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What Determines the Vertical Displacement of the Body During Normal Walking?

Gard, Steven A. PhD; Childress, Dudley S. PhD

JPO Journal of Prosthetics and Orthotics: September 2001 - Volume 13 - Issue 3 - p 64-67
Biomechanics And Gait
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Conventional wisdom states that the vertical excursion of the body is reduced by several of six “determinants” of gait to minimize the energy expenditure of walking. However, we have shown that pelvic obliquity and stance-phase knee flexion—the second and third determinants of gait—have little or no effect on the magnitude of the body’s vertical excursion during normal walking because the timing of these actions is wrong for reduction of vertical movement to occur. We believe that stance-phase knee flexion and pelvic obliquity provide shock absorption in normal walking during the loading response phase of gait. Our data show that for a given individual the vertical displacement of the body is determined by effective leg length, foot rocker radius, and step length. Using a rocker-based inverted pendulum model of walking, we have derived equations relating walking parameters such as the vertical excursion, step length, cadence, and walking speed. Results from our theoretical analysis compared favorably with actual measurements from able-bodied ambulators walking across a range of speeds from about 0.8 to 2.0 m/sec. We believe that some pathological gaits may be improved through modification of the foot rocker shape and by making adequate provisions for shock absorption.

STEVEN A. GARD, PhD, is a research health scientist with the VA Chicago Health Care System–Lakeside Division, the director of the VA Chicago Motion Analysis Research Laboratory, and a research assistant professor in the Departments of Biomedical Engineering and Physical Medicine and Rehabilitation, Northwestern University, Chicago, IL.

DUDLEY S. CHILDRESS, PhD, is a research health scientist with the VA Chicago Health Care System–Lakeside Division, the director of the Northwestern University Prosthetics Research Laboratory and Rehabilitation Engineering Research Program, a professor in the Departments of Biomedical Engineering and Physical Medicine and Rehabilitation, Northwestern University, and the executive director of the Northwestern University Prosthetic-Orthotic Center, Chicago, IL.

Correspondence to: Steven Gard, PhD, Northwestern University Prosthetics Research Laboratory and Rehabilitation Engineering Research Program, 345 E. Superior, RIC 1441, Chicago, IL 60611. Phone: (312) 238-6500; Fax: (312) 238-6510; E-mail: sgard@northwestern.edu

Normal human walking is characterized by a smooth vertical rise and fall of the trunk, occurring once with each step or twice during a gait cycle. The body is at its lowest elevation during the time of double support and rises to its highest position during midstance. The peak-to-peak amplitude of the trunk’s vertical displacement, defined as the vertical excursion, is typically 4 to 5 cm for freely selected gait (∼1.4 m/sec for adults). Vertical excursion of the trunk is related to walking speed, ranging from about 3 cm at slow walking speeds (∼0.8 m/sec) to about 8 cm at the fastest walking speeds (∼2.2 m/sec).

Many conventional ideas about normal human walking originate from concepts that were first presented in a landmark article 1 entitled “The Major Determinants in Normal and Pathological Gait.” The authors identified six determinants of normal gait that were claimed to minimize the displacement of the body’s center of mass (BCOM) and smooth its trajectory, thereby saving energy. The six determinants of gait are pelvic rotation, pelvic obliquity, stance-phase knee flexion, foot-ankle mechanisms, ankle and knee interactions, and lateral displacement of the pelvis. The authors asserted that a bipedal gait without these six determinants—referred to as compass gait—would be characterized by excessive vertical excursion of the BCOM, which would waste energy. The first three determinants of gait were believed to reduce the vertical excursion of the BCOM by half. The fourth and fifth determinants further smoothed the BCOM’s trajectory, and the sixth was concerned with reducing medial-lateral displacement of the BCOM. These six determinants and their supposed effect on gait have been generally well accepted by gait clinicians and researchers, seemingly to the point that their influence on vertical body motion is often no longer considered to be hypothetical but is instead regarded as fact. We believe that critical examination of these ideas is important, not only for understanding normal walking but also for management of prosthetic and orthotic gait.

Results from our research challenge the theory that pelvic obliquity and stance-phase knee flexion—the second and third determinants of gait—reduce the vertical excursion of the body during normal walking. We have used gait analysis to measure the effects of pelvic obliquity and stance-phase knee flexion on the vertical excursion of the trunk in normal gait. Contrary to the theory of the six determinants of gait, we found that these movements have no effect on the magnitude of the trunk’s vertical excursion due to their timing during the gait cycle. 2,3 We, and others, 4,5 believe that these actions reduce shock at initial contact and during the loading response phase of walking. We show that the vertical excursion of the body can be completely accounted for by geometrical constraints imposed by the legs and feet of a simple theoretical model. 6,7 Results from our work suggest that improvements to prosthetic and orthotic gaits may be realized through modification of the foot roll-over shape and by making adequate provision for shock absorption.

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METHODOLOGY

Our investigation of vertical trunk movement during normal walking consisted of both experimental data obtained from gait analyses performed on able-bodied subjects and theoretical data derived from a rocker-based inverted pendulum model of walking. Kinematic data were acquired from three adult male volunteers who walked with a normal gait, using methods described in detail elsewhere. 2,3 All of the subjects provided informed consent. Reflective markers were placed on bony prominences on the legs and pelvis of each subject, and the positions of these markers were tracked using a motion analysis system. Data were acquired as the subjects walked at speeds distributed across their range of comfortable speeds. The marker position data enabled us to calculate the vertical displacement of the trunk due to pelvic obliquity and stance-phase knee flexion. By using this data, with direct measurements of vertical trunk movement during gait, we were able to determine the effects of pelvic obliquity and stance-phase knee flexion on the trunk’s vertical excursion.

We have developed a rocker-based inverted pendulum model of walking that incorporates the fundamental structural elements of normal gait (Figure 1). The single foot rocker, or roll-over shape, can be considered to be the cumulative effect of the heel, ankle, and forefoot rockers described by Perry. 4 In this model, we assume that the vertical movements of the BCOM and the trunk are identical. Previous studies have shown that vertical BCOM movement can be approximated with a single marker on the trunk. 8–10 The model (Figure 1) has been shown to be useful for deriving equations that relate walking parameters, such as vertical excursion (h), step length (Sl), cadence, and walking speed.

Figure 1

Figure 1

It can be shown that in the rocker-based inverted pendulum model, the leg is effectively lengthened by the foot rocker. 11 The trajectory of the body in the rocker-based inverted pendulum model can be approximated by a conventional inverted pendulum with a virtual leg length on a virtual walking surface (Figure 1). The relationship between the anatomical leg length (L), the foot rocker radius (r), and the virtual leg length (Lv) can be estimated by Equation 1:

where ρ is the “roll factor,” which we have found to be approximately 1.7 to 1.9 for normal gait based on measurements we have made in our motion analysis laboratory. This effective lengthening of the leg serves to flatten the trajectory of the trunk during gait. Furthermore, as shown in Equation 2, the model predicts that the vertical excursion, h, will be a function of only L, ρ, and the step length, Sl:

Results from our theoretical analysis were compared with gait data that we acquired from able-bodied subjects.

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RESULTS

Data from the gait analyses of three able-bodied subjects indicated that the vertical excursion of the trunk varied from about 25 to 85 mm over the range of walking speeds (about 0.9 to 2.3 m/sec). Over this range of speeds, pelvic obliquity ranged from about 6° to 20°, and stance-phase knee flexion ranged from about 20° to 36°. Both pelvic obliquity and stance-phase knee flexion were observed to be maximum at about the time of opposite toe-off and were significantly decreased by the time the body reached its peak vertical displacement (Figure 2). Furthermore, we observed that the magnitudes of pelvic obliquity and stance-phase knee flexion at the time of the trunk’s peak vertical displacement were approximately equal to those that occurred at the time of the trunk’s minimum vertical position. We determined that as a result of the relative magnitudes and the timing between these waveforms, pelvic obliquity and stance-phase knee flexion both lower the average vertical position (ie, elevation) of the trunk slightly, but neither action significantly decreased the trunk’s vertical excursion. 2,3

Figure 2

Figure 2

Equation 2 is shown graphically in Figure 3 for values of L = 0.96 m and ρ = 1.8. Empirical data are plotted with the theoretical curve. Figure 3 demonstrates that there is general agreement between the experimental measures and the theory. The rocker-based inverted pendulum model (Figure 1) does not specifically include pelvic obliquity and stance-phase knee flexion, but these are not required because analysis of the empirical data showed that the amplitude of the trunk’s vertical excursion is not reduced by these actions. Furthermore, we observed that the calculated trunk trajectory without the effects of pelvic obliquity and stance-phase knee flexion closely resembled the theoretical trajectory of the rocker-based inverted pendulum model.

Figure 3

Figure 3

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DISCUSSION

Our results indicate that both pelvic obliquity and stance-phase knee flexion commence with initial contact of the foot during normal gait. Both motions increase during the loading response phase, consistent with a shock-absorbing action as load is transferred from the trailing to the leading leg. Pelvic obliquity and stance-phase knee flexion reach their maximum values at about the time of opposite toe-off, and then they return to their minimum values as the body reaches its peak vertical displacement. Therefore, due to the timing of these waveforms with the trunk’s vertical displacement during the gait cycle, the magnitude of the body’s vertical excursion is essentially unchanged by pelvic obliquity and stance-phase knee flexion.

Our theoretical rocker-based inverted pendulum model indicates that the vertical excursion of the body in normal walking is determined by step length and foot and leg geometry. In fact, for a particular individual in whom foot rocker radius and leg length are constants, the trunk’s vertical excursion is a function of step length only (Equation 2). The trajectory of the trunk without pelvic obliquity and stance-phase knee flexion closely approximates the theoretical trajectory of the rocker-based inverted pendulum model.

It has been suggested that a mass moving on a level trajectory requires the least expenditure of energy; for this reason, a bipedal ambulator reduces his or her body’s vertical excursion during walking to minimize energy expenditure. 1 However, this idea neglects the principle of conservation of energy, which in the case of human walking involves an exchange between gravitational potential energy (energy of position) and forward kinetic energy (energy of motion). Typical bipedal ambulators must move up and down when they walk because of the approximate inverted pendulum nature of their locomotor mechanism. During steady-state walking, we are at our lowest forward velocity when we are at our highest vertical position in midstance, and we are at our highest forward velocity when we are at our lowest vertical position during double support. The total mechanical energy of the trunk—the sum of the gravitational potential and forward kinetic energies—is nearly constant during able-bodied walking. Therefore, vertical displacement of the body is not inefficient if it is used as a means to store and return energy during walking, as it does in typical walking. Of course, atypical walking, in which vertical displacement is excessive, such as vaulting, is often not efficient.

We believe that some prosthetic and orthotic gaits may be improved by creating an appropriate roll factor, or foot roll-over shape, 12 and by ensuring sufficient shock absorption during the loading response phase of gait. In prosthetic fittings, the roll-over shape is determined by prosthetic foot design. We believe that roll-over shape is important to foot function, foot alignment, and foot design. 12

Shock absorption can be improved by fitting clients with prostheses and orthoses that facilitate a normal pattern of pelvic obliquity and stance-phase knee flexion. Additional shock absorption can be obtained by fitting amputee clients with a shock-absorbing pylon or a stance-phase knee flexion unit. Current shock-absorbing pylons are not physiological because of their axial shortening, and because their shortening action is carried beyond the loading response phase of walking. We believe designs of future prosthetic shock absorbers may perform better if they more closely mimic the time course of shock absorption that is observed in normal walking.

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CONCLUSIONS

Our results indicate that, contrary to the theory of the six determinants of gait, pelvic obliquity and stance-phase knee flexion do not significantly decrease vertical trunk excursion during normal walking. Instead, both pelvic obliquity and stance-phase knee flexion are believed to provide shock absorption during the loading response phase of walking. Our rocker-based inverted pendulum model indicates that the vertical motion of the body comes from the foot roll-over shape, leg geometry (ie, length), and step length.

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ACKNOWLEDGMENTS

This work was supported by the National Institute on Disability and Rehabilitation Research of the United States Department of Education under grant H133E980023. The opinions in this publication are those of the grantee and do not necessarily reflect those of the Department of Education.

Some of this material is the result of work supported with resources and the use of facilities at the Veterans Affairs Chicago Motion Analysis Research Laboratory of the Veterans Affairs Chicago Health Care System–Lakeside Division, Chicago, IL.

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REFERENCES

1. Saunders JB, Inman VT, Eberhart HD. The major determinants in normal and pathological gait. J Bone Joint Surg (Am). 1953; 35A: 543–558.
2. Gard SA, Childress DS. The effect of pelvic list on the vertical displacement of the trunk during normal walking. Gait Posture. 1997; 5: 233–238.
3. Gard SA, Childress DS. The influence of stance-phase knee flexion on the vertical displacement of the trunk during normal walking. Arch Phys Med Rehabil. 1999; 80: 26–32.
4. Perry J. Gait Analysis: Normal and Pathological Function. Thorofare, NJ: SLACK, Inc.; 1992.
5. Sutherland DH, Kaufman KR, Moitoza JR. Kinematics of normal human walking. In: Rose J, Gamble E, eds. Human Walking, 2nd ed. Baltimore: Williams & Wilkins; 1994: 23–44.
6. Childress DS, Gard SA. Vertical movement of the trunk in human walking. In: Proceedings of the 17th Congress of the International Society of Biomechanics, Calgary, Alberta, Canada, August 8–13, 1999.
7. Gard SA, Childress DS. What determines vertical motion of the human body during normal gait? Proceedings of the Fifth Annual Meeting of the Gait and Clinical Movement Analysis Society, April 12–15, 2000, Rochester, MN. Gait Posture. 2000;11:125–126.
8. Saini M, Kerrigan DC, Thirunarayan MA, Duff-Raffaele M. The vertical displacement of the center of mass during walking: a comparison of four measurement methods. J Biomech Eng. 1998; 120: 133–139.
9. Thirunarayan MA, Kerrigan DC, Rabuffetti M, Croce UD, Saini M. Comparison of three methods for estimating vertical displacement of center of mass during level walking in patients. Gait Posture. 1996; 4: 306–314.
10. Whittle MW. Three-dimensional motion of the center of gravity of the body during walking. Human Mov Sci. 1997; 16: 347–355.
11. Morawski JM, Wojcieszak I. Miniwalker: a resonant model of human locomotion. In: Asmusser E, Jorgensen K, eds. Biomechanics VI-A, Int Series on Biomechanics: Proceedings of the Sixth International Congress of Biomechanics. July, 1977, Copenhagen, Denmark. Baltimore, MD: University Park Press; 1978: 445–451.
12. Hansen AH, Childress DS, Knox EH. Prosthetic foot roll-over shapes with implications for alignment of trans-tibial prostheses. Prosthet Orthot Int. 2000; 24: 205–215.
Keywords:

Gait; walking; pelvic obliquity; knee flexion; vertical excursion

© 2001 Lippincott Williams & Wilkins, Inc.