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Ontogenetic scaling of burrowing forces in the earthworm Lumbricus terrestris

Ontogenetic scaling of burrowing forces in the earthworm Lumbricus terrestris. Kim Quillin J Exp Biol 203, 2757-2770 (2000). Anatomy of the earthworm. Earthworm Locomotion. F R. F R. F A. Dead-end burrow setup. Open burrow setup. Apparatus for measuring burrowing forces.

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Ontogenetic scaling of burrowing forces in the earthworm Lumbricus terrestris

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  1. Ontogenetic scaling of burrowing forces in the earthworm Lumbricus terrestris • Kim Quillin • J Exp Biol 203, 2757-2770 (2000)

  2. Anatomy of the earthworm

  3. Earthworm Locomotion FR FR FA

  4. Dead-end burrow setup Open burrow setup Apparatus for measuring burrowing forces

  5. (1) Burrow diameter (2) Soil Properties Apparatus controls

  6. Measured force traces

  7. mb1/3 mb2/3 L L2 L3 Scaling Laws leg length segment length height surface area cross-sectional area muscle force volume mass weight mb1

  8. Scaling Laws y = some Parameter y ∝ mbb what is b? Isometric Scaling if y ∝ L, measure b = 1/3 if y ∝ L2, measure b = 2/3 if y ∝ L3, measure b = 1 Allometric Scaling if the condition for isometry is not met (i.e. any other value for b)

  9. log y Parameter (y) log mb Body Mass (mb) Scaling Laws y = some Parameter y ∝ mbb what is b? y = ambb [log y] = b [log mb] + C

  10. b = 1 b = 2/3 log y b = 1/3 log mb Scaling Laws y = some Parameter y ∝ mbb what is b? b is the slope of the log-log plot

  11. Force σCt Force 1 σCt 1 Δp r b = 2/3 b = 1/3 If wall thickness scales with length: b = 2/3 b = 1/3 If wall thickness (t), max stess (σC) constant: F ∝ L2 ∝ mb0.67 F ∝ L ∝ mb0.33 Δp = Δp = C = = ∝ ∝ ∝ ∝ σL σC σC r r r Area Area 2 t log Force log mb Laplace’s Law: If muscle properties constant during development: F ∝ muscle cross sectional area F ∝ mb0.67 b = 2/3 Scaling Laws y = Burrowing Force y ∝ mbb what is b?

  12. L2 L2 Scaling of burrowing force H0: b = 0.67 Actual: b ≈ 0.5 - Radial burrow-enlarging forces >> radial anchoring forces - Axial and radial enlarging forces about same magnitude ∝ ∝ C mb0

  13. L2 L2 Force Force Force a b H0: b = -0.33 H0: b = 0 ∝ ∝ = ∝ ∝ ∝ ∝ Pressure L-1 C mb-1/3 mb0 Weight L3 L2 Area* Area Scaling of burrowing force *Area of plane of the force transducer ⊥ to the force

  14. Scaling of burrowing force Burrowing force does not scale isometrically: Small worms can push 500 times body weight, large worms can only push 10 times body weight Hypotheses for cause of relatively weak large worms: 1) Muscle area might not increase isometrically with body size 2) Muscle stress might not be constant across body sizes 3) Mechanical advantage of segments might change with body size 4) Burrowing kinematics different for small & large worms 5) Soil deformation resistance might depend on scale of deformation

  15. HA: H0: F ∝ CSA of muscle CSA ∝ mbb CSA ∝ mb0.67 b < 0.67 1) Muscle Area Actual: b > 0.67

  16. L2 Force Force untested ∝ = ∝ ∝ σmuscle C mb0 L2 Area* Area *Area of muscle cross-section 2) Muscle Stress H0: σmuscle constant across all body sizes HA: σmuscle less in large worms

  17. A b Length ∝ = = MA MA B a diameter 3) Mechanical Advantage Quillin (1998) L = 102 mb0.34 d15 = 5.3 mb0.34 d50 = 4.2 mb0.32 Length and diameter both scale isometrically → no expected change in MA

  18. untested 4) Burrowing Kinematics larger worms→fewer strides per second larger worms→more elongated during crawling HA: Muscles of larger worms working at higher strains→produce less force

  19. untested 5) Soil Properties

  20. Scaling of burrowing force Burrowing force does not scale isometrically: Small worms can push 500 times body weight, large worms can only push 10 times body weight Hypotheses for cause of relatively weak large worms: 1) Muscle area might not increase isometrically with body size 2) Muscle stress might not be constant across body sizesTEST: σmuscle ↓ during development 3) Mechanical advantage of segments might change with body size 4) Burrowing kinematics different for small & large wormsTEST: larger earthworm muscles working at larger strains 5) Soil deformation resistance might depend on scale of deformation

  21. Maximum forces in earthwormscompared with other animals

  22. point here is that lever-like systems can’t scale with BOTH geometric and static stress similarity -- but hydrostatic skeletons can; worms grow isometrically, so these and dynamic stresses scale.

  23. Length A b ∝ = = MA MA diameter B a 3) Mechanical Advantage Quillin (1998) L = 102 mb0.34 d15 = 5.3 mb0.34 d50 = 4.2 mb0.32 Length and diameter both scale isometrically → no expected change in MA

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