Optimization of the mechanical performance of a two-duct semicircular duct system--part 3: the positioning of the ducts in the head.

In the majority of vertebrates, the horizontal duct of the vestibular system lies approximately in the yawing plane of the head. The positioning of the vertical ducts, however, is not in the pitch- and roll planes but the vertical ducts generally lie under an angle of about 30-45 degrees relative to the medial plane. Using the equations for a hydrodynamically interconnected two-duct system, optimal positions of the vertical and horizontal ducts in different vertebrate groups can be derived. It was stated that the mean response of the vertical ducts should be optimized. This leads to a symmetrical positioning of the vertical ducts with respect to the medial plane. In all observed vertebrate groups, a solution of mu =(pi-alpha)/2 is found (mu is the angle of the vertical ducts relative to the medial plane, alpha is the angle between the vertical duct planes). For alpha=90 degrees, this provides an equal sensitivity for pitch- and roll- movements. For alpha>90 degrees, a larger sensitivity for pitch movements is obtained, at the expense of a lower sensitivity for roll movements. It is argued that the angle alpha between the vertical ducts may vary from 90 to 120 degrees. In most vertebrates, the centre of mass is stabilized by e.g. fins, tri- or quadrupedal stability, a crawling body or upside-down resting positions (e.g. bats). Birds are generally biped, so in walking they are also rather sensitive to roll. These features are related to labyrinth positioning in the head.