Major moving biological fluids, or biofluids, are blood and air that cooperate to bring oxygen to the body’s cells and eliminate carbon dioxide produced by these cells. Blood is conveyed in a closed network composed of 2 circuits in series — the systemic and pulmonary circulation —, each constituted by arteries, capillaries, and veins, under the synchronized action of the left and right cardiac pumps, respectively. Air is successively inhaled from and exhaled to the atmosphere through the airway openings (nose and/or mouth). In the head, blood generates the cerebrospinal fluid in choroid plexi of all compartments of the ventricular system and receives it in arachnoid villi. Other biofluids are either secreted, such as bile from the liver and breast milk that both transport released substances with specific tasks, or excreted, such as urine from kidneys or sweat from skin glands that both convey useless materials and waste produced by the cell metabolism. In addition to the convective transport, peristalsis, which results from the radial contraction and relaxation of mural smooth muscles, propels the content of the lumen of the muscular bioconduit (e.g., digestive tract) in an anterograde direction. Blood circulation and air flow in the respiratory tract are widely explored because of their vital functions. Note that inhaled air is transported through the respiratory tract by two processes: convection down to bronchioles and diffusion down to pulmonary alveoli.1 Furthermore, investigations of these physiological flows in deformable bioconduits give rise to models such as the Starling resistance that themselves become object of new study fields in physics and mechanics (e.g., collapsible tubes) as well as of new developments in math- ematical modeling and scientific computing. Whereas fluid–structure interaction problems in aeronautics and civil engineering deal with materials of distinct properties, blood stream and vessel wall correspond to two domains of nearly equal physical properties, as both blood and vessels have densities close to that of water. New processing strategies must then be conceived.