The *lung* (adjectival form: pulmonary) is the essential respiration organ in all air-breathing animals. The lung's structure has evolved to efficiently enable gas exchange between biological cells and the atmosphere. Read here about how tensegrity concepts explain this structure in humans and other animals.
In mammals the two lungs are located in the chest on either side of the heart. Their principal function is to transport oxygen from the atmosphere into the bloodstream, and to release carbon dioxide from the bloodstream into the atmosphere. This exchange of gases is accomplished in the mosaic of specialized cells that form millions of tiny, exceptionally thin-walled air sacs called alveoli. To completely explain the anatomy of the lungs, it is necessary to discuss the passage of air through the mouth to the alveoli. Once air progresses through the mouth or nose, it travels through the oropharynx, nasopharynx, the larynx, the trachea, and a progressively subdividing system of bronchi and bronchioles until it finally reaches the alveoli where the gas exchange of carbon dioxide and oxygen takes place. 
The drawing and expulsion of air (ventilation) is driven by muscular action. The musculoskeletal system in the lung is structured so that it is stable, yet elastic. In humans, breathing is largely driven by the muscular diaphragm at the bottom of the thorax. Contraction of the diaphragm pulls the bottom of the cavity in which the lung is enclosed downward, increasing volume and thus decreasing pressure, causing air to flow into the airways. The lung tissues and enclosing rib cage itself are structured to expand and contract and enable breathing, like a blacksmith's bellows is structured to inflate and deflate.
Sleep apnea, for example, results when the structure is not stable enough, and the sleeper is periodically oxygen deprived. Lazopoulosa invokes some tensegrity concepts when he describes the upper faryngeal area and its elastic connections. See article.
Bird Lung Tensegrity Structuring
Birds lungs obtain fresh air during both exhalation and inhalation. Avian lungs do not have alveoli, as mammalian lungs do, but instead contain millions of tiny passages known as parabronchi, connected at either ends by the dorsobronchi and ventrobronchi. Air flows through the honeycombed walls of the parabronchi into air vesicles, called atria, which project radially from the parabronchi. These atria give rise to air capillaries, where oxygen and carbon dioxide are traded with cross-flowing blood capillaries by diffusion.
J. N. Maina at the School of Anatomical Sciences, Johannesburg, South Africa, researches the bird's lungs with other colleagues.
Maina described the mechanical requirements of this tensegrity, particularly the rigidity or strength required.
"Among the air-breathing vertebrates, the respiratory system of birds, the lung-air sac system, is remarkably complex and singularly efficient. The most perplexing structural property of the avian lung pertains to its exceptional mechanical strength, especially that of the minuscule terminal respiratory units, the air- and the blood capillaries. In different species of birds, the air capillaries range in diameter from 3 to 20 μm: the blood capillaries are in all cases relatively smaller. Over and above their capacity to withstand enormous surface tension forces at the air–tissue interface, the air capillaries resist mechanical compression (parabronchial distending pressure) as high as 20 cm H2O (2 kPa). The blood capillaries tolerate a pulmonary arterial vascular pressure of 24.1 mmHg (3.2 kPa) and vascular resistance of 22.5 mmHg (3 kPa) without distending. The design of the avian respiratory system fundamentally stems from the rigidity (strength) of the lung. The gas exchanger (the lung) is uncoupled from the ventilator (the air sacs), allowing the lung (the paleopulmonic parabronchi) to be ventilated continuously and unidirectionally by synchronized bellows like action of the air sacs. Since during the ventilation of the lung the air capillaries do not have to be distended (dilated), i.e., surface tension force does not have to be overcome (as would be the case if the lung was compliant), extremely intense subdivision of the exchange tissue was possible. Minuscule terminal respiratory units developed, producing a vast respiratory surface area in a limited lung volume. I make a case that a firm (rigid) rib cage, a lung tightly held by the ribs and the horizontal septum, a lung directly attached to the trunk, specially formed and compactly arranged parabronchi, intertwined atrial muscles, and tightly set air capillaries and blood capillaries form an integrated hierarchy of discrete network system of tension and compression, a tensegrity (tensional integrity) array, which absorbs, transmits, and dissipates stress, stabilizing (strengthening) the lung and its various structural components." 
Role of Collagen Fibers
Maina later explicated the tensegrity structure of the common rooster's lung, identifying collagen fibers as the compressive elements.
"To identify the forces that may exist in the parabronchus of the avian lung and that which may explain the reported strengths of the terminal respiratory units, the air capillaries and the blood capillaries, the arrangement of the parabronchial collagen fibers (CF) of the lung of the domestic fowl, Gallus gallus variant domesticus was investigated by discriminatory staining, selective alkali digestion, and vascular casting followed by alkali digestion. On the luminal circumference, the atrial and the infundibular CF are directly connected to the smooth muscle fibers and the elastic tissue fibers. The CF in this part of the parabronchus form the internal column (the axial scaffold), whereas the CF in the interparabronchial septa and those associated with the walls of the interparabronchial blood vessels form the external, i.e. the peripheral, parabronchial CF scaffold. Thin CF penetrate the exchange tissue directly from the interparabronchial septa and indirectly by accompanying the intraparabronchial blood vessels. Forming a dense network that supports the air and blood capillaries, the CF weave through the exchange tissue. The exchange tissue, specifically the air and blood capillaries, is effectively suspended between CF pillars by an intricate system of thin CF, elastic and smooth muscle fibers. The CF course through the basement membranes of the walls of the blood and air capillaries. Based on the architecture of the smooth muscle fibers, the CF, the elastic muscle fibers, and structures like the interparabronchial septa and their associated blood vessels, it is envisaged that dynamic tensional, resistive, and compressive forces exist in the parabronchus, forming a tensegrity (tension integrity) system that gives the lung rigidity while strengthening the air and blood capillaries." 
References and Links
 Maina, 2006, avian lung tensegrity article online
2] Implicit mechanistic role of the collagen, smooth muscle, and elastic tissue components in strengthening the air and blood capillaries of the avian lung by John N. Maina, Sikiru A. Jimoh, Margo Hosie, article first published online: 6 SEP 2010, DOI: 10.1111/j.1469-7580.2010.01279.x
 Wikipedia on Avian Lungs, http://en.wikipedia.org/wiki/Bird_anatomy
 Wikipedia on Lungs, http://en.wikipedia.org/wiki/Lungs