KATHERINE M. KEARSE, LARA D. LADAGE, BRITTNEY L. MANGES
Division of Mathematics & Natural Sciences, Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601, USA
ABSTRACT
The gastrocnemius muscle is the main muscle in the calf that flexes the foot and knee, and partially generates force during a jump. A muscle’s contractile force can be influenced by many factors including muscle thickness, the angle between the muscle body and the muscle fibers (pennation angle), and the length of the muscle fibers. During contraction, the fascicles shorten and rotate to greater pennation angles to generate force for movement. While much is known about the behavior and force generation of individual muscles, it’s less clear how the orientation of the muscle in relation to other bones and muscles affects the generation of force during contraction. Therefore, the focus of this experiment was to determine the orientation, or angle, of the gastrocnemius that would generate the greatest contractile force when stimulated. Four different orientations of the frog gastrocnemius were used to determine which generated the greatest contractile force. In this experiment, we assessed the contractile force generated across leg configurations that would occur during a jump. The muscle was stimulated with an electrode and force from muscle contraction was measured using a force transducer. The results from the overall model showed no significant differences in contractile force among the positions tested (p = 0.071). Using this information can help us understand how frogs generate such great contractile forces. This would be beneficial to understanding the mechanisms underlying jumping in this species, as well as inform future research about contractile force and kinematics that occur during jumping in other species.
INTRODUCTION
The skeletal muscles of vertebrates are an important part of the musculoskeletal system and are responsible for voluntary movements such as walking, swimming, and jumping. Skeletal muscles are composed of a collection of muscle fibers, which are composed of thick (myosin) and thin (actin) filaments that overlap. It is these thick and thin filaments that are responsible for the contraction of a muscle (e.g., Huxley, 1969). The force that is generated when a muscle contracts is called contractile force. Not all muscle contractions are equal, thus the contractile force generated differs as well. One study found that the greatest force is achieved when sarcomere length allows for optimal overlap of these filaments and that the force decreases when the overlap is shorter or longer than the optimum (MacIntosh, 2017). It has been found that contractile force in skeletal muscles increases as muscle thickness decreases and as pennation angles decrease (Dick et al., 2017). A pennation angle is the angle between the longitudinal axis of a muscle and its internal muscle fibers. As muscles contract, the muscle fibers rotate to greater pennation angles and the muscle shortens. For the muscle to maintain its volume, the muscle must increase in thickness when it is shortened (Dick et al., 2017).
Due to their capabilities of generating high contractile forces, frogs have tremendous jumping abilities, with the rear legs providing most of the force for forward propulsion. They are capable of jumping horizontal distances exceeding 30 times their body length (Moo et al., 2017) and execute these long jumps in a very short amount of time. A greater contractile force is beneficial for frogs when jumping as it allows them to jump quickly and far to escape predators and catch prey. For them to be able to do this, their hind leg muscles must produce a large amount of force. The gastrocnemius muscle, posterior of the lower leg, allows for flexion at the ankle and knee joints and is partially responsible for generating the contractile force used to jump these large distances. Understanding the physical conformation of the leg muscles during different points during jumping is important to understanding which part of a jump generates the greatest force.
Previous studies have observed the generated force of the gastrocnemius muscle. For example, in a study done by Herzog et al. (1992) on cats in situ, the peak contractile force of the gastrocnemius muscle occurred when the ankle was at an 80° angle and decreased as the ankle angle increased. An additional study looked at the force generated during jumping in vivo in frogs (Moo et al., 2017). This study found that that the gastrocnemius muscle produced the highest contractile force during the propulsion phase of the jump, when the frog is pushing off the ground to propel the body into the air. While the previous experiments examined in vivo differences in leg orientations, it remains unclear if more controlled experiments done in vitro on leg orientations can produce differences in force generation during gastrocnemius contraction.
The goal of this study was to examine the in vitro contractile force of the frog gastrocnemius muscle at four different leg orientations in the American bullfrog, Lithobates catesbeianus, to determine the orientation of the leg that produces the greatest contractile force. As the leg straightens, the muscle is less contracted, with decreased pennation angles and muscle thickness. Knowing this, we tested if the gastrocnemius muscle will generate more contractile force as the leg straightens. We predicted that the highest contractile force will be observed at the end of a frog’s jump, when the leg is almost completely straight.
METHODS
Materials
Anuran species differ in primary locomotor mode (jump, hop, swim, walk/run; Danos and Azizi 2015) so we chose an easily accessible jumping species, the American bullfrog, as our model species. Four adult bullfrogs were acquired from a vendor and used in this experiment. The enclosure that the frogs were held in measured 40 cm x 25 cm x 10 cm. It contained large aquarium pebbles and water. The frogs were held in captivity for four days and fed ten large meal worms twice a day while housed. The frogs were housed under a light cycle of 10 hours of light and 14 hours of darkness. All procedures were approved by the Pennsylvania State University’s Institutional Animal Care and Use Committee (protocol #201546456).
A force transducer was mounted onto a ring stand, with a femur clamp securely mounted to the bottom of the ring stand. A stimulating electrode for inducing muscle contractions was then connected to a separate ring stand. The force transducer and stimulating electrode were connected to a data acquisition program (PowerLab, Ad Instruments, Sydney, Australia) to collect data on generated contractile force. The force transducer was calibrated to give the data in Newtons and to correct any residual offset voltage.
Techniques
The frogs were humanely sacrificed, and the gastrocnemius muscle was then dissected away from the tibiofibular bone and was left attached to the tibiofemoral joint (knee) and calcaneus (heel). One end of a 15-cm piece of thread was tied to the Achilles tendon with the other end attached to a force transducer. The femur bone was cut just above the tibiofemoral joint, leaving the tibiofibular bone and talocrural joint (ankle) behind. The small portion of femur left was placed in the femur clamp mounted to the ring stand.
Figure 1. Four frog leg positions during stimulation of the gastrocnemius. For Position A, the knee-ankle joint and the ankle-tarsometatarsal joint were maneuvered into angles of 180° and 54°, respectively. Position B had the angles of the knee-ankle joint and the ankle-tarsometatarsal joint at 10° and 75°, respectively. For Position C, the angle between the knee and ankle joint was 25° and the angle between the ankle and tarsometatarsal bones was 150°. For Position D, the angles of the knee-ankle joint and the ankle-tarsometatarsal joint was 50° and 170°, respectively. Figure was redrawn based on Figure 5 in Moo et al. (2017).
The frog leg was maneuvered into four different positions based on previous analysis of leg positions during jumping (e.g., Moo et al., 2017), focusing on manipulating the position between the knee and ankle joints, as well as the position between the ankle and tarsometatarsal joints (Figure 1). Angels were measured using a protractor. For Position A, the angle between the knee and ankle joint was 180° and the angle between the ankle and tarsometatarsal bones was 54°, representing the loading phase of a jump. The takeoff phase of a jump was represented by Position B, with the angles of the knee-ankle joint and the ankle-tarsometatarsal joint 10° and 75°, respectively. For Position C, the angle between the knee and ankle joint was 25°, while the angle between the ankle and tarsometatarsal bones was 150°, representing the propulsion, or midjump, phase of a jump. Lastly, for Position D, the angle between the knee and ankle joint was 50° and the angle between the ankle and tarsometatarsal bones was 170°. This position represents the aerial phase of a jump, when the frog has completely left the surface from which it jumped. The gastrocnemius muscle was kept moist with lactated Ringer’s solution (200-250 mOsm, 6.6 g/L NaCl, 0.15 g/L KCl, 0.15 g/L CaCl2, 0.2 g/L NaHCO3) throughout the experiment.
For each muscle, in a neutral leg position, we calculated a supramaximal stimulus value, which was the minimum voltage required to generate maximum contraction multiplied by 1.5. This voltage was used to stimulate the muscle in each of the four leg positions. The gastrocnemius muscles from both legs of each frog were stimulated and data on contractile forces for each leg position were collected, thus this technique was repeated a total of eight times. A counterbalanced design was used to reduce the effect of fatigue over the four different tests for each leg.
Statistical Tests
Since data were collected on both legs of each subject, the contractile force of the two legs were averaged for each position, giving four averaged values per leg position. Because the predictor was continuous and data were collected on the same muscle for four different leg configurations, the differences in force among the four positions were assessed with a repeated-measures general linear model (GLM). A Mauchly’s Test of Sphericity was done to indicate whether the assumption of equality of variances was violated or not. Fischer's least significant difference was used for post-hoc pairwise comparisons. We considered all results to be statistically significant if p ≤ 0.05. All analyses were conducted with SPSS for Windows, v. 27 (IBM Corp., Armonk, NY, U.S.A.).
RESULTS
Figure 2. The average contractile force (± SD) of the gastrocnemius muscle in Lithobates catesbeianus at different leg positions. There were no significant differences in contractile forces among leg positions (p = .071).
The average contractile forces for Positions A, B, C and D were 5.6626 N, 11.829 N, 5.9556 N, and 6.4736 N, respectively. The Mauchly’s Test of Sphericity indicated that the assumption of sphericity was not violated (χ25 = 11.279, p = 0.0790). For the overall model, the results indicated no statistically significant difference in contractile force among the leg positions tested (F3,1 = 106.321, p = 0.071; Figure 2). Normally, no further tests would be done on the data because the statistical test of the overall model showed no significance. However, since the overall model was approaching significance, the post-hoc analyses were probed. It was found that all comparisons with Position B had p-values less than 0.179 while other pairwise comparisons between the other three positions were non-significant (all comparisons p ≥ 0.83, all ρ < 0.13).
DISCUSSION
The hypothesis for this experiment was that the greatest contractile force would be generated when the frog leg was straightest, representing the propulsion stage during a frog jump. The results of this experiment demonstrated no significant difference in contractile force among the four different configurations, although it appears that Position B trended towards having a greater contractile force compared to the others. As seen in Figure 2, there was a trend between the position of the leg and the generated contractile force such that Position B produced the greatest force, followed by Positions D, then C, then finally A. Statistically, however, the full model was not statistically significant and thus the hypothesis put forward was rejected.
Previous studies have examined the generated contractile force of the gastrocnemius muscle in situ and in vivo. For example, Herzog et al. (1992) exposed the gastrocnemius muscle of anesthetized cats and placed force transducers on the tendon of the muscle in situ. The researchers measured the force of the entire gastrocnemius muscle by stimulating it using a nerve cuff electrode placed around the tibial nerve. The peak contractile force of the gastrocnemius muscle happened when the ankle was at an angle of 80° and decreased as the ankle angle increased (Herzog et al., 1992). In our study, there was a trend that showed that the greatest contractile force was generated during Position B, when the angle between the knee and ankle joint was 10° and the angle between the ankle and tarsometatarsal bones was 75°, more similar to that found in Herzog et al. (1992). However, statistical tests showed no significant difference in the contractile forces between the four leg positions of this experiment. Studies contradicting each other or not finding similar results illustrates the need for further research. This and the Herzog et al. (1992) study may have arrived at different results due to other reasons as well, including that the kinematics may differ in the jumping mechanics between cats and frogs as well as different points of electrode placement and stimulation.
In a different study, Moo et al. (2017) implanted sonomicrometry crystals, EMG electrodes, and a force transducer directly into the belly of the plantaris longus of Rana pipiens. The researchers then let the frog jump normally and measured the contractile force. They found that the muscle produced the highest contractile force during the propulsion phase of the jump (Moo et al., 2017). The results from this study indicate that Position C in the current experiment may have generated the highest contractile force, however we did not find that Position C varied in contractile force when compared to the other positions. This may be due to species differences or measuring contractile force in vitro vs. in vivo. There are likely differences in generation of contractile forces when the muscles are in highly controlled conditions versus in an actual moving animal. In fact, previous studies have found that muscles and tendons can be pre-loaded, like a catapult, representing stored potential energy that can couple with the muscles’ contractile forces during movement (e.g., Astley and Roberts, 2011, 2014; Mayfield et al., 2016). In our study, because our animals had been sacrificed, we could not account for pre-loading on the resultant contractile force. Another study also found that accounting for the angle at the sacral joint can be important for generating different dynamics during jumping (Richards et al., 2018); the current study did not manipulate this joint, and it thus remains unclear the contribution that this joint makes on contractile force. Contraction of and support by other muscles, pre-loading force, and components of the musculoskeletal system likely change the contractile forces in the gastrocnemius during movement and we may not expect the results to be similar between a stationary, highly controlled leg position versus a whole animal moving in vivo (e.g., Peplowski and Marsh, 1997; Wade et al., 2019).
Although the results of this study trended towards some previous research, such as that of Herzog et al. (1992), they did not align with what was found in some other prior experiments on frogs, such as what Moo et al. (2017) found. Our non-significant results could be attributable to factors specific to our study. A few possible causes include the sample size used in this experiment being very small, as it consisted of only four frogs. If the experiment were to be done with a larger sample size, it is possible that the data would better represent what was found in the literature. Furthermore, the experiment could have been impacted because the orientation of the frog leg may have moved slightly during stimulation. More advanced equipment that can precisely assess angle and assure little to no deviation during stimulation would create more accuracy in the data. Finally, because frogs are ectothermic, it may be that the temperature at which we stimulated the muscles affected contractile properties. Previous studies have found that temperature can impact the power output by the legs during jumping (e.g., Peplowski and Marsh, 1997, Johnston and Temple, 2002); because we did not control for temperature, it may have affected our results in some way.
The purpose of this study was to determine what phase in the frog’s jump produced the greatest contractile force. Understanding this contributes to our knowledge about how frogs are capable of jumping such outstanding distances. From a comparative standpoint, using a different species would be useful in understanding the evolution of muscles used in jumping and propulsion. In frog species, changing the species of frog would affect the size and structure of the gastrocnemius muscle, which would also change the force generated during contraction. Further, examining locomotor modalities among frog species (e.g., species that jump, walk, swim) can provide a functional view of the relationship among limb configuration, contractile force generated, and locomotor mode. An extreme species comparison would be looking at kangaroos, which are also known for their tremendous jumping abilities. Understanding the similarities and differences among vastly differences jumping species can help in understanding the mechanisms underlying jumping and how those mechanisms have evolved over time. Finding the similarities between two animals that are both known for jumping can help narrow down future research about contractile force and other mechanistic aspects of jumping. Research conducted on the mechanisms of jumping is significant because it allows us to understand how species can jump great distances and how this is beneficial to their survival and reproduction.
The data of this experiment did not show that a significant difference in contractile force as the leg position changed, or that one position generated a significantly greater contractile force than the others. Therefore, we could not conclusively demonstrate in which angle or orientation of the leg would generate the greatest contractile force in the gastrocnemius. However, future research could use the basis of this study to repeat the study or change other variables to ascertain if they affect gastrocnemius muscle contraction. Because there are fewer controlled studies on manipulation of leg orientations in static positions, it is unclear the relationship between those and contractile force generated in moving animals.
ACKNOWLEDGMENTS
We would like to thank Cori Biddle, Penn State Altoona’s assistant librarian, for help with finding literature and Mark Oswalt, the Biology lab manager, for helping set up the experiment.
CONFLICTS OF INTEREST/DISCLOSURE
The authors declare no conflicts of interest.
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