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Multi-functionality of the cat medical gastrocnemius during locomotion
ARTICLE IN PRESS
Journal of Biomechanics 38 (2005) 1291–1301 www.elsevier.com/locate/jbiomech www.JBiomech.com
Multi-functionality of the cat medical gastrocnemius during locomotion Motoshi Kaya, Azim Jinha, Tim R. Leonard, Walter Herzog Faculty of Kinesiology, Human Performance Laboratory, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4 Accepted 20 June 2004
Abstract The functional role of biarticular muscles was investigated based on direct force measurement in the cat medial gastrocnemius (MG) and analysis of hindlimb kinematics and kinetics for the stance phase of level, uphill, and downhill walking. Four primary functional roles of biarticular muscles have been proposed in the past. These functional roles have typically been discussed independently of each other, and biarticular muscles have rarely been assigned more than one functional roles for different phases of the work cycle. The purpose of this study was to elucidate the functional role of the biarticular cat MG during locomotion. It was found that MG forces were primarily associated with the moment requirements at the ankle for most of the stance phase, but also helped to satisfy the moments at the knee in the initial phase of stance. In the second half of stance, MG transferred mechanical energy from the knee to the ankle from the knee to the ankle, while simultaneously producing a substantial amount of mechanical work. Based on these results, we hypothesize that MG’s primary function is that of an ankle extensor. However, because of the coupling of the ankle extensor moment with a knee flexor moment in the initial, and a knee extensor moment in the final phase of stance, MG satisfies two joint moments in early stance, and transfers mechanical energy from the knee to the ankle in late stance. We conclude that cat MG has multiple functional roles during the stance phase of locomotion, and speculate that such multifunctionality also exists in other bi- and multi-articular muscles. r 2004 Elsevier Ltd. All rights reserved. Keywords: Muscle coordination; Biarticular muscle; Joint moment; Cat locomotion
1. Introduction The redundant nature of musculoskeletal systems allows for a specific task to be performed with an infinite number of muscular coordination patterns. Yet, it has been known for a long time that skilled movements are performed in a stereotyped manner. Similar patterns of muscular coordination have been observed within and across subjects for movement tasks, such as human walking (e.g., Winter and Yack, 1987; Dietz et al., 2001), cycling (e.g., van Ingen Schenau et al., 1995; Neptune and Herzog, 2000), and cat locomotion (e.g., Walmsley et al., 1978; Hodgson, 1983, Herzog et al., 1993). Corresponding author. Tel.:+1-403-220-8525; fax: +1-403-284-3553
E-mail address: [email protected] (W. Herzog). 0021-9290/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2004.06.009
In humans and animals, mono-, bi-, and multiarticular muscles have often been associated with distinct and different functional roles. An understanding of these roles might provide novel insight into the mechanisms of muscular coordination and movement control. An obvious advantage of biarticular muscles is that force from one muscle can produce movements at two joints. Therefore, one might think of biarticular muscles to be preferentially activated when the moments they produce about both joints coincide with the moment requirements of the actual movement. Such a functional role of biarticular muscles has been proposed for human (Fujiwara and Basmajian, 1975; Prilutsky and Gregor, 1997; Prilutsky et al., 1998) and animal movement (Jacobs and Macpherson, 1996; Gregor et al., 2001). However, this proposed role may have severe
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limitations. For example, moments produced by biarticular muscles at a joint are often associated with a rotational movement in the same direction. If so, a biarticular muscle would shorten because of its action at both joints, and its contractile speed would be greater than that of corresponding monoarticular muscles, thus reducing its force capacity in accordance with the forcevelocity relationship (Hill, 1938). However, the contractile velocity of biarticular muscles may be smaller than that of corresponding monoarticular muscles in situations in which shortening at one joint is offset by lengthening at the other joint. This reduced contractile velocity of biarticular muscles allows for favorable contractile conditions during fast locomotion (e.g., cat gastrocnemius and plantaris during trotting and galloping, Prilutsky et al., 1996). Therefore, biarticular muscles are sometimes thought of as nearly ‘‘isometric’’ structures that transport mechanical energy from one joint to the adjacent rather than producing substantial work themselves (Bobbert and van Ingen Schenau, 1988; Mai and Lieber, 1990; Jacobs et al., 1996). van Ingen Schenau et al. (1992) proposed that monoarticular muscles are preferentially activated when movement direction involves shortening, while biarticular muscles are preferentially activated to control the direction of external forces by adjusting the moments in the two joints they span. Thus, biarticular muscles were thought to be highly activated when they produce an external force component, whose direction is similar to the direction of the required external force. This proposed function of biarticular muscles (van Ingen Schenau et al., 1992) is mechanically equivalent to the first one mentioned above, if the inertial effects of a movement are small, and thus can be neglected in the equations of motion, such as during static leg extension (Jacobs and van Ingen Schenau, 1992, Prilutsky and Gregor, 1997), slow isokinetic leg extension (Doorenbosch and van Ingen Schenau, 1995), and cat walking (Kaya et al., 2003b). Finally, Dul et al. (1984) suggested that biarticular muscles, such as the cat medial gastrocnemius (MG, biarticular ankle extensor/knee flexor), may be considered monoarticular muscles (ankle extension), based on electromyographical (EMG) patterns (Wetzel et al., 1973) and reflex connections (Goslow et al., 1973). Therefore, biarticular muscles might be used primarily to satisfy the moments at a single joint, while being relatively insensitive to the mechanical requirements at the other joint. From the above arguments, it can be seen that biarticular muscles have been associated with at least four distinctly different functional roles. Much of the evidence in support of these functional roles is based on the anatomy of the musculoskeletal system, activation patterns as observed through EMG recording, or
indirect estimates of muscle force. However, musculoskeletal anatomy may lead to paradoxical conclusion (Lombard, 1903), and the relationship between EMG and muscle force in dynamic situations is highly nonlinear (Bigland-Ritchie 1981; Guimaraes et al., 1994a, b), and contains a variable time delay (Guimaraes et al., 1995). Furthermore, adequate EMG-force relationships seem only possible using powerful numerical approaches (e.g., artificial neural networks, Savelberg and Herzog, 1997; Liu et al., 1999), and indirect force estimates may contain massive errors (Herzog and Leonard, 1991). For these reasons, there is little accurate, quantitative evidence about the role of biarticular muscles during voluntary movements. Interestingly, the idea that biarticular muscles may satisfy different functional roles, depending on the instantaneous movement requirements, has not been considered systematically. The purpose of this study was to elucidate the role of the biarticular cat MG during a variety of locomotor conditions, based on measured MG forces, and the external kinematics and kinetics.
2. Methods 2.1. Subjects and muscle force measurement Six outbred, male, adult cats (5.371.2 kg) were trained to walk on a walkway that was positioned at different slopes: level (n ¼ 24 individual trials for N ¼ 5 animals), upslope at 301 (n ¼ 25, N ¼ 6), 451 (n ¼ 25, N ¼ 6), and 601 (n ¼ 12, N ¼ 5), and downslope at -301 (n ¼ 28, N ¼ 6). These walking conditions were chosen, since characteristics of the required ankle and knee joint moments change substantially between level, uphill, and downhill walking (e.g., Gregor et al., 2001), and so provide a large range of conditions for studying the functional role of MG. Each cat was surgically implanted with buckle-type tendon force transducers (Walmsley et al., 1978) onto the separated tendons of the MG and soleus (SOL) (Herzog et al., 1993). MG and SOL were chosen, since force measurements are straight forward, and comparable results are available in the literature (Walmsley et al., 1978; Hodgson, 1983, Whiting et al., 1984; Fowler et al., 1993; Herzog et al., 1993; Prilutsky et al., 1994; Gregor et al., 2001). All signals were transmitted by telemetry to a custom-built amplifier and stored on a PC at 2000 Hz. After implantation of the sensors, training was resumed one day following surgery to prevent the formation of adhesions around the ankle, and to accelerate the recovery process. Measurements were carried out when cats had completely recovered from surgery based on the assessment of kinematics and kinetics (ground reaction force (GRF) and resultant joint moment) of the implanted hindlimb. All surgical procedures were
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performed according to the guidelines of the Canadian Council on Animal Care, and were approved by the Life Sciences Animal Ethics Committee of the University of Calgary. For a more detailed description of the surgical procedures and measurement of tendon forces, see Herzog et al. (1993) and Kaya et al. (2003a). 2.2. Hindlimb kinematics and kinetics Reflective markers were placed over the hip, knee, ankle, metatarsophalangeal (MP) joint, and toe of the instrumented hindlimb to obtain knee, ankle, and MP joint angles. The positions of these markers for level and uphill walking were collected using a motion analysis system (60 Hz; VP310, Motion Analysis Cooperation, Santa Rosa, CA, USA), and those for downhill walking were recorded using a high-speed camera (200 Hz; V14B, NAC, Inc., Tokyo, Japan) and were manually digitized using a custom-designed program written in MATLAB (Math Works, Inc., Natick, MA, USA). In order to avoid artifacts caused by skin marker movement, the location of the knee joint center was calculated using an optimization procedure, in which the estimated location of the knee marker was optimized to be closest to the measured knee marker location, with the constraint that the distances from the estimated knee joint center to the measured ankle and hip joint were the same as the measured shank and thigh length, respectively. GRFs of the instrumented hindlimb were measured using two force platforms located in the center of the walkway (DRMC36, AMTI, Newton, MA, USA). They were collected simultaneously with the muscle forces and stored on a PC at 2000 Hz. The resultant joint moments at ankle and knee were calculated using the inverse dynamics approach (Andrews, 1995) with hindlimb kinematics and ground reaction forces obtained directly, and inertial properties of body segments estimated using equations given by Hoy and Zernicke (1985). In this study, extensor moments were defined as positive. In order to quantify the moment demands at ankle and knee that could be satisfied by MG, the knee moment was subtracted from the ankle moment (e.g., Prilutsky et al., 1998). Since extensor moments are defined as positive, the difference between ankle and knee moments becomes greater when both (either) the ankle extensor moment and (or) the knee flexor moment increases. 2.3. Data analysis Correlation coefficients were calculated to evaluate the relationships between MG forces and resultant ankle/knee moments. This analysis was performed at every 10% of the stance phase between 10% and 90% of stance. For a given walking condition, individual step
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3. Results Typical examples of the time-histories of knee and ankle joint moment for 301 downhill, level, and 451 uphill walking are shown with the corresponding MG and SOL forces in Fig. 1. Compared to level walking (black lines in Fig. 1A, B), uphill walking is associated with greater ankle extensor and knee flexor moments (gray lines in Fig. 1A, B), while downhill walking is associated with smaller ankle extensor and greater knee extensor moments (dashed lines in Fig. 1A, B) in the first part of stance. In the second part of stance, greater ankle and knee extensor moments are required for uphill compared to level and downhill walking, while downhill walking is associated with an ankle flexor and a small knee extensor moment. Both shape and magnitude of MG force curves changed systematically with the corresponding ankle extensor moment curves for the entire stance phase (Fig. 1B, C). MG forces were greatest for uphill walking throughout stance (Fig. 1C), and peak forces were shifted relative to level walking from early to midstance, similar to the shift for the peak ankle extensor moments (Fig. 1B). For downhill walking, MG force became very small (for some animals, even zero) when the ankle moment switched from extensor to flexor in the latter part of stance. In contrast, SOL forces were less sensitive to changes in the ankle moment requirements (Fig. 1B, D). For instance, SOL force did not decrease as quickly as MG force in the latter part of stance of downhill walking, and some animals showed a decrease in SOL forces from level to uphill walking when ankle extensor moments and MG forces increased (e.g., gray line in Fig. 1D). The relationships between MG force and ankle moment at 10% increments of the stance phase (10–90%) from a single animal across all walking conditions are shown in Fig. 2. The corresponding correlation coefficients between MG force and ankle moment for all individual animals are shown as a function of the percent of stance phase in Fig. 3. MG forces were positively correlated with ankle extensor moments in the initial 80% of stance across all animals, and strong positive correlations were observed up to 70% of the stance phase (Fig. 3). Ankle extensor moments were typically greater for uphill walking (filled symbols in Fig. 2) than for level and downhill walking (empty symbols in Fig. 2). The relationships between MG force and knee moment at 10% increments of the stance phase (10–90%) from a single animal across all walking conditions are shown in Fig. 4. The corresponding
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Fig. 1. Mean time-histories of (A) knee moment; (B) ankle moment; (C) MG force; and (D) SOL force curves as a function of percent of the stance phase for 301 downhill, level, and 451 uphill walking from a single animal. Note, that the MG force curves are similar in shape and vary in a similar way in magnitude with the corresponding ankle moment curves, while SOL force curves do not.
correlation coefficients between MG force and knee moment for individual animals are shown as a function of the percent of stance phase in Fig. 5. MG forces were negatively correlated with knee extensor moments in the initial 30% of stance, while they were positively correlated with knee extensor moments in the second half of stance, except for one animal (cat 1) (Fig. 5). Cat 1 was an exceptional animal in that it produced smaller knee extensor moments than the remaining five animals in the late part of stance for uphill compared to level and downhill walking. The relationships between MG force and the difference between ankle and knee moments at 10% incre-
The functional role of biarticular muscles has been debated for decades. The following arguments have crystallized from these discussions: (i) biarticular muscles primarily function to simultaneously satisfy the moment requirements at the two joints they span. (e.g., Prilutsky et al., 1998; Gregor et al., 2001). (ii) Biarticular muscles function to transfer energy from one joint to the other (e.g., Bobbert and van Ingen Schenau, 1988). (iii) Biarticular muscles function to control the direction of external forces (van Ingen Schenau et al., 1992). Note that the functional role proposed under point (i) constitutes a sub-set of the functional role of point (iii); i.e., the case when all inertial effects are negligible or are ignored. (iv) Biarticular muscles function essentially as monoarticular muscles to satisfy the resultant joint moment at one of the two joints exclusively (Dul et al., 1984). The four functional roles proposed here have been put forward independently in the past. Below, we discuss whether cat MG can be associated with any of these roles. (i) Biarticular muscles function to satisfy moments at two joints. The positive correlations between MG force and the difference between ankle and knee moments were greatest in the first half of the stance phase (10–50%) (Fig. 7), since MG forces increased with increasing ankle extensor moments (positive correlation, Fig. 3), and also increased with increasing knee flexor moments (negative correlation, Fig. 5). For the second half of the stance phase, the positive correlations between MG force and the difference between ankle and knee moments decreased, and eventually, became negative (Fig. 7), suggesting that MG functions to satisfy ankle and knee moments for the first half of the stance phase, but definitely not for the second half. (ii) Biarticular muscles function to transfer energy from one joint to the other joint. For the second half of stance, MG forces were mostly positively correlated with the knee extensor (Fig. 5) and the ankle extensor moments (Fig. 3). These joint kinetics were consistently associated with ankle and knee extension in this period of stance, implying that MG functions to transfer energy from the knee to ankle for the second half of the stance phase. However, MG also shortens substantially during the
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Fig. 2. Relationships between MG force and ankle moment at (A) 10%, (B) 20%, (C) 30%, (D) 40%, (E) 50%, (F) 60%, (G) 70%, (H) 80%, and (I) 90% of the stance phase. Data were obtained from a single animal (cat 3) across all walking conditions. Extensor moments are defined as positive.
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second half of stance (Fig. 8). Therefore, it does not only transfers energy, but also produces a substantial amount of mechanical energy in this phase.
(iii) Biarticular muscles function to control the direction of external force. This functional role is mechanically almost equivalent to the first one, because inertial effects play a minor role during cat locomotion (Kaya et al, 2003b). MG may be considered to satisfy this functional role for the first half of the stance phase, for the reasons described above under point (i). (iv) Biarticular muscles function to satisfy moments at a single joint. The great positive correlations between MG forces and ankle moments for most (70-80%) of the stance phase suggest that MG functions as an ankle extensor (Fig. 3) with little regard for the mechanical requirements at the knee (Fig. 7). This suggestion is further supported by the close agreement of the shape of the time-histories of MG forces and ankle extensor moments for the entire stance phase (Fig. 1). Interestingly, MG forces became very small or zero when the ankle moment switched from extensor to flexor in the late phase of stance in downhill walking (Fig. 1B, C),
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Fig. 4. Relationships between MG force and knee moment at (A) 10%, (B) 20%, (C) 30%, (D) 40%, (E) 50%, (F) 60%, (G) 70%, (H) 80%, and (I) 90% of the stance phase. Data were obtained from a single animal (cat 6) across all walking conditions. Extensor moments are defined as positive.
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whereas SOL forces remained substantial (Fig. 1D). In three animals, peak SOL forces decreased for uphill compared to level walking, despite an increase in ankle
extensor moments (e.g., Fig. 1B, D), possibly because SOL force is limited in uphill walking by its fast speed of shortening and lack of active-lengthening (Kaya et al., 2003a). Therefore, MG seems strongly related to the ankle extensor but not the knee flexor requirements, while SOL is relatively insensitive to the magnitude of the ankle moment, and thus, might be associated with ankle joint stability or stiffness, rather than ankle moments. The idea that MG functions primarily as an ankle extensor is consistent with the greater moment arm of MG at the ankle (50–100% greater) compared to the knee (Burkholder and Nichols, 1998). 4.1. Multi-functionality of biarticular muscles During locomotion, cat MG appears to function as a monoarticular ankle extensor. This result is based on the high, positive correlations between MG force and ankle extensor moment for most of the stance phases of gait
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Fig. 6. Relationships between MG force and the difference between ankle and knee moment at (A) 10%, (B) 20%, (C) 30%, (D) 40%, (E) 50%, (F) 60%, (G) 70%, (H) 80%, and (I) 90% of the stance phase. Data were obtained from a single animal (cat 3) across all walking conditions.
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Fig. 7. Correlation coefficients between MG force and the difference between ankle and knee moment as a function of percent of the stance phase for all animals. The positive correlations imply that MG forces increase with increasing demands for ankle extensor and knee flexor moments.
(Figs. 2 and 3), the surprising similarity in shape of the MG force-time histories and the resultant ankle moment-time histories, and finally, and probably most
Fig. 8. Mean time-histories of MG muscle-tendon length curves for 301 downhill, level, and 451 uphill walking from a single animal.
convincingly, by the loss of MG force in the late stance phase of downhill walking, at the instant when the resultant ankle moment switches from extensor to flexor (Fig. 1B, C). This proposed monoarticular action of the cat MG is consistent with previous suggestions of a primary ankle extension function based on EMG patterns (Wetzel et al., 1973) and reflex connections (Goslow et al., 1973), and is consistent with earlier
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treatments of the cat MG when investigating its forcesharing contribution with other agonistic muscles (Dul et al., 1984; Herzog and Leonard, 1991). However, in the first half of the stance phase, MG is also negatively correlated with the resultant knee extensor moment, because its force variations closely match the knee flexor requirements (Fig. 5). In this first part of stance, the resultant GRF vector is located in front of the ankle and knee. For a given hindlimb configuration and GRF magnitude, the ankle extensor and knee flexor moments are given by the direction of the GRF vector, since inertial effects of the hindlimb may safely be ignored during cat locomotion (Kaya et al., 2003b). Ankle extensor and knee flexor moments are thus highly coupled in the first part of the stance phase. Therefore, by virtue of this ‘‘geometrical’’ coupling, it is obvious that if MG force is highly correlated with the ankle extensor moment, it would also have to be highly correlated with the knee flexor moment. We conclude from this analysis that cat MG functions as an ankle extensor in the first half of the stance phase, but because of the geometrical coupling of ankle and knee moments, MG also helps to satisfy the knee flexor requirements in this phase of stance. Because of the negligible inertial effects, this result immediately implies that MG’s contribution to the GRF is in a similar direction as the resultant GRF. However, it should be emphasized that the correlations of MG force with the difference between ankle and knee moments are only positive for the first half of stance (Figs. 6 and 7). Therefore, satisfying two joint moments (Prilutsky and Gregor, 1997; Prilutsky et al., 1998; Gregor et al., 2001), and/or controlling the direction of the GRF (van Ingen Schenau et al., 1992; Jacobs and van Ingen Schenau, 1992; Doorenbosch and van Ingen Schenau, 1995), is only MG’s functional role for the first part of stance, and not the second part. For movement tasks associated with great inertial effects on joint kinetics, such as ballistic arm movements, it was found that biarticular muscle activities were primarily associated with the direction of joint movement, rather than the direction of the external force (Welter and Bobbert, 2002), providing further evidence that the control of external forces is not necessarily the exclusive role of biarticular muscles. Furthermore, we propose that satisfying both, the ankle and knee moment requirements in early stance, is a function of cat MG that is caused by MG’s function in ankle extension and the geometric coupling of the two moments. In the second half of the stance phase, ankle and knee extension, as well as ankle and knee extensor moments prevail. In this phase, MG force is highly correlated with the resultant knee extensor moment. Since MG produces a knee flexor moment when contracting, it appears that it functions in this part of the stance phase to transfer mechanical energy produced by the knee
extensors to the ankle. It has been argued that biarticular muscles may primarily function as essentially ‘‘inextensible bands’’ that transfer energy from one joint to the next (Bobbert and van Ingen Schenau, 1988; Mai and Lieber, 1990; Jacobs et al., 1996). However, MG also shortens substantially during the second half of stance (Fig. 8), and thus does not only transfer energy, but also produces a substantial amount of mechanical work. The results of Cat 1 differed from those of the other five animals shown in Figs. 5 and 7. These differences were caused by the unusually large knee extensor moment of Cat 1 for downhill compared to level and uphill walking. Cat 1 had equal or greater knee extensor moments for downhill (Fig. 9, dashed line) than uphill walking (gray line) in the late stance phase. All other animals showed greater knee extensor moments for uphill than downhill walking. The results obtained from Cats 2–6 are consistent with findings published by Gregor et al. (2001) who also reported that knee extensor moments were greater for uphill than downhill walking in cats. Thus, based on our results and those by Gregor et al. (2001), it appears that the results of Cat 1 are abnormal. Cat 1 walked downhill in a more crouched position than all the other animals (e.g., Fig. 10A). This crouched walking style was associated with a greater breaking force for Cat 1 compared to the other animals (thick black line in Fig. 10B). Thus, the crouched walking position and the greater breaking force produced by Cat 1 caused an exaggerated knee extensor moment for downhill walking in Cat 1 that was not observed in the five other animals of this study, or the results presented by Gregor et al. (2001). Therefore, it appears that Cat 1 adopted a different downhill walking strategy compared to the preferred walking style of the remaining animals. 4.2. Neurophysiological interpretations Previous studies have shown that modulation of cat MG activity is more closely related to the hindlimb dynamics than modulation of SOL activity. For instance, MG activity systematically increases 3–4 times from slow walking to fast walking/trotting/running (Walmsley et al., 1978; Pierotti et al., 1989; Kaya et al., 2003a) or steep uphill walking (Kaya et al., 2003a), and dramatically increases for jumping (E20 fold; Walmsley et al., 1978) and paw shaking (E10 fold; unpublished). In contrast, SOL activity varies much less for this range of movements: 20–30% increase from slow to fast walking/running (Smith et al., 1977; Kaya et al., 2003a) or steep uphill walking (Kaya et al., 2003a); and 50% increase for jumping (Smith et al., 1977; Walmsley et al., 1978). During paw shaking, SOL activity is virtually zero (Smith et al., 1980, Fowler et al., 1988). Furthermore, Nichols (1999) argued that SOL
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activation is progressively inhibited by increasing MG forces to enhance the coupling of hindlimb joint movements, causing an increase in limb stiffness. Since MG is a biarticular muscle, it can accommodate different mechanical requirements in an efficient way at different times during stance, while the monoarticular SOL cannot.
5. Conclusion Cat MG satisfies all functions that have typically been associated independently with biarticular muscles. It is closely associated with the ankle extensor moments throughout stance. Because of the geometric coupling of knee and ankle moments, MG helps knee flexion and the control of the direction of the GRF in early stance, and the transfer of energy from the knee extensors to the ankle in late stance. We propose that cat MG is a multifunctional muscle, and that other bi- and multi-articular muscles may be multi-functional, too. We assume that the relative importance of the functional roles associated
here for cat MG may change for other bi- and multiarticular muscles, but we disagree with much of the published literature that associated biarticular muscles with a single role, at the exclusion of others, based on anatomy, EMG recordings, or theoretical predictions of muscle forces, rather than direct recordings of the in vivo forces. Furthermore, many previous interpretations on the functional roles of biarticular muscles were based on analysis of segments of a work task (e.g., early stance for locomotion), rather than the full work cycle, or isolated movements (e.g., a static leg extension). Such restricted analyses may not capture the multitude of possible functions of biarticular muscles.
Acknowledgments The authors are grateful to Hoa Nguyen and Andrzej Stano for their technical support. This work was supported by the Alberta Heritage Foundation for Medical Research, NSERC of Canada, and the Olympic Oval Endowment Fund, University of Calgary.
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References Andrews, J.G., 1995. Euler’s and Lagrange’s equations for linked rigid-body models of three-dimensional human motion. In: Allard, P., Stokes, I.A.F., Blanchi, J.P. (Eds.), Three-Dimensional Analysis of Human Movement Human Kinetics. Champaign, IL, pp. 145–175. Bigland-Ritchie, B., 1981. EMG/force relations and fatigue of human voluntary contractions. Exercise and Sport Sciences Reviews 9, 75–117. Bobbert, M.F., van Ingen Schenau, G.J., 1988. Coordination in vertical jump. Journal of Biomechanics 21, 249–262. Burkholder, T.J., Nichols, T.R., 1998. A three dimensional model of the cat hindlimb. In: Proceedings of NACOB 98. The Third American Congress on Biomechanics, Waterloo, ON, Canada, pp. 207-208. Dietz, V., Fouad, K., Bastiaanse, C.M., 2001. Neuronal coordination of arm and leg movements during human locomotion. European Journal of Neuroscience 14, 1906–1914. Doorenbosch, C.A.M., van Ingen Schenau, G.J., 1995. The role of mono- and bi-articular muscles during contact control leg tasks in man. Human Movement Science 14, 279–300. Dul, J., Johnson, G.E., Shavi, R., Townsend, M.A., 1984. Muscular synergism—II, A minimum-fatigue criterion for load sharing between synergistic muscles. Journal of Biomechanics 17, 675–684. Fowler, E.G., Gregor, R.J., Roy, R.R., 1988. Differential kinetics of fast and slow ankle extensors during the paw-shake in the cat. Experimental Neurology 219-224. Fowler, E.G., Gregor, R.J., Hodgson, J.A., Roy, R.R., 1993. Relationship between ankle muscle and joint kinetics during the stance phase of locomotion in the cat. Journal of Biomechanics 26, 465–483.
Fujiwara, M., Basmajian, J.V., 1975. Electromyographic study of twojoint muscles. American Journal of Physical Medicine 54, 234–242. Gregor, R.J., Smith, J.L., Smith, D.W., Oliver, A., Prilutsky, B.I., 2001. Hindlimb kinetics and neural control during slope walking in the cat: Unexpected findings. Journal of Applied Biomechanics 17, 277–286. Goslow, G.E., Reinking, R.M., Stuart, D.G., 1973. The cat step cycle: hindlimb joint angles and muscle lengths during unrestrained locomotion. Journal of Morphology 141, 1–41. Guimaraes, A.C.S., Herzog, W., Hulliger, M., Zhang, Y.T., Day, S., 1994a. EMG-force relationship of the cat soleus muscle sudied with distributed and non-periodic stimulation of ventral root filaments. Journal of Experimental Biology 186, 75–93. Guimaraes, A.C.S., Herzog, W., Hulliger, M., Zhang, Y.T., Day, S., 1994b. Effect of muscle length on the EMG-force relation of the cat soleus muscle using non-periodic stimulation of ventral root filaments. Journal of Experimental Biology 193, 49–64. Guimaraes, A.C.S., Herzog, W., Hulliger, M., Zhang, Y.T., Day, S., 1995. EMG-force relation of the cat soleus muscle during locomotion, and its association with contractile conditions. Journal of Experimental Biology 198, 975–987. Herzog, W., Leonard, T.R., 1991. Validation of optimization models that estimate the forces exerted by synergistic muscles. Journal of Biomechanics 24, 31–39. Herzog, W., Leonard, T.R., Guimaraes, A.C.S., 1993. Forces in gastrocnemius, soleus, and plantaris tendons of the freely moving cat. Journal of Biomechanics 26, 945–953. Hill, A.V., 1938. The heat of shortening and the dynamic constants of muscle. Proceedings of the Royal Society of London. Series B: Biological Sciences (London) 126, 136–195. Hodgson, J.A., 1983. The relationship between soleus and gastrocnemius muscle activity in conscious cats—a model for motor unit recruitment? Journal of Neurophysiology 337, 553–562. Hoy, M.G., Zernicke, R.F., 1985. Modulation of limb dynamics in the swing phase of locomotion. Journal of Biomechanics 18, 49–60. Jacobs, R., van Ingen Schenau, G.J., 1992. Control of an external force in leg extensions in humans. Journal of Physiology 457, 611–626. Jacobs, R., Macpherson, J.M., 1996. Two functional muscle groups during postural equilibrium tasks in standing cats. Journal of Neurophysiology 76, 2402–2411. Jacobs, R., Bobbert, M.F., van Ingen Schenau, G.J., 1996. Mechanical output from individual muscles during explosive leg extensions: The role of biarticular muscles. Journal of Biomechanics 29, 513–523. Kaya, M., Leonard, T., Herzog, W., 2003a. Coordination of medial gastrocnemius and soleus forces during cat locomotion. Journal of Experimental Biology 206, 3645–3655. Kaya, M., Leonard, T., Herzog, W., 2003b. A kinetics-based classification of the stance phase of walking. In: XIXth Congress of the International Society of Biomechanics, University of Otago, Dunedin, New Zealand, p. 196. Lombard, W.P., 1903. The action of two-joint muscles. American Physical Education Review 9, 141–145. Liu, M.M., Herzog, W., Savelberg, H.H., 1999. Dynamic muscle force predictions from EMG: an artificial neural network approach. Journal of Electromyography and Kinesiology 9, 391–400. Mai, M.T., Lieber, R.L., 1990. A model of semitendinosus muscle sarcomere length, knee and hip joint interaction in the frog hindlimb. Journal of Biomechanics 23, 271–279. Neptune, R.R., Herzog, W., 2000. Adaptation of muscle coordination to altered task mechanics during steady-state cycling. Journal of Biomechanics 33, 165–172. Nichols, T.R., 1999. Receptor mechanisms underlying heterogenic reflexes among the triceps surae muscles of the cat. Journal of Neurophysiology 81, 467–478.
ARTICLE IN PRESS M. Kaya et al. / Journal of Biomechanics 38 (2005) 1291–1301 Pierotti, D.J., Roy, R.R., Gregor, R.J., Edgerton, V.R., 1989. Electromyographic activity of cat hindlimb flexors and extensors during locomotion at varying speeds and inclines. Brain Research 481, 57–66. Prilutsky, B.I., Herzog, W., Allinger, T.L., 1994. Force-sharing between cat soleus and gastrocnemius muscles during walking: Explanations based on electrical activity, properties, and kinematics. Journal of Biomechanics 27, 1223–1235. Prilutsky, B.I., Herzog, W., Allinger, T.L., 1996. Mechanical power and work of cat soleus, gastrocnemius and plantaris muscles during locomotion: possible functional significance of muscle design and force patterns. Journal of Biomechanics 199, 801–814. Prilutsky, B.I., Gregor, R.J., 1997. Strategy of muscle coordination of two- and one-joint leg muscles in controlling an external force. Motor Control 1, 92–116. Prilutsky, B.I., Isaka, T., Albrecht, A.M., Gregor, R.J., 1998. Is coordination of two-joint leg muscles during load lifting consistent with the strategy of minimum fatigue? Journal of Biomechanics 31, 1025–1034. Savelberg, H.H.C.M., Herzog, W., 1997. Prediction of dynamic force from electromyographic signals: an Artificial Neural Network Approach. Journal of Neuroscience Methods 78, 65–74. Smith, J.L., Edgerton, V.R., Betts, B., Collatos, T.C., 1977. EMG of slow and fast ankle extensors of cat during posture, locomotion, and jumping. Journal of Neurophysiology 40, 503–513.
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Smith, J.L., Betts, B., Edgerton, V.R., Zernicke, R.F., 1980. Rapid ankle extension during paw shakes: selective recruitment of fast ankle extensors. Journal of Neurophysiology 432, 612–620. van Ingen Schenau, G.J., Boots, P.J.M., de Groot, G., Snackers, R.J., van Woensel, W.W.L.M., 1992. The constrained control of force and position on multi-joint movements. Neuroscience 46, 197–207. van Ingen Schenau, G.J., Dorssers, W.M.M., Welter, T.G., Beelen, A., de Groot, G., Jacobs, R., 1995. The control of mono-articular muscles in multijoint leg extension in man. Journal of Physiology 484, 247–254. Walmsley, B., Hodgson, J.A., Burke, R.E., 1978. Forces produced by medial gastrocnemius and soleus muscles during locomotion in freely moving cats. Journal of Neurophysiology 41, 1203–1216. Welter, T.G., Bobbert, M.F., 2002. Initial muscle activity in planar ballistic arm movements with varying external force directions. Motor Control 6, 32–51. Wetzel, M.C., Gerlach, R.L., Stern, L.Z., Hannapel, L.K., 1973. Behavior and histochemistry of functionally isolated cat ankle extensors. Experimental Neurology 39, 223–233. Whiting, W.C., Gregor, R.J., Roy, R.R., Edgerton, V.R., 1984. A technique for estimating mechanical work of individual muscles in the cat during treadmill locomotion. Journal of Biomechanics 17, 685–694. Winter, D.A., Yack, H.J., 1987. EMG profiles during normal human walking: stride-to-stride and inter-subject variability. Electroencephalography and Clinical Neurophysiology 67, 402–411.
Journal of Biomechanics 38 (2005) 1291–1301 www.elsevier.com/locate/jbiomech www.JBiomech.com
Multi-functionality of the cat medical gastrocnemius during locomotion Motoshi Kaya, Azim Jinha, Tim R. Leonard, Walter Herzog Faculty of Kinesiology, Human Performance Laboratory, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4 Accepted 20 June 2004
Abstract The functional role of biarticular muscles was investigated based on direct force measurement in the cat medial gastrocnemius (MG) and analysis of hindlimb kinematics and kinetics for the stance phase of level, uphill, and downhill walking. Four primary functional roles of biarticular muscles have been proposed in the past. These functional roles have typically been discussed independently of each other, and biarticular muscles have rarely been assigned more than one functional roles for different phases of the work cycle. The purpose of this study was to elucidate the functional role of the biarticular cat MG during locomotion. It was found that MG forces were primarily associated with the moment requirements at the ankle for most of the stance phase, but also helped to satisfy the moments at the knee in the initial phase of stance. In the second half of stance, MG transferred mechanical energy from the knee to the ankle from the knee to the ankle, while simultaneously producing a substantial amount of mechanical work. Based on these results, we hypothesize that MG’s primary function is that of an ankle extensor. However, because of the coupling of the ankle extensor moment with a knee flexor moment in the initial, and a knee extensor moment in the final phase of stance, MG satisfies two joint moments in early stance, and transfers mechanical energy from the knee to the ankle in late stance. We conclude that cat MG has multiple functional roles during the stance phase of locomotion, and speculate that such multifunctionality also exists in other bi- and multi-articular muscles. r 2004 Elsevier Ltd. All rights reserved. Keywords: Muscle coordination; Biarticular muscle; Joint moment; Cat locomotion
1. Introduction The redundant nature of musculoskeletal systems allows for a specific task to be performed with an infinite number of muscular coordination patterns. Yet, it has been known for a long time that skilled movements are performed in a stereotyped manner. Similar patterns of muscular coordination have been observed within and across subjects for movement tasks, such as human walking (e.g., Winter and Yack, 1987; Dietz et al., 2001), cycling (e.g., van Ingen Schenau et al., 1995; Neptune and Herzog, 2000), and cat locomotion (e.g., Walmsley et al., 1978; Hodgson, 1983, Herzog et al., 1993). Corresponding author. Tel.:+1-403-220-8525; fax: +1-403-284-3553
E-mail address: [email protected] (W. Herzog). 0021-9290/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2004.06.009
In humans and animals, mono-, bi-, and multiarticular muscles have often been associated with distinct and different functional roles. An understanding of these roles might provide novel insight into the mechanisms of muscular coordination and movement control. An obvious advantage of biarticular muscles is that force from one muscle can produce movements at two joints. Therefore, one might think of biarticular muscles to be preferentially activated when the moments they produce about both joints coincide with the moment requirements of the actual movement. Such a functional role of biarticular muscles has been proposed for human (Fujiwara and Basmajian, 1975; Prilutsky and Gregor, 1997; Prilutsky et al., 1998) and animal movement (Jacobs and Macpherson, 1996; Gregor et al., 2001). However, this proposed role may have severe
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limitations. For example, moments produced by biarticular muscles at a joint are often associated with a rotational movement in the same direction. If so, a biarticular muscle would shorten because of its action at both joints, and its contractile speed would be greater than that of corresponding monoarticular muscles, thus reducing its force capacity in accordance with the forcevelocity relationship (Hill, 1938). However, the contractile velocity of biarticular muscles may be smaller than that of corresponding monoarticular muscles in situations in which shortening at one joint is offset by lengthening at the other joint. This reduced contractile velocity of biarticular muscles allows for favorable contractile conditions during fast locomotion (e.g., cat gastrocnemius and plantaris during trotting and galloping, Prilutsky et al., 1996). Therefore, biarticular muscles are sometimes thought of as nearly ‘‘isometric’’ structures that transport mechanical energy from one joint to the adjacent rather than producing substantial work themselves (Bobbert and van Ingen Schenau, 1988; Mai and Lieber, 1990; Jacobs et al., 1996). van Ingen Schenau et al. (1992) proposed that monoarticular muscles are preferentially activated when movement direction involves shortening, while biarticular muscles are preferentially activated to control the direction of external forces by adjusting the moments in the two joints they span. Thus, biarticular muscles were thought to be highly activated when they produce an external force component, whose direction is similar to the direction of the required external force. This proposed function of biarticular muscles (van Ingen Schenau et al., 1992) is mechanically equivalent to the first one mentioned above, if the inertial effects of a movement are small, and thus can be neglected in the equations of motion, such as during static leg extension (Jacobs and van Ingen Schenau, 1992, Prilutsky and Gregor, 1997), slow isokinetic leg extension (Doorenbosch and van Ingen Schenau, 1995), and cat walking (Kaya et al., 2003b). Finally, Dul et al. (1984) suggested that biarticular muscles, such as the cat medial gastrocnemius (MG, biarticular ankle extensor/knee flexor), may be considered monoarticular muscles (ankle extension), based on electromyographical (EMG) patterns (Wetzel et al., 1973) and reflex connections (Goslow et al., 1973). Therefore, biarticular muscles might be used primarily to satisfy the moments at a single joint, while being relatively insensitive to the mechanical requirements at the other joint. From the above arguments, it can be seen that biarticular muscles have been associated with at least four distinctly different functional roles. Much of the evidence in support of these functional roles is based on the anatomy of the musculoskeletal system, activation patterns as observed through EMG recording, or
indirect estimates of muscle force. However, musculoskeletal anatomy may lead to paradoxical conclusion (Lombard, 1903), and the relationship between EMG and muscle force in dynamic situations is highly nonlinear (Bigland-Ritchie 1981; Guimaraes et al., 1994a, b), and contains a variable time delay (Guimaraes et al., 1995). Furthermore, adequate EMG-force relationships seem only possible using powerful numerical approaches (e.g., artificial neural networks, Savelberg and Herzog, 1997; Liu et al., 1999), and indirect force estimates may contain massive errors (Herzog and Leonard, 1991). For these reasons, there is little accurate, quantitative evidence about the role of biarticular muscles during voluntary movements. Interestingly, the idea that biarticular muscles may satisfy different functional roles, depending on the instantaneous movement requirements, has not been considered systematically. The purpose of this study was to elucidate the role of the biarticular cat MG during a variety of locomotor conditions, based on measured MG forces, and the external kinematics and kinetics.
2. Methods 2.1. Subjects and muscle force measurement Six outbred, male, adult cats (5.371.2 kg) were trained to walk on a walkway that was positioned at different slopes: level (n ¼ 24 individual trials for N ¼ 5 animals), upslope at 301 (n ¼ 25, N ¼ 6), 451 (n ¼ 25, N ¼ 6), and 601 (n ¼ 12, N ¼ 5), and downslope at -301 (n ¼ 28, N ¼ 6). These walking conditions were chosen, since characteristics of the required ankle and knee joint moments change substantially between level, uphill, and downhill walking (e.g., Gregor et al., 2001), and so provide a large range of conditions for studying the functional role of MG. Each cat was surgically implanted with buckle-type tendon force transducers (Walmsley et al., 1978) onto the separated tendons of the MG and soleus (SOL) (Herzog et al., 1993). MG and SOL were chosen, since force measurements are straight forward, and comparable results are available in the literature (Walmsley et al., 1978; Hodgson, 1983, Whiting et al., 1984; Fowler et al., 1993; Herzog et al., 1993; Prilutsky et al., 1994; Gregor et al., 2001). All signals were transmitted by telemetry to a custom-built amplifier and stored on a PC at 2000 Hz. After implantation of the sensors, training was resumed one day following surgery to prevent the formation of adhesions around the ankle, and to accelerate the recovery process. Measurements were carried out when cats had completely recovered from surgery based on the assessment of kinematics and kinetics (ground reaction force (GRF) and resultant joint moment) of the implanted hindlimb. All surgical procedures were
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performed according to the guidelines of the Canadian Council on Animal Care, and were approved by the Life Sciences Animal Ethics Committee of the University of Calgary. For a more detailed description of the surgical procedures and measurement of tendon forces, see Herzog et al. (1993) and Kaya et al. (2003a). 2.2. Hindlimb kinematics and kinetics Reflective markers were placed over the hip, knee, ankle, metatarsophalangeal (MP) joint, and toe of the instrumented hindlimb to obtain knee, ankle, and MP joint angles. The positions of these markers for level and uphill walking were collected using a motion analysis system (60 Hz; VP310, Motion Analysis Cooperation, Santa Rosa, CA, USA), and those for downhill walking were recorded using a high-speed camera (200 Hz; V14B, NAC, Inc., Tokyo, Japan) and were manually digitized using a custom-designed program written in MATLAB (Math Works, Inc., Natick, MA, USA). In order to avoid artifacts caused by skin marker movement, the location of the knee joint center was calculated using an optimization procedure, in which the estimated location of the knee marker was optimized to be closest to the measured knee marker location, with the constraint that the distances from the estimated knee joint center to the measured ankle and hip joint were the same as the measured shank and thigh length, respectively. GRFs of the instrumented hindlimb were measured using two force platforms located in the center of the walkway (DRMC36, AMTI, Newton, MA, USA). They were collected simultaneously with the muscle forces and stored on a PC at 2000 Hz. The resultant joint moments at ankle and knee were calculated using the inverse dynamics approach (Andrews, 1995) with hindlimb kinematics and ground reaction forces obtained directly, and inertial properties of body segments estimated using equations given by Hoy and Zernicke (1985). In this study, extensor moments were defined as positive. In order to quantify the moment demands at ankle and knee that could be satisfied by MG, the knee moment was subtracted from the ankle moment (e.g., Prilutsky et al., 1998). Since extensor moments are defined as positive, the difference between ankle and knee moments becomes greater when both (either) the ankle extensor moment and (or) the knee flexor moment increases. 2.3. Data analysis Correlation coefficients were calculated to evaluate the relationships between MG forces and resultant ankle/knee moments. This analysis was performed at every 10% of the stance phase between 10% and 90% of stance. For a given walking condition, individual step
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3. Results Typical examples of the time-histories of knee and ankle joint moment for 301 downhill, level, and 451 uphill walking are shown with the corresponding MG and SOL forces in Fig. 1. Compared to level walking (black lines in Fig. 1A, B), uphill walking is associated with greater ankle extensor and knee flexor moments (gray lines in Fig. 1A, B), while downhill walking is associated with smaller ankle extensor and greater knee extensor moments (dashed lines in Fig. 1A, B) in the first part of stance. In the second part of stance, greater ankle and knee extensor moments are required for uphill compared to level and downhill walking, while downhill walking is associated with an ankle flexor and a small knee extensor moment. Both shape and magnitude of MG force curves changed systematically with the corresponding ankle extensor moment curves for the entire stance phase (Fig. 1B, C). MG forces were greatest for uphill walking throughout stance (Fig. 1C), and peak forces were shifted relative to level walking from early to midstance, similar to the shift for the peak ankle extensor moments (Fig. 1B). For downhill walking, MG force became very small (for some animals, even zero) when the ankle moment switched from extensor to flexor in the latter part of stance. In contrast, SOL forces were less sensitive to changes in the ankle moment requirements (Fig. 1B, D). For instance, SOL force did not decrease as quickly as MG force in the latter part of stance of downhill walking, and some animals showed a decrease in SOL forces from level to uphill walking when ankle extensor moments and MG forces increased (e.g., gray line in Fig. 1D). The relationships between MG force and ankle moment at 10% increments of the stance phase (10–90%) from a single animal across all walking conditions are shown in Fig. 2. The corresponding correlation coefficients between MG force and ankle moment for all individual animals are shown as a function of the percent of stance phase in Fig. 3. MG forces were positively correlated with ankle extensor moments in the initial 80% of stance across all animals, and strong positive correlations were observed up to 70% of the stance phase (Fig. 3). Ankle extensor moments were typically greater for uphill walking (filled symbols in Fig. 2) than for level and downhill walking (empty symbols in Fig. 2). The relationships between MG force and knee moment at 10% increments of the stance phase (10–90%) from a single animal across all walking conditions are shown in Fig. 4. The corresponding
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ments of the stance phase (10–90%) from a single animal across all walking conditions are shown in Fig. 6. The corresponding correlation coefficients for all animals as a function of percent of stance are shown in Fig. 7. MG forces and the difference between ankle and knee moments were positively correlated for approximately the initial 50% of stance, while they were negatively correlated from 80–90% of stance, except for one animal (cat 1) (Fig. 6 and 7).
(B)
1.5
MG force [N]
-30deg
30 20 10 0 0
20
Percent of stance phase [%]
Fig. 1. Mean time-histories of (A) knee moment; (B) ankle moment; (C) MG force; and (D) SOL force curves as a function of percent of the stance phase for 301 downhill, level, and 451 uphill walking from a single animal. Note, that the MG force curves are similar in shape and vary in a similar way in magnitude with the corresponding ankle moment curves, while SOL force curves do not.
correlation coefficients between MG force and knee moment for individual animals are shown as a function of the percent of stance phase in Fig. 5. MG forces were negatively correlated with knee extensor moments in the initial 30% of stance, while they were positively correlated with knee extensor moments in the second half of stance, except for one animal (cat 1) (Fig. 5). Cat 1 was an exceptional animal in that it produced smaller knee extensor moments than the remaining five animals in the late part of stance for uphill compared to level and downhill walking. The relationships between MG force and the difference between ankle and knee moments at 10% incre-
The functional role of biarticular muscles has been debated for decades. The following arguments have crystallized from these discussions: (i) biarticular muscles primarily function to simultaneously satisfy the moment requirements at the two joints they span. (e.g., Prilutsky et al., 1998; Gregor et al., 2001). (ii) Biarticular muscles function to transfer energy from one joint to the other (e.g., Bobbert and van Ingen Schenau, 1988). (iii) Biarticular muscles function to control the direction of external forces (van Ingen Schenau et al., 1992). Note that the functional role proposed under point (i) constitutes a sub-set of the functional role of point (iii); i.e., the case when all inertial effects are negligible or are ignored. (iv) Biarticular muscles function essentially as monoarticular muscles to satisfy the resultant joint moment at one of the two joints exclusively (Dul et al., 1984). The four functional roles proposed here have been put forward independently in the past. Below, we discuss whether cat MG can be associated with any of these roles. (i) Biarticular muscles function to satisfy moments at two joints. The positive correlations between MG force and the difference between ankle and knee moments were greatest in the first half of the stance phase (10–50%) (Fig. 7), since MG forces increased with increasing ankle extensor moments (positive correlation, Fig. 3), and also increased with increasing knee flexor moments (negative correlation, Fig. 5). For the second half of the stance phase, the positive correlations between MG force and the difference between ankle and knee moments decreased, and eventually, became negative (Fig. 7), suggesting that MG functions to satisfy ankle and knee moments for the first half of the stance phase, but definitely not for the second half. (ii) Biarticular muscles function to transfer energy from one joint to the other joint. For the second half of stance, MG forces were mostly positively correlated with the knee extensor (Fig. 5) and the ankle extensor moments (Fig. 3). These joint kinetics were consistently associated with ankle and knee extension in this period of stance, implying that MG functions to transfer energy from the knee to ankle for the second half of the stance phase. However, MG also shortens substantially during the
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Fig. 2. Relationships between MG force and ankle moment at (A) 10%, (B) 20%, (C) 30%, (D) 40%, (E) 50%, (F) 60%, (G) 70%, (H) 80%, and (I) 90% of the stance phase. Data were obtained from a single animal (cat 3) across all walking conditions. Extensor moments are defined as positive.
1
cat1 cat2 cat3 cat4 cat5 cat6
Correlation coefficient
0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0
20
40
60
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100
Percent of stance phase [%] Fig. 3. Correlation coefficients between MG force and ankle moment as a function of percent of the stance phase for all animals.
second half of stance (Fig. 8). Therefore, it does not only transfers energy, but also produces a substantial amount of mechanical energy in this phase.
(iii) Biarticular muscles function to control the direction of external force. This functional role is mechanically almost equivalent to the first one, because inertial effects play a minor role during cat locomotion (Kaya et al, 2003b). MG may be considered to satisfy this functional role for the first half of the stance phase, for the reasons described above under point (i). (iv) Biarticular muscles function to satisfy moments at a single joint. The great positive correlations between MG forces and ankle moments for most (70-80%) of the stance phase suggest that MG functions as an ankle extensor (Fig. 3) with little regard for the mechanical requirements at the knee (Fig. 7). This suggestion is further supported by the close agreement of the shape of the time-histories of MG forces and ankle extensor moments for the entire stance phase (Fig. 1). Interestingly, MG forces became very small or zero when the ankle moment switched from extensor to flexor in the late phase of stance in downhill walking (Fig. 1B, C),
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Fig. 4. Relationships between MG force and knee moment at (A) 10%, (B) 20%, (C) 30%, (D) 40%, (E) 50%, (F) 60%, (G) 70%, (H) 80%, and (I) 90% of the stance phase. Data were obtained from a single animal (cat 6) across all walking conditions. Extensor moments are defined as positive.
1
cat1 cat2 cat3 cat4 cat5 cat6
Correlation coefficient
0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0
20
40
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100
Percent of stance phase [%] Fig. 5. Correlation coefficients between MG force and knee moment as a function of percent of the stance phase for all animals.
whereas SOL forces remained substantial (Fig. 1D). In three animals, peak SOL forces decreased for uphill compared to level walking, despite an increase in ankle
extensor moments (e.g., Fig. 1B, D), possibly because SOL force is limited in uphill walking by its fast speed of shortening and lack of active-lengthening (Kaya et al., 2003a). Therefore, MG seems strongly related to the ankle extensor but not the knee flexor requirements, while SOL is relatively insensitive to the magnitude of the ankle moment, and thus, might be associated with ankle joint stability or stiffness, rather than ankle moments. The idea that MG functions primarily as an ankle extensor is consistent with the greater moment arm of MG at the ankle (50–100% greater) compared to the knee (Burkholder and Nichols, 1998). 4.1. Multi-functionality of biarticular muscles During locomotion, cat MG appears to function as a monoarticular ankle extensor. This result is based on the high, positive correlations between MG force and ankle extensor moment for most of the stance phases of gait
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MG muscle-tendon length [cm]
Fig. 6. Relationships between MG force and the difference between ankle and knee moment at (A) 10%, (B) 20%, (C) 30%, (D) 40%, (E) 50%, (F) 60%, (G) 70%, (H) 80%, and (I) 90% of the stance phase. Data were obtained from a single animal (cat 3) across all walking conditions.
14 -30 deg 13.5
level 45 deg
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Fig. 7. Correlation coefficients between MG force and the difference between ankle and knee moment as a function of percent of the stance phase for all animals. The positive correlations imply that MG forces increase with increasing demands for ankle extensor and knee flexor moments.
(Figs. 2 and 3), the surprising similarity in shape of the MG force-time histories and the resultant ankle moment-time histories, and finally, and probably most
Fig. 8. Mean time-histories of MG muscle-tendon length curves for 301 downhill, level, and 451 uphill walking from a single animal.
convincingly, by the loss of MG force in the late stance phase of downhill walking, at the instant when the resultant ankle moment switches from extensor to flexor (Fig. 1B, C). This proposed monoarticular action of the cat MG is consistent with previous suggestions of a primary ankle extension function based on EMG patterns (Wetzel et al., 1973) and reflex connections (Goslow et al., 1973), and is consistent with earlier
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treatments of the cat MG when investigating its forcesharing contribution with other agonistic muscles (Dul et al., 1984; Herzog and Leonard, 1991). However, in the first half of the stance phase, MG is also negatively correlated with the resultant knee extensor moment, because its force variations closely match the knee flexor requirements (Fig. 5). In this first part of stance, the resultant GRF vector is located in front of the ankle and knee. For a given hindlimb configuration and GRF magnitude, the ankle extensor and knee flexor moments are given by the direction of the GRF vector, since inertial effects of the hindlimb may safely be ignored during cat locomotion (Kaya et al., 2003b). Ankle extensor and knee flexor moments are thus highly coupled in the first part of the stance phase. Therefore, by virtue of this ‘‘geometrical’’ coupling, it is obvious that if MG force is highly correlated with the ankle extensor moment, it would also have to be highly correlated with the knee flexor moment. We conclude from this analysis that cat MG functions as an ankle extensor in the first half of the stance phase, but because of the geometrical coupling of ankle and knee moments, MG also helps to satisfy the knee flexor requirements in this phase of stance. Because of the negligible inertial effects, this result immediately implies that MG’s contribution to the GRF is in a similar direction as the resultant GRF. However, it should be emphasized that the correlations of MG force with the difference between ankle and knee moments are only positive for the first half of stance (Figs. 6 and 7). Therefore, satisfying two joint moments (Prilutsky and Gregor, 1997; Prilutsky et al., 1998; Gregor et al., 2001), and/or controlling the direction of the GRF (van Ingen Schenau et al., 1992; Jacobs and van Ingen Schenau, 1992; Doorenbosch and van Ingen Schenau, 1995), is only MG’s functional role for the first part of stance, and not the second part. For movement tasks associated with great inertial effects on joint kinetics, such as ballistic arm movements, it was found that biarticular muscle activities were primarily associated with the direction of joint movement, rather than the direction of the external force (Welter and Bobbert, 2002), providing further evidence that the control of external forces is not necessarily the exclusive role of biarticular muscles. Furthermore, we propose that satisfying both, the ankle and knee moment requirements in early stance, is a function of cat MG that is caused by MG’s function in ankle extension and the geometric coupling of the two moments. In the second half of the stance phase, ankle and knee extension, as well as ankle and knee extensor moments prevail. In this phase, MG force is highly correlated with the resultant knee extensor moment. Since MG produces a knee flexor moment when contracting, it appears that it functions in this part of the stance phase to transfer mechanical energy produced by the knee
extensors to the ankle. It has been argued that biarticular muscles may primarily function as essentially ‘‘inextensible bands’’ that transfer energy from one joint to the next (Bobbert and van Ingen Schenau, 1988; Mai and Lieber, 1990; Jacobs et al., 1996). However, MG also shortens substantially during the second half of stance (Fig. 8), and thus does not only transfer energy, but also produces a substantial amount of mechanical work. The results of Cat 1 differed from those of the other five animals shown in Figs. 5 and 7. These differences were caused by the unusually large knee extensor moment of Cat 1 for downhill compared to level and uphill walking. Cat 1 had equal or greater knee extensor moments for downhill (Fig. 9, dashed line) than uphill walking (gray line) in the late stance phase. All other animals showed greater knee extensor moments for uphill than downhill walking. The results obtained from Cats 2–6 are consistent with findings published by Gregor et al. (2001) who also reported that knee extensor moments were greater for uphill than downhill walking in cats. Thus, based on our results and those by Gregor et al. (2001), it appears that the results of Cat 1 are abnormal. Cat 1 walked downhill in a more crouched position than all the other animals (e.g., Fig. 10A). This crouched walking style was associated with a greater breaking force for Cat 1 compared to the other animals (thick black line in Fig. 10B). Thus, the crouched walking position and the greater breaking force produced by Cat 1 caused an exaggerated knee extensor moment for downhill walking in Cat 1 that was not observed in the five other animals of this study, or the results presented by Gregor et al. (2001). Therefore, it appears that Cat 1 adopted a different downhill walking strategy compared to the preferred walking style of the remaining animals. 4.2. Neurophysiological interpretations Previous studies have shown that modulation of cat MG activity is more closely related to the hindlimb dynamics than modulation of SOL activity. For instance, MG activity systematically increases 3–4 times from slow walking to fast walking/trotting/running (Walmsley et al., 1978; Pierotti et al., 1989; Kaya et al., 2003a) or steep uphill walking (Kaya et al., 2003a), and dramatically increases for jumping (E20 fold; Walmsley et al., 1978) and paw shaking (E10 fold; unpublished). In contrast, SOL activity varies much less for this range of movements: 20–30% increase from slow to fast walking/running (Smith et al., 1977; Kaya et al., 2003a) or steep uphill walking (Kaya et al., 2003a); and 50% increase for jumping (Smith et al., 1977; Walmsley et al., 1978). During paw shaking, SOL activity is virtually zero (Smith et al., 1980, Fowler et al., 1988). Furthermore, Nichols (1999) argued that SOL
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activation is progressively inhibited by increasing MG forces to enhance the coupling of hindlimb joint movements, causing an increase in limb stiffness. Since MG is a biarticular muscle, it can accommodate different mechanical requirements in an efficient way at different times during stance, while the monoarticular SOL cannot.
5. Conclusion Cat MG satisfies all functions that have typically been associated independently with biarticular muscles. It is closely associated with the ankle extensor moments throughout stance. Because of the geometric coupling of knee and ankle moments, MG helps knee flexion and the control of the direction of the GRF in early stance, and the transfer of energy from the knee extensors to the ankle in late stance. We propose that cat MG is a multifunctional muscle, and that other bi- and multi-articular muscles may be multi-functional, too. We assume that the relative importance of the functional roles associated
here for cat MG may change for other bi- and multiarticular muscles, but we disagree with much of the published literature that associated biarticular muscles with a single role, at the exclusion of others, based on anatomy, EMG recordings, or theoretical predictions of muscle forces, rather than direct recordings of the in vivo forces. Furthermore, many previous interpretations on the functional roles of biarticular muscles were based on analysis of segments of a work task (e.g., early stance for locomotion), rather than the full work cycle, or isolated movements (e.g., a static leg extension). Such restricted analyses may not capture the multitude of possible functions of biarticular muscles.
Acknowledgments The authors are grateful to Hoa Nguyen and Andrzej Stano for their technical support. This work was supported by the Alberta Heritage Foundation for Medical Research, NSERC of Canada, and the Olympic Oval Endowment Fund, University of Calgary.
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Fig. 10. (A) Stick figure representation of the cat hindlimb with the resultant GRFs at 10%, 30%, 50%, 70%, and 90% of the stance phase of downhill walking. Stick figures were compared between Cat 1 and Cat 3. Note that Cat 1 walked with a more crouched position than Cat 3 throughout the stance phase of downhill walking. (B) Mean timehistories of the GRF component parallel to the surface of the walkway (i.e., breaking force) for downhill walking. The ground reaction force was normalized relative to the body weight (BW) of each animal. Note that cat 1 had the greatest relative breaking force of all animals in this study.
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