Whole limb kinematics are preferentially conserved over individual joint kinematics after peripheral nerve injury

In nature, animals maintain stable legged locomotion despite encountering unpredictable terrain from one step to the next. Adjustments are regularly made to counteract naturally occurring joint deviations and may go unnoticed with casual observation. When a limb is injured, however, individual joint function can be compromised and this can lead to noticeable deficits. The ability to exploit a pre-existing compensation mechanism for counteracting joint deviations and conserving normal whole limb function may help retain locomotor performance after injury. Intralimb gait compensation involves responses of some joints that act to attenuate the effects of deficits at other joints. This assumes that a task level goal, such as consistency of whole limb kinematics, guides the overall compensation process.

Findings from biomechanical and neurophysiological studies suggest that conserving limb-level function is an important goal during locomotion. For decades, researchers have studied steady state legged locomotion to yield biomechanical models that predict the locomotor dynamics of walking and running gaits across diverse taxonomic groups. The inverted pendulum model for walking (Cavagna et al., 1977; Griffin et al., 2004) and the mass-spring model for running (Blickhan,1989; McMahon and Cheng,1990) each provide low-degree of freedom behavioral templates that can describe whole body movements during legged locomotion(Full and Koditschek, 1999). These biomechanical models reduce the neuromusculoskeletal complexity of the legs to the simple function of a rigid strut or a linearly elastic spring rotating about a point mass. Neurophysiological studies also support a neural basis for the importance of limb-level function in locomotion. Recent studies have indicated that the central nervous system directly encodes whole limb kinematics rather than individual joint kinematics. Dorsal spinocerebellar tract (DSCT) neurons in the cat spinal cord integrate and carry sensory information to the cerebellum and are known to influence locomotion and posture. In vivo recordings from these DSCT neurons revealed that the majority of the ascending DSCT activity reflected the cat's overall limb orientation and limb length kinematics rather than providing specific information about an individual joint(Bosco and Poppele, 2000; Bosco and Poppele, 2003; Bosco et al., 2000). Although the importance of whole limb behavior to locomotion is clear, we do not have a good understanding about how the joints act in concert to conserve limb-level function during locomotion and particularly whether such a compensation strategy is engaged after neuromuscular injury.

In the cat, surgical transection and immediate repair of individual nerves supplying the muscles of the triceps surae group of ankle extensors reliably results in a brief paralytic stage of approximately one month followed by complete self-reinnervation of the affected muscles after 9–12 months(Cope et al., 1994; Cope and Clark, 1993). The self-reinnervated muscle regains full efferent motor function with a permanent disruption of the short-latency, proprioceptive reflex pathways from the reinnervated muscle commonly referred to as the monosynaptic stretch reflex. This peripheral nerve injury results in increased ankle joint flexion, or yield, during the initial weight-bearing portion of the stance phase of gait when the muscle is in the paralytic stage(Abelew et al., 2000; Maas et al., 2007). After self-reinnervation, measurable joint-level deficits can persist for years after the injury, particularly during down-slope walking when engaging the short-latency pathways are more critical to joint function. These studies have focused on the deficits to joint range of motion rather than comparing joint function relative to whole limb function over the entire gait cycle. We used this surgically precise, peripheral nerve self-reinnervation model to gain insights into locomotor compensation strategies at different stages of injury and recovery. This approach also allowed us to compare injuries across different muscles as a first test of the fundamental nature of these compensation principles.

Our main objective was to test the general hypothesis that a locomotor compensation strategy exists such that joint angle combinations are selected that achieve consistency, or a minimum change, in limb kinematics (see Fig. 1). We made two predictions related to our general hypothesis about both long-term locomotor compensation and short-term locomotor compensation. First, we defined long-term compensation as the conservation of mean limb kinematics trajectories across all individuals at the expense of changes to mean joint kinematics trajectories. We tested this long-term compensation by comparing the consistency of the mean trajectory shapes of limb and individual joint kinematics after neuromuscular injury. We predicted that the majority of the mean post-injury limb kinematics trajectory could be explained by the pre-injury kinematics for all cats (R²>0.50), whereas the mean joint angle trajectories would follow new and different trajectories resulting in lower R² values. Second, we defined short-term compensation as the minimization of the step-by-step variance of limb kinematics that is concomitant with an increased variance in joint kinematics. We tested for short-term compensation by comparing the total variance of limb orientation and joint angles on a step-by-step basis. We predicted that total variance of the joint angles would be greater than that for limb orientation, indicating that the combined effect of these greater step-by-step joint angle deviations is to counteract and minimize deviations in limb orientation.

We performed all procedures according to an approved protocol by the Emory University Institute for Animal Care and Use Committee. Five adult cats(Felis catus L.; mean body mass=3.91±0.64 kg) were selected based on friendliness and ability to train for food rewards. All animals were socially housed in a colony within a single large room that exceeded NIH recommendations for space requirements(Institute for Laboratory Animal Research,1996). Dry food and water were provided ad libitum within the colony; treadmill locomotion training rewards consisted of wet food.

We trained the animals over a 1–3 month period until they could walk on command at 0.8 m s^–1 for a minimum of 60 s on a custom treadmill. Food rewards were given after each completed trial. We constructed the treadmill frame from an extruded aluminum chassis (Varco, Greenwood, SC,USA) with a 0.32 cm thick aluminum bed supporting a low-friction 0.32 cm Teflon surface (Fluoro-Plastics, Philadelphia, PA, USA) over which a 0.24 m wide treadmill belt (Regional Supply, Marietta, GA, USA) could easily slide. A 0.5 hp DC brushless motor with reversible digital controller and speed readout(Cole Electric, Atlanta, GA, USA) turned a custom-lathed aluminum drive shaft. The general treadmill construction followed a design similar to one previously developed for human studies (Kram et al.,1998), but was appropriately scaled to the dimensions of a cat. A clear acrylic enclosure (0.95 m×0.34 m×0.62 m) was constructed to fit over the treadmill without affecting belt movement. An additional adjustable wall-spacer further restricted lateral position on the treadmill such that the walking surface for each cat was approximately 0.16 m×0.95 m to ensure steady, forward locomotion.

A peripheral nerve injury was generated in each animal through a previously described surgical procedure (Cope et al.,1991). Briefly, the cat was placed under general anesthesia(isoflurane gas) within a sterile surgical field. We exposed the tibial nerve with a longitudinal incision in the popliteal fossa of the left hindlimb. We then identified the distal-most portion of the nerve branch innervating the lateral head of the gastrocnemius and soleus muscles. Through a dissecting microscope, we cut the epineurium and divided the approximately three to four individual nerve bundles supplying the soleus muscle for two cats. We verified the innervation of these nerve bundles through electrical stimulation of the bundles with bipolar hook electrodes. For the three remaining cats, in addition to the soleus the individual nerve branches innervating the lateral and medial heads of the gastrocnemius muscle were also identified in a similar fashion. Each of the individual nerve branches (or bundles) identified during surgery was independently transected and the cut ends were immediately reattached with 10-0 non-absorbable monofilament suture (S&T AG,Neuhausen, Switzerland). Since these nerve branches and bundles were cut and reattached at their most distal point of entry into the muscle belly, we minimized any chance of cross-reinnervation into an inappropriate muscle as is common for injuries made proximal to major branch points(English, 2005). While in the operating room, we verified the loss of innervation to the muscle through electrical stimulation of the individual nerve branches proximal to the repair site. We did not observe any response from repaired muscles but did observe clear activation when testing neighboring unaffected muscles. Consequently,the wound site was closed using sterile sutures and the cat was allowed to heal in isolation over the next 7 days, after which the animal was returned to the general colony. Although it was not critical to the hypotheses directly tested in this study, we later verified the sensory loss in the reinnervated muscle during a terminal procedure using a well-described method(Huyghues-Despointes et al.,2003a; Huyghues-Despointes et al., 2003b; Nichols,1989; Nichols,1999). Also during the terminal procedure, we directly measured hindlimb bony segment lengths for use in our kinematics model and independently weighed the four major ankle extensor muscles (soleus, medial and lateral gastrocnemius heads, and plantaris muscles) from both hindlimbs to test for symmetry.

Prior to any behavioral testing, the cats were injected intramuscularly with 0.06 mg kg^–1 of medetomidine (Domitor®, New York,NY, USA), a reversible veterinary sedative-analgesic commonly used for minor diagnostic procedures not requiring general anesthesia. While sedated, the animals' hindquarters were shaved to allow for accurate palpation and ink marking of anatomical landmarks. Regardless of animal size, we intramuscularly injected 0.10 ml of atipamozole (Antisedan®, Pfizer) to reverse the effects of the medetomidine. Cats were typically alert, upright and walking within 10–20 min of injection of the reversal agent. With the cat in a standing position and using the marked skin as a guide, we attached retroreflective markers to the skin at the superior iliac crest, greater trochanteric notch, lateral epicondyle of the femur, lateral malleolus of the fibula, fifth metatarsal head, and the proximal interphalangeal joint of the left leg (Fig. 2).

Pre-injury control data were collected on two separate days before the nerve injury surgery was performed. Post-injury data were collected 1-month post-surgery during the muscle paralytic stage and at 14 months post-surgery during the muscle self-reinnervated stage. The self-reinnervated stage data reported here reflect the 14-month post-injury stage for all but one cat,which did not complete the 14-month collection. Instead, 9-month self-reinnervated stage data were successfully collected and are reported for this individual. During all data collection trials, the cats walked on our treadmill at 0.8 m s^–1 until a steady gait was observed. Three-dimensional (3-D) marker positions on the left hindlimb were recorded at 125 Hz for 16 s with a two-camera motion capture system (Peak Performance Technologies, Denver, CO, USA) and saved to a computer for later analysis. Animals were allowed to rest for at least 2–5 min between the two to four trials collected for each day of collection. A typical 16-s trial consisted of approximately 25 stride cycles; however, we excluded any portions of a trial that was not at constant speed to minimize any acceleration effects. Although constant speed was a criterion for data inclusion, this did not require the animals to place their paws on the treadmill belt in the same relative anteroposterior position with each step. Given the general relationship between speed, step frequency and step length, an infinite number of different limb orientations at ground contact could have resulted in the same constant walking speed. Additionally, for any given limb orientation, an infinite number of limb lengths can be achieved by simply varying the joint angles in an accordion-like fashion. It is important to point out that the mechanics of constant speed treadmill locomotion are identical to that of over ground locomotion (van Ingen Schenau,1980) and results in comparable kinematics and kinetics(Riley et al., 2007). Therefore, it is reasonable to expect numerous options with respect to limb positions and kinematics trajectories over the step cycle as one might during over ground locomotion. The data from all trials were pooled for each condition and on average we analyzed 38 steps (±25; ±s.d.) per cat and condition with a range of 17–100 strides across all cats and conditions.

Marker position data were low-pass filtered (zero-lag, fourth order Butterworth filter, 7 Hz cut-off) and reconstructed to 3-D positions using commercial motion analysis software (Peak Motus 8.0, Peak Performance Technologies, Denver, CO, USA). The sagittal plane knee joint center was determined by calculating the two intersection points of two circles whose centers were defined by the hip and ankle joints and whose radii were defined by the segment lengths of the femur and tibia, respectively(Fowler et al., 1993; Goslow et al., 1973). From these two points of intersection, only one provided an anatomically appropriate solution and was used as the knee joint center. From the marker positions, 2-D sagittal plane joint angles were calculated for the hip, knee,ankle and metatarsalphalangeal (MTP) joints(Fig. 2). We performed a subsequent check on our data to verify that out-of-plane limb movements were minimal. The animals were killed with an overdose of sodium pentobarbital(Nembutal, 150 mg kg^–1), and the hindlimb was dissected and bone segment lengths of the femur and tibia were directly measured to use in our knee triangulation procedure. Using calipers, we measured the femoral segment length as the distance between the center of the femoral head to the estimated knee joint center between the lateral femoral epicondyle and lateral tibial plateau. We measured the tibial segment length as the distance between the same point between lateral femoral epicondyle and lateral tibial plateau to the apex of the lateral malleolus of the fibula. We defined the whole limb position as a vector drawn from the toe marker to the pelvic marker(Fig. 2). From this limb vector, we could calculate the kinematics of the limb orientation and limb length over each gait cycle. The trajectories of each joint angle and limb position component were then time-normalized and averaged over the gait cycle.

All cats showed morphological symmetry across right and left hindlimbs with respect to bony segment lengths and post-injury muscle masses. Our cadaveric measurements after the terminal procedure yielded nearly symmetrical hindlimb segment lengths for all animals with the greatest mean difference between left and right segment lengths measuring only 1.6±2.9 mm(Table 1), which we did not find to be significant (P=0.28). We found a small but significant difference of 0.9±0.6 mm in the left tibial segment (P=0.04)Nevertheless, this difference amounted to less than a 1% difference in segment length. The mean differences for all respective segments of the left and right limbs averaged less than 3%. The ankle extensor muscle masses from the affected left hindlimb did not show any asymmetries across cats when compared with their corresponding muscle in the contralateral limb(Table 1). We observed the largest difference in the lateral gastrocnemius muscle mass, with that of the left limb being on averaged 1.4 g lighter than that of the right limb,resulting in a 12% difference that was not statistically significant(P=0.09). We verified, through video observation, that all cats walked with symmetrical gait patterns for all trials and conditions. The overall symmetry in muscle masses also suggests that there were no gross architectural changes related to asymmetric gait patterns, such as atrophy or hypertrophy in the affected muscles or their synergists.

We calculated the means of the kinematics trajectories across all strides for each cat and condition (Matlab, Natick, MA, USA). We quantified the consistency of the mean post-injury kinematics data relative to the mean pre-injury kinematics by performing linear regressions on each of the two sets of mean post-injury trajectories (Paralytic and Self-Reinnervated Stages)versus the mean pre-injury trajectories (Matlab). We performed these linear regressions over the initial yield phase of stance as determined by the ankle joint (∼15% of stride) and also over the entire stance phase (∼60% of stride). We then used the coefficient of determination(R²) from each variable regression to quantify the consistency of the mean kinematics trajectory after injury for one animal. The R² values were then averaged across all cats at each injury stage (R̄²). If R̄²>0.50, then we could say that the majority of the trajectory shape after injury can be explained by the same pattern observed before injury for all cats (one-tailed, t-test, α=0.05, JMP, SAS Institute, Cary, NC, USA). This metric allowed us to test whether the trajectory of each of the kinematics variable persisted after injury and whether this was a common feature across all cats. Mean kinematics trajectories over multiple steps provide us with an estimate of what the kinematics goals may be during locomotion. Comparing pre-injury mean trajectories to their corresponding post-injury data would indicate whether the kinematic targets for that variable had changed due to the injury.

We calculated the variance of the different kinematics variables defined in our hindlimb model (Fig. 2)across all strides for each cat and condition. We then cumulatively summed the variance over the entire stride cycle to obtain a single metric we termed`total variance'. We compared total variance for each joint angle and for limb orientation angle across all cats and data collection stages (pre-injury,paralytic stage, and self-reinnervated stage). Pooling variance data across all joints and recalculating a single mean total variance value for all joints, we performed a one-tailed t-test to assess differences between joint angles and limb orientation angles (α=0.05). We performed a single factor ANOVA for each total variance measurement (limb orientation and pooled joint angles) over the data collection stages (pre-injury,paralytic stage, and self-reinnervated stage) to test for an effect over time. When we detected a significant effect, we performed a Tukey–Kramer HSD post-hoc test to further discriminate between time stages.

Prior to peripheral nerve injury, our joint kinematics data were comparable with data reported in the literature for healthy intact cat locomotion(Goslow et al., 1973; Maas et al., 2007; Smith et al., 1998). Post-injury, we observed clear changes in mean joint kinematics trajectories for each cat compared with pre-injury (Fig. 3). Nerve injuries to ankle extensor muscles had clear effects on other joints of the limb. The directions and magnitudes of joint deficits after injury, however, could sometimes be unpredictable depending on injury condition and animal.

As expected, paralyzed triceps surae muscles resulted in a large ankle flexion, or yield, during the weight acceptance period of the stance phase(Fig. 3). This was consistent across all three triceps-injured animals. In these animals, the other joints of the limb were also affected in response to the altered ankle kinematics. Notably, the MTP and hip joint trajectories of all three triceps-injured cats showed the same changes with greater MTP flexion and hip extension throughout the stance phase compared with pre-injury. By contrast, the knee joint trajectory showed some variation with cat 4 showing relatively little effect at the knee whereas cats 3 and 5 showed increased peak knee extension during the paralytic stage. With muscle self-reinnervation, there were fewer consistent trends across individuals. For example, MTP joint trajectories of the three triceps-injured cats showed three different patterns after muscle self-reinnervation (Fig. 3).

The soleus nerve injury group displayed more subtle deficits at both paralytic and self-reinnervated stages. We still observed notable deficits at the MTP joint, but they were not consistent between animals. MTP kinematics of the two soleus-injured animals provided an exemplary case of inter-animal variability after nerve injury (Fig. 3, two bottom-left panels). Cat 1 showed a clear post-injury response favoring decreased (more hyper-extended) MTP joint angles across the gait cycle. By contrast, Cat 2 adopted increased (less hyper-extended) MTP joint angles. Differences in MTP kinematics remained after soleus self-reinnervation.

Interjoint coordination was affected by both muscle paralysis and self-reinnervation. We observed drastic changes as indicated by angle–angle plots during the paralytic stage, followed by more subtle post-injury changes in joint range of motion during the self-reinnervated stage (Fig. 4). These data suggest relatively unique post-injury mean joint kinematics for each animal. In cat 3 for example, stance phase knee joint range of motion returned to normal after triceps surae self-reinnervation (shaded regions in Fig. 4A,B) while baseline shifts occurred in hip and ankle joint ranges of motion. By contrast, with the same injury cat 4 preserved stance phase hip and ankle joint ranges of motion while that of the knee shifted (shaded regions in Fig. 4D,E).

Mean kinematics trajectories of limb orientation and limb length were far less affected after nerve injury compared with individual joints(Fig. 5). Mean limb orientation trajectories of all cats followed the same pattern and magnitudes of stance phase retraction and swing phase protraction across all injury conditions. Mean limb length trajectories before and after injury displayed a brief period of limb shortening during the initial weight-bearing, or yield, phase of stance followed by lengthening throughout the rest of stance. Mean limb length dramatically shortened over the first half of swing phase and extended as it approached paw contact of the next stride cycle. Despite small post-injury differences, these trajectory patterns were well conserved across all animals in both shape and magnitude.

Post-injury kinematics data matched pre-injury data better for limb orientation and limb length trajectories than for individual joint angles. A linear regression of post-injury mean kinematics trajectories as a function of mean pre-injury kinematics provided a quantitative metric of the consistency of the trajectory pattern after nerve injury(Fig. 6). A perfectly unchanged mean trajectory would correspond to a regression that matches the line of identity, or an R²=1.0. A post-injury mean trajectory that did not match pre-injury kinematics would result in a R²equal to zero. R² values averaged across all animals(R̄²) indicated invariant mean limb kinematics after injury (Fig. 7). During the paralytic stage, only limb orientation(R̄²=0.93±0.89, P=0.0002) and limb length(R̄²=0.82±0.11, P=0.0017) kinematics were preserved(R̄²>0.50) over the yield phase of stance and only limb orientation(R̄²=0.99±0.002, P<0.0001) was preserved over the entire stance phase. After muscle self-reinnervation, R̄²values of both limb orientation (0.91±0.09, P=0.0012) and limb length (0.84±0.14, P=0.0094) remained high over the yield phase. After self-reinnervation, both limb orientation(R̄²=0.97±0.05, P=0.0001) and limb length(R̄²=0.83±0.24, P=0.0352) trajectories were preserved over the entire stance phase.

In comparison, no individual joint angle trajectories were preserved during the paralytic stage (Fig. 7). After self-reinnervation, only the knee joint trajectory over the yield phase had returned for all cats(R̄²=0.77±0.20, P=0.0373) but a normal knee joint trajectory did not persist over the entire stance phase(R̄²=0.54±0.32, P=0.4014). R² values for ankle joint(R̄²=0.69±0.46, P=0.2375) and hip joint(R̄²=0.24±0.48, P=0.8208) trajectories, in contrast, were not high for all cats over the yield phase of stance, but were over the remainder of stance phase(R̄²=0.81±0.24, P=0.0389; and R̄²=0.95±0.06, P=0.0004, respectively).

Regardless of the type of injury, the individual joints of the hindlimb exhibited greater step-by-step variability than the entire limb. At each of the pre-injury, paralytic and self-reinnervated stages, the cumulatively summed variance, or total variance, of individual joint angles was always greater than the total variance of limb orientation(Fig. 8). Prior to nerve injury, intact cats exhibited greater total variance in individual joint angles (0.58±0.57 rad²) compared with the total variance of limb orientation (0.25±0.14 rad², P=0.027). All animals during the paralytic stage also exhibited greater joint angle total variance (0.80±0.24 rad²) compared with limb orientation total variance (0.37±0.24 rad², P=0.016). After muscle self-reinnervation, all animals again demonstrated greater total variance in joint kinematics (1.49±0.87 rad²) compared with total variance of limb orientation (0.53±0.27 rad², P<0.001).

The total variance of limb orientation did not change after injury as a result of muscle paralysis or self-reinervation[F_(3,15)=1.95, P=0.18]. The step-by-step total variance of joint angles, however, did increase after injury[F_(3,60)=10.07, P<0.001]. Although total variance of joint angles increased in both post-injury stages, only the self-reinnervated stage was significantly different (α=0.05; Fig. 8).

Step-by-step deviations observed at the limb level were not equally sensitive to the deviations of individual limb elements. Limb orientation was most sensitive to deviations in shank and thigh segment angles, and least sensitive to deviations of the forefoot and pelvis angles(Fig. 9A). Positive values of limb orientation sensitivity indicated that an increase in any of the five segment angles would result likewise in an increase in limb orientation. Although the relative magnitudes of sensitivity were modulated across the gait cycle, individual patterns changed little after injury(Fig. 9A–C) and were similar across all cats (Fig. 9D,E). Limb length was also most sensitive to shank and thigh angle deviations, however, these had opposite effects as indicated by the opposite signs for sensitivity (Fig. 9F). This means an increase in shank segment angle would increase limb length, whereas the same increase in thigh segment angle would decrease limb length.

In a given animal, peripheral nerve injury results in clear changes to mean joint kinematics, which are often referred to as locomotor deficits in cases of pathological gait. Although varied responses occur between animals at some joints, some consistent trends also exist. The magnitude of the joint deficit is related to the severity of the injury. Paralysis resulted in greater changes to mean joint angles compared with self-reinnervation. The polyarticular characteristics of remaining unaffected muscles also had an effect on resulting joint deficits.

A large biomechanical constraint exists when the plantaris muscle remains as the only major ankle extensor as a result of paralyzed triceps surae muscles. Although extrinsic foot muscles such as flexor hallucis longus can be significant contributors to ankle extension(Lawrence et al., 1993), the larger plantaris muscle with its substantial ankle extensor muscle moment arm probably takes over the majority of ankle extension duties when the triceps surae group is paralyzed. The plantaris muscle is a powerful ankle extensor used during normal cat locomotion(Prilutsky et al., 1996),however, it is also a significant flexor of the MTP joint because of its continuous insertion onto the flexor digitorum brevis muscle(Crouch, 1969). Owing to this triarticular nature, an increased ankle extensor role for plantaris would create a biomechanical coupling between the ankle and MTP joints such that greater ankle extension would correlate with greater MTP angles (i.e. less hyperextension). As expected, all three triceps surae-paralyzed animals displayed increases in MTP joint angles because of the increased role played by the plantaris muscle as an ankle extensor. When only soleus is paralyzed,it is possible for either the triarticular plantaris or biarticular gastrocnemius muscles to take over any lost ankle extensor function. Cat 2 showed the same increase in MTP joint angles as the triceps injured cats suggesting this animal probably relied more on plantaris after injury. By contrast, cat 1 displayed smaller MTP joint angles (i.e. increased hyperextension) suggesting more reliance on the gastrocnemius muscle at the ankle joint, which does not cross the MTP joint.

With muscle self-reinnervation, mean joint angle trajectories approach more normal, pre-injury kinematics compared with the paralytic stage, but some deficits remain (Fig. 7). After great disruption during the paralytic stage, interjoint coordination approaches pre-injury values after self-reinnervation with some lingering deficits in mean joint kinematics (Fig. 4). These lingering joint deficits become more obvious and consistent across animals when these cats walk down an incline(Abelew et al., 2000; Maas et al., 2007) because of the greater reliance on length and force feedback, which are effectively lost after muscle self-reinnervation (Cope et al., 1994). Although mean joint kinematics are altered during level walking, individual cats exhibit individual variation in mean kinematics patterns over the gait cycle.

In contrast to the joint kinematics, mean trajectories of the limb kinematics are highly conserved across animals after peripheral nerve injury. Pre-injury mean limb orientation and limb length trajectories persist during both paralytic and self-reinnervated stages (Figs 5 and 6). Maintaining the same limb position trajectory is of primary importance during locomotion after neuromuscular injury. Furthermore, these data suggest that preservation of pre-injury limb orientation and limb length trajectories is accomplished through the long-term compensatory changes occurring across all of the individual joints. This long-term compensation strategy exploits the neuromechanical redundancy in the limbs to coordinate different combinations of joint angles that result in the same net global limb kinematics(Fig. 8). We see this to be the case in four different neuromuscular injury conditions: soleus muscle paralysis, soleus muscle self-reinnervation, triceps surae group paralysis,and triceps surae group self-reinnervation. This suggests that the coordination of joint kinematics to preserve limb kinematics may be a fundamental guiding principle of long-term locomotor compensation in cats.

At the joint-level, there is no return to pre-injury mean joint angle trajectories during the paralytic stage. After self-reinnervation, only three instances of joint angle trajectory are preserved. After self-reinnervation,mean knee angle trajectory returns to its pre-injury state, but only over the yield phase (Fig. 7A). When we consider the rest of stance phase, only mean ankle and hip joint kinematics return to pre-injury states (Fig. 7B). These data suggest the knee joint may have an important function during the yield phase of stance and that the ankle and hip joints may be critical over the remainder of stance. These notions, however, require further testing to confirm. The lack of persistence of any joint angle trajectories during the paralytic stage, however, suggests that maintaining joint-level tasks are of secondary importance relative to maintaining invariant limb function.

Our long-term compensation data suggest that after neuromuscular injury,different individual cats will arrive at different solutions, or combinations of joint kinematics patterns, that satisfy the common goal of maintaining invariant limb kinematics. These joint-level kinematic changes occur over weeks and months while accommodating the changing sensorimotor abilities associated with peripheral nerve injury and recovery. Long-term locomotor compensation to chronically adjust mean joint kinematics in this way could utilize a pre-existing short-term compensation strategy that explores and exploits numerous possible combinations of joint angles to minimize variability of limb kinematics on a step-by-step basis.

In addition to a long-term compensation strategy that uses altered mean joint angle trajectories to maintain invariant mean limb kinematics, we found a short-term compensation strategy that minimizes step-by-step variability of limb kinematics despite an increase in joint angle variability. Step-by-step total variance of all joint angles is consistently greater than total variance of limb orientation at all three injury stages. Limb orientation is sensitive to changes in each limb segment, so many combinations of joint deviations could result in increased limb total variance. Yet, this does not occur. Limb orientation is defined kinematically by the net combination of joint angles and segment lengths. Although joint angles vary significantly from one step to the next, they are selected in combinations that tend to keep overall limb orientation invariant. A short-term compensation strategy to decrease step-by-step limb variability is similar in concept to the long-term compensation strategy that preserves mean limb kinematics trajectories through the selection of appropriate mean joint kinematics. In both cases, redundancy in joint angle combinations that result in the same net limb position is exploited to overcome challenges due to nerve injuries occurring over months or natural step-by-step variations occurring over seconds.

Surprisingly, the step-by-step joint variance increased throughout the study period, or across injury stages (Fig. 8). One might have predicted that step-to-step variance might come back to pre-injury levels with muscle self-reinnervation, especially since the mean joint trajectories returned closer to pre-injury values. One possible explanation for this is that the cats had increased their reliance on using joint covariance after injury to maintain a consistent limb kinematics trajectory. Although there is some evidence of increased goal-equivalent joint variability with pathological gait (Black et al., 2007), this is a relatively unexplored area and deserves further attention. The finding that consistent limb kinematics are achieved through greater joint variability provides interesting evidence that the recovery process after injury does not include returning to the same neuromuscular state before injury. Locomotor recovery may then be more appropriately viewed as the persistence of limb-level function through enhancement of joint-level compensatory processes, or altered motor control strategies. The ability for locomotor compensation could be a heritable form of behavioral plasticity and represent an evolutionary adaptation for physiologically adaptive behavior(Bronmark and Miner, 1992; Bronmark and Pettersson, 1994; Gotthard and Nylin, 1995; Wagner, 1996). Although an intriguing possibility, to thoroughly test such an idea would require much more work than is possible here.

Deliberation over what guides these compensatory responses after injury may require a broader view of what functional tasks are being met with each step. Although a peripheral nerve injury may directly affect only muscles acting at the ankle joint, concomitant responses occur across all major joints of the limb. An appealing proposition is that stabilization of limb-level kinematics alone are attended to at higher supraspinal levels of the nervous system. These limb-level control signals then descend and guide lower levels of organization that select and regulate individual joint kinematics through a more automated process. The anatomical locations of these higher-level control centers are unknown, but remain an active area of research(Drew et al., 2008; Ting, 2007; Ting and McKay, 2007). At lower levels of the locomotor system, regulation of joint kinematics to consistently satisfy higher-level commands might include a mixture of active neural processes, such as autogenic and heterogenic spinal reflex pathways,and passive biomechanical mechanisms, such as the mechanical coupling associated with biarticular muscles and interaction torques. It is likely that both active and passive mechanisms are involved.

Preferential conservation of limb-level kinematics over joint-level kinematics over long and short time scales suggests that a neuromechanical representation of whole limb function may guide joint-level locomotor compensations. This intralimb compensation mechanism exploits the abundance of joint-angle combinations that are goal-equivalent for the limb-level tasks of orientation and length control. With muscle paralysis, when none of the individual joints could match pre-injury kinematics, limb-level function remained invariant across all cats (Fig. 7). Although the functional role of individual joint trajectories over the stance phase may require more study, the persistence of joint-level function appeared to be of secondary importance compared with the preservation of whole limb function.

Our findings support previous work that suggests neural representations of whole limb position (orientation and length) in the cat are encoded at the level of the spinal cord (Bosco and Poppele, 2000; Bosco and Poppele, 2003; Bosco et al.,2000). This sensory representation of whole limb position ascends spinal tracts to higher brain centers and is probably an important determinant of locomotor control of the limbs. Recent work also suggests that the increased cortical activity associated with more complex walking tasks is due to modifications made during gait(Beloozerova and Sirota, 1993a; Beloozerova and Sirota, 1993b; Beloozerova and Sirota, 1998; Drew et al., 2008). This suggests the central nervous system may use neural representations of limb-level kinematics to assemble goal-equivalent, joint-level compensatory responses that correct and stabilize normal limb function on a step-by-step basis, both before and after injury.

Both neural and mechanical processes may regulate these immediate joint-level compensations. Heterogenic force feedback pathways can contribute to such a compensation mechanism between muscles crossing adjacent joints. Heterogenic reflex pathways that affect the knee and ankle joints have been identified in the cat to affect interjoint coordination(Nichols et al., 1999; Wilmink and Nichols, 2003). For example, increased force production in the triceps surae muscles related to inadvertent ankle extension would increase inhibition of the quadriceps muscles and result in a compensatory decrease in knee extension. A recent modeling study of the cat hindlimb indicates heterogenic reflexes result in greater stability or maintenance of limb position against perturbations(Bunderson et al., 2007). These and other yet to be identified reflex pathways probably function to regulate automatic joint-level responses to preserve goal-equivalence at the limb level.

In addition to neural mechanisms, passive mechanics may improve compensatory action in the joints. The role of biarticular muscles and interaction torques across limb segments is implicated in stabilizing the shoulder-elbow complex in arm reaching movements(Cabel et al., 2001; Kurtzer et al., 2006; Sangani et al., 2007) and in helping explore goal-equivalent kinematic solutions during other human arm movements (Martin et al.,2009). In human hopping, simply adopting a more extended limb position can help stabilize limb-level force production on the ground despite high joint torque variances (Yen and Chang, in press).

The invariance of whole limb function that results from joint-level compensatory actions may also help explain why simple biomechanical models,such as the inverted pendulum model for walking and the spring-mass model for running, can robustly predict the dynamics of legged locomotion across so many species with complex and different morphologies(Blickhan, 1989; Full and Koditschek, 1999; McMahon, 1990; Srinivasan and Ruina, 2006). These biomechanical models grossly oversimplify the complex neuromusculoskeletal features of the limbs during locomotion. Yet, along with the studies suggesting neural representations of whole limb position, our results suggest these simple biomechanical templates for limb function may reflect actual performance variables controlled by higher levels of the locomotor system.

A coordinated, joint-level response can minimize the effect of limb-destabilizing deviations experienced by any single joint. For example,humans minimize the variability of end-point position or end-point force by exploiting goal-equivalent variability in the joints during upper extremity reaching movements (Scholz and Schöner, 1999; Tseng et al., 2002; Tseng and Scholz,2005) and finger force production tasks(Kang et al., 2004; Shinohara et al., 2003; Shinohara et al., 2004),respectively. In a locomotor task, similar compensation strategies exist for lower limb control during human hopping(Auyang et al., 2009; Yen et al., 2009)(Yen and Chang, in press). Humans hopping in place coordinate joint-level kinematics to minimize the effects of natural cycle-to-cycle joint-level variance on limb orientation and limb length (Auyang et al.,2009). To the best of our knowledge, this is the first evidence that task-oriented goals such as limb position in the cat may be driving joint-level locomotor compensations after neuromuscular injury.

In summary, limb-level kinematics are preferentially maintained over individual joint-level kinematics after multiple types of peripheral nerve injury in cat ankle extensor muscles. Limb orientation and limb length are functionally relevant locomotor tasks stabilized by goal-equivalent compensatory actions at the joints and appear to guide long-term locomotor compensation after injury and short-term locomotor compensation on a step-by-step basis. This suggests animals exploit motor redundancy in the limbs to stabilize limb function with each step, and that this compensation strategy can persist over temporary and permanent disruptions of joint function.