Roll-over shapes of human locomotor systems: effects of walking speed
Introduction
The musculo-skeletal lower limb system of a non-disabled human is a mechanism of immense complexity. In particular, the human foot is an intricate structure comprised of numerous bones, muscles, and ligaments. The human foot has been studied in terms of its function, its disorders, and its evolution (Morton, 1935; Hiss, 1937; Steindler, 1955; Susman, 1983). Numerous experiments and models have been developed to examine narrow biomechanical questions about the foot (Ker et al., 1987; Scott and Winter, 1993; Salathe et al., 1986; Patil et al., 1993; Simkin and Leichter, 1990; Kim and Voloshin, 1995). While undoubtedly useful for insight into specific clinical problems, these models are difficult to use for the development of lower limb orthoses and prostheses––the devices aimed at accommodating or replacing disabled or amputated lower limb systems. For locomotion and rehabilitation applications, a simpler more global understanding of non-disabled lower limb systems could be useful. Rocker-like (cam-like) properties of lower limb systems may provide the simple global understanding needed to answer a number of questions in the fields of locomotion and rehabilitation.
The foot and ankle have been modeled as rockers by several investigators. Perry (1992) has described the function of the foot and ankle during stance as three qualitative rockers: the heel, ankle, and forefoot rockers. Ju (1986); Ju and Mansour (1988) and Koopman, 1989, Koopman, 1995 used rocker models of the foot in computer models of walking and found that their models were sensitive to the effective shape of the foot. Analyses of walking toys (Morawski and Wojcieszak, 1978), prosthetic feet (Stein and Flowers, 1987; Knox, 1996; Hansen et al., 2000), physiologic ankle–foot (AF) systems (Knox, 1996; Hansen, 2002), and mathematical and physical models of walking (McGeer, 1990; Gard and Childress, 2001) have used rockers to describe the function of the foot and/or ankle–foot complex. Stein and Flowers (1987) used the invariant relationship of center of pressure (CoP, in the forward progression direction) and shank angle to conclude that the solid-ankle cushioned heel (SACH) prosthetic foot could be modeled effectively as a cam; although measurement of the cam was not shown. Knox (1996) later developed similar methods as those shown in this paper to measure the effective cam shapes of prosthetic feet and of non-disabled ankle–foot systems.
We believe that the goals of non-disabled lower limb systems for walking are to conform to simple geometries over which the body can roll, making use of passive dynamics of a rocker-based inverted pendulum (McGeer, 1990; Gard and Childress, 2001). The purpose of this paper is to investigate rocker shapes during walking and to examine the hypothesis that they do not change with walking speed. This hypothesis was based on a rocker-based inverted pendulum model of walking (Gard and Childress, 2001) and preliminary walking data of three non-disabled subjects. The rockers are defined here as roll-over shapes, because they are the effective geometries that the corresponding lower limb systems conform to during the “roll-over” phase of gait, i.e. between heel contact (HC) and opposite heel contact (OHC). After OHC, focus can be shifted to the other lower limb system (i.e. the leading limb). Between OHC and toe off, other goals likely exist for the trailing limb, which is being rapidly unloaded, and ceases to act as a rocker (Hansen, 2002). Three different kinds of roll-over shapes are presented and the effects of walking speed on these three roll-over shapes are shown. The three kinds of roll-over shapes are named foot, ankle–foot, and knee–ankle–foot (KAF) to conform with naming conventions used for lower-limb orthoses (foot orthoses, FOs, ankle–foot orthoses, AFOs, and knee–ankle–foot orthoses, KAFOs). Potential uses of roll-over shapes in the field of rehabilitation and implications of walking speed results are discussed.
Section snippets
Methods
The basic premise of roll-over shape measurement can be illustrated using a simple rolling wheel (see Fig. 1). As the wheel rolls it utilizes a series of contact points. These points, if measured in a world-based coordinate system, are in a straight line on the rolling surface (see Fig. 1). If these same contact points are measured relative to a coordinate system fixed on the wheel (i.e. a wheel-based coordinate system), the points indicate the rolling geometry or cam-shape of the wheel (see
Results
The mean foot, ankle–foot, and knee–ankle–foot roll-over shapes for all subjects combined are shown in Fig. 4 for five walking speed ranges using thick black lines. The center of pressure locations of the ground reaction force in the three coordinate systems following opposite heel contact (OHC) are also shown using thin lines. The standard errors of the roll-over shapes are shown using a gray band of error behind the roll-over shapes and unloading shape portions (this band is a series of error
Discussion
The statistical analyses used in this study show that the knee–ankle–foot roll-over shapes change in position with walking speed. However, the amount of the changes in position may not be clinically significant for rehabilitation concerns. Median forward shifts of the best-fit arcs change by less than half a percent of body height over the speed range tested. Radii of the roll-over shapes did not change significantly with walking speed although the median values of radii and Fig. 5 indicate
Conclusions
Non-disabled lower limb systems adapt to changing conditions associated with different walking speeds to maintain similar effective roll-over geometries (roll-over shapes). This finding is promising to the field of rehabilitation because it provides a simplified set of goals for the design of walking aids such as prostheses and orthoses. Comparing roll-over shapes of disabled persons' affected lower limbs to the invariant shapes of non-disabled systems may also provide insight toward surgical
Acknowledgements
The authors would like to acknowledge the use of the VA Chicago Motion Analysis Research Laboratory of the VA Chicago Health Care System, Chicago, Illinois.
The work described in the paper was partially supported by the Department of Veterans Affairs, Rehabilitation Research and Development Service and is administered through the VA Chicago Health Care System, Chicago, Illinois.
This work was also funded by the National Institute on Disability and Rehabilitation Research (NIDRR) of the US
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