Foot trajectory in human gait: a precise and multifactorial motor control task.

Foot Trajectory in Human Gait: A Precise and Multifactorial Motor Control Task

The trajectory of the heel and toe during the swing phase of human gait were analyzed on young adults. The magnitude and variability of minimum toe clearance and heel-contact velocity were documented on 10 repeat walking trials on 11 subjects. The energetics that controlled step length resulted from a separate study of 55 walking trials conducted on subjects walking at slow, natural, and fast cadences. A sensitivity analysis of the toe clearance and heel-contact velocity measures revealed the individual changes at each joint in the link-segment chain that could be responsible for changes in those measures. Toe clearance was very small (1.29 cm) and bad low variability (about 4 mm). Heel-contact velocity was negligible vertically and small (0.87 m/s) horizontally. Six joints in the link-segment chain could, with very small changes ([+ or -] 0.86 [degrees] - [+ or -] 3.3 [degrees], independently account for toe clearance variability. Only one muscle group in the chain (swing-phase hamstring muscles) could be responsible for altering the heel-contact velocity prior to heel contact. Four mechanical power phases in gait (ankle push-off, hip pull-off, knee extensor eccentric power at push-off, and knee flexor eccentric power prior to heel contact) could alter step length and cadence. These analyses demonstrate that the safe trajectory of the foot during swing is a precise end-point control task that is under the multisegment motor control of both the stance and swing limbs. [Winter DA. Foot trajectory in human gait: a precise and multi-factorial motor control task. Phys Ther. 1992;72:45-56.]

Key Words: Kinesiology/biomechanics, gait analysis; Lower-limb trajectory, measurements; Slipping; Tripping.

Walking is primarily a lower-extremity control activity, and researchers have recognized this by focusing their research on the kinematics and kinetics of the lower limb. The upper body (head, arms, and trunk [HAT]) has received limited attention, and that has dealt mainly with kinematic descriptions.[1] Some recent focus has been placed on the HAT's large inertial load, as it affects balance,[2] and on the HAT's large gravitational load, as it affects collapse.[3] The role of the lower extremity in controlling both balance and collapse was identified as unique stance-phase tasks. The detailed role of the lower extremity in achieving forward progression has been limited, however, to kinematic descriptions and a number of kinetic analyses. Forward progression is essentially a lower-extremity task and begins late in stance during push-off[4] and continues throughout swing. The detailed energetics that decide the magnitude of step length and the precise trajectory of the foot during swing have not been analyzed and were the subject of this research.

Review of Literature

To date, there has been considerable effort focused on the kinematics of the lower limb during normal walking. Joint angle data have most commonly been reported.[5-12] Absolute segment kinematics (linear and angular displacements, velocities, and accelerations) are not commonly reported.[12] Other than the occasional "stick-diagram" plot and a few individual trajectory plots,[13] there has not been a comprehensive study that has examined the trajectory of the foot (heel and toe), especially critical variables such as toe clearance and heel-contact velocity. Several energy-related motor patterns have been identified as influencing the magnitude of step length.[14] Because the swing limb constitutes the major energy demand in walking,[15,16] we must look at the mechanical energy-generating and energy-absorbing phases that accelerate and decelerate the lower limb immediately prior to and during swing. Energy generation during push-off by the plantar flexors is the largest single work phase in the gait cycle[4] and is responsible for the upward and forward acceleration of the lower limb. Simultaneous with this plantar-flexor contraction (during 40%-60% of the walking stride), the knee is flexing under the control of the eccentrically acting quadriceps femoris muscle. During late stance (50% of stride), the hip flexors commence a concentric contraction, initiating a "pull-off" power phase that continues past toe-off (TO) into mid-swing (80% of stride). Finally, the major deceleration of the leg and foot is achieved by the hamstring muscles, which contract eccentrically to reduce the foot velocity to near-zero prior to heel contact (HC). What is not known is how these energy-generating and energy-absorbing phases vary as stride length (and cadence) varies in normal level gait.

Methodology

Biomechanical Model

The precision of any task must be considered relative to the number of segments involved, their size and mass, and the number of degrees of freedom. The link chain for the control of the foot during swing begins with the stance foot and proceeds up to the hip, across the pelvis, and down to the distal end of the swing foot/phalangeal segment. This chain can be considered to consist of seven segments (or nine if a phalangeal segment is considered), with 12 major angular degrees of freedom at the ankle, knee, and hip that can influence the displacement of the heel or toe during the swing phase of gait. Figure 1 represents this anatomical model with those important degrees of freedom indicated. For a typical adult male subject (mass=70 kg, height=1.8 m), the length of this chain exceeds 2 m. If we consider the large number of muscles crossing those joints, the end-point control of the heel and toe trajectories is a challenging task.

Procedure and Subjects

The experimental evidence presented in this report was taken from gait laboratory data collected from young adults. Some analyses were based on individual walking trials, and other analyses were based on repeat trials conducted over a period of 1 hour. Details of the kinematic and kinetic systems have been reported previously[4,12,14,16] and have recently been summarized in a recent report on walking pattern changes in the elderly.[17] For the foot-trajectory component of this study, a group of young adults (six men, five women), who ranged in age from 21 to 28 years (X [Bar] = 24.9), were analyzed. Their average height was 1.73 m, and their average weight was 69.2 kg. Each subject walked at his or her natural cadence on a level walkway a minimum of 10 times; repeat trials were conducted over a period of 1 hour (one trial every 5 or 6 minutes). For the analysis of the energetic factors that affect step length, data were taken from analyses performed over the past 10 years using 55 young subjects averaging 22.6 years of age. Their average height was 1.75 m, and their average weight was 71.2 kg. The data-collection protocol of this analysis was identical to that of the foot-trajectory analysis, except each subject underwent only one walking trial at his or her natural cadence, at a fast cadence (defined as the subject's natural cadence+20 steps/min), or at a slow cadence (defined as the subject's natural cadence--20 steps/min). A total of 19 subjects were analyzed at slow and natural cadences, and 17 subjects were analyzed at fast cadences. Each subject provided informed consent before participation in the study.

Data Analysis

The trajectories of the heel and toe markers were plotted over the stride period, which was normalized to 100%, with HC at 0% and 100%. These heel and toe profiles were then averaged over the 10 repeat walking trials to assess intrasubject variability. Each intrasubject average was then ensemble-averaged to produce an intersubject average. Based on the variability measurements recorded at minimum toe clearance, each critical degree of freedom in the link chain was varied independently to demonstrate the sensitivity of the toe trajectory to small angular variations at each joint in the chain. In this way, the fine control necessary at each of the joints was documented. In a similar manner, the velocities of the heel in the vertical and horizontal directions were calculated in order to assess the rapid reduction in velocity of the heel during the latter half of swing and after HC. A similar sensitivity analysis on the angular velocities of all segments in the link chain were examined at HC to determine their individual contributions to the slowing down of the heel at this potentially dangerous impact time. Finally, the joint mechanical power patterns immediately prior to and during swing were assessed[4] to determine how they changed as cadence and step length increased.

Results

Figure 2 plots the average vertical trajectory and both horizontal and vertical velocities of the toe for 11 subjects over the stride period. The toe trajectory showed the toe to reach its lowest point at about 56% of stride as the toe pushed downward during the final phase of push-off. This minimum on each trial was considered to be zero toe clearance for the purpose of plotting this displacement profile. After TO, the toe reached a height of a few centimeters. During mid-swing, the toe dropped to its minimum clearance; for these subjects, this mean clearance averaged 1.29 cm. During the latter half of swing, the toe rose to its maximum of about 15 cm just prior to HC. The mean intra-subject variability for this minimum toe clearance was 0.45 cm. Figure 2 shows that this minimum clearance was achieved when the forward velocity of the toe was at its maximum (ie, about 4.6 m/s). Figure 3 demonstrates the position of the stance and swing limbs and the upper body at this potentially dangerous tripping time during one representative walking trial. The forward velocity of the body was 1.4 m/s at this time, and the center of gravity of the HAT was just forward of the stance foot. The combination of this center-of-gravity location and the body's forward momentum means that, if a trip occurs, there is no possibility that the support limb can recover to return the body's center of gravity within the safe borders of the foot. The only possible safe recovery is by a safe placement of the swing limb itself. It is noted that the coefficients of variation (CVs) of these intersubject ensemble averages (Fig. 2) are quite low and indicate considerable consistency in this small group of young adults. The sensitivity analysis of the kinematics from one of the subjects examined all joints in the link segment that had a potential for influencing the toe trajectory at the time of minimum toe clearance: swing ankle, swing knee, swing hip, stance hip abductor (pelvic list), stance knee, and stance ankle. The sensitivity analysis calculated the angular changes that, at each joint by itself, would cause the [+ or -] 0.45-cm toe clearance variability. These results are reported in Table 1, and one typical calculation is presented in Figure 4. According to this interpretation of the results, if all the remaining joints remained unchanged, a change of [+ or -] 0.86 degree at this time in stance hip abduction alone could be responsible for all of the variability seen in toe clearance. Figure 5 plots the average vertical trajectory and both horizontal and vertical velocities of the heel for these same subjects over the stride period. The heel began rising in mid-stance at heel-off and reached a maximum of about 25 cm just after TO, then decreased rapidly, reaching about 1 cm above the ground at 90% of the stride period. During the last 10% of the stride prior to HC, the trajectory was almost horizontal; the horizontal velocity also decreased drastically from 4 m/s, reaching about 0.87 m/s at HC. This forward velocity decreased to zero at about 4% of the stride, indicating a small skidding of the heel of the shoe immediately after HC. Figure 6 demonstrates the position of the body at HC, especially the heel velocity vectors relative to the forward velocity of HAT, during one representative walking trial. A further sensitivity analysis of the kinematics of the link chain at this time of HC was completed to assess the angular velocity changes that, by themselves, would be necessary to reduce the forward heel velocity by 0.87 m/s, thus reducing it to exactly zero at HC. The potential angular velocities to which heel velocity is sensitive are swing foot, swing leg, swing thigh, pelvic horizontal velocity (controlled by hip rotators), stance thigh, stance leg, and stance foot. The necessary angular velocity changes are summarized in Table 2 with an indication of what muscle group would be responsible in each case (remembering that during stance the muscles at either the proximal or distal end of each segment can control). One typical calculation of the velocity sensitivity is presented in Figure 7. The variability of the heel trajectories, as demonstrated by the CVs in the ensemble averages presented in Figure 5, is quite low. Again, this low variability is indicative of consistency in this small group of young adults. Figures 8 through 10 present mechanical power profiles drawn from the database from subjects walking at three different cadences and at different step lengths. The 19 natural-cadence walkers had a mean cadence of 105.3 steps/min and a mean step length of 1.51 m (walking velocity = 1.33 m/s). The 19 slow walkers had a cadence of 86.8 steps/min and a step length of 1.38 m (walking velocity = 1.00 m/s), and the 17 fast walkers had a cadence of 123.1 steps/min and a step length of 1.64 m (walking velocity = 1.68 m/s).

Discussion

Toe clearance has been considered to be a major responsibility of the swing leg dorsiflexors, and, as expected, it is quite sensitive to small angular changes ([+ or -] 2.07 [degrees]) of the swing ankle. The sensitivity analysis results (Tab. 1), however, show that the end-point toe trajectory is also very sensitive to small angular changes at five other joints in the total link-segment chain. Toe clearance is sensitive to even smaller angular changes at the knee ([+ or -] 1.35 [degrees]) and during stance hip abduction and adduction ([+ or -] 0.86 [degrees]). Clinically, it is important to observe each walking patient and note any clearance problems and at which joint compensations are taking place. Thus, it is not surprising that certain patients, such as those with below-knee amputations, adapt to achieve a safe foot clearance with increased knee flexion and "hip hiking" (increased stance hip abduction). Circumduction is also a common adaptation, but, because of the low sensitivity of the swing hip abductors, an appreciable angular change is required to make a significant change in toe clearance. The trajectory velocity of the heel immediately prior to HC is virtually zero vertically and low in the horizontal direction; such findings raise the question as to why many researchers refer to this initial contact as "heel-strike." With the exception of the swing foot, the angular velocity changes necessary to reduce the heel forward velocity to zero were well within the range of biomechanically determined angular velocities during natural walking.[18] Functionally, however, some of the potential controls implied by the results of Table 2 must be discarded. A rapid plantar flexion of the foot (12.3 radians/s) immediately prior to HC is not a valid solution, because this movement would result in a rapid foot-slap rather than a controlled lowering of the foot after HC. The analysis also suggests the stance thigh's forward velocity could be decelerated by increased knee flexor activity at the same time as the stance leg was decelerated by increased knee extensor activity. Obviously, this is not an anatomically possible combination. Similarly, the tabulated results suggest that the stance ankle plantar flexors would have to increase their activity to decelerate the forward-rotating leg at the same time as they decreased activity to decrease foot plantar flexion. Again, this is not a compatible solution. Another possibility is hip extensor control of the stance thigh, but such control is not likely, because the stance hip extensors are not reported to be active at this time.[19,20] Thus, the knee flexors, hip extensors, and stance hip external rotators are the only muscle groups that have the potential for decelerating the heel immediately prior to HC (Tab. 2). The most compatible combination of those three muscle groups are the knee flexors and the hip extensors, which means that the biarticulate hamstring muscles would be predicted to decelerate both the swing thigh and leg and therefore are the major decelerators of the foot. Electromyographic profiles show the hamstring muscles to be active in late swing.[19,20] Mechanical power analyses have also shown this to be true in both walking[4] and running,[21] during which the eccentric work done at the knee during the latter half of swing was dominant. In running,[21] a small, short-duration burst of positive power immediately followed this K4 negative work and was due to a concentric contraction as these same hamstring muscles momentarily accelerated the leg backward. This finding does not mean that the foot was traveling backward at this time. Rather, the body had a forward velocity of about 3 m/s, and, to reduce the foot velocity to near-zero, the foot would need a momentary backward velocity of about 3 m/s relative to the center of mass of the body. The central nervous system obviously recognizes the energetics of this fine control. The third possible muscle group noted in Table 2 that could control the swing limb's forward velocity are the stance hip external rotators. Because the angular rotation and velocity of the pelvis in the transverse plane were quite small, these rotators would have only minimal potential for control. The clinical significance of this HC velocity analysis relates to the potential for a patient to slip at this critical phase of the gait cycle. Heel contact usually involves weight bearing on a small surface area of the heel, and, if the ground contact area is wet or slippery, there is an increased probability of slipping. In a study on fit and non-disabled elderly subjects, we have documented that their HC velocity was 1.15 m/s, which is significantly higher (P<.01) than for the younger adults in this study. Thus, these elderly individuals are at a greater risk for slipping, even though their walking velocity was significantly lower than that of the younger adults in this study (1.29 versus 1.43 m/s, respectively). To date, we have not documented the HC velocity for patients who are prone to fall; such studies are currently ongoing. Four of the power bursts (ie, A2, K3, K4, and H3) shown in Figures 8 through 10 demonstrated drastic changes during push-off and swing that could influence step length. The ankle push-off burst (A2 in Fig. 8) showed a dramatic increase as the subjects accelerated their lower limb prior to TO to achieve a longer step length. Almost simultaneous to this push-off impulse was an increasing absorption of energy at the knee (K3 in Fig. 9) by the eccentrically acting quadriceps femoris muscle. This absorption represents a necessary loss of energy to prevent too rapid a knee flexion prior to TO (60% of stride) resulting from the forceful upward acceleration of the leg caused by A2. At mid-double support (50% of stride), the hip flexors contracted concentrically to commence a pull-off of the lower limb (H3 in Fig. 10), which continued past TO until midswing. This impulse of pull-off energy also increased dramatically with increased cadence and step length. In mid-swing, the swinging lower limb (mainly leg and foot) reached its maximum energy, which must be removed prior to HC. The K4 burst (Fig. 9) showed the knee flexors (hamstring muscles) to be eccentrically acting, mainly to remove the kinetic energy from the swinging leg and foot. Thus, increased step length (and cadence) is normally achieved with an increase in both positive work by the ankle plantar flexors and hip flexors and a matched increase in the negative work by the knee extensors during late stance and the knee flexors during late swing. The influence of these energy bursts on the gait patterns of fit and nondisabled elderly subjects has also been demonstrated recently.[17] These elderly subjects were seen to have the same natural cadence as the younger adults in this study, but a significantly (P<.01) shorter stride length. Two motor pattern changes responsible for this reduction were a significantly reduced push-off power (A2 burst) and a significant increase in quadriceps femoris muscle absorption (K3 burst).

Conclusions

The trajectory of the foot during gait is a precise end-point control task. It is under the multisegment motor control of both stance and swing limbs. Toe clearance of slightly more than 1 cm was found to be sensitive to fine control by at least six muscle groups in the link-segment chain. Heel-contact velocity was virtually zero in the vertical direction, with a low horizontal velocity. The dominant muscle group responsible for reducing that velocity was the hamstrings. The magnitude of step length was found to be under the control of four concentric and eccentric motor patterns during late stance and swing. Step length and walking velocity were increased by increased plantar-flexor power during push-off and by increased hip-flexor power during "pull-off." Step length can be reduced by increased eccentric quadriceps femoris muscle activity during late stance and by increased eccentric hamstring muscle activity during late swing. In spite of the consistency in the foot trajectory profiles for this small group of young adults, more research may be necessary to quantify any differences in larger groups of young adults and in other age groups.

Acknowledgment 

I acknowledge the technical assistance of Mr Paul Guy. [Tables 1 and 2 Omitted]

PHOTO : Figure 1. Stick diagram of link-chain system of seven segments of the support limb, pelvis, and swing limb involved in the control of the toe and heel trajectories. The 12 major degrees of free dom at the six joints that influence those trajectories are indicated.

PHOTO : Figure 2. Ensemble-averaged displacement and velocities of the toe over one stride of 11 subjects walking a their natural cadence. Heel contact was at 0% and 100% of stride, and toe-off (TO) was at 60% of stride. Minimum toe vertical displacement for each subject was set at zero at the minimum reached as the toe pressed downward into the floor immediately before TO. (CV = coefficient of variation.)

PHOTO : Figure 3. Position of body at the instant of minimum toe clearance for one representative walking trial showing the high forward toe velocity (4.6 m/s) and center of gravity of the head, arms, and trunk located ahead of the stance foot. (R represents the ground-reaction-force vector, and mg represents the body's center-of-gravity vector.)

PHOTO : Figure 4. Example of sensitivity calculation to determine the angular change ([+ or -] [Delta] [Theta]) necessary at the knee alone to cause the [+ or -] 0.45-cm displacement variability seen at the toe at the instant of minimum toe clearance.

PHOTO : Figure 5. Ensemble-averaged displacement and velocities of the heel of the same 11 subjects as represented in Fig. 2 over one stride, from heel contact (HC) to HC. Horizontal heel velocity reached a peak in mid-swing and decreased to virtually zero in the vertical direction and to a low value horizontally at HC. (CV = coefficient of variation; TO = toe-off.)

PHOTO : Figure 6. Position of body at heel contact for one representative walking trial showing the low heel velocities relative to the forward velocity of the body's center of mass. (R represents the ground-reaction-force vector, and mg represents the body's center-of-gravity vector.)

PHOTO : Figure 7. Example of calculation to determine the sensitivity of the heel contact (HC) velocity to the velocity of the individual segment. ([Delta] [Omega] = angular velocity change that, by itself, could reduce the horizontal velocity of the heel at HC from its average value [0.87 m/s] to zero; [Delta] V = change in velocity.)

PHOTO : Figure 8. Mechanical power generation and absorption profiles at the ankle for three walking-speed cadences: natural, slow, and fast. The push-off power (A2 burst) by the plantar flexors drastically increased from slow to fast walking cadences and represents over 75% of all energy generated in the stride period. The A1 power phase was the absorption of energy as the plantar flexors lengthen as the leg rotates forward over the foot. (TO = toe-off.)

PHOTO : Figure 9. Mechanical power absorption and generation at the knee for the same three cadence groups as represented in Fig. 8. The K3 burst was the power associated with the eccentrically contracting quadriceps femoris muscle necessary to control knee flexion caused by the "piston-like" push-off by the ankle in late stance. The K4 burst was due to the eccentrically contracting hamstring muscles decelerating the swinging leg prior to heel contact. Both K3 and K4 increased as cadence and stride length increased. The K1 burst was the absorption by the knee extensors as they lengthen when the knee flexes. The K2 burst was the generation by the same knee extensors as the knee extends during mid-stance. (TO = toe-off.)

PHOTO : Figure 10. Mechanical power generation and absorption at the hip for the samethree cadence groups as represented in Fig. 8. The H3 burst represents the "pull-off" power generation by the hip flexors. This positive work began in late stance (50%), continued into mid-swing (80%), and increased drastically as cadence increased. The H1 power phase resulted from the hip extensors shortening immediately after heel contact. The H2 power burst resulted from the hip flexors; lengthening during mid-stance to decelerate the backward-rotating thigh. (TO) = toe-off.)

References

[1]Thorstensson A, Nilsson J, Carlson H, Zomlefer MR. Trunk movements in human normal walking. Acta Physiol Scand. 1984;121:9-22. [2]Patla AE, Frank JS, Winter DA. Assessment of balance control in the elderly: some issues. Physiotherapy Canada. 1990;42:89-98. [3]Winter DA. Overall principle of lower limb support during stance phase of gait. J Biomech. 1980; 13:923-927. [4]Winter DA. Energy generation and absorption at the ankle and knee during fast, natural and slow cadences. Clin Orthop. 1983;197:147-154. [5]Finley FR, Karpovick PV. Electrogoniometric analysis of normal and pathological gaits. Research Quarterly. 1964;35:379-384. [6]Murray MP, Drought AB, Kory RC. Walking patterns of normal men. J Bone Joint Surg [Am]. 1964;46: 335-360. [7]Murray MP. Gait as a total pattern of movement. Am J Phys Med. 1967;46:290-333. [8]Murray MP. Walking patterns of normal women. Arch Phys Med Rebabil. 1967;51:637-650. [9]Johnston RC, Smidt GI. Measurement of hip-joint motion during walking. J Bone Joint Surg [Am]. 1969;51:1083-1094. [10]Lamoreux LW. Kinematic measurements in the study of human walking. Bulletin of Prosthetics Research. Spring 1971:3-84. [11]Sutherland DH, Hagy JL. Measurement of gait movements from motion picture film. J Bone Joint Surg [Am]. 1972;54:787-797. [12]Winter DA, Quanbury AO, Hobson DA, et al. Kinematics of normal locomotion: a statistical study based on TV data. J Biomech. 1974;1:479-486. [13]Murray MP, Clarkson BH. The vertical pathways of the foot during level walking, II: clinical examples of distorted pathways. Phys Ther. 1966;46:590-599. [14]Winter DA. Concerning scientific basis for the diagnosis of pathological gait and for rehabilitation protocols. Physiotherapy Canada. 1985;37:245-252. [15]Ralston HJ, Lukin L. Energy levels of human body segments during level walking. Ergonomics. 1969;12:39-46. [16]Winter DA, Quanbury AO, Reimer GD. Analysis of instantaneous energy of normal gait. J Biomech. 1976;9:253-257. [17]Winter DA, Patla AE, Frank JS, Walt SE. Biomechanical walking pattern changes in the fit and healthy elderly. Phys Ther. 1990;70:340-347. [18]Winter DA. Biomechanics and Motor Control of Human Gait. Waterloo, Ontario, Canada; University of Waterloo Press; 1987:25-26. [19]Winter DA, Yack HJ. EMG profiles during normal human walking: stride-to-stride and inter-subject variability. Electroencephalogr Clin Neurophysiol. 1987;67:402-411. [20]Shiavi R. Electromyographic patterns in adult locomotion: a comprehensive review. J Rehabil Res Dev. 1985;22:85-97. [21]Winter DA. Moments of force and mechanical power in slow jogging. J Biomech. 1983;16:91-97.

DA Winter, PhD, PEng, is Professor, Department of Kinesiology, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.