Abstract
Independent control of the right and left ankles (differentiation) may be a motor control mechanism linking impaired coordination and mobility limitations. We tested the hypotheses that motor control differentiation of the ankles, as measured using Cross-Sample Entropy, during antiphase coordination at two movement frequencies, is associated with impaired coordination (high ankle coordination variability) and mobility limitations (Short Physical Performance Battery score ≤9). We conducted a cross-sectional study of community-dwelling older adults (N=133) aged 80.04 (±4.67) years. In linear regression modeling, low ankle Cross-Sample Entropy (low motor control differentiation) was associated with poor (i.e., high) coordination variability at the slower (P = 0.026), but not the faster (P = 0.447), ankle movement frequency. In logistic regression modeling, low Cross-Sample Entropy at the slower (OR = 1.67; 95% CI: 1.07–2.59) and faster (OR = 2.38; 95% CI: 1.43–3.94) ankle movement frequencies were associated with increased odds for mobility limitations. Our findings support the hypothesis that ankle differentiation may be a motor control mechanism that links impaired coordination with mobility limitations.
Keywords: ankle, coordination, differentiation, mobility
Introduction
An estimated 25% of adults aged 70 years and older have mobility limitations that negatively impact their ability to perform activities such as walking, balancing, and rising from a chair [28]. Worldwide, almost two thirds of people over 70 years of age suffer from gait disorders [43]. Because of the progressively ageing population, increasing pressure on health care systems is expected in the coming years due to mobility limitations [43]. Impairments in strength, range of motion, and balance have been identified as contributors to mobility limitations [1]. Central factors, such as white matter hyperintensities, gray matter atrophy, and altered functional connectivity are also associated with mobility limitations [16, 35, 36]. Despite advances in the understanding of the factors that contribute to mobility limitations in older adults, further study is needed to clarify the mechanisms by which altered motor control contributes to mobility limitations.
Rhythmic antiphase ankle coordination is a recently identified impairment that contributes to mobility limitations [17, 18]. Rhythmic ankle coordination is the ability to produce consistently timed movements of the ankles. Antiphase coordination is simultaneous movement of limb segments in opposite directions. While impaired coordination has been identified as a contributor to mobility limitations, the motor control mechanisms by which this type of impairment contributes to mobility limitations have not been well established. In this paper we extend this research by investigating one possible neural mechanism that may mediate the relationship between impaired coordination and mobility limitations.
The ability to produce antiphase (alternate bilateral muscle activation) interlimb coordination is dependent upon the neural inhibition of the default inphase (simultaneous bilateral muscle activation) coupling of body segments [26, 45]. Neural dedifferentiation has been associated with decreased interhemispheric inhibition during motor task performance [25]. Neural dedifferentiation is brain activation that is more diffuse and bilaterally symmetrical among older adults, compared to young adults, during motor and cognitive tasks [2, 5, 6, 32, 44] that correlates with decreased task performance.
It is possible that neural dedifferentiation, and the consequent decreased interhemispheric inhibition [12, 25, 26], may contribute to decreased motor control differentiation. Motor control differentiation is the degree to which body segments are controlled independently, rather than as a single degree of freedom. Neural dedifferentiation may contribute to decreased inhibition of the inphase neural coupling of limbs, resulting in poor performance of antiphase coordination. It is currently unknown if less differentiated control of body segments is associated with impaired coordination or mobility limitations among older adults.
On the one hand, the neuromotor system harnesses the numerous degrees of freedom (e.g., muscles, body segments) into lower dimensional units of control [3], which could lead to speculation that less differentiated control could be associated with better mobility. On the other hand, the relationship between motor control differentiation and motor performance has been shown to depend upon the type of task [29, 42], and prior research has shown that less differentiated motor control is associated with poorer (i.e., more variable) antiphase coordination [19]. These findings suggest that less differentiated motor control may be associated with poorer mobility.
To address this question, we conducted a cross-sectional study of community-dwelling older adults to test the hypotheses that low ankle differentiation is associated with high ankle coordination variability and mobility limitations, even after adjustment for several possible confounders. We examined ankle coordination performance at two movement frequencies, as coordination variability [20, 24] and attentional cost [11, 23] vary as a function of movement frequency.
Method
Participants
Community-dwelling older adults aged 67 to 94 years were recruited for this study. The study was approved by the Institutional Review Board at the University of Massachusetts Lowell and all participants provided written informed consent. The study was performed in accordance with relevant guidelines and regulations.
Inclusion/exclusion criteria
Inclusion criteria were age 65 years or older, ability to speak and understand English, able to walk 20 feet without personal assistance, sufficient vision to read written material, and sufficient hearing to synchronize movements with auditory metronome tones. Exclusion criteria were moderate to severe cognitive impairment defined as a Mini-Mental State Examination (MMSE) score of less than 18 [9], diagnosis of a terminal disease, Parkinson’s disease, Alzheimer’s disease, stroke, multiple sclerosis, any neuromuscular, cardiopulmonary, or orthopedic condition that would impair movement of the ankles.
Ankle Coordination Task Procedure
Participants were positioned supine on a physical therapy table with their knees and lower legs supported to allow unrestricted movement of the ankles. Orthoses that confined ankle movements to dorsi-plantarflexion were placed on each foot and lower leg. A Qualisys (Gothenburg, Sweden) 8-camera motion capture system with reflective markers collected kinematic data on the angular position of the ankles at a sampling rate of 100 Hz. A standard coordination synchronization protocol [20] was used to assess antiphase (moving the right and left ankles simultaneously in opposite directions) coordination variability. Participants were instructed to move their right and left ankles in antiphase coordination in synchronization with auditory metronome tones paced for movement frequencies of 0.5 and 1.0 Hz. We selected 0.5 and 1.0 Hz movement frequencies as older adults are more likely to spontaneously transition from antiphase to inphase coordination at higher movement frequencies [12]. Participants performed one trial at each movement frequency.
Assessment of Mobility Limitations
Mobility limitations were assessed using the Short Physical Performance Battery (SPPB). The SPPB is a well-validated measure of mobility performance that has been shown to predict hospitalization and disability [13, 14, 30]. The SPPB includes measures of usual-paced walking speed, time to rise from a chair five times, and standing balance [14]. Higher SPPB scores (maximum score = 12) represent better performance. Presence of mobility limitations was defined according to an established cut-point, a total SPPB score ≤ 9 [14].
Demographics and Comorbidities
Demographic characteristics examined were age, gender, race, and educational level. Several potential confounders of the relationship between ankle differentiation, ankle coordination variability, and mobility limitations were measured. Body Mass Index (BMI) was calculated as measured weight in kilograms divided by height in meters squared. Cognitive status was measured using the MMSE [10]. Executive function was estimated as the difference between the Trail Making Tests Part A and B (TMT Delta). The Trail Making Test (TMT) Part A consists of numbered targets that must be connected sequentially, and provides information about visual attention and psychomotor speed [27, 41]. TMT Part B consists of numbered and lettered targets that are to be connected in alternating succession. A shorter time on each TMT test reflects better performance. The TMT Delta provides an estimate of executive functioning [4, 7, 8] and is sensitive to the presence of frontal-executive cognitive impairment and cerebrovascular risk [31]. TMT Delta was calculated by subtracting the time to perform Part A from Part B. Taking the difference between these times controls for motor speed.
Participants were asked if a physician had ever told them that they had heart disease (myocardial infarction, atrial fibrillation, pacemaker, angina, or congestive heart failure), high blood pressure, high cholesterol, diabetes, gastric ulcer, kidney disease, liver disease, anemia, cancer, depression, osteoarthritis, spinal stenosis, rheumatoid arthritis, gout, lung disease (asthma, emphysema, chronic bronchitis, or chronic obstructive lung disease), multiple sclerosis, or eye disease (such as glaucoma, cataracts, or macular degeneration).
Data analysis
Rhythmic ankle coordination variability was measured using an established measure of interlimb coordination, the standard deviation of the relative phase between right and left body segments [22]. Relative phase was calculated from angular position data using the established point estimate method [21] from the first 20 relative phase values of both flexion and extension. Ankle control differentiation was assessed using Cross-Sample Entropy Cross-Sample Entropy is a nonlinear time series measure of the asynchrony between two signals (e.g., movements of the right and left ankles) and provides an estimate of the degree of differentiation in the control of two body segments [39, 42]. We calculated Cross-Sample Entropy using parameter values of m = 2 and r = 0.2 SD [33]. Lower Cross-Sample Entropy values indicate body segments are controlled more as a single degree of freedom, whereas higher values indicate body segments are controlled more independently.
Statistical analyses
Initially, we calculated the frequencies and proportions for categorical variables and the means and standard deviations for continuous variables. Evaluation of the assumption of normality of residuals was confirmed by inspection and possible collinearity of independent variables was examined. We conducted an interquartile-range analysis to search for potential outliers in the data. We then created a multivariable linear regression model evaluating the association of Cross-Sample Entropy with ankle coordination variability. Third we created a multivariable logistic regression model evaluating the association of Cross-Sample Entropy and ankle coordination variability and mobility limitation, generating adjusted odds ratios and 95% confidence intervals. In each model we adjusted for age, gender, number of chronic conditions, MMSE score, and TMT Delta. Inferential statistical analysis was performed using IBM SPSS software (version 22) with a Type I error rate of 0.05.
Results
Characteristics of the study sample are presented in Table 1. Participants with mobility limitations were an average age of 81 years (range 70 to 89 years) of age, slightly older than those without limitations who had a mean age of 79 years (range 67 to 94 years). The test for outliers resulted in no outliers being found. Those with and without mobility limitations were 62%, and 64% female, respectively. Those with and without mobility limitations had an average of 5 and 4 chronic conditions, respectively. During the antiphase coordination task no participants transitioned to inphase coordination.
Table 1.
Demographic and health characteristics of study participants.
| Mobility limitations (n = 37) | No mobility limitations (n = 96) | ||
|---|---|---|---|
| Characteristics | Mean ± SD (Range) |
Mean ± SD (Range) |
P |
| Age (years) | 81.16 ± 4.12 (70–89) |
79.44 ± 4.66 (67–94) |
0.041 |
| % Female | 62.20 | 63.50 | 0.885 |
| Education (years) | 13.84 ± 2.17 (10–19) |
13.11 ± 2.67 (7–19) |
0.111 |
| BMI | 27.98 ± 5.11 (16.97–41.13) |
26.97 ± 4.82 (17.85–41.38) |
0.307 |
| # chronic conditions | 5.35 ± 3.66 (1–16) |
4.06 ± 2.37 (0–9) |
0.053 |
| MMSE score | 27.00 ± 2.68 (19–30) |
27.76 ± 2.12 (22–30) |
0.127 |
| Trail Making Test A (sec) | 44.21 ± 16.19 (18.63–86.19) |
35.27 ± 11.35 (19.44–75.44) |
0.003 |
| Trail Making Test B (sec) | 114.36 ± 51.97 (44.12–239.00) |
83.41 ± 29.67 (26.53–155.00) |
0.001 |
| Trail Making Test Delta (sec) | 70.15 ± 42.94 (9.00–166.70) |
48.14 ± 25.79 (3.60–120.50) |
0.005 |
| Gait speed (m/s) | 0.87 ± 0.20 (0.31–1.28) |
1.11 ± 0.20 (0.54–1.53) |
<0.001 |
| SPPB score | 7.08 ± 2.29 (1–9) |
11.03 ± 0.80 (10–12) |
<0.001 |
| Mean deviation of relative phase from 180° (deg) | |||
| 0.5 Hz | 16.27 ± 12.23 (0.90–40.93) |
10.33 ± 8.98 (0.00–45.93) |
0.014 |
| 1.0 Hz | 19.24 ± 15.79 1.78–68.95 |
11.02 ± 9.79 (0.00–57.7) |
0.005 |
| Ankle coordination variability (deg) | |||
| 0.5 Hz | 28.90 ± 7.00 (17.48–49.52) |
28.01 ± 9.45 (10.41–53.25) |
0.556 |
| 1.0 Hz | 28.50 ± 7.11 (16.06–52.82) |
24.46 ± 7.55 (10.44–44.41) |
0.005 |
| Cross-Sample Entropy | |||
| 0.5 Hz | 2.83 ± 0.26 (2.15–3.33) |
2.96 ± 0.27 (2.07–3.60) |
0.018 |
| 1.0 Hz | 2.59 ± 0.11 (2.33–2.77) |
2.69 ± 0.15 (2.28–3.07) |
<0.001 |
Abbreviations: BMI = Body Mass Index; Hz = Hertz; Max = maximum; Min = minimum; MMSE = Mini-Mental State Examination; SD = standard deviation.
Table 2 presents the adjusted multivariable linear regression models evaluating the association of Cross-Sample Entropy with coordination variability at the 0.5 and 1.0 Hz coordination task frequencies. TMT Delta was associated with ankle coordination variability at the faster (β = 0.006; 95% CI: 0.001 – 0.011), but not the slower (β = 0.001; 95% CI: −0.005 – 0.006) movement frequency. Cross-Sample Entropy was associated with ankle coordination variability at the slower (β = −0.184; 95% CI: −0.356 – −0.012) but not the faster (β = 0.009; 95% CI: −0.169 – 0.186) movement frequency.
Table 2.
Multivariable linear regression evaluating the association of Cross-Sample Entropy with ankle coordination variability.
| Variable | Estimate | SE | 95% CI | P |
|---|---|---|---|---|
| Model 1: 0.5 Hz movement frequency. | ||||
| Age | 0.016 | 0.020 | −0.023 – 0.087 | 0.416 |
| Sex | −0.468 | 0.178 | −0.820 – −0.116 | 0.010 |
| # chronic conditions | −0.033 | 0.030 | −0.093 – 0.027 | 0.281 |
| MMSE score | −0.010 | 0.039 | −0.087 – 0.068 | 0.808 |
| Trail Making Tests Delta | 0.001 | 0.003 | −0.005 – 0.006 | 0.786 |
| Cross-Sample Entropy | −0.184 | 0.087 | −0.356 – −0.012 | 0.036 |
| Model 2: 1.0 Hz movement frequency. | ||||
| Age | 0.014 | 0.020 | −0.025 – 0.053 | 0.483 |
| Sex | −0.110 | 0.179 | −0.465 – 0.244 | 0.539 |
| # chronic conditions | 0.020 | 0.030 | −0.040 – 0.080 | 0.513 |
| MMSE score | −0.013 | 0.039 | −0.065 – 0.091 | 0.740 |
| Trail Making Tests Delta | 0.006 | 0.003 | 0.001 – 0.011 | 0.045 |
| Cross-Sample Entropy | 0.009 | 0.090 | −0.169 – 0.186 | 0.924 |
Abbreviations: Hz = Hertz; MMSE, Mini-Mental State Examination. N = 133 in both models.
Coefficients are based on 1 standard deviation units of ankle coordination and Cross-Sample Entropy.
Table 3 presents the adjusted multivariable logistic regression models evaluating the odds for having mobility limitations. TMT Delta was associated with mobility limitations in regression models f both the slow (OR = 1.020; 95% CI: 1.006 – 1.034) and fast (OR =. 1.019; 95% CI: 1.005 – 1.034) ankle movement frequencies. The odds for having mobility limitations based on a 1 standard deviation difference in ankle coordination variability were significant at the faster (OR = 1.595; 95% CI: 1.009 – 2.521) but not the slower (OR = 0.998; 95% CI: 0.647 – 1.538) movement frequency. The odds for having mobility limitations based on a 1 standard deviation difference in ankle Cross-Sample Entropy were significant for the slower (OR = 1.680; 95% CI: 1.059 – 2.665) and faster (OR = 2.401; 95% CI: 1.386 – 4.159) movement frequencies.
Table 3.
Association between Cross-Sample Entropy and ankle coordination variability with mobility limitations (SPPB score ≤ 9).
| Variable | OR (95% CI)* | P |
|---|---|---|
| Model 1: 0.5 Hz movement frequency | ||
| Age | 1.053 (0.952 – 1.164) | 0.316 |
| Sex | 0.780 (0.309 – 1.968) | 0.599 |
| # chronic conditions | 1.189 (1.015 – 1.393) | 0.032 |
| MMSE score | 0.897 (0.740 – 1.088) | 0.269 |
| Trail Making Tests Delta | 1.020 (1.006 – 1.034) | 0.004 |
| Ankle coordination variability | 0.998 (0.647 – 1.538) | 0.992 |
| Ankle Cross-Sample Entropy | 1.680 (1.059 – 2.665) | 0.028 |
| Model 2: 1.0 Hz movement frequency | ||
| Age | 1.025 (0.923 – 1.138) | 0.643 |
| Sex | 0.750 (0.287 – 1.959) | 0.558 |
| # chronic conditions | 1.200 (1.025 – 1.406) | 0.024 |
| MMSE score | 0.929 (0.758 – 1.139) | 0.480 |
| Trail Making Tests Delta | 1.019 (1.005 – 1.034) | 0.010 |
| Ankle coordination variability | 1.595 (1.009 – 2.521) | 0.046 |
| Ankle Cross-Sample Entropy | 2.401 (1.386 – 4.159) | 0.002 |
Abbreviations: CI, confidence interval; Hz = hertz; MMSE, Mini-Mental State Examination; OR, odds ratio. N = 133 in both models.
Odds ratios presented are based on a 1 standard deviation difference in ankle coordination and a −1 standard deviation difference in Cross-Sample Entropy.
Results from logistic regression with adjustment for gait speed are presented in Table 4. TMT Delta was associated with mobility limitations in regression models of both the slow (OR = 1.020; 95% CI: 1.006 – 1.035) and fast (OR =. 1.019; 95% CI: 1.004 – 1.034) ankle movement frequencies. The odds for having mobility limitations based on a 1 standard deviation difference in the variability of ankle coordination at the slower (OR = 0.888; 95% CI: 0.555 – 1.422) and faster (OR = 1.526; 95% CI: 0.960 – 2.426) were not significant. The odds for having mobility limitations based on a 1 standard deviation in ankle Cross-Sample Entropy were significant for the slower (OR = 1.976; 95% CI: 1.181 – 3.307) and faster (OR = 2.321; 95% CI: 1.340 – 4.019) movement frequencies.
Table 4.
Association between Cross-Sample Entropy and ankle coordination variability with mobility limitations (SPPB score ≤ 9), with adjustment for gait speed.
| Variable | OR (95% CI)* | P |
|---|---|---|
| Model 1: 0.5 Hz movement frequency | ||
| Age | 0.994 (0.890 – 1.111) | 0.919 |
| Sex | 1.129 (0.416 – 3.061) | 0.812 |
| # chronic conditions | 1.088 (0.912 – 1.299) | 0.350 |
| MMSE score | 0.920 (0.756 – 1.121) | 0.408 |
| Trail Making Tests Delta | 1.020 (1.006 – 1.035) | 0.006 |
| Gait speed | 1.420 (1.098 – 1.836) | 0.008 |
| Ankle coordination variability | 0.888 (0.555 – 1.422) | 0.622 |
| Ankle Cross-Sample Entropy | 1.976 (1.181 – 3.307) | 0.010 |
| Model 2: 1.0 Hz movement frequency | ||
| Age | 0.972 (0.866 – 1.091) | 0.634 |
| Sex | 0.913 (0.330 – 2.527) | 0.861 |
| # chronic conditions | 1.127 (0.952 – 1.335) | 0.165 |
| MMSE score | 0.956 (0.777 – 1.177) | 0.673 |
| Trail Making Tests Delta | 1.019 (1.004 – 1.034) | 0.012 |
| Gait speed | 1.356 (1.046 – 1.759) | 0.022 |
| Ankle coordination variability | 1.526 (0.960 – 2.426) | 0.074 |
| Ankle Cross-Sample Entropy | 2.321 (1.340 – 4.019) | 0.003 |
Abbreviations: CI, confidence interval; Hz = hertz; MMSE, Mini-Mental State Examination; OR, odds ratio. N = 133 in both models.
Odds ratios presented are based on a 1 standard deviation difference in ankle coordination and a −1 standard deviation difference in Cross-Sample Entropy.
Discussion
The findings supported our hypotheses that low ankle control differentiation is associated with poor (high) ankle coordination variability (at the slower movement frequency) and mobility limitations. Prior research in young adults found that less variable (better) rhythmic interlimb antiphase coordination is associated with more differentiated limb control [19]. To our knowledge, the present study is the first to observe this relationship among older adults, and to demonstrate that less differentiated motor control is associated with mobility limitations.
Low ankle control differentiation consists of controlling the two ankles more as a single unit, rather than more independently. Low ankle differentiation may be a motor control mechanism that links the previously found association of poor ankle coordination with mobility limitations [17, 18]. Ankle coordination variability was associated with mobility limitations only at the faster movement speed, while ankle control differentiation at both movement frequencies was associated with limitations. This may indicate that ankle differentiation has a more consistent and sensitive association with mobility limitations than does coordination variability. This conclusion is supported by the finding that ankle control differentiation at both ankle movement frequencies was associated with mobility limitations even after adjustment for gait speed. The latter finding also suggests that ankle control differentiation may be associated with performance on the SPPB tasks other than gait speed (chair rise and balance), though further work is needed to confirm this.
We found that decreased ankle control differentiation is associated with mobility limitations and higher ankle coordination variability (at the slower movement frequency). Neural dedifferentiation has been associated with decreased interhemispheric inhibition [12, 25, 26] and neural inhibition of the bilateral inphase coupling of the ankles to produce antiphase coordination [26, 45]. We speculate that low ankle control differentiation may reflect the decreased interhemispheric inhibition that accompanies neural dedifferentiation of the neuromotor system. If this is the case, it may be that neural dedifferentiation is a mechanism of coordination impairment [38] that contributes to mobility limitations among older adults.
Prior research has shown older adults have a higher attentional cost during a slow, compared to faster, movement frequencies during arm-leg coordination [11] and finger tapping [23]. These findings may lead one to expect better executive function to be associated with better coordination performance at a slower movement frequency. However, we found executive function to be associated with coordination variability at the faster, but not the slower, movement frequency. This discrepancy could be due to the type of cognitive assessment used (TMT Delta vs. reaction time), the body segments involved (ankle coordination vs. arm-leg coordination and finger tapping), or to the limited range of movement frequencies we examined.
We found that executive function, but not ankle differentiation, is associated with coordination variability at the faster ankle movement frequency. This may indicate that, at the faster movement frequency, better executive function acts in a compensatory fashion for poor (i.e., low) ankle differentiation to decrease coordination variability. Executive function is known to compensate for other motor deficits such as in gait [15, 37, 46]. We speculate that these findings may indicate the simultaneous presence of neural dedifferentiation and compensation. Future research is needed to examine the effects of cognitive functions on coordination performance and the possible co-occurrence of neural dedifferentiation and compensation among older adults. Factors such as task difficulty or preferred movement speed [24, 40], that were not controlled for in the present study, may limit the compensatory use of executive function at the slower movement speed. These findings may have implications for rehabilitative care for mobility limitations. For example, rehabilitation that targets ankle control differentiation, rather than ankle coordination variability, may produce different neural adaptations that have different effects on mobility limitations.
No participants transitioned from antiphase to inphase coordination during performance of the coordination task. This is consistent with prior research that found an absence of phase transitions in rhythmic antiphase foot coordination, even at high movement frequencies [34]. While this finding remains to be replicated, it indicates possible differences in the coupling of lower limbs, compared to upper limbs. Future research is needed to clarify differences in the neural control of upper and lower limb coordination.
The present study has several strengths. To our knowledge, this is the first study to examine the associations of motor control differentiation with mobility limitations and control among older adults. The study also included a measure of executive function and coordination variability, which allowed the determination of ankle control differentiation as an independent contributor to mobility limitations. A limitation of this study is its cross-sectional nature. This limits conclusions regarding causality.
Another limitation is that we did not include strength as a variable. This was not examined due to the minimal strength requirements for the foot coordination task. However, there has been a lack of research on associations between strength and motor differentiation. Because we cannot assess the contribution of strength to motor differentiation we are unable to determine the extent to which strength may mediate the relationship between motor differentiation and mobility limitations.
Conclusions
We conclude that ankle control differentiation is associated with ankle coordination performance and is independently associated with mobility limitations among community-dwelling older adults. These findings support the general hypothesis that ankle control differentiation is a motor control mechanism linking impaired ankle coordination and mobility limitations among community-dwelling older adults.
Figure 1.
Exemplar data of angular foot position during 0.5 Hz foot coordination. A. a participant with no mobility limitation and Cross-Sample Entropy = 3.18. B. a participant with mobility limitation and Cross-Sample Entropy = 2.15.
Highlights.
Low foot differentiation is associated with high coordination variability
Low foot differentiation is associated with mobility limitations
Low foot differentiation may be a mechanism of mobility limitations
Acknowledgement of financial support
This work was supported by the National Institute on Aging (K01AG053461 to E.J.; R01AG041525-05 to S.L.); the National Institute of Child Health and Human Development (K24HD070966-04) to J.B.).
Footnotes
Competing financial interests: The authors declare no competing financial interests.
Declarations of interest: none
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