Abstract
[Purpose] This study aimed to investigate the usefulness of a quality index in gait for proximal femur fractures. [Participants and Methods] In this study, 20 females with postoperative proximal femur fracture in the preparation phase for discharge (femur fracture group) aged ≥60 years (63.0 ± 3.0 years) and 20 healthy older females (healthy group) participated (75.7 ± 7.7 years) (n=40). Measurements were conducted at comfortable and maximal gait speeds. Power spectrum entropy (PSE), harmonic ratio (HR), and modified HR (mHR), which are smoothness indices, were calculated from the measured data in each of the three axial directions and compared. [Results] The healthy and femur fracture groups showed significant differences in the PSE, HR, and mHR for comfortable and maximal gait speed in the lateral and vertical directions. Furthermore, all directions between the HR and mHR in the femur fracture group had significant differences. [Conclusion] The usefulness of the PSE, HR, and mHR as quality evaluation indices of gait was demonstrated in patients with postoperative femur fractures after unilateral disability.
Keywords: Power spectrum entropy, Harmonic ratio, Accelerometer
INTRODUCTION
The world’s aging population is aging at a rapid rate1). Frailty is observed in many older adults, and these individuals are at a high risk of falls, hospitalization, and impaired activities of daily living (ADLs)2). Furthermore, the need for reducing the disability risk of frailty has been reported3), and the need for rehabilitation is increasing. In rehabilitation, improving walking ability is important to improve the performance of ADLs4). In general, methods for evaluating gait in clinical settings are extensively used to assess comfortable gait speed, maximum gait speed, step length, and cadence using a stopwatch and are considered quantitative indices. In particular, maximum walking speed has been reported to be a useful indicator for evaluating physical performance5). In contrast, recently, the number of reports on the use of accelerometers to evaluate the quality of motion has been increasing6). The smoothness of motion is considered a quality index, and power spectrum entropy (PSE) and harmonic ratio (HR) are representative indices.
The PSE evaluates smoothness based on the probability of overlapping high frequencies and has been reported to provide information about the physical function of individuals who have experienced falls that quantitative measures do not provide7). In this connection, a study using the PSE reported that a task to learn the sensation of load by repeated standing and sitting movements in asymmetrical postures was performed on healthy adults and the smoothness of the quality index improved after the amount of load, a quantitative index, was stabilized8). The HR has been reported to assess regularity, harmony, and symmetry of movements; discriminate between the gait of younger adults and that of older adults9); and elucidate the fall experience of older adults10). In this regard, the reliability and usefulness of HR as an assessment of regularity and asymmetry in gait for unilateral disability after stroke have been reported11, 12). Furthermore, Wada et al.13) reported that preoperative and postoperative gait evaluation of females with osteoarthritis of the hip joint showed improved HR; however, their HR values were lower than those of healthy participants, suggesting residual asymmetry. This suggests that asymmetric motor control and learning are advanced in unilateral disability by repetition of movements in ADL. However, to the best of our knowledge, no studies have reported on postoperative hip injuries, the incidence of which increases rapidly after 60 years of age. Patients with proximal femur fractures are expected to have residual instability and asymmetry in gait. Therefore, this study aimed to investigate the usefulness of quality assessment in gait activities in older healthy participants and patients undergoing hip fracture surgery.
The hypothesis is that the proximal femur fracture group with possible residual instability will have lower gait smoothness than the healthy group. As a result, the proximal femur fracture group will have a lower HR and a higher PSE than the healthy group.
PARTICIPANTS AND METHODS
We conducted a cross-sectional study involving 20 healthy females aged 60 years or older (healthy group) (63.0 ± 3.0 years) and 20 females with proximal femur fracture (femur fracture group) (75.7 ± 7.7 years) (Table 1). The exclusion criteria for the healthy group were as follows: psychiatric, neurological, or musculoskeletal disorders; and history of disease that would affect gait activity. The exclusion criteria for the femur fracture group were as follows: previous history of dementia and the Mini-Mental State Examination (MMSE) score of <24. This study was conducted after receiving approval (2020-012) from the Ethics Committee of Kumamoto Kenhoku Hospital. Ethical consideration was provided to all participants according to the Declaration of Helsinki, and consent was obtained after explaining the content and significance of the study in paper form.
Table 1. Comparison of baseline data of the participants.
| Characteristics | Healthy group (n=20) | Femur fracture group (n=20) | |
| Height (cm) | 154.6 ± 4.9 | 151.1 ± 5.4 | * |
| Age (years) | 63.0 ± 3.0 | 75.7 ± 7.7 | *** |
| Weight (kg) | 53.6 ± 9.3 | 45.7 ± 6.7 | ** |
| BMI (kg/m2) | 22.3 ± 3.3 | 20.0 ± 2.7 | * |
| MMSE (points) | 27.6 ± 2.3 | ||
| Type of hip fracture | |||
| Trochanteric fracture after OLIF | 9 | ||
| Subtrochanteric fracture after OLIF | 2 | ||
| Neck fracture | 9 | ||
| Type of surgery | |||
| OLIF | 3 | ||
| BHA | 3 | ||
| THA | 3 | ||
| Laterality | |||
| Right | 8 | ||
| Left | 12 | ||
| Gait aid | |||
| None without | 20 | 11 | |
| Cane | 0 | 9 | |
| Date of measurement (days after surgery) | 45.8 ± 10.8 | ||
Mean ± SD, *p<0.05, **p<0.01, ***p<0.001.
BMI: body mass index; MMSE: mini-mental state examination, OLIF: open reduction internal fixation; BHA: bipolar hemiarthroplasty, THA: total hip arthroplasty.
Measurements were taken using the 9-axis wireless motion sensor SS-MS-HMA16G15 (Sports Sensing Inc., Fukuoka, Japan). The nine axes comprised acceleration (16G) (3 axes), angular velocity (1,500 degrees/second) (3 axes), and geomagnetic sensor (10 Gauss) (3 axes). An elastic band was attached to the motion sensors so that these motion sensors were positioned at the third lumbar spinous process (L3) of the participants according to the method proposed by Moe-Nilssen14). The sampling frequency was set to 100 Hz. Gait was measured for a steady 10-m gait with a 3-m auxiliary path in front of and behind the participants. Two types of task motions were used: comfortable speed (CS) and maximum speed (MS) gait. The instructions were “please walk as usual” for CS gait and “please walk as fast as possible” for MS gait. Rest periods between the tasks were at least 10 s, and no fatigue was verbally confirmed before moving on to the next measurement. The femur fracture group was measured seven weeks postoperatively during the preparation for discharge from the hospital at the level of independence in walking activities.
The analysis parameters were the PSE and HR. Analysis was performed after Butterworth low-pass filter processing at 20 Hz15). For gait analysis, the effect of gravity was corrected by the average value of acceleration in each of the three axes in the resting standing position in triaxial acceleration data15, 16). Steps were cut out with the heel contact as the point of peak before the acceleration in the longitudinal direction changed from positive to negative17). For triaxial composite direction analysis, the acceleration in each of the three directions was squared and the square root of the added values was used.
The PSE was calculated from time series spectra obtained by fast Fourier transform using Hanning’s window function, excluding the first component, and normalized7, 18). Analysis intervals were cut out using 4–5 gait cycles as a guide7) and calculated from 512 points (5.12 s) in between.
The HR was discrete Fourier transformed (DFT) for one gait cycle to evaluate the regularity and harmonicity of each step, and the 20th harmonic coefficients were included in the analysis. The HR was calculated as odd/even for the lateral direction and even/odd for the vertical direction, longitudinal direction, and triaxial composite15, 19, 20). Then, two gait cycles were used for DFT to evaluate discipline and harmony per gait cycle, and the modified HR (mHR) was calculated up to the 40th harmonic coefficient for analysis. The mHR was calculated as even/odd for all directions. The representative values of the HR and mHR were the average of the values calculated from five gait cycles of triaxial acceleration data.
The normality of the data was assessed using the Shapiro–Wilk test, and equal variance was checked using the Levene test. Gait speed was compared between the femur fracture and healthy groups using a two-sample t-test and analysis of covariance adjusted for age and body mass index (BMI) as covariates. To compare the HR and PSE, the two-sample t-test and Mann–Whitney U-test were used. The mHR was compared using the Wilcoxon signed-rank test. The effect size was calculated as (r), where r=0.1, 0.3, and 0.5 for small, medium, and large, respectively. The significance level was set to 5%. Statistical analyses were performed using R4.2.1 (CRAN, freeware) for Windows. The sample size for this study was calculated using G*Power 3.1.9.7 (Heinrich Heine University, Dusseldorf, Germany)21). The significance level was set to α=0.05, power was set to 1-β=0.8, effect size (d)=0.916 was assumed in a pilot study of 10 participants, and the minimum number of participants in the group was recommended to be 20.
RESULTS
In a comparison of gait speeds, the healthy group was significantly faster than the femur fracture group in both CS (p<0.001, r=0.76) and MS (p<0.001, r=0.83) gait. The results of the analysis of covariance showed significant differences in MS gait (p<0.020), although the effects of age and BMI were excluded (Table 2).
Table 2. Comparison of gait speed between healthy group and femur fracture group.
| Gait speed (m/s) | Healthy group | Femur fracture group | † | Effect size | ‡ |
| CS | 1.44 ± 0.18 | 0.95 ± 0.18 | *** | 0.76 | |
| MS | 1.89 ± 0.23 | 1.13 ± 0.29 | *** | 0.83 | * |
Mean ± SD, *p<0.05, ***p<0.001.
†: two-sample t-test, ‡: analysis of covariance.
CS: comfortable speed; MS: maximum speed; SD: standard deviation.
PSE comparisons showed that the healthy group had significantly lower CS gait values in all directions (lateral: p<0.001, r=0.64; vertical: p<0.001, r=0.74; longitudinal: p=0.010, r=0.40; triaxial: p<0.001, r=0.76). MS gait was significantly lower in the healthy group, except for the longitudinal direction (lateral: p<0.001, r=0.59; vertical: p=0.002, r=0.48; triaxial: p=0.003, r=0.46) (Table 3).
Table 3. Comparison of PSE estimated for CS and MS gait motions.
| PSE (bit) | Healthy group | Femur fracture group | Effect size | |
| CS | ||||
| Lateral | 5.81 ± 0.21 | 6.10 ± 0.12 | *** | 0.64 |
| Vertical | 5.49 ± 0.19 | 5.90 ± 0.15 | *** | 0.74 |
| Longitudinal | 5.72 ± 0.21 | 5.88 ± 0.15 | * | 0.40 |
| Triaxial | 5.65 ± 0.21 | 5.92 ± 0.09 | *** | 0.76 |
| MS | ||||
| Lateral | 5.85 ± 0.19 | 6.09 ± 0.15 | *** | 0.59 |
| Vertical | 5.65 ± 0.24 | 5.88 ± 0.19 | ** | 0.48 |
| Longitudinal | 5.82 ± 0.21 | 5.90 ± 0.16 | 0.27 | |
| Triaxial | 5.75 ± 0.16 | 5.89 ± 0.13 | ** | 0.46 |
Mean ± SD, *p<0.05, **p<0.01, ***p<0.001.
PSE: power spectrum entropy; CS: comfortable speed, MS: maximum speed; SD: standard deviation.
HR comparisons showed that the healthy group had significantly higher CS (lateral: p<0.001, r=0.73; vertical: p<0.001, r=0.76; longitudinal: p<0.001, r=0.71; triaxial: p<0.001, r=0.69) and MS (lateral: p<0.001, r=0.68; vertical: p<0.001, r=0.58; longitudinal: p<0.001, r=0.56; triaxial: p<0.001, r=0.51) gait values in all directions (Table 4).
Table 4. Comparison of HR estimated for CS and MS gait motions.
| HR | Healthy group | Femur fracture group | Effect size | |
| CS | ||||
| Lateral | 2.82 ± 0.68 | 1.71 ± 0.44 | *** | 0.73 |
| Vertical | 3.83 ± 0.75 | 2.23 ± 0.65 | *** | 0.76 |
| Longitudinal | 3.71 ± 1.05 | 2.11 ± 0.67 | *** | 0.71 |
| Triaxial | 2.87 ± 0.63 | 1.80 ± 0.52 | *** | 0.69 |
| MS | ||||
| Lateral | 3.01 ± 0.86 | 1.72 ± 0.53 | *** | 0.68 |
| Vertical | 3.11 ± 0.85 | 2.08 ± 0.68 | *** | 0.58 |
| Longitudinal | 3.80 ± 1.51 | 2.37 ± 0.83 | *** | 0.56 |
| Triaxial | 2.53 ± 0.69 | 1.83 ± 0.51 | *** | 0.51 |
Mean ± SD, ***p<0.001.
HR: harmonic ratio; CS: comfortable speed, MS: maximum speed; SD: standard deviation.
Regarding mHR comparisons, the healthy group had significantly higher CS gait values in all directions (lateral: p<0.001, r=0.72; vertical: p<0.001, r=0.67; longitudinal: p<0.001, r=0.72; triaxial: p<0.001, r=0.59). The maximum gait speed was significantly higher in the healthy group, except for the triaxial composite (lateral: p<0.001, r=0.60; vertical: p=0.036, r=0.33; longitudinal: p=0.017, r=0.38) (Table 5).
Table 5. Comparison of mHR estimated for CS and MS gait motions.
| mHR | Healthy group | Femur fracture group | Effect size | |
| CS | ||||
| Lateral | 3.38 ± 0.92 | 2.22 ± 0.52 | *** | 0.72 |
| Vertical | 3.98 ± 0.70 | 2.81 ± 0.63 | *** | 0.67 |
| Longitudinal | 4.20 ± 0.68 | 2.88 ± 0.62 | *** | 0.72 |
| Triaxial | 3.14 ± 0.77 | 2.35 ± 0.46 | *** | 0.59 |
| MS | ||||
| Lateral | 3.28 ± 0.87 | 2.21 ± 0.55 | *** | 0.60 |
| Vertical | 3.62 ± 1.05 | 2.95 ± 0.88 | * | 0.33 |
| Longitudinal | 3.83 ± 1.10 | 3.03 ± 0.91 | * | 0.38 |
| Triaxial | 2.80 ± 0.79 | 2.45 ± 0.66 | 0.24 |
Mean ± SD, *p<0.05, ***p<0.001.
mHR: modified harmonic ratio; CS: comfortable speed, MS: maximum speed; SD: standard deviation.
Regarding HR and mHR comparison, the HR was significantly lower in the healthy group for CS gait in the lateral direction (p=0.030, r=0.48). The femur fracture group had significantly lower HR values in all directions for both CS (lateral: p=0.030, r=0.62; vertical: p=0.003, r=0.61; longitudinal: p<0.001, r=0.67; triaxial: p=0.002, r=0.64) and MS gait (lateral: p=0.008, r=0.56; vertical: p<0.001, r=0.74; longitudinal: p=0.029, r=0.48; triaxial: p<0.001, r=0.67) (Table 6).
Table 6. Comparison of HR and mHR in healthy group and femur fracture group.
| HR | mHR | Effect size | ||
| Healthy group | ||||
| CS | ||||
| Lateral | 2.82 ± 0.68 | 3.38 ± 0.92 | * | 0.48 |
| Vertical | 3.83 ± 0.75 | 3.98 ± 0.70 | 0.16 | |
| Longitudinal | 3.71 ± 1.05 | 4.20 ± 0.68 | 0.42 | |
| Triaxial | 2.87 ± 0.63 | 3.14 ± 0.77 | 0.27 | |
| MS | ||||
| Lateral | 3.01 ± 0.86 | 3.28 ± 0.87 | 0.37 | |
| Vertical | 3.11 ± 0.85 | 3.62 ± 1.05 | 0.39 | |
| Longitudinal | 3.80 ± 1.51 | 3.83 ± 1.10 | 0.02 | |
| Triaxial | 2.53 ± 0.69 | 2.80 ± 0.79 | 0.29 | |
| Femur fracture group | ||||
| CS | ||||
| Lateral | 1.71 ± 0.44 | 2.22 ± 0.52 | * | 0.62 |
| Vertical | 2.23 ± 0.65 | 2.81 ± 0.63 | ** | 0.61 |
| Longitudinal | 2.11 ± 0.67 | 2.88 ± 0.62 | *** | 0.67 |
| Triaxial | 1.80 ± 0.52 | 2.35 ± 0.46 | ** | 0.64 |
| MS | ||||
| Lateral | 1.72 ± 0.53 | 2.21 ± 0.55 | ** | 0.56 |
| Vertical | 2.08 ± 0.68 | 2.95 ± 0.88 | *** | 0.74 |
| Longitudinal | 2.37 ± 0.83 | 3.03 ± 0.91 | * | 0.48 |
| Triaxial | 1.83 ± 0.51 | 2.45 ± 0.66 | *** | 0.67 |
Mean ± SD, *p<0.05, **p<0.01, ***p<0.001.
HR: harmonic ratio; mHR: modified harmonic ratio, CS: comfortable speed; MS: maximum speed; SD: standard deviation.
DISCUSSION
A systematic review reported that CS was 1.24 m/s for females in their 60s and 1.13 m/s for females in their 70s22). Alcazar et al.23) reported that MS was 1.9 m/s for females above 60 years of age (mean age, 73.0 years). In Japan, it has been reported that CS is 1.06 m/s and MS is 1.64 m/s in females above 65 years of age, and that the rate of decline in gait ability increases after 70 years of age24). CS and MS of the femur fracture group in this study were 0.95 m/s and 1.13 m/s, respectively, which tended to be lower than those reported in previous studies. In particular, significant differences in MS using age and BMI as covariates were observed in the analysis of covariance, suggesting the possibility of residual effects of proximal femur fracture.
The PSE has been reported to be smoother with lower values7, 18). In this study, CS was significantly lower in the healthy group in all directions, although MS was not significantly different in the longitudinal direction. Furthermore, the effect size (r) in the longitudinal direction was 0.4 for CS and 0.27 for MS, which were lower than those in the other directions. The PSE is reported to be unaffected by gait speed7). However, the difference in MS between the two groups in this study was larger than that reported in a previous study, suggesting that the PSE in the longitudinal direction is more sensitive to speed than what was shown in the previous study. Nevertheless, the PSE in the lateral, vertical, and triaxial composite directions in CS and the PSE in the lateral direction in MS were suggested to be useful indices with a large effect size (r).
The HR decreases in all directions in participants at a high risk of falls10). In this study, the healthy group had significantly higher values and larger effect sizes (r) in all directions for CS and MS. Thus, the femur fracture group was considered at a high risk of falls because of decreased smoothness, although they were independent in mobility and were preparing for discharge from the hospital. Furthermore, the HR has been reported to quantify symmetry19), and the lateral HR in the femur fracture group was lower than that in the vertical and longitudinal directions, suggesting a significant loss of symmetry in the lateral direction.
For the mHR, we evaluated two steps (one stride) as one cycle, whereas the HR evaluated one step as one cycle. Bellanca et al.19) stated that harmonic coefficients should be increased as required. In this study, the frequency band was adjusted to include up to 40 harmonic coefficients in the analysis because this approximately doubles the number of data used to calculate a single mHR. The results showed an increase in the mHR values in the femur fracture group compared to HR values, and no significant difference was observed in the triaxial composite of MS. Therefore, our results suggest that it is useful to assess the mHR in addition to the HR for evaluation after unilateral disability.
Regarding the comparison between the HR and mHR, Kavanagh et al.25) reported less smoothness in the mediolateral direction in older adults, and Brach et al.8) reported a decrease in the HR in the longitudinal direction even in older adults without a decrease in gait speed. These findings suggest that older healthy females have decreased symmetry and smoothness. Significant differences in the lateral direction were observed in the healthy group of this study, suggesting a decrease in symmetry and smoothness in one step. In contrast, the healthy group showed no significant differences in CS in the vertical, longitudinal, and triaxial composite directions and MS in all directions, whereas the femur fracture group showed significant differences in CS and MS in all directions. This suggests that in healthy older participants, the HR values for symmetry and smoothness at one step and the mHR values analyzed up to 40 harmonic coefficients for symmetry and smoothness at one stride are comparable in value. Furthermore, the comparison of the HR and mHR in the femur fracture group showed significant differences in all directions, indicating that the mHR was improved in the condition of hospital discharge preparation. Therefore, if one step per improvement is insufficient, the HR will be low. However, if the strategy for each stride was acquired, the mHR would improve. These results suggest that mHR may serve as an indicator of the acquisition of mobility.
This study has some limitations. First, we compared a group of healthy older females ≥60 years of age and a femur fracture group, and removing all significant baseline differences in different factors, such as age and BMI, was difficult, and thus, generalizing the results of this study is difficult.
Funding and Conflict of interest
None.
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