Methods
Photoelastic stress analysis
Photoelastic stress analysis, common in materials engineering, has been used to measure forces of moving organisms1,2. To restrict wall effects while still clearly visualizing animals and stress fields, a 21-L (5.5-gallon) aquarium was filled with gelatin mixed with seawater at double the normal concentration (28.35 g gelatin/L seawater). A photographic light table produced a uniform light field. We adapted previous methods2 from two to three dimensions by assuming that the light field was bilaterally symmetrical and using data only from worms travelling straight downward with the crack oriented perpendicular to the camera. Because we were more interested in magnitude than direction of forces, we used circularly, rather than linearly, polarized light. This procedure eliminates isoclinic fringes, which provide information about directions of stresses, to more clearly show isochromatic fringes, which provide information about magnitudes3. Light from the light table went through a linear polarizer, then a quarter-wave retardation plate to become circularly polarized, through the gelatin, through another quarter-wave retardation plate, and finally a linear polarizing filter. Forces were calculated from the videotaped area of the stress field in individual frames over time.
Using a weighted test tube containing known volumes of water resting on the gelatin surface, we calibrated stress-field areas. Least-squares regression between force (mass of test tube plus water x gravity) per unit area of the test tube touching the surface (measured from frame grabs via Image J) and area of the stress field (thresholded using Matlab to the same value as the stress field around worms) predicted stress. We assumed that force exerted by the round bottom of the test tube against the flat surface of the gelatin accurately mimicked force exerted by the curved pharynx against the relatively flat wall of the crack. Stresses were converted to forces by multiplication with the area of the everted pharynx (from a dorsal view, calculated with Image J). Because we could not see the area of the pharynx exerting the force while the pharynx was being everted and retracted, we scaled the maximum area by the ratio of dorso-ventral thickness at a given time to thickness at full eversion (squared, to convert length to area). The ratio varied from approximately 1/3 when the pharynx was retracted to unity at full eversion. Care was taken to match the range of stresses caused by test-tube weight to those exerted by the worm, although often when the pharynx was retracted, no pixels exceeded threshold value. We conservatively assumed when no light was detected that the maximum stress possible without detection was present. Calculated work in any case is small from these threshold forces because of the small distances involved.
Works Cited
1.Harris, J. K. A photoelastic substrate technique for dynamic measurements of forces exerted by moving organisms. Journal of Microscopy 114, 219-228 (1978).
2.Full, R. J., Yamauchi, A. & Jindrich, D. L. Maximum single leg force production: cockroaches righting on photoelastic gelatin. Journal of Experimental Biology 198, 2441-2452 (1995).
3.Sharples, K. Photoelastic Stress Analysis. Chartered Mechanical Engineer (1981).