs act much like balloons in that there is some effort involved to inflate them, but when the inflating pressure is released, the recoil of the elastic walls provides the pressure necessary to deflate them. The lungs are suspended in the thoracic cavity which is normally at a slight negative pressure. When the diaphragm is lowered, that pressure becomes more negative and the lungs expand into the cavity. Air from the atmosphere moves into the resulting partial vacuum and inflates the alveoli. One is aware of the effort, but it is not extreme as in the case of the baby's first breath . Once the alveoli are fully inflated, exhalation can be accomplished by merely relaxing the diaphragm, since the wall tension in all the tiny alveoli will act to force the air out of them. By forcing the diaphragm upward, we can exhale forcefully by adding the diaphragm effort to the recoil of the elastic alveoli. In diseases like emphysema, the elasticity of the alveoli is lost and exhalation becomes a laborious process.
IndexLaPlace's law conceptsReferenceShier, et al.Ch 19
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The Baby's First Breath Everyone knows that it is much more difficult to blow up a balloon for the first time. Why is that? For one thing, the applied pressure does not create much tension in the walls of a small balloon to start the stretching process necessary for inflation. According to LaPlace's law, the wall tension will be twice as large for a balloon of twice the radius. If it takes a certain applied pressure to overcome the elasticity of the large balloon and cause it to expand further, it will take twice as much pressure to start to expand the smaller balloon. All this makes it difficult for the baby to take its first breath -- all the balloons are small! The alveoli of the lungs are collapsed in the fetus and must be inflated in the process of inhalation. Thus the traditional spank on the bottom of the newborn to make him/her mad enough to make the effort for the first breath. Further difficulties are encountered by premature infants because the surfactant fluid which coats the alveoli to give them the appropriate wall tensions is formed in the later stages of pregnacy. Until that point, the alveoli are coated with fluid which has essentially the surface tension of water, much higher than that of the normal surfactant.
Emphysema The disease of the lungs called emphysema or chronic obstructive pulmonary disease (COPD) results in the enlargement of the alveoli of the lungs as some are destroyed and others either enlarge or combine. The disease is one of the destructive effects of long-term smoking, but sometimes occurs in non-smokers. If the normal inhalation process inflates the alveoli to a larger radius, the implications of LaPlace's law are that the wall must have lost much of its elasticity. Normally it would take twice the pressure to inflate a constant tension membrane to twice its radius. Typically, the wall tension of the healthy alveoli is determined by the surface tension of the liquid which coats them, and with a uniform coating (called a surfactant), they will all inflate to a similar radius. The enlarged alveoli in the emphysema patient imply less elastic recoil during the process of exhalation. Exhalation requires effort from the diaphragm and in advanced stages of the disease, a patient will not be able to blow out a match. Besides the loss of elasticity of the alveolar walls, the larger size of the compartments implies a smaller surface area for a given volume. Because the oxygen exchange from the air to the blood is proportional to the area of the exchange membrane, this diminishes the rate of oxygen transfer.
Tension in Arterial Walls The tension in the walls of arteries and veins in the human body is a classic example of LaPlace's law. This geometrical law applied to a tube or pipe says that for a given internal fluid pressure, the wall tension will be proportional to the radius of the vessel. The implication of this law for the large arteries, which have comparable blood pressures, is that the larger arteries must have stronger walls since an artery of twice the radius must be able to withstand twice the wall tension. Arteries are reinforced by fibrous bands to strengthen them against the risks of an aneurysm. The tiny capillaries rely on their small size.
Demonstration with balloon
Capillary Walls The walls of the capillaries of the human circulatory system are so thin as to appear transparent under a microscope, yet they withstand a pressure up to about half of the full blood pressure. LaPlace's law gives insight into how they are able to withstand such pressures: their small size implies that the wall tension for a given internal pressure is much smaller than that of the larger arteries. Given a peak blood pressure of about 120 mmHg at the left ventricle, the pressure at the beginning of the capillary system may be on the order of 50 mmHg. The large radii of the large arteries imply that for pressures in that range they must have strong walls to withstand the large resulting wall tension. The larger arteries provide much less resistance to flow than the smaller vessels according to Poiseuille's law, and thus the drop in pressure across them is only about half the total drop. The capillaries offer large resistances to flow, but don't require much strength in their walls
Danger of Aneurysms The larger arteries of the body are subject to higher wall tensions than the smaller arteries and capillaries. This wall tension follows the dictates of LaPlace's law, a geometrical relationship which shows that the wall tension is proportional to the radius for a given blood pressure. If an artery wall develops a weak spot and expands as a result, it might seem that the expansion would provide some relief, but in fact the opposite is true. In a classic "vicious cycle", the expansion subjects the weakened wall to even more tension. The weakened vessel may continue to expand in what is called an aneurysm. Unchecked, this condition will lead to rupture of the vessel, so aneurysms require prompt medical attention.A localized weak spot in an artery might gain some temporary tension relief by expanding toward a spherical shape, since a spherical membrane has half the wall tension for a given radius. Minimizing membrane tension is why soap bubbles tend to form a spherical shape. But for an expanding artery, forming a near-spherical shape cannot be depended upon to give sufficient tension relief. Demonstration with balloo
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