Model and measurement studies on stages of prosthetic gait.   

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Chapter 3

Prosthetic limb swing
Principles of obstacle avoidance with a transfemoral prosthetic limb
Helco G. van Keeken, Aline H. Vrieling, At L. Hof, Klaas Postema, Bert Otten,
In Med Eng Phys, 2011. [bib] [pdf] [doi]  
 
NOTICE: this is the author's version of a work that was accepted for publication in J Med Eng Phys. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.
Prosthetic limb swing without (l) and with (r) ground friction.
Notice the temporal and spatial differences.

Principles of obstacle avoidance with a transfemoral prosthetic limb.

In this study, conditions that enable a prosthetic knee flexion strategy in transfemoral amputee subjects during obstacle avoidance were investigated. This study explored the hip torque principle and the static ground principle as object avoidance strategies. A prosthetic limb simulator device was used to study the influence of applied hip torques and static ground friction on the prosthetic foot trajectory. Inverse dynamics was used to calculate the energy produced by the hip joint. A two-dimensional forward dynamics model was used to investigate the relation between the obstacle-foot distance and the necessary hip torques utilized during obstacle avoidance. The study showed that a prosthetic knee flexion strategy was facilitated by the use of ground friction and by larger active hip torques. This strategy required more energy produced by the hip compared to a knee extension strategy. We conclude that when amputees maintain sufficient distance between the distal tip of the foot and the obstacle during stance, they produce sufficiently high, yet feasible, hip torques and use static ground friction, the amputees satisfy the conditions to enable stepping over an obstacle using a knee flexion strategy.
 
transfemoral prosthetic limb, obstacle avoidance, hip torques, ground friction, knee flexion, computer simulations

Introduction

Stepping safely over obstacles is a common daily living activity 1. During obstacle avoidance, the stance limb must establish a base of support that appropriately maintains stability to avoid slipping or falling. The swing limb must clear the obstacle successfully to avoid tripping 2; 3. The applied joint moments of the swing limb and the obstacle-foot distance during stance determine the clearance achieved during obstacle avoidance 4. Flexion of the knee in the swing limb is the most important motor strategy used by able-bodied (AB) subjects for foot clearance. This knee flexion is achieved by an increase in the force of the knee flexors 5; 6; 7; 8; 9 and through kinetic coupling by the hip flexors. The amputation of a lower limb results in a deficiency in sensory input and an absence of muscles and joint(s). A person with a lower limb prosthesis must adapt to a mechanical device to become functionally independent again 10. Transtibial (TT) amputee subjects increase swing hip elevation and hip and knee flexion as a function of obstacle height during obstacle avoidance. An increase of the knee flexion on the prosthesis side is achieved by modulating the work performed at the hip, not at the knee, as seen on the amputee’s sound side 11; 12. In addition, the stance limb hip flexion, knee flexion and (on the sound side) ankle plantarflexion increase slightly with increased obstacle height, but the stance limb hip elevation does not. Hill et al. ( 1997) concluded that modulations of the stance limb served to position the pelvis further back from the obstacle as the height of the obstacle increased.
Transfemoral (TF) amputee subjects make use of adjustment strategies to compensate for the loss of muscles and sensory input in their prosthetic limb during obstacle avoidance, and they learn to cope with bilaterally delayed and decreased obstacle avoidance responses in both limbs 13. Vrieling et al. (2007; 2009) found that the prosthetic knee flexion during obstacle avoidance of transfemoral amputee subjects was reduced in comparison with unimpeded walking and compared to TT amputees and able-bodied subjects. The lack of knee strategy in TF amputee subjects is compensated for by circumduction at the hip on the prosthesis side and by plantar flexion on the sound side 14. These results suggest that TF amputee subjects use an extension strategy: their knee is fixed in extension, which is combined with hip abduction and exorotation. This strategy has an advantage over the knee flexion strategy. The extended prosthetic knee eases the transition from swing to stance. However, the extension strategy also has disadvantages. Not only does it reveal the use of a prosthetic limb, but also changes in the gait cycles are necessary when accelerating and decelerating the prosthetic limb in a lateral direction. Therefore, more degrees of freedom must be controlled. Additional free space is necessary for the clearance as the foot moves farther outward. Possible reasons for choosing the extension strategy over the flexion strategy are 1) a reduced gait velocity of the TF amputee subjects, which impedes the initiation of the pendulum motion of the prosthetic limb or 2) not being able to produce a sufficient flexion moment at the hip joint. To reduce the number of falls of amputees, Vrieling et al. suggested that it is important to train amputees in complex motor tasks, such as stepping over an obstacle, during the rehabilitation period. This training should be aimed at improving knee flexion or the execution of adjustment strategies. Although TF amputee gait and obstacle avoidance include many out of plane actions, including trunk sway 16; 17; 18 and the previously reported circumduction strategy 14; 15, we believe it is of interest to study the possibility of crossing an obstacle with a knee flexion strategy as this strategy reduces the changes in gait cycles and masks the use of a prosthetic limb. In theory, crossing an obstacle with an upper leg prosthesis, which is confined to the sagittal plane, can be executed in four ways, where the prosthetic limb is either leading or trailing with the artificial knee joint either in flexion (flexion strategy) or fixed in extension and combined with hip abduction and exorotation (extension strategy).
In the present study, we asked how the hip torques and static ground friction 19 contributed to a flexion strategy in obstacle avoidance and what the costs are of this strategy. We hypothesized that to move a prosthetic foot using a knee flexion strategy over an obstacle that is close by, it is preferable to use ground friction and large hip torques. This combination helps to achieve height with less forward motion compared to a combination of small hip torques and without the use of static ground friction. To achieve sufficient obstacle-foot clearance during the knee flexion strategy, the TF amputee subject must overcome the extension spring force that keeps the prosthetic knee in extension. The applied hip torque and the static ground friction on the prosthetic foot can help overcome the extension spring force. Consequently, the following knee flexion lowers the moment of inertia of the prosthetic limb by bringing the foot and the lower leg shaft closer to the hip joint. These changes may be useful when stepping over an obstacle. In the current study, we limited the modeling to the sagittal plane, as crossing an obstacle with a flexed upper leg prosthesis is confined to the sagittal plane.
In the first part of this study, we experimentally investigated the relationship among the static ground friction on a prosthetic foot, a wide range of hip torques and the trajectory of the prosthetic foot. The temporal (duration) and spatial (forward motion) data, the inverse dynamics (energy produced by the hip, the hip torques and the mean angular velocities of the upper leg) and the statistical relationships among fast or slow hip flexion to move the foot 0.1 m upward, with and without static ground friction conditions, were investigated. In the second part of this study, we used a two-dimensional forward dynamics model to investigate obstacle avoidance for which we focused on a) the influence of a constant hip torque on the first part of the prosthetic foot trajectory, with and without the use of static ground friction and b) the relation between the obstacle-foot distance and the associated necessary time varying hip torques in the sagittal plane while stepping over an obstacle. Testing for these discrete parameters in human subjects, without the interference of compensation strategies, was not feasible; therefore, it was decided to approach this problem in a theoretical way. The outcome and insights we gained from this study can be used to understand why TF amputee subjects prefer to use the knee extension strategy during obstacle avoidance and to provide insights into what we should take into account when teaching a knee flexion strategy during obstacle avoidance to TF amputee subjects who have a prosthetic limb.

Methods & Results

Informed consent was obtained from all subjects before testing.

Part I - Measurements

In first part of this study, we investigated the relationships among static ground friction, hip torques and the trajectory of the prosthetic foot.

Hip torques

A wide range of hip torques driving a prosthetic limb was produced by four naive AB male subjects (mean 30 y (SD 7); mean 80 kg (SD 7.3); mean 1.87 m (SD 0.08)), with no previous experience using a prosthetic limb. A kneewalker transfemoral prosthetic simulator was used 20; 21. To obtain a high degree of equivalence for the comparison, we used a kneewalker prosthetic limb that was relatively short compared to the length of the sound limb, with the same properties, alignment settings and segments length for all four subjects. To make contact with the ground, the leg length difference between the sound leg and the prosthetic leg was compensated for by flexing the sound stance limb. The kneewalker prosthetic limb consisted of an Otto Bock Habermann modular four-bar linkage knee joint (3R36), an Otto Bock dynamic foot with toes (1D10, size 26) and a shoe (size 43 / 9, toe-heel length 0.30 m) (figure 1). The artificial knee was equipped with an extension spring. The spring served two main functions. First, the spring supported the forward motion of the foot and the shaft at the end of the swing phase. Second, the spring enabled the prosthetic limb user to raise the prosthetic limb forward against gravity without flexion of the knee, assuming that the motion is not performed at a high acceleration. This second feature provided a prosthetic limb user control over the passive knee when positioning the prosthetic foot for the stance phase. When using the extension spring, the prosthetic knee remains locked in full extension. The spring generates a moment between 45 and 0 degrees of flexion. The amount of moment is inversely related to the amount of flexion, which decreases to 0 Nm at a 45 degree flexion. Hyperextension of the prosthetic knee is prevented by a mechanical stop, i.e., a very high stiffness. The spring produces a maximal moment of 12.4 Nm in full extension. The length of the shaft can be adjusted to match the contralateral leg length. The mass of the knee-shaft-socket system is 2.08 kg. The prosthetic ankle-foot system of the prosthetic leg is relatively stiff. The upper leg socket of the kneewalker prosthetic limb is constructed in such a way that the prosthetic limb is connected to the upper and lower leg, which is fixed at a 90 degree flexion at the knee joint. Because of this construction, the AB subjects are able to put weight on the kneewalker via their knee and the socket/leg connection, so that the prosthesis can be used in a comparable manner to prostheses for knee-exarticulation amputees. All subjects used the same shoe under the prosthetic foot. The heel-toe length was 0.3 m.


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Figure 1: Kneewalker prosthesis for able-bodied subjects.
The black dots indicate the position of the retroreflective markers.


Measurement

We used a PRIMAS 3D motion capture camera system, Bertec force plates and the kneewalker. The 3D motion capture camera system consisted of 6 infrared cameras that recorded at 100 Hz. A total of 8 retroreflective markers were positioned on the spina illiaca posterior superior (1), the socket (3: upper leg, knee joint and lower leg), the shaft (2: proximal and distal) and the foot (2: heel and toe) (figure 1). The motion data were filtered using a third-order 5 Hz low-pass zero time-lag Butterworth filter. The three-dimensional forces and the center of pressure position were sampled at 100 Hz using Bertec force plates.

Procedure

The subjects were instructed to stand at ease on the force plates. Subsequently, they had to flex their hip at the prosthesis side at four speeds, which varied from slow to very fast, while standing on their sound limb. The subjects performed this task in two conditions: with and without ground friction on the prosthetic foot, i.e., with the foot on the floor and the foot above the floor. Under the ground friction condition, no instructions were given regarding how much body weight should be placed on the prosthetic limb. The subjects were allowed a maximum of five trials to produce the four different speeds. The subject decided which trial was excluded if he or she used five trials. Only the first part of the motion, from the beginning of motion, until the lowest point of the foot (either the heel or toe) reached a height of 0.10 m above the starting position, was used for the analysis. During the movement, the displacement of the pelvis had to be kept at a minimum to limit the compensation strategies. The data from the force plates were used to verify whether the swing foot was in contact with the ground in the two conditions. The data from the optical marker system were used to verify that pelvis displacement had a standard deviation that was less than 0.04 m in any direction. Only the trials that met these criteria were selected. The selected trials were grouped according to conditions with and without ground friction. The two conditions were then subdivided into fast and slow trials, which were based on the time it took to move the foot upward until the lowest point of the foot reached a height of 0.10 m above the starting position. The trials were divided at the median of that duration (0.36 s).

Outcome parameters

The outcome parameters were the percentage of trials that resulted in flexion of the knee, the duration of the trials, the forward motion of the lowest point of the foot, the energy produced by the hip, the hip torque, the mean angular velocity of the upper leg during the trial, and whether the motion resulted in flexion or extension of the knee. The motion-captured kinematic data and the force plate data were used in a planar inverse dynamics model. The model was based on a Newton-Euler approach with constraint equations, previously presented by Otten (2003), which consisted of three linked elements with a 4 bar linkage knee to calculate the energy, the torques and the mean angular velocity in the sagittal plane. A non-parametric method, i.e., the Kruskal-Wallis test, was used to determine significant differences (p<0.05) between the conditions.

Results


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Figure 2: Minimal (left panels) and maximal torques (right panels) produced during the trials in the conditions with (lower panels) or without static ground friction (upper panels).



Table 1: Overview of the temporal (duration) and spatial (forward motion) data and the inverse dynamics (energy produced by the hip and the mean angular velocities of the upper leg) results of the 4 conditions (fast or slow hip flexion, with and without static ground friction) under which the foot was raised foot 0.10 m.







Group Forward motionEnergy Duration Angular velocity meanFlexion
(m) (J) (s) (rad/s) (% of trials)







Without Static Friction, Slow0.36 (0.08)12.86 (2.40)0.59 (0.20) 0.77 (0.34)38
Without Static Friction, Fast 0.22 (0.05) 29.31 (6.15)0.32 (0.03)2.04 (0.26)100
With Static Friction, Slow 0.21 (0.07) 21.36 (4.14) 0.48 (0.09)1.57 (0.39)100
With Static Friction, Fast 0.14 (0.05)29.12 (7.86)0.29 (0.04)†‡ 2.43 (0.42)†‡ 100







Significant differences between the pairs of conditions (Group, first column) are marked with , and (p<0.05).



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Figure 3: Trajectories of the toe of the kneewalker prosthetic limb during fast and slow hip flexion in the conditions with and without static ground friction. The foot was raised upward, until the lowest point of the foot (either the heel or toe) reached a height of 0.10 m above starting position. The numbers at the bottom the graphs represent the average duration and standard deviation in seconds of the motions. Notice that the trajectories of the slow movement without static ground friction are larger because the heel is the lowest point of the foot.


Figure 2 shows the minimal and maximal torques of the wide range of hip torques that were used in the conditions with and without ground friction. Some trials were excluded because of too much hip motion or ground contact. For the without ground friction condition, 14 trials met the inclusion criteria; for the with static ground friction condition, 18 trials met the criteria. The average hip position standard deviation of the selected trials was 0.02 m in both conditions. Figure 3 shows the trajectories of the toe of the kneewalker prosthetic limb during fast and slow hip flexion in the conditions with and without static ground friction. The foot moved upward until the lowest point of the foot reached a height of 0.10 m above the starting position. An overview of the temporal (duration) and spatial (forward motion) data, the inverse dynamics (energy produced by the hip, the hip torques and the mean angular velocities of the upper leg) results, the statistical relationship among fast and slow hip flexion in the conditions with and without static ground friction, for the foot travelling 0.10 m upward, and the result of the motion (flexion or extension of the knee) are presented in table 1.
This experiment shows that by making use of more energy and static ground friction, the foot moved a smaller distance forward (0.20 m) compared to when less energy is produced and no static ground friction is used. Making use of these two factors shortened the upwards motion duration significantly and increased the angular velocity of the upper leg. The lack of ground friction with fast upper leg motions made no difference in the energy produced nor the duration of the motion, but it almost doubled the forward motion of the foot. In all of the fast trials and the slow trials that made use of static ground friction, flexion of the prosthetic knee was found. In 5 out of the 8 slow trials that did not make use of the static ground friction, the knee was maintained in an extended position.

Part II - Simulations

In the second part of this study, we used the two-dimensional forward dynamics model to investigate obstacle avoidance in a theoretical way, in which we focused on a) the influence of a constantly applied hip torque on the first part of the prosthetic foot trajectory with and without the use of static ground friction for 0.2 s and b) the relationship between the obstacle-foot distance and the associated necessary time to vary hip torques in the sagittal plane when stepping over an obstacle.

Model

The forward dynamics model is a planar system of three linked elements based on a Newton-Euler approach with constraint equations, as presented by Otten (2003). The model consists of an upper leg, a lower leg and a foot with joint torques and forces (figure 4). We adjusted the model to simulate the dynamics of a prosthesis that was connected to an upper leg stump. The settings of the model were in the range of the kneewalker prosthetic limb. The stump and socket connection was modeled as a single rigid body. For the sake of simplicity, the model utilized frictionless single axis joints. Values were selected based on numerical stability. The ranges of the ankle joint and knee joint were limited with linear counter torque springs and dampers. The counter torque springs are related to the joint angles. The dampers in the joints damp the motion of the joint based on the joint velocity. The knee counter torque spring, which limits the flexion and extension range of motion of the knee, provided a maximal stiffness of 5000 Nm rad-1. The free range of the knee joint was 100 to 0 degrees (fl / ext). The extension damper factor of the knee was set to 10 Nm s rad-1. The flexion damper factor was set to 1 Nm s rad-1. The ankle counter torque spring provided a maximal counter torque of 1000 Nm rad-1. The free range of the ankle joint was -1 to +1 degrees (plantar fl / dorsal fl; almost stiff ankle). The ankle damper factor was set to 4 Nm s rad-1.


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Figure 4: A two-dimensional planar system of four linked elements with joint torques and forces in a floor and obstacle environment.


The hip joint moved with a constant forward velocity. The torques on the hip joint and the translations of the moveable point in the sagittal plane were variables in the model of which the influences can be studied. The hip joint was the origin of the first element in the chain. Translation and rotation of a parent element effected the connected child element. The proximal (heel) and distal (toe) part of the foot were used as possible contact-points with the external environment. The ground reaction forces, which the model takes into account, were formed in these points during collision. The external environment consisted of a floor and an obstacle of 0.10 m high and 0.10 m wide. The socket and shaft elements were modeled as slender rods. The foot was modeled as a triangle. The masses and lengths of the kneewalker prosthetic limb were set as constants in the model (socket: 8 kg, 0.45 m; shaft 3 kg, 0.53 m; foot 1 kg, 0.31 m; horizontal heel-toe length 0.24 m; foot sole-ankle height 0.07 m). There was no weight support implemented. Other constants in the model included the stiffness of the floor and the obstacle (105 N/m). The positions of the elements and their angles, velocities and angular velocities were calculated during the simulation using the Euler integration method with an integration step size of 0.001 s. An extension assist spring, as found in modern artificial knee joints, was added to the model. The modeled spring was active in the range of 15 to 0 degrees flexion. The spring provided a counter torque of 0 Nm at 15 degrees of flexion and increased linearly to 25 Nm at 0 degrees of flexion.

Simulation

Computer simulations (ΔT = 0.001 s) were performed using Matlab (The MathWorks, Inc; Version 7, R14).

Procedure

The model was used to investigate a) the influence of the applied hip torques and the static ground friction on the foot trajectory and b) the relationship between the obstacle-foot distance and the necessary torques for obstacle clearance.

Part IIa The influence of the applied hip torques was investigated using a simulation in which the prosthesis hung with the hip joint fixed in the two-dimensional space (figure 5-left). The prosthetic limb was positioned high above the ground. The foot did not touch the ground. In the initial state, the socket / stump element and the shaft element were hanging vertically. Torques ranging from 0 Nm to 100 Nm in the flexion and extension direction were applied to the hip joint to create flexion and extension moments on the hip. These torques were constant during the simulation. The influence of static ground friction on prosthetic foot trajectory was investigated using a situation in which the prosthetic limb hung vertically with the foot in contact with the ground. The angular velocities of the segments were zero at the beginning of the simulations. We applied the highest flexion torque (100 Nm), as used in the previous simulation, on the hip. The duration of the simulations was 0.2 s (figure 5-right).


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Figure 5: Left panel: The influence of various hip flexion and extension torques applied to the model. The numbers in the graph represent the applied hip torques and the end position of the ankle after 0.2 s of simulation. The stick figures represent the end positions at the various values of the hip moment (flexion). Although the mass and inertial properties of the foot were taken into account, the foot is not shown in the figure for clarity reasons.
Right panel: Prosthetic limb trajectory of the model with (A) and without (B, dashed line) static ground friction (hip torque: 100 Nm; duration: 0.2 s).

Part IIb The model was also used to study the relation between the obstacle-foot distance and the needed torques for foot clearance. This object was placed at several distances in front of the toe of the prosthetic foot, ranging from 0.1 m to 0.7 m, in steps of 0.1 m. Hip torque profiles, which vary during a step and are needed to steer the prosthetic limb over an obstacle placed at a specific distance, were searched for in a sequence of trials with a simulated annealing algorithm. For every distance, the model was set with initial parameters. The forward horizontal velocity of the hip was set to 0.9 m s-1 constant velocity (unimpeded TF gait velocity: 1.0 m s-1 14; 15). The vertical hip velocity was set to zero. The angular velocities of the segments were zero at the start of the simulations. The distance the model had to cover was set to 1.4 m. The start and end positions of the prosthesis and the desired minimal clearance (0.05 m) from the prosthetic foot over the obstacle (height: 0.10 m; depth: 0.10 m) were set as objectives for the model. Using a hip torque profile as the input argument, the simulated annealing algorithm 23 searched for the lowest error value, which was the outcome of the obstacle avoidance with the prosthetic limb simulation during a sequence of 3000 trials per distance. The error value to be minimized by the algorithm was based on the knee angle (in rad) and the distance between the foot and the floor in the final position (in m), the clearance of the foot over the object (in m), the number of contacts made with the ground and the obstacle (discrete number), the length of the hip, the knee and foot trajectories (in m) and the total distance traveled (in m). These error values were unweighted sums. Therefore, the error values of the knee angle and the number of ground contacts had a great deal of influence on the final outcome. When searching, the hip torque profile that produced the lowest error value during the previous simulation trials was used as an input for the next trial. This torque profile input was adjusted based on random values, whose magnitudes decreased over the trials, resulting in a new error value. At the beginning of the trials, the torque profile changed more than at the end of the trials, due to the decrease in the magnitude of the random values. This procedure helped to identify an optimal local minimum, and therefore the optimal hip torque profile. The profile that was used the input for the algorithm was the result of a cubic spline-based interpolation over time of five adjustable torque values. These five torque values were on a fixed time interval between the start and the end of the simulation. The values between these discrete points were interpolated, which resulted in a smooth cubic spline curve over time. The range of the possible hip torques was limited to the maximal flexion and extension hip torques that were produced by our subjects and in accordance with literature ranging from 0 and 100 Nm 24.

Results

The simulations showed that the applied hip torques and the static ground friction influenced the foot trajectory. The torque profiles needed for stepping over an obstacle were based on these factors.

Part IIa The forward dynamics simulations with the model showed that when the applied torque changes, the resulting trajectory of the foot also changes. When a hip extension torque is applied to a prosthesis that is hanging freely, the foot follows the trajectory of a pendulum. The knee joint locks the prosthesis in extension, therefore ’converting’ the double pendulum into a single pendulum. Larger torque values result in a longer trajectory of the foot, that is caused by the higher velocity of the foot in the same time interval. When a flexion torque is applied the trajectory of the foot is quite different. As long as the torque is small, the trajectory is still similar to the trajectory of a pendulum. However, when a larger torque is applied, the trajectory changes. The curves in figure 5-left show that when large torques are applied, the foot gains not only more forward velocity but also for a more upward velocity. In figure 5-right, the influence of the static ground friction is visualized. When the prosthetic foot makes contact with the ground, the trajectory of the prosthetic foot with the same torque applied differs from the trajectory when no contact is made. Due to static ground friction, the tip of the foot (toe) becomes the point of rotation of the lower leg for the first period of the simulation. The horizontal forward trajectory distance of the foot after losing contact with the ground is less compared to the situation without static ground friction. However, the vertical upward trajectory distance is larger.

Part IIb The trajectories that were found with the simulated annealing algorithm corresponded to the imposed criteria. The simulations of the model show that the torque profiles (figure 6), that are needed for stepping over an obstacle positioned at different distances from the initial starting position from the prosthetic foot are comparable for almost all distances, except when the object is very close to the distal tip of the foot (<0.10 m). An obstacle-foot distance of 0.2 m was sufficient to step over the obstacle with normal human hip torques (range: 56 to 83 Nm) (figure 6). At very close distances contact with the obstacle can only be avoided when torques that are outside the range of the torques produced by our subjects are applied. A starting torque of more than 100 Nm is needed to steer the prosthetic limb in flexion over the obstacle (figure 6, line 0.10 m, starting at 150 Nm). The clearance over the object deviated on average by 0.02 m (SD 0.02) from the imposed 0.05 m. This relatively large standard deviation was caused by the trials in which the object was close to the foot (<0.60 m).


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Figure 6: Profiles of the hip torques that are needed for stepping over an obstacle while using static ground friction as a result of a simulated annealing algorithm. The numbers in the graph represent the distance between the foot and the obstacle at the beginning of the simulation. When the object is too close to the foot (0.1 m) unrealistic flexion moments are required (dashed line).

Discussion

We hypothesized that to move a prosthetic foot using a knee exion strategy over an obstacle that is close by, it is preferable to use ground friction and large hip torques. This combination helps to achieve height with less forward motion compared to a combination of small hip torques and without the use of static ground friction. The current study confirmed the above hypothesis. Both the experiment and the model showed that the generated trajectory is the result of the duration and the amount of the applied hip torques and the use of static ground friction. When the foot is not too close to the obstacle (>0.15 m) it should be possible for TF amputee subjects to generate the adequate knee flexion motion with the available hip torques and the use of static ground friction. Of course, it should be taken into account that this specific finding is only valid for this specific prosthetic limb. Other studies have shown that changes in the stiffness and damping of prosthetic joints 25, weight (distribution) 26; 27, the composition of the knee joint 28; 29, gait velocity and the shape of the socket 14 influence the trajectory of the foot or the needed hip torques. Although the results of this study have to be verified by future studies of other prosthetic limbs and in TF amputees with comorbidity, some explanations for the choices made in obstacle avoidance strategies can be reasoned based on the hip torque and static ground friction principles that were identified. Earlier results have suggested that during obstacle avoidance, TF amputee subjects use a knee extension strategy with an externally rotated and abducted limb 14; 15. A possible explanation for this choice of strategy is that the distance between the prosthetic foot and the object are too small for safe clearance during obstacle avoidance. In that case, the subjects should be taught to use the prosthetic limb as the leading limb during the obstacle clearance, which would result in a sufficient distance between the foot and the object 14. Another possible explanation for the choice of this strategy might be the amount of energy that is necessary to employ the strategy. According to our study, a flexion strategy that is seen in the fast hip motion trials or when static ground friction is used demands more hip energy compared the slow motion without using static ground friction condition, in which the knee remains extended in most of the trials. The needed energy may be the reason for this choice, although one could image that standing on one limb for a longer period, moving the prosthetic limb in a direction perpendicular to the direction their walking and losing forward velocity is more energy demanding than the fast motion and making use of static ground friction. We were not able to verify this with our data. The third possible explanation is that making use of static ground friction or the application of large hip torques results in increased upper leg angle velocity, which may feel less controlled with no active control over the passive prosthetic knee joint. Learning to cope with a flexing passive knee joint can only be possible when the subject is able to fit the prosthetic limb perfectly into his body scheme and when the properties of the limb are suited to the needs of the user. If the subject is not able to fit the prosthetic limb into his body scheme, he or she will learn that when he or she uses small hip torques, the prosthetic limb remains in an extended knee joint position. An extension spring in the knee enables the patient to slowly lift the limb over an obstacle, without flexion of the knee, which results in controlled clearance over the obstacle. In the knee extension strategy the static ground friction on the prosthetic foot is not used during obstacle avoidance. The last possible explanation for not using a knee flexion strategy when the prosthetic limb is the trailing limb is that the TF amputee subject has no visual control over the prosthetic foot, to compensate the lack of mechanoreceptors in the knee, as long as it is behind or under the body. Therefore, the TF amputee subject does not know if foot clearance is adequate. A study with AB subjects showed that limb elevation over an obstacle was increased for a greater safety margin after removing vision 30. Leading limb control is modifiable on-line when vision is available during obstacle avoidance. In contrast, trail limb control is based primarily on feedforward visual information and on-line kinesthetic sensory output. The extension strategy enables the TF subject with a diminished on-line kinesthetic sensory output to have more visual control when the limb is trailing.
There are a few limitations to this study. The group of subjects was small in number. This group was used to investigate the foot trajectory of the prosthetic limb when applying hip torques and using static ground friction on the prosthetic foot. We were not interested in the performances of the AB subjects, only the trajectory of the prosthetic foot driven by the subjects. The number of trials made by the subjects was sufficient to test our hypothesis. It can also be argued that the AB subjects using the kneewalker prosthetic limb cannot be compared with TF amputees. However, Lemaire et al. reported that AB subjects use the same compensation strategies as inexperienced prosthetic limb users and that kinematic and kinetic analyses results were similar to gait analysis of people with TF amputations 20, which makes the use of a kneewalker prosthetic limb valid in our study. A limitation in the theoretical part of this study is that we used a constant hip forward velocity when steering the prosthesis over the obstacle in the simulations. Prosthetic limb users do not use constant velocities. Complex combinations of accelerations and decelerations are applied on the hip while walking with a prosthesis 31 and during obstacle avoidance 11; 12; 14; 15. These hip accelerations do not only influence the motion of the prosthetic components, but they also have a direct influence on foot clearance. If a TF amputee subject elevates or tilts his or her hip or pelvis 0.01 m, the foot will also gain 0.01 m of foot clearance. This hip elevation or tilt strategy is very often used during obstacle avoidance; AB subjects achieve approximately 22% of toe clearance by utilizing hip elevation 32, but this factor was not taken into account in this study. We expect that hip elevation or tilt strategy will contribute to the reduction of the needed hip torques for obstacle avoidance. However, the model shows that this strategy is not necessary in obstacle avoidance when the correct hip torques and static ground friction are used. Note that the minimum and maximum torques found in these simulations deviate slightly from human hip torques. As we did not include a complete muscle model, the simulated profiles show a sudden onset of torque at the beginning of the movement, whereas human torque profiles normally show a slow onset for the first 100 ms 33. Another limitation in this simulation is that we used a simulated annealing algorithm, which is a stochastic procedure. Although this algorithm does not give a set of unique solutions, there is sufficient convergence of the torque profiles to be useful for testing our hypothesis (figure 6). The last limitation is that the models in this study were two-dimensional models, which limits motion to the sagittal plane. To study the influence of non-planar obstacle avoidance solutions, which may necessitate knee extension strategies and hip joint motion with abduction and exorotation, three-dimensional models should be constructed. As obstacle avoidance is confined to the sagittal plane, we feel that a two-dimensional model is acceptable for an analysis of normal swing phase kinematics and for gaining insights into the influence of hip torques and ground friction on the trajectory of the prosthetic foot. The model we used for the forward dynamics simulation consisted of a single axis knee joint for parsimonious reasons. Although this knee joint is still used in prostheses, this knee joint is not representative for all modern prosthetic knee joints. Most modern prosthetic knee joints consist of at least four bar linkage knee joints or are computer controlled. These types of knee joints influence the trajectory of the foot 28; 29; 34. Nevertheless, to gain insight into the prosthetics dynamics, the single axis knee joint satisfies our requirements.

Conclusions

The study showed that the trajectory of the prosthetic foot is influenced by both the hip torques and the static ground friction on the prosthetic foot. Based on our findings, we report that the following factors contribute to a successful clearance using a knee flexion strategy during obstacle avoidance by TF amputee subjects: 1) maintaining a sufficient distance between the foot and the obstacle at the start of the swing phase, 2) producing sufficient hip torques, and 3) making use of the static ground friction on the prosthetic foot.

Competing Interests

There are no competing interests related to this study.

Acknowledgement

The authors wish to acknowledge the OIM foundation, Beatrixoord foundation and Anna Foundation for their financial support.

Ethical Approval

The medical ethics committee of the University Medical Center Groningen approved the study protocol (reference number 2004.176). All subjects signed an informed consent before testing.

References

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Perspective

via Healio.com O&P Business News.

We have a reasonably good understanding about how prosthesis users walk on level surfaces, but we currently have a poor understanding about how they walk up and down stairs or slopes and step over obstacles. This paper makes a significant contribution about how transfemoral prosthesis users avoid obstacles while walking. I enjoyed this article and thought it was a well-designed and executed study for several different reasons: First of all, the authors utilized a multifaceted approach, collecting experimental data and performing computer simulations. Both methods yielded valuable information about the different strategies that were complementary and served to present a more complete picture than if either approach had been used alone. The results produced by each method were generally in agreement, serving to validate the two approaches while verifying the assumptions of each. Secondly, I think there is much to be learned by utilizing able-bodied individuals for simulating characteristics of prosthetic and orthotic gaits. Unless strict inclusion/exclusion criteria are employed, recruiting actual prosthesis users for studies of this type often produces data with considerable variability, making interpretation challenging. Finally, I appreciate that the authors not only recognized the clinical implications of their work, but recommended that gait training for transfemoral amputees emphasize appropriate principles for safe, efficient obstacle avoidance during ambulation.

Steven Gard, PhD

Executive director, Northwestern University Prosthetics-Orthotics Center
Research associate professor, dept. of physical medicine and rehabilitation,
Feinberg School of Medicine, Northwestern University,
Research health scientist, Jesse Brown VA Medical Center, Dept. of Veterans Affairs
 
Disclosures: Gard has no relevant financial disclosures.

 

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