#### INTRODUCTION

Skilled motor performance is characterized by an increased mechanical efficiency (ME) because the task is performed with reduced energy expenditure.^{1,2} ME is relatively constant over a wide range of workloads for children with typical development (TD) and adults. Mechanical efficiency for stair climbing and uphill running ranges from 20% to 30%.^{3} It is assumed that inefficient motor behavior of adults or children with cerebral palsy (CP) or other forms of motor dysfunction reflects abnormal motor control and posture related to impaired coordination and neuromuscular function. Previous studies have reported significantly lower ME in children with CP (2%–5%) compared with children with TD (∼20%).^{4,5} Other studies have shown that ME is reduced in CP^{6} and other types of dysfunction in children and adults.^{7,8}

A number of studies of adults who are physically fit demonstrated improved ME after training and motor learning, indicating that movement patterns become more efficient with practice and repetition.^{9,10} This suggests that the measurement of ME during a work task can be useful for assessing development stages and evaluating intervention outcomes and changes with motor learning and practice. A recently developed stair-climbing test shows promise for the measurement of ME during ambulatory tasks in children with CP^{4} and may be used when other specific tasks, such as cycling, may be impossible to perform. A simplified, more convenient, clinical version of the stair-climbing test that might be applicable in children’s natural environments was also developed and validated.^{5} The latter study assessed ME_{net}, with oxygen consumption (V̇o_{2}) estimated from the heart rate (HR) increase and body weight, during a self-paced 4-minute stair-climbing test in children with a range of motor function abilities. It demonstrated that stair-climbing V̇o_{2} above the resting level could be reasonably predicted for children with CP from the corresponding increase in HR above rest (dHR), resulting in a correlation of *r* = +0.96 between directly measured and predicted ME_{net}.^{5} In the first study of ME,^{4} with directly measured V̇o_{2}, it was found that gross ME showed less variability than ME_{net} obtained by subtracting the resting metabolic rate. This was in agreement with a previous study of walking efficiency.^{11} However, the subsequent study^{5} using indirectly determined V̇o_{2} showed less variability for ME_{net}, and therefore, that procedure was evaluated.

The stair-climbing task has a potential advantage over walking on a horizontal surface, in that it requires a greater amount of external work that is easily and accurately measured, potentially resulting in lower variability and higher repeatability of metabolic cost within subjects. A cycling task has the disadvantage that it is difficult for children with CP to pedal continuously for a sufficient duration to approach a steady metabolic state. Also, a large number of children with CP cannot pedal despite being ambulatory.^{12}

The aim of this study was to determine the smallest magnitude of change in ME_{net} during self-paced stair climbing that is required to indicate a significant change resulting from interventions. We also wished to determine the ability of ME_{net} to discriminate between levels II and III of the Gross Motor Function Classification System (GMFCS) in children with CP. For comparison, the smallest change that would be significant was also determined for a small group of children with TD.

#### METHODS

The ME_{net} during stair climbing was used as an outcome measure in a study of different treatments in children with CP; 2 tests were done at baseline to document its repeatability and determine the smallest change that could be considered significant beyond the error of measurement.

##### Participants

The children’s parents gave written informed consent for them to participate in a study designed to evaluate “the effect of a motor learning approach in improving walking functions” and for publication of the results. An ethics committee at each of the 3 study sites approved the study. The investigators involved in the subsequent study and the personnel that administered these and other tests were given extensive standardized instructions and practice before the study. A 3-day instructional course was conducted for the researchers of all 3 sites, wherein they learned how to perform the measurements and collect the data, including the computerized collection, downloading, and transferring of data files to the principal investigator. The principal investigator serially supervised the data collection procedures at the 3 sites before the study onset.

The study population for the repeatability tests included 51 children with a diagnosis of diplegic CP. Twenty-one children were classified at level II using GMFCS and 30 at level III.^{13} Nine children with TD were also tested (Table 1) for comparison but were not included in the computation of the smallest significant change for the CP group. The TD group did not differ significantly in age and body mass index (BMI) but were significantly taller and heavier than the children with CP.

##### Stair-Climbing Test and Equipment

The stair-climbing test and equipment have been described in detail in an earlier report.^{5} The dynamic stair trainer (DPE Medical, Shoeva, Israel) was used for measuring external work. It has 4 steps, adjustable from 1 to 17 cm, with adjustable handrails. The stair height was set according to each child’s climbing ability during pretest trials. The height of the steps and the hand rails was chosen to allow the child to use them most effectively, based on the child’s size and leg and arm motor capabilities and reduce the effects of fatigue over the 4-minute duration of the task. The HR was monitored continuously by a Polar Pulsimeter (model S-810; Polar Electro Co., Kempele, Finland). In summary, the external work was calculated from the vertical displacement of the body during stair climbing. The force is the body weight, and the external work is the product of weight and vertical displacement. The number of ascents in a measured time interval (eg, 4 minutes) is counted, and the number of descents is ignored. The energy cost is V̇o_{2} during stair climbing minus resting V̇O_{2} (dV̇O_{2}), calculated in units equivalent to external work (kilojoules). ME_{net} is the resulting external work/energy cost ratio expressed as a percent. Predicted V̇o_{2} for stair climbing, as determined from the previous study,^{5} was calculated as dV̇O_{2} = −251.9 + 7.14 (dHR per minute) + 14.37 (weight in kilograms). Other mechanical factors such as variations of velocity and force exerted by the feet, extraneous arm and torso movements, or horizontal component of the body’s progression will increase the metabolic cost but are not included in the calculation of total external work.^{14}

##### Testing Protocol

Each child was given a detailed explanation of the equipment and then practiced stair climbing. The test was then done twice for familiarization and for setting the height of the stairs. After a sitting rest period of >10 minutes, baseline measurements were made while sitting for 5 minutes on a chair with a backrest and being told a story. Children then walked up and down the stairs continuously for approximately 4 minutes at a self-paced speed, using handrails for assistance if desired. After ascending to the top step, they turned and descended the stairs. Each stair-climbing test was performed twice with a minimum sitting rest period of 30 minutes between tests and after confirming that the resting HR had returned to baseline.

##### Statistics

Paired and unpaired *t* tests and regression analyses were used to analyze data and compute confidence intervals (CIs) and statistical significance (*p* < 0.05). Repeatability was also quantified by the intraclass correlation coefficient (ICC) for unordered pairs, [ICC = (MS_{between} − MS_{within})/(MS_{between} + MS_{within})], and the variability of average scores for each pair as a percentage of total variability (η^{2} = SS_{between}/SS_{total}).

#### RESULTS

The mean and standard deviation (SD) values for ME_{net} (%), external work (kilojoules) and V̇O_{2} (kilojoules) for each group and both combined are given in Table 2. The 51 children with CP demonstrated a strong tendency to increase ME_{net} on test 2 (T2) (*p* = 0.054), which resulted from a nonsignificant 8% increase in external work and a 4% reduction in energy cost compared with test 1 (T1). In the TD group, both external work and energy cost increased significantly from T1 to T2, resulting in minimal change in ME_{net}. The work done was 5.7 times greater for the TD group, but the energy cost was only 1.4 times higher, resulting in 4.3 times greater ME_{net} for children with TD than for the children with CP. Regressions of the T2-T1 difference (*y* axis) versus the mean (*x* axis) were only significant (positive) for external work for the total group.

For quantifying the agreement of ME_{net} values of the 2 tests, the ICC and η^{2} values were 0.93 and 0.96, respectively, for the 51 children with CP (Table 3). For the 9 children with TD and all 60 subjects combined, the ICC values were 0.78 and 0.97 and the η^{2} values were 0.88 and 0.98, respectively. The lower ICC for the TD group resulted from their mean scores being relatively more homogeneous, indicated by their lower coefficient of variation (0.21 vs 0.73 for the children with CP).

Table 3 Image Tools |
Fig. 2 Image Tools |

The percentage scores for ME_{net} for the 2 tests on each of the subject groups are shown in Figure 1. The slope values for the 51 children with CP, the 9 children with TD, and all subjects combined were 1.01, 0.92, and 0.96, respectively, and all not significantly different from 1.00 (*p* > 0.20). Although the mean point of the 9 children with TD is near the overall regression line, a greater variability of ME_{net} between the test pairs is apparent for this group, represented by a significantly larger standard error of the estimate for these 9 children versus the CP group of 51 (*p* < 0.001). To take into account the difference in variability between the high and low scores within and between groups, the percentages of differences [100 × (T2 − T1)/((T1 + T2)/2)] are plotted versus the mean [(T1 + T2)/2] of the scores in Figure 2 for the 51 children with CP, with the scores for the 9 children with TD also shown. This served to reduce the SD of the 30 highest scores to be more similar to the 30 lowest scores, making it possible to more precisely define the test-retest reliability.^{15} For these data, this calculation was superior to the common logarithmic transformation to equalize the variability related to the mean score.^{16}

In Table 3, the CIs of the scores depicted in Figure 2 are summarized for each group, expressed both as the percentage of difference and measured ME_{net} score difference. It is apparent that the CIs for the percentage of differences are more similar between the 2 groups than the differences between the measured scores.

The resultant CI for the percentage of difference in the test scores for the 51 pairs with CP is −38.8% to 54.3%. As the slope value of the regression shown in Figure 2 does not approach significance, it was assumed to be zero. Therefore, an individual with an ME_{net} score of 3.87% on T1 (the mean T1 value for the 51 children) would be expected to score between 2.6% [T1 (200 − 38.8)/(200 + 38.8)] and 6.8% [T1 (200 + 54.3)/(200 − 54.3)] on T2. Similarly, from the CI for the TD group, the T2 score for a T1 of 17.8% (mean from Table 2) would be expected to lie between 12.5% and 24.0%, and T2 for a T1 of 6.0% (the overall mean) would be between 4.0% and 10.1%. Estimates of T2 scores that would be significant were computed from the CI for a sampling distribution from the mean percentage of difference and 1.96× SEM of the difference. For the 51 children with CP, with a SD of percentage of difference of 23.8% (Fig. 2), the percentage of increase in T2_{2} above T1_{2} required to achieve significance is 13.4% [1.68 (one-tailed paired *t* value for significance) × 23.8/√51 + 7.8]. For a T1 score of 3.87%, T2 would need to be >4.39%.

The difference of ME_{net} between levels II and III of GMFCS for the 51 children with CP was significant (*p* < 0.001) with little overlap, with respective means (SD) of 1.2% (1.0%) versus 7.0% (1.0%). Only 1 of the 30 subjects at level III had a score higher than the 2 lowest scores of the 21 children at level II.

#### DISCUSSION

The increase in ME_{net} from T1 to T2 for children with CP could represent a learning effect because there was no increase in TD. ME is a stable index demonstrating the ability to function optimally. The greater heterogeneity in the movements of the children with CP probably allowed for a greater range of options in performing the motor task that might increase ME. For them, each trial could provide neuromotor feedback on how they could optimize their next climbing trial. The children with TD already function with their optimal ME capabilities. On their second trial, the children with CP tried to improve stair climbing, as evidenced by their significantly increased external work. This significantly increased their V̇O_{2} and resulted in unchanged ME values. The percentage of improvement [(T2 − T1)/T1] indicated a trend to be associated with the T1 score for all 60 subjects combined (*r* = −0.22, *P* = 0.09); a negative correlation would be expected if those with lower function had a greater tendency to improve.

The repeatability according to the ICC and η^{2} values seem acceptable; however, it is the CI that must be considered in studies that aim to attribute significant effects of interventions beyond the smallest significant change. If ME_{net} was measured in another group of 51 subjects with CP (T1_{2}) and then measured again after a course of therapy (T2_{2}) to determine improvement, the difference must exceed that predicted from the CI of this repeatability study. The estimated increase in T2 score required for significance for the 51 children with CP was 13.4%. With only 26 subjects (*t*_{0.05} = 1.71), the increase would need to be at least 15.8% (ME_{net} >4.48%) and 19.5% for 13 subjects (ME_{net} >4.62%). For a mean T1 of ME_{net} for the TD group of 17.8%, identical to that in this study, T2 would need to be 1.86 × 16.5/√9 − 3.0 = 7.2% higher or >19.1%. The differences between T1 and T2 from this study can also be used to determine the number of subjects needed to obtain significance for a desired percentage of difference (power test).

As pointed out by Verschuren et al,^{17} objective field tests for CP are lacking. They developed a shuttle test and compared it with treadmill running in 25 subjects and noted acceptable repeatability for exercise time and peak HR. However, their test requires a maximal effort by children and is applicable only to children at GMFCS levels I and II. Bowen et al^{18} determined reproducibility of the physiological cost index and directly measured V̇O_{2} while walking in children with CP. They concluded that directly measured V̇O_{2} was more reproducible than the physiological cost index (average variability of 13.2% and 20.3%, respectively). These values are about twice those found in the current study.

The ME_{net} scores indicated that this test could distinguish between levels II and III of GMFCS. This is in agreement with Johnston et al,^{19} who reported a significant inverse correlation between the energy cost of walking and GMFCS levels I to IV in 30 children, including a 43% higher value in level III than level II. Oeffinger et al^{20} also reported significant associations between GMFCS levels I to III and the energy cost of walking, with a 63% higher value for level III than II. Our percentages of differences of ME_{net} are an order of magnitude higher, indicating a better resolution for a range of motor abilities.

##### Limitations of the Study

The quantification of repeatability described here for children with CP pertains to those having the age, size, and disability characteristics described in Table 1. Values for the small group of children with TD may not be representative because of the small sample size and are given for general comparison only.

##### Summary

Convenience of HR measurement and submaximal, self-paced effort of stair climbing are major advantages of the current test for children with motor dysfunction. This stair-climbing test has demonstrated an acceptable difference of 7.8% in the repeated ME_{net} score in children with CP. From this study, ME_{net} predicted by HR and body weight showing a change of >13.4% (>0.55% of measured ME_{net} score) can account for changes other than test-retest measurement variability in future studies dealing with maturation, treatment, and therapy interventions. This suggests that the metabolic cost of a stair-climbing task, which need not be identical to that used here, can be reasonably sensitive in measuring changes in gross motor function.