The conventional theory about the snail shell shape of the mammalian cochlea is that it evolved essentially and perhaps solely to conserve space inside the skull. Recently, a theory proposed that the spiral's graded curvature enhances the cochlea's mechanical response to low frequencies. This article provides a multispecies analysis of cochlear shape to test this theory and demonstrates that the ratio of the radii of curvature from the outermost and innermost turns of the cochlear spiral is a significant cochlear feature that correlates strongly with low-frequency hearing limits. The ratio, which is a measure of curvature gradient, is a reflection of the ability of cochlear curvature to focus acoustic energy at the outer wall of the cochlear canal as the wave propagates toward the apex of the cochlea.inner ear ͉ function ͉ mammalian evolution ͉ spiral I t is often thought that mammalian cochleae are coiled to pack a longer organ into a small space inside the skull and that the cochlear coil increases the efficiency of blood and nerve supply through a central shaft (1). Although these spatial advantages of a coiled cochlea have been generally accepted, understanding the effect of shape on hearing itself has been a challenge.Cochlear coiling is absent in reptiles, birds, and monotreme mammals, and it appears to have originated in the marsupial and placental mammal lines (2). Coiling allowed the cochlea to become longer, increasing the potential octave range, whereas uncoiled cochleae have been associated with relatively limited hearing ranges. Earlier studies suggested that the evolution of coiling enhanced high-frequency hearing (3). This suggestion, however, is not wholly satisfactory for several reasons. Above all, increased hearing ranges extended both high-frequency and low-frequency (LF) hearing abilities in mammals compared with birds and reptiles and improved sensitivities compared with even LF specialist fishes (4). Further, the highest-frequency waves are resolved near the base (entrance) before they propagate far enough into the spiral to ''feel'' the cochlear curvature; it is the lowest-frequency waves that propagate along the cochlea's coils.Earlier work on land mammal ear anatomy (5) found a strong correlation between the LF hearing limit of each species and the product of basilar membrane length and number of spiral turns, but did not adduce a mechanistic explanation for this relationship. Other data suggested also that longitudinal curvature of the cochlear duct generates radial fluid pressure gradients (6) and enhances radial movement of hair cells (1, 7).Recently, a new theory proposed that the cochlea's graded curvature actually enhances LF hearing (8), similar to a whispering gallery in which sounds cling to the concave surface of the lateral wall (9). The cochlear spiral shape redistributes wave energy toward the outer wall, particularly along its innermost, tightest, apical turn, and thereby enhances sensitivity to lowerfrequency sounds.In this article, we test this theory morphometrically. W...

Endothelial cells, when cultured on gelled basement membrane matrix exert forces of tension through which they deform the matrix and at the same time they aggregate into clusters. The cells eventually form a network of cord-like structures connecting cell aggregates. In this network, almost all of the matrix has been pulled underneath the cell cords and cell clusters. This phenomenon has been proposed as a possible model for the growth and development of planar vascular systems in vitro. Our hypothesis is that the matrix is reorganized and the cellular networks form as a result of traction forces exerted by the cells on the matrix and the latter's elasticity. We construct and analyze a mathematical model based on this hypothesis and examine conditions necessary for the formation of the pattern. We show cell migration is not necessary for pattern formation and that isotropic, strain-stimulated traction is sufficient to form the observed patterns.