We would like to thank Galloway for his commentary and the opportunity to expand on some of the ideas advanced in the article. We have organized the response to address the specific questions raised by Galloway.
Selection Theory
The problem of selection versus constraint is indeed difficult to test experimentally, and it is confounded by the fact that there are other constraints due to the task demands (eg, speed, accuracy) and by environmental factors that surely influence the movement patterns. Our view is that rather than “selection” of a stiffness or force variable, a movement pattern emerges as a function of the interplay of task demands, available dynamic resources (energy-generating and energy-conserving capabilities), and environment. In our view, the child with cerebral palsy learns about (explores) his or her dynamic resources within a given environment (eg, uneven surfaces, slippery floors, underwater) and under specific task demands (eg, walking, running, jumping). On each occasion, a number of viable patterns are available. The pattern that emerges (rather than being selected) is optimal from the perspective of stability, metabolic cost, and mechanical efficiency. Thus, although the child explores his or her mass, strength, stiffness, or body segment lengths, the “selection” occurs at the level of movement pattern. The stiffness observed in children with cerebral palsy is the product of muscle and connective tissue properties that developmentally change according to their patterns of use.1,2 In this sense, stiffness itself is a property that cannot serve as the basis for a selection process. Patterns of movements, however, provide enough diversity and, consequently, selection theory can be applied.
The major difference between our proposal and the traditional view of neural and mechanical constraints is that we look at the resources the child brings to the task and understand the observed movement pattern, not as an abnormal feature of a damaged central nervous system, but as a viable solution given the capabilities for force generation and conservation (dynamic resources) possessed by the child. In this view, the negative “constraint approach” is substituted by a positive perspective that seeks to understand the observed movement pattern as an adaptive behavior that facilitates the development of, and is facilitated by, the available resources.
Vertical Stiffness Calculation
As pointed out, we calculated stiffness as the slope of the linear regression between vertical acceleration and displacement of the center of mass, assuming a linear relationship as expected in a linear spring. The regression plots of these 2 variables revealed a fairly linear relationship, with R2 varying from .61 to .96. This relationship was stronger in children with cerebral palsy than in normally developing children. Some of the plots of vertical acceleration by vertical displacement of the center of mass demonstrated that the observed curves were typical of a vertical stiffness produced by a nonlinear “hard spring.” However, even these plots had a large linear portion in the middle of the curve. Despite these possible problems, similar results were obtained with different forms of stiffness calculations. In a study of people carrying backpacks while walking at different speeds, Holt et al3 showed that knee joint vertical and global stiffness measures were equivalent.
Although the contribution of the lower-limb joints to the overall stiffness might have clinical interest, the model proposed cannot be used to identify the stiffness distribution across the joints. Due to the large variability of severity, types of impairment, and topographic distribution of altered tone observed in children with cerebral palsy, it would be very difficult to show a specific pattern of stiffness distribution across lower-limb joints. In addition, individual differences in energy-generating and energy-conserving capabilities (dynamic resources) among children with cerebral palsy may result in a different stiffness contribution of each joint, but reveal a similar overall behavior.
Changes With Speed
Data published previously on global stiffness and impulsive force demonstrated a linear relationship between these variables and speed, but with different slopes.4 In our study, the magnitude of the variables was a function of speed in both groups. Because there was a speed difference between groups, we believe normalization to walking speed was necessary to allow meaningful comparisons between groups or limbs. Our results varied according to the speed of walking. However, at the preferred speed, the only variable that did not show an expected difference, according to the proposed hypotheses, was vertical stiffness. This lack of difference in vertical stiffness at the preferred speed (P=.06) might have been influenced by the small sample size used in our study. In other studies,4,5 it has been shown that at the preferred speed children with cerebral palsy demonstrated greater stiffness of their affected limbs when compared with typically developing children. In relation to differences in potential energy (K/P energy) at the preferred speed in the more affected lower extremity, it is important to note that, according to the model presented, no difference was expected between groups. A difference in K/P energy, however, was observed at all speeds in the less affected lower extremity, as we had hypothesized. Therefore, our results seem to explain the walking pattern of children with cerebral palsy at the preferred speed.
Role of Plantar-Flexed Ankle
We believe Galloway is correct when he states that differences in stiffness, K/P energy, and landing angle could be the result of changes in range of motion (ROM), stiffness, or ability to generate force at the trunk or any joint of the children's lower extremity. From a traditional therapeutic perspective, one could argue that we must treat these impairments in order to minimize the functional limitation. Many of the therapeutic measures the medical profession uses do exactly that. Examples include serial casting and tendon-lengthening surgeries. If a ROM limitation is indeed the primary cause of a gait deviation in a person with cerebral palsy, then identifying that limitation would be important. Conversely, if changes in pattern (including, for example, increased ability to generate force or power in the noninvolved limb, increasing joint stiffness, or adaptive ROM limitations) are compensations for inadequate resources (eg, lack of muscle force needed to overcome gravity or to provide joint stability), as we suspect, then treating an individual component may not be appropriate, because it is an attempt to remove an adaptation to the underlying cause (the changed dynamic resource).
As children become older, the adaptations may indeed become structural in the sense that, for example, the triceps surae muscle-tendon length ratio is reduced and there is more connective tissue embedded in the muscle.6–8 Nevertheless, we would argue that the benefits of treating individual components by, for example, tendon lengthening to get improved ROM at the ankle are short-lived at best and that the procedures are more likely to cause pain, weakness, or other gait deviations. Our suggestion is that early intervention at the level of dynamic resources can avoid many of the structural limitations seen after years of adaptive use of particular structures in particular patterns.
We used the term “landing angle” instead of the more easily understood term “step length” because we contend that this variable could be the result of several body motion combinations, as it depends on the behavior of the center of mass. Thus, despite small differences in the kinematic details of the walking pattern of children with cerebral palsy, a simple biomechanical model that takes into consideration the dynamic resources available to these children can capture their overall waking behavior. In this sense, interventions should not focus only on specific limitations in lower-extremity passive or active ROM, but on providing the dynamic resources needed to better accomplish a functional behavior.
We thank Galloway for his insightful and thoughtful review of our work. We hope that the responses and arguments presented here may help clarify our understanding of the mechanisms underlying functional performance in children with cerebral palsy.
- Physical Therapy
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