Leg mechanics contribute to establishing swing phase trajectories during memory-guided stepping movements in walking cats: a computational analysis

Abstract

When quadrupeds stop walking after stepping over a barrier with their forelegs, the memory of barrier height and location is retained for many minutes. This memory is subsequently used to guide hind leg movements over the barrier when walking is resumed. The upslope of the initial trajectory of hind leg paw movements is strongly dependent on the initial location of the paw relative to the barrier. In this study, we have attempted to determine whether mechanical factors contribute significantly in establishing the slope of the paw trajectories by creating a four-link biomechanical model of a cat hind leg and driving this model with a variety of joint-torque profiles, including average torques for a range of initial paw positions relative to the barrier. Torque profiles for individual steps were determined by an inverse dynamic analysis of leg movements in three normal cats. Our study demonstrates that limb mechanics can contribute to establishing the dependency of trajectory slope on the initial position of the paw relative to the barrier. However, an additional contribution of neuronal motor commands was indicated by the fact that the simulated slopes of paw trajectories were significantly less than the observed slopes. A neuronal contribution to the modification of paw trajectories was also revealed by our observations that both the magnitudes of knee flexor muscle EMG bursts and the initial knee flexion torques depended on initial paw position. Previous studies have shown that a shift in paw position prior to stepping over a barrier changes the paw trajectory to be appropriate for the new paw position. Our data indicate that both mechanical and neuronal factors contribute to this updating process, and that any shift in leg position during the delay period modifies the working memory of barrier location.

Keywords: leg mechanics; model leg movement; obstacle avoidance; walking; working memory.

Figure 1

Four-link modeling of cat hind leg. (A) The cat hind leg was modeled by four uniform rods for the thigh, shank, paw, and toes connected at the hip joint (h), knee joint (k), ankle joint (a), and paw joint (p). The model was used to calculate torques at these four joints when the animal stepped over a remembered barrier (dotted rectangle), and to simulate leg movements when driven by different torque profiles. The barrier (filled rectangle) was lowered after the forelegs have stepped over it. The slope of the toe trajectory (dotted line) was calculated over distance of 2 cm soon after the swing phase commenced. (B) Parameters used to determine the equations of motion for a single segment (see text for details). This segment represents the first segment in a kinematic chain starting from the origin (O), which is the hip joint in the model. Note that for each segment the segment angle (θ) is measured in the anti-clockwise direction from the positive X-axis proximal to the segment. By convention, positive torques are in the anti-clockwise direction. The reaction torque and forces at the distal joint are in the opposite directions to those at the proximal joint.

Figure 2

Verification of accuracy of numerical integration of the forward mechanical model. (A) The kinematics of the hind leg of a cat stepping over a barrier (actual kinematics) were used in an inverse dynamic analysis to first calculate the torque profiles at the four joints. These torque profiles were then used as inputs to the forward model to yield a simulated leg movement (model kinematics). Note the high degree of similarity of the stick figures for the actual and simulated leg movements. (B) Plot of the slopes of the actual and simulated toe trajectories showing a very close correspondence.

Figure 3

Slope of toe trajectories increase with shorter initial toe distances from the barrier in the behaving animal (dash lines and open squares) and in the forward model (solid line and filled circles) driven by averaged torque profiles calculated for a subset of trials starting with toe-to-barrier distances in the range of 16–25 cms. The initial geometry of the leg in each simulated trial was the same as initial geometry of the leg in the corresponding trial of the behaving animal. Note the divergence of the best best-fitting curves as the initial toe-to-barrier distance decreases due to the lower dependence of the modeled slopes on initial distance from the barrier. The three data sets are from three different animals.

Figure 4

Slopes of toe trajectories produced by the simulation are generally lower than the slopes for the observed toe trajectories. Each data point in the scatter plots represents the slope of toe trajectory from the simulation (simulated slope) and the slope observed (observed slope) for a single trail. The three sets of data are from trials in three different animals. Note the divergence from the identity line (dashed) as slope increases. The matching of the data points at the low slopes is because the simulations were driven by average torque profiles of a subset of trials at long toe-to-barrier distances that are associated with low slopes (see Figure 3).

Figure 5

The knee torque at the beginning of swing increases with shorter initial toe distance from the barrier. (A) Averaged torque profiles hip, knee, and ankle joints for the first 200 ms of the swing phase for long (solid lines) and short (dashed lines) initial toe-to-barrier positions. Note the knee torque is larger for shorter distances for approximately the first 30 ms of swing (shaded area), whereas the initial torques at the ankle and hip joints are very similar at swing onset for both conditions. Knee flexion torques are negative for the geometry of the leg used in the inverse dynamic analysis, while hip and ankle flexion torques are positive. (B) Scatter plot of data from another animal showing the increase in the knee torque at swing onset with decreasing toe-to-barrier distance.

Figure 6

The magnitude of EMG activity in knee flexor muscles semitendinosus (ST) and medial sartorius (Sart_m) increases with shorter initial toe distance from the barrier. The magnitudes of the EMGs were measured over the first 150 ms of burst onset. Data in (A) and (B) are from two different animals. EMG amplitudes measured in arbitrary units (AU).