Article Figures & Tables
Figures
- Fig. 1.
(A) Outline sketch (right lateral view) of the hindlimb skeleton of Pseudemys concinna illustrating the lines of action of the major muscle groups contributing to stresses in the femur during the stance phase of terrestrial locomotion. Pelvic girdle bones and tail vertebrae are colored black and femur is shaded grey. Some proximal hip muscles that do not span the femoral midshaft and do not contribute directly to femoral stress (e.g. puboischiofemoralis externus, ischiotrochantericus) have been omitted for clarity. Rotational forces exerted by caudi-iliofemoralis (dashed arrow) were not calculated (see text). (B) Outline sketch of the right femur and tibia (same as in A) of P. concinna illustrating the planes defining the anatomical frame of reference for force platform analyses. Both surfaces of the plane are labeled, with solid arrows and filled circles indicating surfaces in view and dashed arrows and open circles indicating surfaces hidden from view (i.e. surfaces that can only be seen if the planes are transparent). A, anterior; P, posterior; D, dorsal; V, ventral; L, lateral; M, medial.
- Fig. 2.
Representative kinematic profiles of right hindlimb joints for river cooter turtles (P. concinna) during a walking step over a force platform. Top to bottom: femoral (hip) protraction (Pro.)/retraction (Ret.) angle, femoral (hip) abduction (Ab.)/adduction (Add.) angle, knee angle and ankle angle (Ext., extension; Flex., flexion). Kinematic profiles represent mean (±s.e.m.) angles averaged across all four turtles (N=18–21 trials per individual, 78 total steps per data point). Note that axis scales differ for these plots to provide increased resolution for smaller angles.
- Fig. 3.
Mean ground reaction force (GRF) dynamics of the right hindlimb from an individual cooter. All plots show means (±s.e.m.) over N=21 trials. (A) Vertical, anteroposterior (AP) and mediolateral (ML) GRF components in body weight (BW), with positive values indicating upward, anterior and lateral forces, respectively (top to bottom). Axis scales differ for these plots to provide increased resolution for the small AP and ML forces. All trials were normalized to the same duration, allowing values to be graphed against the fraction of time through the contact interval. (B) Limb segment positions at the mean time of peak net GRF (41% contact) during a representative step by P. concinna, with the direction and magnitude of the GRF vector illustrated. The femur is highlighted by bolder lines; note that it is foreshortened in lateral view. H, hip; K, knee; A, ankle. (C) AP and ML orientations of the net GRF vector. AP angles were determined relative to vertical at 0° (90° indicates GRF horizontal, pointing forwards;<0° indicates posteriorly directed GRF). ML angles were determined relative to vertical at 0° (positive values indicate laterally directed GRF; negative values indicate medially directed GRF).
- Fig. 4.
Moments exerted by the GRF about the hindlimb joints and the long axis of the femur from an individual cooter. All plots show means (±s.e.m.) over N=20 trials. Note that axis scales differ for these plots to provide increased resolution for smaller moments. Directions of moments are labeled to the right of the figure plots. Hip AP, the GRF moment about the hip in the anatomical anterior and posterior directions; Hip DV, the GRF moment about the hip in the anatomical dorsal and ventral directions; Right prox. clock., torsional GRF moment, clockwise when viewing the right femur from the proximal end; Right prox. counter., torsional GRF moment, counterclockwise when viewing the right femur from its proximal end.
- Fig. 5.
Components of bending stress in the femur induced by muscles and GRF components from an individual cooter. All data are mean (±s.e.m.) stresses over N=21 trials. Stresses plotted are those occurring on the dorsal surface for forces acting to cause dorsoventral (DV) bending, and those occurring on the anterior surface for forces acting to cause anteroposterior (AP) bending. Tensile stress is positive and compressive stress is negative. `Muscles' indicates stresses induced by major muscle groups in the direction indicated; `external' indicates stresses induced by the GRF acting in the direction indicated; `axial' indicates stresses induced by the axial component of the GRF due to bone curvature in the direction indicated. Bending stresses induced by axial forces are very small and overlap along the zero line for the DV and AP directions. Note that the retractor moment generated by the GRF for most of stance (Fig. 4) precludes calculation of muscular contributions to AP bending stress in the femur, but that resulting stress underestimation is minimized to the extent possible (see Appendix).
- Fig. 6.
(A) Maximum tensile (σt, open circles) and compressive (σc, filled circles) stresses acting in the right femur and neutral axis angle from the anatomical AP axis of the femur from an individual cooter. Plots show means (±s.e.m.) over N=20 trials. Frame stills show limb position at the time of maximum tensile stress (left image) and at the time of peak net GRF magnitude (right image). Solid vertical lines mark the relative timing of these loading events. (B) Schematic cross-sections of a right femur illustrating neutral axis orientations for bending (red line and values) at peak tensile stress (upper) and peak net GRF (lower). Neutral axis is illustrated offset from the centroid (dark circle) due to axial compression superimposed on bending loads. Mean rotation of the neutral axis> 45° over the course of a walking step indicates that the `posterior' cortex of the femur experiences compression (shaded) and the `anterior' cortex experiences tension (unshaded), placing the plane of bending nearly parallel with the anatomical dorsoventral (DV) axis of the bone. The curved black arrow indicates the inward rotation of the femur during a step, which shifts the anatomical plane of bending to align more closely with the anatomical DV axis.
Tables
- Table 1.
Anatomical data from hindlimb muscles of experimental animals (P. concinna)
pc04 pc05 pc07 pc08 Muscle A θ rm A θ rm A θ rm A θ rm Hip retractors Pubotibialis + FTI* 82.9 8 7.1h, 8.1k 103.7 10 14.4h, 8.3k 56.9 10 12.0h, 11.7k 69.5 10 8.8h, 5.5k FTE 51.9 20 17.2h, 8.4k 81.2 20 12.5h, 19.0k 54.2 20 11.3h, 14.4k 34.7 20 8.0h, 9.6k Caudi-iliofemoralis 132.5 0 9.5h 111.7 0 11.1h 62.4 0 12.9h 83.0 0 9.1h Ischiotrochantericus 86.5 0 11.1h 76.1 0 9.7h 65.6 0 8.5h 37.9 0 6.4h Hip adductors Adductor femoris 18.7 15 5.5h 26.7 15 12.2h 17.6 15 8.5h 12.4 15 5.9h PIFE 73.6 0 5.6h 185.2 0 9.9h 115.8 0 7.4h 74.1 0 6.7h Knee extensors Iliotibialis 18.3 15 4.2k 28.2 10 4.2k 13.3 12 2.9k 12.9 12 3.5k Femorotibialis 67.4 0 5.1k 89.1 0 2.7k 63.0 0 3.1k 56.6 0 2.5k Ankle extensors Gastrocnemius (lateral) 12.1 0 6.4a, 5.9k 21.4 0 3.4a, 9.0k 20.9 0 2.7a, 7.2k 9.5 0 3.6a, 4.9k Gastrocnemius (medial) 19.4 0 2.9a 19.4 0 3.2a 5.9 0 3.7a 9.8 0 3.2a FDL 43.6 0 3.5a, 3.8k 56.1 0 2.7a, 5.7k 38.1 0 3.1a, 4.1k 25.8 0 3.0a, 3.6k Pronator profundus 50.7 0 2.3a 39.1 0 4.1a 61.3 0 3.1a 14.4 0 2.0a -
A, cross-sectional area of muscle (mm2); θ, angle between the muscle and the long axis on bone (degrees); rm, moment arm of the muscle (mm) about the joint indicated by the superscript letter (h, hip; k, knee; a, ankle); PIFE, puboishiofemoralis externus; FTI, flexor tibialis internus; FTE, flexor tibialis externus; FDL, flexor digitorum longus
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↵* Measurements of pubotibialis and FTI were combined in analyses due to their close association
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- Table 2.
Anatomical data from femora of experimental animals (P. concinna)
Measurement pc04 pc05 pc07 pc08 Length (mm) 51.9 66.9 57.1 40.5 A (mm2) 16.5 17.1 10.7 6.0 rc(AP) (mm) –1.1 –0.5 –0.4 –0.9 rc(DV) (mm) 1.4 1.7 1.6 1.3 yAP (mm) 1.9 1.9 1.8 1.6 yDV (mm) 2.8 2.3 2.3 1.8 IAP (mm4) 24.2 57.6 24.9 7.9 IDV (mm4) 18.2 38.4 18.9 6.3 J (mm4) 42.4 96.0 43.7 14.2 -
In subscript notations, AP denotes the anatomical anteroposterior direction for the femur, and DV denotes the anatomical dorsoventral direction for the femur; A, cross-sectional area of bone; rc, moment arm due to bone curvature; y, distance from neutral axis to cortex; I, second moment of area; J, polar moment of area. Curvature sign conventions for AP: positive, concave posterior; negative, concave anterior; curvature sign conventions for DV: positive, concave ventral; negative, concave dorsal
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- Table 3.
Mean peak ground reaction force data for P. concinna
GRF Animal Vertical (N) AP (N) ML (N) Peak net GRF time (%) net GRF (BW) GRF femur angle (deg.) GRF AP angle (deg.) GRF ML angle (deg.) pc04 (N=20) 11.3±0.2 –0.8±0.1 –0.7±0.1 37.8±1.6 0.57±0.01 94.3±1.0 –4.3±0.6 –3.5±0.4 pc05 (N=18) 16.1±0.4 0.4±0.3 –1.3±0.3 34.8±1.8 0.44±0.01 80.3±2.1 1.7±1.0 –5.0±1.2 pc07 (N=21) 10.4±0.3 1.8±0.3 –1.4±0.2 44.1±2.4 0.54±0.02 90.9±2.5 9.7±1.6 –8.0±1.4 pc08 (N=19) 3.9±0.1 0.3±0.04 –0.6±0.1 47.1±1.2 0.53±0.01 91.8±1.5 4.4±0.5 –8.1±0.6 Mean ± s.e.m. – – – 41.0±1.1 0.52±0.01 89.6±1.1 2.9±0.8 –6.2±0.5 -
GRF femur, angle of ground reaction force to the femur; GRF AP, anteroposterior inclination angle of GRF; GRF ML, mediolateral inclination angle of GRF
Vertical=0° for GRF AP and ML angles of inclination: for GRF AP, negative angles are posteriorly directed and positive angles are anteriorly directed; for GRF ML, negative angles are medially directed. BW, body weight
Values are means ± s.e.m. (N=number of steps analyzed)
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- Table 4.
Mean peak stresses for femora of P. concinna with GRF magnitudes and orientations at peak tensile stress
Peak stress Individual Tensile (MPa) Compressive (MPa) Axial (MPa) Shear (MPa) Peak tens. time (%) Peak comp. time (%) Neutral axis angle from AP (deg.) Net GRF (BW) GRF AP angle (deg.) GRF ML angle (deg.) Speed (CL s–1) pc04 (N=20) 39.1±0.2 –44.7±0.2 –2.9±0.1 19.3±0.5 9.9±1.2 12.1±1.0 17.5±0.9 0.39±0.02 5.3±0.6 –13.2±0.5 0.7±0.10 pc05 (N=18) 15.9±0.8 –20.9±0.5 –3.2±0.1 12.7±0.6 63.3±5.7 62.9±5.7 48.3±10.4 0.27±0.04 3.2±2.7 –9.5±2.3 0.6±0.05 pc07 (N=21) 21.3±0.5 –26.5±0.5 –3.2±0.1 10.8±0.7 50.4±5.6 39.3±6.4 44.2±8.8 0.35±0.05 6.1±2.3 –12.2±1.5 0.9±0.10 pc08 (N=19) 22.2±0.5 –31.3±0.7 –4.7±0.1 11.9±0.4 24.2±3.7 22.2±2.7 24.3±2.2 0.39±0.02 8.1±0.5 –15.6±1.1 0.6±0.05 Mean ± s.e.m. 24.9±1.0 –31.1±1.0 –3.5±0.1 13.7±0.5 36.6±3.2 33.6±3.1 33.4±3.7 0.35±0.01 5.6±0.9 –12.7±0.8 0.7±0.03 -
Shear stresses are reported for counterclockwise rotation of the right femur as viewed from the proximal end
Peak tension (tens.) and compression (comp.) time are shown as a percentage
Deviations of the neutral axis from the anatomical anteroposterior (AP) axis of each bone are counterclockwise in direction (i.e. positive angle from horizontal at 0°)
CL, carapace length; ML, mediolateral
Peak stresses were determined from force platform loading data; N=number of steps analyzed
Values are means ± s.e.m.
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- Table 5.
Mechanical properties and safety factors for femora and tibiae of P. concinna
Bending Torsion Bone N Yield stress (MPa) Safety factor mean N Yield stress (MPa) Safety factor mean Femur 3 305.9±66.3 13.9 3 78.1±6.6 6.3 Tibia 4 143.4±22.1 6.5* – – – -
Yield stress values are means ± s.e.m.
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↵* Tibial safety factor calculated from tibia yield stress and average peak locomotor stresses of the femur
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- Table 6.
Results of regressions of peak tensile stress in the femur during locomotion on kinematic and force variables for P. concinna and I. iguana
P. concinna I. iguana Variable RMA slope R P F RMA slope R P F FemTV angle (+) (deg.) –0.17 0.44 0.001* 13.68 1.44 0.33 0.10 3.01 FemHZ angle (–) (deg.) –0.57 0.35 0.01* 8.02 –0.97 0.36 0.07 3.61 Knee angle (+) (deg.) –0.27 0.37 0.005* 8.61 –1.82 0.29 0.15 2.26 Ankle angle (+) (deg.) 0.21 0.11 0.43 0.62 –1.72 0.11 0.59 0.29 Fm kext (+) (BW) 3.29 0.36 0.01* 8.35 0.97 0.88 <0.0001* 82.40 Fm add (–) (BW) –4.81 0.57 <0.0001* 26.94 –0.18 0.00 0.99 0.00 Fm aext (+) (BW) 4.69 0.65 <0.0001* 41.83 1.49 0.62 0.001* 15.26 Rhip (+) (CL) 48.99 0.29 0.03* 4.90 0.95 0.03 0.88 0.02 Rknee (–) (CL) –74.53 0.24 0.07 3.37 0.51 0.35 0.08 3.31 Rankle (+) (CL) 186.06 0.29 0.03* 5.08 –0.51 0.12 0.55 0.36 Net GRF (+) (BW) 20.42 0.48 0.0001* 17.06 0.04 0.74 <0.0001* 29.44 GRF AP angle (+) (deg.) –0.49 0.05 0.71 0.14 1.07 0.20 0.32 1.04 GRF ML angle (–) (deg.) –0.41 0.10 0.47 0.54 –0.65 0.14 0.48 0.51 Speed (+) (CL s–1) –45.01 0.01 0.94 0.01 0.05 0.34 0.09 3.19 -
All force and kinematic variables were determined at the time of peak tensile stress
Muscle force and moment arm data normalized for body weight (BW) and carapace length (CL), respectively, for P. concinna only
FemTV, hip protraction/retraction angle; FemHZ, hip abduction/adduction angle; Fm, force exerted by a muscle group; kext, knee extensors; add, femoral adductors; aext, ankle extensors; R, moment arm of GRF about a limb joint; net GRF, magnitude of resultant GRF vector; GRF AP, anterioposterior angle of GRF vector (in direction of travel); GRF ML, mediolateral angle of GRF vector (orthogonal to direction of travel)
Positive variables (+): positive slopes indicate increasing values with increased stress; negative slopes indicate decreasing values with increased stress
Negative variables (–): positive slopes indicate decreasing values with increased stress; negative slopes indicate increasing values with increased stress
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↵* RMA slopes significant at P<0.05; N=58 for all P. concinna regressions; N=26 for all I. iguana regressions (data from Blob and Biewener, 2001)
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