The notochord of hagfish Myxine glutinosa: visco-elastic properties and mechanical functions during steady swimming

SUMMARY To determine the possible locomotor functions of the hagfish notochord, we measured its flexural stiffness EI (N m -2 ) and flexural damping C (kg m 3 s -1 ), under in vitro conditions that mimicked the body curvature and bending frequency measured during steady undulatory swimming. To assess the notochord9s contribution to the mechanical behavior of the whole body, we also measured EI and C of the whole body, the body with skin removed, and the notochord with the outer fibrous sheath removed. When subjected to dynamic bending at angular frequencies from π to 6π rad s -1 and midline curvatures from 11 to 40 m -1 , 1 cm in situ body segments ( N =4), located at an axial position of 37% of the body length, showed significant changes in EI, C , the Young9s modulus or material stiffness ( E , MPa), the net work to bend the body over a cycle ( W , J) and resilience ( R , % energy return). When skin, muscles and the outer fibrous sheath of the notochord were removed sequentially, each structural reduction yielded significant changes in mechanical properties: C decreased when the skin was removed, E increased when the muscles were removed, and EI and R decreased when the outer fibrous sheath was removed. Although occupying only a small portion of the cross-sectional area, the notochord provides the body with 75% of its total EI and 80% of total C , by virtue of its high E , ranging from 4 to 8 MPa, which is an order of magnitude greater than that of the whole body. Thus, as the body9s primary source of EI and C , the notochord determines the passive (i.e. internal, non-muscular) mechanical behavior of the swimming hagfish. EI and C covary inversely and non-linearly such that as C increases, EI decreases. However, the bending moments M (Nm) produced by each property increase proportionally, and the ratio of stiffness to damping moments, also known as the amplification ratio at resonance, is nearly invariant (approximately 7) with changes in driving frequency. If the body operates in life at or near resonance, the variables EI and C interact over a range of swimming speeds to produce passive mechanical stability.