Volume 27, Issue 5, Pages 673-679 (March 2017) Two Levels of Waviness Are Necessary to Package the Highly Extensible Nerves in Rorqual Whales  Margo A. Lillie, A. Wayne Vogl, Kelsey N. Gil, John M. Gosline, Robert E. Shadwick  Current Biology  Volume 27, Issue 5, Pages 673-679 (March 2017) DOI: 10.1016/j.cub.2017.01.007 Copyright © 2017 Elsevier Ltd Terms and Conditions

Current Biology 2017 27, 673-679DOI: (10.1016/j.cub.2017.01.007) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 1 Nerve Orientation and Elongation during a Lunge of a Fin Whale (A) During lunge feeding, the ventral groove blubber (VGB) overlying the ventral pouch expands 162% circumferentially and 38% axially [9]. The underlying VGB nerves (yellow) lengthen and recoil with the VGB. (B) Internal surface of the left side of the VGB. The ventral midline is down; rostral is right. VGB nerves lie in a fascial plane over the VGB muscle. θ is the nerve angle from the body axis (double arrow). (C) Physiological nerve stretch is predicted to increase with nerve orientation. Stretch was predicted from the VGB expansions shown in (A), using the relationship λpred=((2.62sinθ)2+(1.38cosθ)2−1)×100%. Current Biology 2017 27, 673-679DOI: (10.1016/j.cub.2017.01.007) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 2 Two-Phase Response of VGB Nerves in Tensile Tests (A) Response of two VGB nerves showing variation in initial, low-stress elongation (phase one) and a sharp increase in stiffness at the transition to phase two (inset). Rat sciatic nerve response is shown for comparison. Arrows indicate the peak predicted physiological stretch for the VGB (upper) and rat sciatic nerves (lower). (B) Elongation at the transition from phase one to two increased with nerve orientation. A spline fit to the mechanical data (broken line) fell about 30% below the predicted physiological elongation (solid line). Core waviness from micro-CT scans predict core straightening at the transition. Waviness in partially dissected nerves disappeared at the transition. (C) Maximum elongation increased with orientation. Spline fit to the mechanical data (broken line) overlay the predicted physiological stretch (solid line). The total waviness obtained from micro-CT scans matched or exceeded the physiological elongation. Current Biology 2017 27, 673-679DOI: (10.1016/j.cub.2017.01.007) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 3 Waviness in Core and Fascicles of VGB Nerves (A) Dissection of fresh nerve showing outer epineurial sheath and wavy inner core. Some epineurium remained attached to core. Nerve orientation θ = 60°. (B) Axial micro-CT slice through a nerve trunk showing tortuous course of core through thick epineurium. Adipose tissue is bright. θ = 64°. (C) Three-dimensional reconstructions of two nerve cores from micro-CT scans. θ = 87° left, 85° right. The outer sheath has been removed with software. The image of the left core is made as a negative and shows endoneurial space as bright. ϕ is the local angle of the nerve core relative to the main axis. Drawing shows calculation of bending strain (ε) as the ratio of the distance from the neutral axis (y) and the radius of curvature (R). (D) Structural waviness within a nerve core in a histological section. Double arrow identifies one fascicle cut largely longitudinally but also caught close to cross-section at left. Within the fascicles, axons (arrowheads) and ample endoneurial collagen (dark pink) are seen in both cross and longitudinal section. Nuclei are stained black. En, endoneurium; Ep, epineurium. No distinct perineurium is identifiable. Tissue stained with Verhoeff’s Van Gieson. (E) Close-up of three-dimensional reconstruction showing waviness of fascicles. θ = 64°. (F) Axial micro-CT slice through relatively straight section of core showing variation in fascicle waviness. θ = 69°. (G) Bending strains differ on inner and outer curvature when there is no shear between structural elements (drawing). Fascicles were relatively straight at outer curvature of core bend and very wavy at inner curvature (lower panels). θ = 85° top, 69° bottom. (H) Bending strains are minimal on inner and outer curvature when shear allows relative movement between structural elements (drawing). Structural lines within two fascicles run in parallel and maintain a constant waviness across bends (lower panel). θ = 69°. See also Figure S1. Current Biology 2017 27, 673-679DOI: (10.1016/j.cub.2017.01.007) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 4 Impact of Bending Strains on Waviness in the Recoiled Nerve (A) Core waviness increased with nerve orientation (p = 0.012), but mean fascicle waviness decreased with nerve orientation (p = 0.01). Lines show linear regressions fit to data. (B) The decrease of fascicle waviness can be quantitatively accounted for by the increase in peak bending strain (p = 0.0027). The broken line shows a slope of −1. (C) Core bending strain increased with core waviness and corresponds to the strains predicted for a sine-generated curve (SGC), but not a sinewave. See also Figure S1. (D and E) The shape of a sine-generated curve, illustrated in (D), is not a sinewave, but the directional angle ϕ it makes relative to the main axis changes sinusoidally along the curve (E). ω is the maximum value of ϕ. Figure modified with permission from [20]. (F) Sinusoidal variation in ϕ indicates cores and fascicles approximate sine-generated curves. Points show data; lines show fitted sinewave. Points with error bars represent mean ± SEM. Current Biology 2017 27, 673-679DOI: (10.1016/j.cub.2017.01.007) Copyright © 2017 Elsevier Ltd Terms and Conditions