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Functional morphology of proximal hindlimb muscles in the frog Rana pipiens

William J. Kargo^1,* and Lawrence C. Rome²

¹ The Neurosciences Institute, 10640 John Jay Hopkins Drive, San Diego, CA 92121, USA
² Department of Biology, University of Pennsylvania, Philadelphia, PA 19129, USA

View larger version (35K): [in a new window]   Fig. 1. Muscle attachment sites in the frog Rana pipiens. (A) Attachment sites on the pelvis. The thigh muscles were dissected, and the proximal portion of each muscle, except CR (cruralis) and SM (semimembranosus) in this particular specimen, was left intact and attached to the pelvis. CR and SM muscles were completely removed from the pelvis. The pelvis/femur/muscle complex was scanned with a three-dimensional laser scanner, and the three-dimensional image is shown. Ventral, dorsal, caudal, lateral and rostral views are shown from top left to bottom right. Muscle attachment sites are marked on the image by the appropriate abbreviations (see below). (B) Attachment sites surrounding the knee joint. Thigh and calf muscles were dissected, and the portion of each muscle attached at the knee joint was left intact. The femur/tibiofibula/muscle complex was scanned with a three-dimensional laser scanner, and the three-dimensional image is shown. Ventral, dorsal, posterior and anterior views are shown from top left to bottom right. Muscle abbreviations are as follows: semimembranosus (SM), gracilus major (GR), adductor magnus dorsal and ventral heads (ADd and ADv), cruralis (CR), gluteus magnus (GL), semitendinosus ventral and dorsal heads (STv and STd), combined distal tendons of STv and STd (ST) iliofibularis (ILf), iliacus externus (ILe), iliacus internus (ILi), sartorius (SA), tensor fascia latae (TFL), tibialis (TA), peroneus (PE) and plantarus (PL), obturator internus and externus (OI and OE), quadratus femoris (QF) and pectineus (Pec).

View larger version (52K): [in a new window]   Fig. 3. Coordinate axes for the hip and knee joints. The hip was modeled as a ball-and-socket joint with three orthogonal axes of rotation. The center of rotation was fixed and located within the femoral head. Rotation about the z-axis was termed hip flexion (counterclockwise) and hip extension (clockwise). Rotation about the y-axis was termed hip adduction (counterclockwise) and hip abduction (clockwise). Rotation about the x-axis was termed hip internal rotation (clockwise) and external rotation (counterclockwise). The kinematics about the z-axis of the knee joint was modeled by a planar, rolling joint. Clockwise rotation about the z-axis of the knee joint was termed flexion, and counterclockwise rotation was termed knee extension.

View larger version (26K): [in a new window]   Fig. 2. The paths of the musculotendon actuators making up the frog model. The muscles include semimembranosus (SM), gracilus major (GR), adductor magnus dorsal and ventral heads (ADd and ADv), cruralis (CR), gluteus magnus (GL), semitendinosus ventral and dorsal heads (STv and STd), iliofibularis (ILf), iliacus externus (ILe), iliacus internus (ILi), sartorius (SA), tensor fascia latae (TFL), obturator internus (OI), quadratus femoris (QF) and pectineus (Pec). Paths are shown only for proximal hindlimb muscles and represent the path between the pelvis attachment site and the distal muscle attachment site. Individual muscles are marked by the appropriate muscle abbreviations. The top row shows four different views, left to right: ventral, lateral, dorsal, rostral, of hip-flexor-related muscles (CR, GL, ILe, ILf, ILi, SA and TFL). The bottom row shows four different views, left to right: ventral, lateral, dorsal, caudal, of hip-extensor-related muscles (ADd, ADv, GR, SM, STd, STv, OI and QF).

View larger version (41K): [in a new window]   Fig. 4. Moment arm measurements about the hip and knee joints. (A) Moment arms about the flexion—extension axis of the hip joint in experimental frogs were measured relative to a starting, test position (see text). Values are means ± 1 S.D., N=8. The color scheme is as follows: ADd, dark gray; ADv, orange; CR, brown; GL, yellow; GR, red; ILe, dark green; ILf, light gray; ILi, purple; SA, light blue; STd, black; SM, light green; TFL, dark blue. FLEX, flexion; EXT, extension. (B) Moment arms about the abduction—adduction axis of the hip joint in experimental frogs. ADD, adduction; ABD, abduction. (C) Moment arms about the internal—external rotation axis of the hip joint in experimental frogs. EX, external rotation; IN, internal rotation. (D) Moment arms about the flexion—extension axis of the frog knee joint were measured relative to a test position (see text). Values are means ± 1 S.D., N=6. (E) Moment arms about the flexion—extension axis of the hip in the model frog. (F) Moment arms about the abduction—adduction axis of the hip in the model frog. (G) Moment arms about the internal—external rotation axis of the hip in the model frog. Muscle abbreviations: semimembranosus (SM), gracilus major (GR), adductor magnus dorsal and ventral heads (ADd and ADv), cruralis (CR), gluteus magnus (GL), semitendinosus ventral and dorsal heads (STv and STd), iliofibularis (ILf), iliacus externus (ILe), iliacus internus (ILi), sartorius (SA) and tensor fascia latae (TFL).

View larger version (30K): [in a new window]   Fig. 5. Moment arms about a single axis of the hip joint depend not only on the rotation angle about that axis but also on rotation angles about the other two hip axes. The left column of each panel (A—C) shows data for the model frog, and the right column shows data measured in experimental frogs. The top row of each panel shows data for semimembranosus (SM) and the bottom row shows data for sartorius (SA). For each plot (four per panel), the right and left horizontal axes represent the hip angles (in degrees) and the vertical axis represents the moment arm (in mm) about the flexion—extension (FLEX/EXT) (A), abduction—adduction (ABD/ADD) (B) and external—internal rotation (EX/IN) (C) axes of the hip. (A) Extensor moment arms for SM were dramatically reduced when the femur was adducted or abducted away from the test position. The peak flexor moment arm for SA was reduced when the femur was adducted or abducted away from the test position. (B) The abduction moment arms for SM varied little across the range of abduction—adduction when the femur was extended, but varied to a much greater extent (by 30-40 %) when the femur was flexed. The opposite effect was observed for SA adduction moment arms. (C) Internal rotation moment arms for SM were largest at extended hip positions and smallest at flexed hip positions. External rotation moment arms for SA were largest at flexed positions and smallest at extended positions.

View larger version (34K): [in a new window]   Fig. 6. Sarcomere excursion ranges measured in the model frog and in experimental frogs. Arrows represent the starting (arrow tail) and final (arrow head) sarcomere lengths predicted by the model frog at the starting and take-off positions of a jump. Sarcomere lengths were predicted by simulating fixed-end contractions at the start position and then at the take-off position. Bars represent ± 1 S.D. (N=6) from the mean sarcomere lengths measured in experimental frogs when placed (and fixed) at the starting and take-off positions of a jump. Each row shows data for one muscle (model, arrow; experimental frogs, bars). The muscles corresponding to each row are shown to the right. Muscle abbreviations are as follows: semimembranosus (SM), gracilus major (GR), adductor magnus dorsal and ventral heads (Add and ADv), cruralis (CR), gluteus magnus (GL), semitendinosus ventral and dorsal heads (STv and STd), iliofibularis (ILf), iliacus externus (ILe), iliacus internus (ILi), sartorius (SA) and tensor fascia latae (TFL). Also plotted is the sarcomere length/tension relationship for frog SA (dashed line; Gordon et al., 1966). In general, the model accurately predicted the starting and final sarcomere lengths of experimental frogs, and most muscles operated over a range where at least 85 % of maximal tetanic force could be produced.

View larger version (44K): [in a new window]   Fig. 7. Three-dimensional force fields produced by the primary hip extensor muscles (A) (semimembranosus, SM, top row; gracilus, GR, middle row; adductor dorsal head, ADd, bottom row) and knee extensor muscles (B) (cruralis, CR, top; gluteus magnus, GL, middle; tensor fascia latae, TFL, bottom). Force fields were constructed by placing the model ankle at different positions in the limb's workspace and maximally activating each muscle (by simulating a fixed-end muscle contraction; see Materials and methods). The peak force produced at each of 80 positions is plotted. The force field produced by each muscle is normalized to the maximum force within each field so that force fields can be compared among muscles. The left columns of A (hip extensors) and B (knee extensor) show a top view and the right columns show a side view of the leg and the muscle force fields. One block in each view represents 10 mm2, i.e. line divisions are 10 mm in length. The force vector at each ankle position has three components: rostral—caudal, medial—lateral and elevation—depression. The rostral—caudal and medial—lateral components are depicted in the left column of A and B; the rostral—caudal components are along the long axis of frog in the horizontal plane, and the medial—lateral components are along the short axis of the frog. The elevation—depression and rostral—caudal components are depicted in the right column of A and B; the elevation—depression components are forces in the plane of gravity. Each muscle produced fields that were a combination of vector components. Most importantly, the magnitude of the force vector components produced by the contraction of each muscle was configuration-dependent.

View larger version (46K): [in a new window]   Fig. 8. Three-dimensional force fields produced by the monoarticular hip flexors (A) (iliacus internus, ILi, top row; iliacus externus, ILe, bottom row), the hip adductor muscles (B) (adductor ventral head, ADv, top row; sartorius, SA, bottom row) and the knee flexor muscles (C) (semitendinosus, ST, top row; iliofibularis, ILf, bottom row). ST is for the combined action of STv and STd. Force fields were constructed as described in Fig. 7 and in the text. The peak force produced at each of 80 positions is plotted. The force field produced by each muscle is normalized to the maximum force within each field so that force fields can be compared among muscles. The left columns of A (hip flexors), B (hip adductors) and C (knee flexors) show a top view and the right columns show a side view of the frog and the muscle force fields. One block in each view represents 10 mm2, i.e. line divisions are 10 mm in length. Each muscle produced force fields that were a combination of elevation—depression, rostral—caudal and medial—lateral functions (see text). The magnitude of the force vector components produced by the contraction of each muscle was configuration-dependent.

View larger version (38K): [in a new window]   Fig. 9. Muscles classified as motors, springs, brakes and struts with respect to contraction type have different qualitative effects on multi-joint limb behavior. Top row, the dot product between the ankle force vector produced by muscle contraction and the instantaneous velocity vector of the ankle during four different behaviors (A, swimming; B, hindlimb wiping; C, defensive kicking; D, jumping). For D, the dot product is calculated between the force vector produced by semitendinosus (ST) contraction (at the tip of the astragalus segment) and the total force vector applied to the ground (see text). Dot products are calculated during periods of muscle activation and shown as circles. Dot products were calculated between the unit vectors (normalized to a magnitude of 1.0). The light gray box represents regions where dot products were greater than 0.5 or the angle between vectors was less than 45°. The dark gray box represents regions where dot products were less than -0.5 or the angle between vectors was greater than 135°. Bottom row, kinematics of the thigh, calf and astragalus segments during the different behaviors. Small arrows represent the direction of ankle movement; the small arrow in D is the direction of body movement. Larger arrows represent the direction of force produced by muscle contraction (gray) and ankle velocity (black) at a time point during the kinematic cycle. In A—C, kinematic parameters are shown at 16.67 ms intervals. In D, kinematic parameters are shown at 5 ms intervals. (A) The ankle forces produced by semimembranosus (SM) contraction during the swimming cycle act to support ankle motion (dot products greater than 0.5). (B) The ankle forces produced by cruralis (CR) contraction during the hindlimb cycle act briefly to oppose and then to support ankle motion (dot products initially less than -0.5 quickly shift to values greater than 0.5). (C) The ankle forces produced by sartorius (SA) contraction during the kicking cycle oppose the entire extension phase (dot products during the 250 ms extension phase were less than -0.5). (D) The forces applied to the ground by semitendinosus (ST) contraction do not clearly support or oppose body motion (dot products between ST forces and the total forces applied to the ground were less than 0.5 but greater than -0.5)

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