The Baby's First Breath

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.

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.