Boyle’s law is a gas law that describes the relationship between the pressure and volume of gas for a mass and temperature. This law is the mechanism by which the human respiratory system functions. Boyle’s law is equivalent to PV = K (P is pressure, V is volume, K is a constant), or one may state that pressure is inversely proportional to the volume.
Issues of Concern
The lungs do not follow Boyle’s law at all volumes. In a resting state with a normal tidal volume, when the alveoli are not collapsed nor are the lungs at maximal capacity, the lungs follow proportional changes of volume and pressure in accordance to Boyle’s law. At low lung volumes, it takes a large pressure change to make small changes in the volume (low compliance of lung tissue). At high volumes within the lung, it takes a more negative pressure to expand the tissue, once again not in compliance with a direct relationship as Boyle’s law dictates. At low and high volumes, the lung has low compliance meaning that the ability of the tissue to expand or its elasticity decreases (compliance = [change in volume]/[change in pressure]).
Organ Systems Involved
The primary organ system involved in the usage of Boyle’s law is the respiratory system. The human body brings air into the lungs by negative pressure. At baseline, the thoracic cavity is in static equilibrium with an intrapleural pressure near -5cmH2O. During inspiration, there is a contraction of inspiratory muscles (diaphragm, external intercostal muscles; additional muscles such as the scalene and sternocleidomastoid can take part under specific circumstances) that increases intrathoracic volume. Due to the combined motion of the lungs and the chest wall, the lungs will begin to expand as the thorax expands during inspiration. According to Boyle’s law, as the volume increases the pressure must decrease, therefore as the intrapleural volume increases, the intrapleural pressure decreases to about -8cm H2O occurs at end inspiration.
At baseline (rest), the alveolar pressure is equal to the atmospheric pressure (0cm H2O), and during inspiration, this pressure will go to -1cmH2O as the volume expands within the alveoli. When the alveolar pressure drops below the atmospheric pressure, air will flow into the lungs for gas exchange.
When the inspiratory muscles relax, the volume within the thorax will decrease, thus the pressure increases and forces out alveolar air back into the atmosphere. With inspiration: lung volume increases, intrapleural pressure decreases. With expiration: lung volume decreases, intrapleural pressure increases.
Intrapleural pressure is the term for pressure within the intrapleural space; alveolar pressure is pressure within the alveoli. As the intrapleural and alveolar pressure become increasingly negative due to the expansion of the chest cavity during inspiration, air from the atmosphere flows into the lungs which allow the lung volume to increase and participate in gas exchange.
Testing related to the mechanism that Boyle’s law works can be applied to the volume within the lung and equations to describe how much air is moving.
The minute ventilation, calculated as the product of tidal volume and respiratory rate, essentially is how much air is inhaled every minute. These two factors control ventilation, which directly depends on the thoracic cavity volume expanding and the decrease in pressure within the intrapleural space and alveoli, allowing for the lungs to fill with air, producing the tidal volume. If there is an adequate tidal volume, a normal respiratory rate will ensure. If the tidal volume is insufficient, there will be a compensatory increase in the respiratory rate in an attempt to maintain normal minute ventilation.
Minute alveolar ventilation is an equation that also depends on Boyle’s law and the inverse relationship of pressure and volume of the thoracic cavity. Alveolar ventilation is the amount of air that reaches the alveoli for gas exchange in each breath; calculated by subtracting the dead space from the tidal volume and then multiplying by the frequency of ventilation.
With a pneumothorax or a hemothorax, there is increased pressure within the intrapleural space. Because of this increased pressure, it moves the resting state of about -5cmH2O to a higher value depending on the degree of disease. As this occurs, it would take a much more significant expansion of the thoracic cavity to create a negative pressure to bring air in from the atmosphere. In a tension pneumothorax, the pressure in the pleural space continually raises the intrapleural pressure, thus decreasing the volume in the lungs. Tension pneumothorax can generate enough pressure to cause a mediastinal shift which eventually interferes with venous return to the right side of the heart and cardiovascular demise.
At birth, newborns are born with no air within their alveoli; thus the volume is zero. The compliance (elasticity of lung tissue) is low at birth. Therefore, the effort to create a negative intrapleural pressure during the initial breaths is high, however, with successive breaths, the lungs fill with air and become more compliant. As the lungs become more compliant, the newborn's lungs will follow Boyle’s law of the inverse relationship of pressure and volume.
Pneumothorax is a clinical condition that can either be primary (typically from trauma) or secondary (patient has a predisposing condition such as COPD). Boyle’s law dictates how air draws into the lungs. As the intrathoracic pressure becomes increasingly negative, the intra-alveolar pressure decreases below atmospheric pressure, causing air to flow into the lungs. In a pneumothorax, there is increased pressure within the intrapleural space, thus causing the need for an increased force to create enough negative pressure for air to come into the lungs.
Boyle’s law also applies when using a medical syringe. When the cylinder on the syringe is empty, it is said to be in a neutral state as there is no air in the syringe. As one pulls back on the plunger, the volume in the cylinder increases, therefore by Boyle’s law the pressure decreases. The liquid is thus drawn into the cylinder to balance the pressure within the syringe and outside of the syringe.
SCUBA divers must be cognizant of Boyle’s law as they descend and ascend to great depths. As a diver descends in the water, the pressure on the person’s lungs increases, and therefore according to Boyle’s law, the volume of air inside the lungs must decrease. As the diver ascends in the water and the pressure on the thoracic cage decreases, the volume of air increases. It is important to exhale steadily to release the volume of the gas if this does not occur the diver can experience pulmonary barotrauma which is overexpansion and alveolar rupture. The diver may have a pneumothorax (chest pain, dyspnea, unilateral decreased breath sounds) or pneumomediastinum (neck pain, pleuritic chest pain, dyspnea, coughing; there may be subcutaneous emphysema causing a crepitation on palpation).