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Scaling of Dynamics in the Earliest Stages of Walking

KG Holt, PT, PhD, is Associate Professor, Department of Physical Therapy and Athletic Training, Sargent College of Health and Rehabilitation Sciences, Boston University, 635 Commonwealth Ave, Boston, MA 02215 (USA). Dr Holt is a fellow at the Center for the Ecological Study of Perception and Action, University of Connecticut, Storrs, Conn
E Saltzman, PhD, is Associate Professor, Department of Physical Therapy and Athletic Training, Sargent College of Health and Rehabilitation Sciences, Boston University. Dr Saltzman is a fellow at the Center for the Ecological Study of Perception and Action, University of Connecticut, and a research scientist at the Haskins Laboratories, New Haven, Conn
CL Ho, PT, ScD, Department of Physical Therapy and Athletic Training, Sargent College of Health and Rehabilitation Sciences, Boston University
BD Ulrich, PhD, is Professor and Dean, Division of Kinesiology, University of Michigan, Ann Arbor, Mich

Address all correspondence to Dr Holt at: kgholt{at}bu.edu

Submitted October 2, 2006; Accepted June 15, 2007

	Abstract

 
Background and Purpose: Although the description of mature walking is fairly well established, less is known about what is being learned in the process. Such knowledge is critical to the physical therapist who wants to teach children with developmental delays. The purpose of this experiment was to test the notion that learning to walk efficiently involves fine-tuning the body’s controllable stiffness (by co-contraction and isometric muscle contractions against gravity) to match (at a 1:1 scaling) the gravitational (pendular) stiffness of the swing leg.

Subjects: The study participants were 7 children with typical development and the newly emerged ability to walk 6 steps without falling (ages 11 months to 1 year 5 months at the onset of walking).

Methods: Pendular stiffness and spring stiffness were estimated from the equations of motion for a hybrid model with kinematic data as children walked over ground. Testing occurred once per month for the first 7 months of walking.

Results: After the first month of walking, children walked with greater spring stiffness than would be predicted by the model. The ratio began to approach the predicted value (1:1) as the months progressed.

Discussion and Conclusion: The results of this and a previous study of the pendular dynamics of gait suggest that learning to walk is a 2-stage process. The first stage involves the child’s discovery of how to conserve energy by inputting a particular muscular force at the correct moment in the cycle. The second stage involves the fine-tuning of the soft-tissue stiffness that takes advantage of the resonance characteristics of tissues. In order to address developmental delays, investigators must discover the dynamic resources used for the activity and attempt to foster their development. A number of interventions that probe this approach are discussed.

	Introduction

Top Abstract Introduction Active and Passive Dynamics... Scaling of Pendular Stiffness... Model and Theory Method Results Discussion and Conclusions References

 
The ability to define developmental delays in the acquisition of gait has important ramifications for physical therapists both from a diagnostic perspective and in planning intervention strategies. The problem lies in discovering an appropriate and useful metric by which to assess developing and mature gait. Furthermore, in order to teach children with developmental delays to walk with mature patterns, therapists must seek to understand what it is that children with typical development learn when acquiring walking ability. To address this problem, we used the concepts and tools of a biomechanical model that reflects the active and passive dynamics of human walking.

	Active and Passive Dynamics of Walking—The Playground Swing Analogy

Top Abstract Introduction Active and Passive Dynamics... Scaling of Pendular Stiffness... Model and Theory Method Results Discussion and Conclusions References

 
Mechanically, walking is analogous to a parent pushing a child on a playground swing. The swing must be pushed at just the right "state" of the swing cycle to be most effective, that is, at the highest point on the swing as it is about to change direction. For the swing, "state" refers to the point at which the velocity of the swing is zero and the amplitude is at a maximum. Thus, "state" is defined by velocity and position. State-dependent forces are called "escapements" and constitute the active dynamics of swinging. A push that is given at the wrong state (eg, as the swing is moving toward the pusher) can slow or even stop the swing. The appropriate escapement in swinging facilitates the conservative passive dynamics of the pendulum. Thus, after the first few pushes to gain amplitude, the swing can be maintained with very little effort from the parent because energy is conserved by the exchange of the kinetic and potential energy of the swing. When pushed in this manner, the swing will oscillate at its natural or resonant frequency, that is, the frequency at which minimal force is required to maintain its oscillations and that is determined by its length.

There are 2 major active dynamic resources for walking. There is a "push," mostly from the gastrocnemius-soleus (G-S) muscle group (about 67% of power, according to Winter¹) of the contralateral limb, as the ipsilateral, lead foot makes initial contact with the ground. Unlike what occurs with the swing, the energy goes into the center of mass (COM) of the body as it oscillates over the planted foot, forming an inverted pendulum. Additionally, in the swing phase of walking, the "push" (or, more appropriately, the "pull") is achieved in the extended hip by brief contraction of the hip flexor muscles to help initiate the forward swing. In addition to energy being conserved in the inverted (stance-leg) pendulum and in the regular (swing-leg) pendulum, the energy in walking also is conserved by the "springiness" of the noncontractile tissues in muscles and in tendons. For example, the G-S muscle group conserves energy by being stretched as the COM passes over the ankle axis in mid-stance and returns that energy to assist in plantar flexion during pushing off.

In a recent experiment, we showed that in the very early stages of walking, children use many different muscle groups to put energy into walking. Some of the energy is input at the appropriate state of the system, but much of it is not. After 1 month, however, children with typical development learn to produce an escapement (a state-dependent force) through plantar-flexion torque at pushing off that is exactly timed to facilitate the use of the passive, energy-conserving capability of the limbs and soft tissues in a hybrid pendulum-spring manner.² Through discovery of the appropriate state at which to input energy, children’s gait begins to look more like that of adults (that is, more like a pendulum) and is more effective in propelling the body toward its goal (usually the mother).

The rich literature on walking development suggests that this is not the whole story. Rather, refinements in the gait pattern occur in a nonlinear manner, at least until the age of 7 to 8 years. For example, Vaughan et al³ showed that the step frequency in walking is not scaled to leg length in the same way as it is in adults until the age of 3 years. Sutherland et al⁴ reported that 5 criteria determined mature gait (single-limb stance period, speed, cadence, step length, and gait width), achieved by about the age of 3 years but not before. Do children learn some other features of their pendulum-spring dynamics that facilitate these changes, and, if so, when does this learning occur?

	Scaling of Pendular Stiffness and Spring Stiffness in Walking

Top Abstract Introduction Active and Passive Dynamics... Scaling of Pendular Stiffness... Model and Theory Method Results Discussion and Conclusions References

 
In older children who are developing typically and in adults walking at preferred walking frequencies, there is a particular relationship between the energy that is conserved in the pendulum action of the swing leg and the energy that is recovered from the stretch ("springiness") of soft tissues. The most efficient way for the 2 "oscillators" (the pendulum and the spring) to work together is for them to have the same or similar natural or resonant frequencies. Imagine trying to push 2 swings of different lengths with the same push. Doing so would not work because the shorter swing would require a higher frequency of pushing because of its higher natural frequency. The factor that determines natural frequency is called "stiffness" and should be equal for the pendulum and the spring. Thus, for optimal performance, the stiffness of the pendulum must be scaled to that of the spring in a 1:1 fashion.^5,6 With this assumption, the preferred walking speed becomes highly predictable from a simple equation derived from the pendulumspring model of the leg (see equation 3 below). This unique scaling relationship results in a predicted stride frequency that is highly stable for head and segmental coordination and metabolically and mechanically efficient.⁷

This particular ratio is not obligatory, however. Although the pendulum characteristics that determine natural frequency are relatively fixed (depending on the mass and length of the segments), the stiffness of the soft-tissue spring can be modulated. For example, the scaling is 1.43:1 (spring stiffness is greater than pendulum stiffness) in children with cerebral palsy because the inherent neuromuscular and morphological stiffness of the soft tissues is greater.⁸ Stiffness also is controllable by co-contraction of muscles around a joint and by the level of isometric contraction of a muscle under an opposing gravitational load. Gait patterns that exploit spring stiffness require more spring action than pendular gait patterns. For example, adult human running is associated with ground reaction forces (GRF) that are 3 to 5 times body weight; in comparison, for walking, the GRF are 1 to 2 times body weight.⁹ The additional torque produced by the GRF around the weight-bearing joints requires increased active contractions of the opposing muscles to prevent collapse. Thus, during running in experienced human adults and bipeds at preferred speeds, the scaling has been shown to be 5:1, reflecting a 4-fold increase in spring stiffness relative to gravitational stiffness^10,11 and a change in pattern that utilizes potential in a spring-like, bouncing pogo stick pattern.¹²

There are 2 lines of evidence suggesting that 1:1 scaling is not achieved in the early stages of walking. First, there is an increase in walking frequency in the first 5 months of walking experience,¹³ contrary to the expectation of pendular systems that speed will decrease as the limbs get longer and the body mass increases. Second, as already noted, walking speed is not scaled to the length and mass of the limbs as it is in adults until a child is 3 years of age.³

Overall, these data lead to the postulate that the development of a mechanically optimal mature gait may be (minimally) a 2-stage, nonlinear process. The first stage is the discovery of the escapement that facilitates an effective sagittal-plane pendulum-spring gait pattern; this stage occurs within the first month of walking.² The second stage is the discovery of the unique scaling of the lengths and masses of the segments to tissue stiffness in a 1:1 ratio that results in an optimally efficient pattern; this stage occurs during later development. If supported, this proposal would provide a dynamic interpretation of the 2-stage process identified by Bril and Breniere,¹³ who observed significant changes in the relationships among stride length, stride frequency, and walking speed in the first 3 to 6 months of independent walking (the "integration phase"), followed by a stabilization of values in the next 18 months (the "tuning phase").

The purpose of this study was to trace the scaling of the pendular stiffness characteristics of the segment to the global spring stiffness as estimated from the regular hybrid pendulum-spring model during the first 7 months of walking in children with typical development. Our prediction was that during this test period, a spring stiffness-to-pendular stiffness ratio of 1:1 would be observed.

	Model and Theory

Top Abstract Introduction Active and Passive Dynamics... Scaling of Pendular Stiffness... Model and Theory Method Results Discussion and Conclusions References

 
The beauty of a mechanical oscillating system operating at resonance is that minimal driving force is required to maintain its oscillations. Any mechanical model also should reflect the dynamic resources available for the task. In human locomotion, these resources include the ability of muscles to generate force, the capability of muscles and soft tissues to conserve and subsequently regenerate elastic energy, and the capability of the limb segments and masses to conserve energy through their pendulum potentials. The hybrid pendulum-spring model^5,11 captures the conservative aspects of these resources. At resonance and for small amplitudes of oscillation, the periodic behavior is governed by the following equation¹¹:

(1)

In this equation, ₀ is the predicted (resonant) stride period; mL² is the moment of inertia of the limb, which is based on the simple pendulum equivalent length of the limb segments (thigh, shank, and foot); mLg is the gravitational torque (pendulum); and kb² is the spring torque (stiffness).

By use of dimensional analysis,¹⁴ mLg and kb² can be divided to produce a dimensionless ratio with constant n. Equation 1 can then be rewritten as follows:

(2)

where L is the simple pendulum equivalent length and g is the acceleration due to gravity. In the special case in which kb²=mLg (1:1 scaling) and by substitution, equation 2 can be rewritten as follows:

(3)

This simple equation has been shown to predict, with good agreement, the preferred walking frequency of adults⁶ and 9-year-old children,⁵ the preferred frequency of leg swinging under various load conditions,¹⁵ and the preferred walking speeds of quadrupeds of various sizes.¹¹ Human walking at the predicted stride frequency results in minimal metabolic cost, maximal stability of the head, and coordination of lower-extremity limb segments.⁷

Equation 3 does not accurately predict the preferred walking speed of children with spastic hemiplegic cerebral palsy, however. The constant n=2.43 must be included in equation 2 to predict the preferred walking period, suggesting, according to the model, a change in the kb²:mLg scaling, to 1.43:1. This value is directionally consistent with the increased stiffness associated with spasticity and tonic contraction of the plantar-flexor muscles in children with spastic hemiplegic cerebral palsy.¹⁶ If animals and humans maintain a resonance based on the kb²:mLg dimensionless ratio, then the constant n is a reflection of the spring stiffness in the model and the global stiffness of the limb. The constant n can be considered a stiffness index.⁷ By rearrangement of equation 2, the value of n can be calculated as follows:

(4)

where _obs is the observed stride period.

	Method

Top Abstract Introduction Active and Passive Dynamics... Scaling of Pendular Stiffness... Model and Theory Method Results Discussion and Conclusions References

 
Subjects

Seven infants who were developing typically participated in the study. The ages at the first visit ranged from 11 months to 1 year 5 months. The following inclusion criteria were met: newly able to perform 3 to 6 consecutive independent steps; no known neurological, cardiovascular, or musculoskeletal diseases; and no known cognitive impairments. The first visit to the laboratory occurred as soon as the parents observed that the child could perform 3 to 6 consecutive independent steps over several repetitions. After the first visit, children and their parents returned for monthly visits up to the seventh month of independent walking. The participants’ anthropometric characteristics (body weight, body height, thigh length, leg length, and foot length) were measured at each visit (Tab. 1). Written informed consent was obtained from the parents of the participants.

Data Analysis

Trials without incidences of falling, stopping, walking off the walkway, or turning around were included in the analysis. The initial contact of the foot in the stance phase was identified by algorithms modified by Ulrich et al¹⁷ from those developed by Hreljac and Marshall.¹⁸ The observed stride period, _obs was calculated as the time difference between successive initial contacts of the right foot. Stride length was determined as the distance covered by forward displacement of the heel marker on consecutive initial contacts of the right foot. Walking speed then was calculated by multiplying stride frequency by stride length. All statistical analyses were carried out with the right foot as the reference.

Thigh, shank, and foot lengths were calculated geometrically from markers on the trochanter, knee, and foot with a custom-written MATLAB program. Segment masses and estimates of the distance of the segment COM from the proximal axis were calculated by use of the estimates of Jensen.¹⁹ These data were then used to calculate the simple pendulum equivalent length as follows.

The thigh-shank-foot is assumed to be a single rigid body attached at the hip joint by a frictionless pin joint. The location of the COM of the lower extremity is calculated with the following equation:

(5)

where h_sys is the distance from the axis of rotation to the COM of the lower extremity, m_i represents the masses of the respective segments, h_i is the distance from the COM of each of the respective segments to the axis of rotation, and M_sys is the total mass of the system (sum of individual segment masses).

Similarly, the moment of inertia of each segment (I_seg) is given by the following equation:

(6)

where m_seg is the segment mass, r is the segment radius of gyration about the segment COM, and h is the distance from segment COM to the axis of the pendulum.

The system moment of inertia about the axis of rotation (I_sys) can then be calculated by use of the parallel-axis theorem as follows:

(7)

where I_i is the segment moment of inertia, m_i is the segment mass, and D_i is the distance from the segment COM to the axis of rotation.

The value for L, the simple pendulum equivalent length, is then calculated as follows:

(8)

The predicted stride period, ₀, is determined by placing the value of L (meters), (3.141), and acceleration due to gravity (g=9.81 ms^–2) into equation 3.

The value of n can also be determined by rearranging equation 2 as follows:

(9)

Statistical Analysis

The Friedman analysis of variance for repeated measures was used to assess the differences in dependent variables from visit 1 to visit 7. This nonparametric test was chosen because the distribution of the data was not normal at each visit, and the variability was not equal among visits. The alpha value was set at .05 for the Friedman analysis of variance. To compare the index n of each visit with a constant of 2 (as predicted by equation 3), Wilcoxon signed-rank procedures were used with an alpha value of .05. Polynomial contrasts were used to test for linear, quadratic, or cubic trends in the change in the index n from visit 1 to visit 7.

	Results

Top Abstract Introduction Active and Passive Dynamics... Scaling of Pendular Stiffness... Model and Theory Method Results Discussion and Conclusions References

 
Anthropometry

Participant anthropometric measurements are shown in Table 1. Weight, height, and segment lengths (with the exception of the thigh) increased significantly across the testing period.

Gait Parameters

Walking speed, stride length, and stride period all increased significantly across the testing period. The median values and the ranges for stride length, stride period, walking speed, observed and predicted stride frequencies, and index n at each visit are shown in Table 2. The mean values for walking speed, stride length, and observed and predicted stride frequencies, the standard deviations, and the P values are shown in Figure 1.

View larger version (16K): [in this window] [in a new window]   Figure 1. Box plots of gait parameters in successive months following walking onset. Horizontal lines in boxes represent median values. (A) Walking speed. (B) Stride length. (C) Stride frequency.

View larger version (18K): [in this window] [in a new window]   Figure 2. Box plots of stride periods in successive months following walking onset. (A) Observed stride period. (B) Predicted (resonant) stride period (0).

View larger version (13K): [in this window] [in a new window]   Figure 3. Box plot of stiffness index n in successive months following walking onset. A value of 2 (dotted line) represents that observed in older children and adults. Values of greater than 2 indicate increased stiffness, and those of less than 2 indicate reduced stiffness.

	Discussion and Conclusions

Top Abstract Introduction Active and Passive Dynamics... Scaling of Pendular Stiffness... Model and Theory Method Results Discussion and Conclusions References

 
As expected, the scaling of the spring stiffness estimate to the pendular component increased (as indexed by n) as a function of time of independent walking during the testing period, in contrast to the prediction of the model that the ratio of the stiffness torque to the gravitational torque should scale at 1:1 as limb lengths and masses increase. After the first month and through the seventh month, the ratio was higher, indicating proportionally greater stiffness. This finding is consistent with the findings of Bril and Breniere¹³ and Vaughan et al³ showing, respectively, increases in the stride or step frequency (increased step frequency is a direct reflection of increased stiffness) of walking and an inability until the age of 3 years to show scaling to body length and mass in the same way as adults.

We argue that the use of the hybrid model adds to this literature by providing an understanding of the learning process that leads to appropriate scaling for optimal performance and suggests an alternative view to the assignment of learning to neuromaturational factors alone.^3,20 The findings of the present study, combined with those for older children and adults, suggest that children’s learning involves 2 stages. In the first stage, "brand-new" walkers discover the escapement that moves the body effectively toward the goal (eg, mother or toy) and, importantly, facilitates use of the energy-conserving (pendulum and spring) properties of limbs and soft tissues.² This "escapement discovery" stage has more profound effects on gait parameters than does the later stage. Marked increases in walking speed (achieved by increases in step length and stride frequency^2,13), decreased step width, and a much greater proportion of motion in the intended line of progression are observed.¹³ In the second stage, fine-tuning involves a reduction in the scaling of soft-tissue controllable stiffness to the pendular masses and lengths of the leg segments. The exact timing of this fine-tuning of dynamic parameters is uncertain and requires further study, but previous research^3,13 suggested that it occurs somewhere between 18 months and 3 years of age. Certainly, by 9 years of age, children have learned to use this scaling ratio, and the result is minimal metabolic cost.^5,8 Our data show that this fine-tuning is in process in the first 7 months of walking as the index n starts to approach the expected value of 2 in the sixth and seventh months (Fig. 3) but has not yet achieved a stable or efficient state.

These findings provide impetus for a different approach to evaluation and interventions for children with atypical development. On the basis of the findings of the present study, it is clear that children with developmental delays should not be expected to find the most efficient step frequency during the first 7 months of independent walking, just as their typically developing peers should not be expected to do so. We hope that our own planned longitudinal studies will provide information about when that type of efficiency might be expected to develop. Prolonged, high step frequency as an indicator of increased stiffness might indicate a developmental delay and would indicate the need to examine that resource. In terms of learning, the implication of these postulates is that the dynamics of pendular masses and lengths in a gravitational field initially "teach," or at least inform, the nervous system at what state of the gait cycle to input muscular impulses to achieve effective progression. Later, optimality criteria, such as minimizing metabolic cost and achieving greater stability, inform the nervous system about the amount of force and coactivation needed to achieve stiffness in the most efficient manner.

This interpretation is in stark contrast to that of Vaughan and colleagues,³ who claimed that scaling (of leg length to step frequency) occurs as a function of neuromaturation (ie, in the primacy of neuromaturation). Furthermore, viewing the scaling issue from our perspective leads to a much different interpretation of disease states. For example, Vaughan et al claimed that the inability of children with cerebral palsy to scale walking speeds to adult values, despite neurosurgical interventions, is attributable to a disruption of their central pattern generator and that there may be "limited opportunities to select favourable networks."^3(p126) Such an interpretation offers little help to the therapist who would like to improve the walking ability of children with cerebral palsy. How would a therapist normalize a (yet to be discovered) central pattern generator or provide opportunities to "select" favorable neural networks?

In contrast, we argue that children with spastic cerebral palsy are unable to scale walking speeds to adult values because they have a different pattern of resources from which to construct their locomotor actions. In particular, the increased stiffness that is associated with the disease process may actually develop as a function of the child’s need to change the gait pattern to compensate for weakness.²¹ This interpretation suggests that if the problem is addressed at the level of dynamic resources (timing and amplitude of active muscle contractions and stiffness control), it may be possible to improve walking ability in these children. For example, in a recent study, we showed that using functional electrical stimulation of the G-S muscle group that is timed to the heel-strike of the involved legs not only improves the amplitude and timing of the contraction²² but also may result in decreased stiffness on the stimulated, involved sides (Ho and colleagues, unpublished research). In principle, it also should be possible to use a metronome or music with a beat that is at the predicted stride period in equation 3 to drive the walking speed of children.

An interesting finding of the present study is that children apparently transition through the 1:1 scaling around the second and third months of walking. That is, in the first month of walking, they walk at a frequency lower than that predicted, and by the fourth month, they have increased to a frequency significantly higher than that predicted (Fig. 3). One may ask why, if they pass through this metabolically optimal state, they are not attracted to and do not maintain this pattern in subsequent months. To answer this question, one must look at the constraints on the walking system. We propose that the primary constraint in the first months of walking development is the successful achievement of task goals. At this stage, the main goal of locomotion is to get to the mother, the candy, or an interesting object without falling and as quickly as possible. Stability of the pattern is essential in order to achieve this goal. The importance of dynamic stability in influencing the gait pattern in early walking has been emphasized by a number of developmentalists.^4,23,24

In contrast, walking in the early months is not done for prolonged periods in any one session; therefore, the need for a metabolically optimal gait is irrelevant or at least secondary to stability constraints. Some authors²⁵ have similarly suggested that there is a trade-off between mechanical economy (in the conservation of pendular energy) and stability in early walking. If metabolic and mechanical costs are not the critical constraints at this stage, then any pattern of parameters that achieves the goal of getting to an object quickly and stably (without falling) is appropriate. Optimal scaling of dynamic parameters is not critical because all combinations are dynamically stable and metabolic cost is not an issue.

The final, most intriguing, and unanswered question with respect to scaling is why unitary dimensionless scaling of spring stiffness torque to gravitational stiffness torque is a signature characteristic of optimal gait. The value has been repeatedly observed in humans of different ages,^5,6 in bipedal walking gait, and even in the walking of quadrupeds of various sizes.¹¹ We suggest that in order for humans to take full advantage of the natural (resonant) frequencies of both the pendulum and the spring, these frequencies must be at or close to the same value. Whenever 2 oscillating systems work together, or entrain, they are affected by 2 tendencies—to be drawn toward their own natural frequency (maintenance tendency) and to be drawn toward each other’s natural frequency (magnetic effect).²⁶ If the natural frequencies are significantly different, then the coordination of their individual actions on the behavior of the legs may lead to greater variability (less stability) as the 2 tendencies compete.²⁷ It is possible that this mechanism is responsible for the finding that the coordination of limb segments is more variable when adults are required to walk at frequencies that do not represent a 1:1 scaling.²⁸

	Footnotes

 
All authors provided concept/idea/research design. Dr Holt, Dr Saltzman, and Dr Ho provided writing and data analysis. Dr Holt and Dr Ulrich provided data collection and fund procurement. Dr Ulrich provided subjects, facilities/equipment, institutional liaisons, and clerical support. Dr Saltzman and Dr Ulrich provided consultation (including review of manuscript before submission).

The authors thank the children and their parents for their participation in the project.

The institutional review boards of the University of Michigan and Boston University approved the study procedures.

This research was funded by National Institutes of Health grant HD 42728.

^* CIR Systems Inc, 60 Garlor Dr, Havertown, PA 19083.

Peak Performance Technologies, 7388 S Revere Pkwy #901, Centennial, CO 80112.

The MathWorks Inc, 3 Apple Hill Dr, Natick, MA 01760.

	References

Top Abstract Introduction Active and Passive Dynamics... Scaling of Pendular Stiffness... Model and Theory Method Results Discussion and Conclusions References

 

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This Article Abstract Full Text (PDF) The Bottom Line The Bottom Line Podcast All Versions of this Article: ptj.20060299v1 87/11/1458    most recent Submit a response Alert me when this article is cited Alert me when Rapid Responses are posted Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Holt, K. G Articles by Ulrich, B. D Search for Related Content PubMed PubMed Citation Articles by Holt, K. G Articles by Ulrich, B. D Related Collections Motor Development Social Bookmarking                      What's this?