Introduction

Walking is a core activity of younger and older persons. Declining walking speed in older persons is associated with negative health outcomes, such as falls [1], frailty [2], hospital admission [3], and mortality [4]. Gait speed is increasingly discussed as the sixth vital sign [5].

There are differences in supervised walking speed assessed in the laboratory and non-supervised gait speed in the real-world environment [6]. Furthermore, assessment methods in the laboratory do not fully reflect real-world walking performance [7]. Therefore, gait speed should also be measured in natural environments to achieve ecological validity and to better understand activity and adaptability. Unfortunately, gait speed estimation using wearable inertial sensors during normal daily activities [8, 9] is influenced by contextual factors and other confounders adding to high complexity and potential inaccuracies in distance estimation when integrating acceleration signals.

So far, the step-frequency is used as a correlate of walking intensity and gait speed and to predict clinical outcomes [10, 11]. Analysing single walking bouts extracted from real-world measurements step-frequency gives further insight into the intensity of gait [12].

A simple method to estimate gait speed in healthy young persons in the free-living condition used the pre-assessed persons walk ratio and showed good agreement between the estimated gait speed and the gait speed measured by an odometer/speedometer combination [13]. The walk ratio represents the step-length/step-frequency relation, which is individually constant over a range of gait speeds [14, 15] and therefore may reflect spatiotemporal coordination of habitual gait during daily activities. Using the individual walk ratio from a laboratory assessment and using in addition the duration of a walking bout and the number of steps during this walking bout (representing step-frequency), free-living gait speed can be calculated. The latter parameters can be provided by wearable sensors during daily activity measurement [16, 17].

This study aims to test the feasibility of gait speed estimation using the persons walk ratio (proof-of-concept) in older adults. Furthermore, this concept of gait speed estimation was compared to the gait speed estimation using the step-frequency.

Methods

Subjects and design

For this cross-sectional validation study, healthy community-dwelling older persons were recruited among social volunteers in a south-west German hospital. The sample size for this feasibility study was set pragmatically [18]. Inclusion criteria were the age of 60 years or more and being able to walk without personal assistance. Exclusion criteria were neurologic diseases (self-report), acute pain affecting walking performance (self-report), poor vision (not recognizing markers on the ground), and terminal illness. All participants gave written informed consent. The study protocol was approved by the ethical committee of the Medical Faculty at the University of Tuebingen (240/2019BO2).

Gait analysis

Although the proposed method of gait speed estimation is intended to be used for data analysis of wearable sensors during activity monitoring, this proof-of-concept study uses an instrumented walk-way because of the high accuracy [19]. Nevertheless, for the estimation of gait speed only those parameters (duration of walking, number of steps) were used, which also can be measured by wearable sensors and which alone are not sufficient to calculate gait speed.

All gait analyses were performed on 8 m long instrumented walk-way (GAITRite, CIR Systems, Franklin NJ, USA). The validity of the system to measure spatiotemporal parameters, including gait speed, step-length, number of steps, heel strike and toe off, has been shown [19]. For the assessment of the persons´ walk ratio, they walked 3-times with normal speed over the walk-way. Thereafter, the person was instructed to walk once a bit slower than normal, once at normal speed and once a bit faster than normal. For each walk, the person walked 3 additional meters before and after the walk-way to exclude acceleration and deceleration effects during the measurements [20].

The person´s walk ratio of the first 3 walks (normal gait speed) was calculated as the step-length divided by step-frequency and the mean walk ratio [cm min] of these 3 walks was used for further calculations. For the next 3 walks (a bit slower than normal speed, normal speed, a bit faster than normal speed; i.e. simulation of free-living condition) the gait speed was estimated in 4 calculation steps using the person’s walk ratio (first 3 walks) and those parameters from the GAITRite system, which validly also could be measured by a wearable sensor system, i.e. duration of walking and number of steps:

  1. 1.

    Step-frequency [steps/min] = number of steps/duration of walking

  2. 2.

    Step-length [m] = walk ratio × step-frequency

  3. 3.

    Distance of walking [m] = step-length × number of steps

  4. 4.

    Mean gait speed [m/s] = distance of walking/duration of walking

These calculated gait speeds of three different target speeds (a bit slower than normal speed, normal speed, a bit faster than normal speed) were compared with the gait speed measured by the GAITRite system as the ground truth.

In order to describe the association between step-frequency and gait speed, these parameters measured by the GAITRite system during the last 3 walks (a bit slower than normal speed, normal speed, a bit faster than normal speed) were correlated.

Descriptive parameters

Person characteristics were described by age, sex, body weight, and height (self-report). The general health status was assessed by the Charlson Comorbidity Index [21] scoring 16 diseases with a weighted score value of 0 (best) to 33 (worst). In addition, the number of falls in the previous year was asked and classified to no fall, 1 or 2 falls or more than 2 falls. Habitual gait speed was used as a capacity marker of global physical performance [22]. The mean walk ratio [cm min], the mean stride-length variability [%], and the mean step-length difference [cm] of the first 3 walks (normal walking) were used as qualitative parameters describing walking performance [22]. The range of the walk ratio was calculated over all 6 walks on the walk-way. Furthermore, the use of walking aids was recorded.

Statistics

The manifestation of parameters was expressed as mean, 95% confidence interval (CI), minimum and maximum. The linear association between estimated and measured gait speed and between measured step-frequency and measured gait speed was expressed as Pearson´s coefficient of correlation. A linear regression model was used to explain the effect of step-frequency on gait speed. With regard to disagreement, CIs were used to show differences between measurements (ground truth versus calculation). All statistics were calculated by open access R-software, version 3.6.1.

Results

Twenty community-dwelling older persons (14 women, 70%) were recruited for the study. Fourteen (70%) reported no fall in the previous year. Five (25%) and 1 person (5%) reported 1 or 2 falls and more than 2 falls, respectively. None of them used a walking aid. The description of the persons in detail is shown in Table 1.

Table 1 Description of all participating community-dwelling older persons (n = 20; 14 women, 70%)
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With regard to gait speed calculation using the walk ratio, the coefficient of correlation between ground truth and calculation was r = 0.98 (Fig. 1). Based on overlapping CIs there was no difference between measured (ground truth) and calculated gait speeds of slow, habitual, and fast walking. Absolute and relative mean differences/errors were smallest for habitual walking (0.03 m/s; 1.97%) and approximately doubled for slow and fast walking but were below 5%. For slow, habitual, and fast walking 4, 1 and 6 individual calculations, respectively, exceeded the 5% difference. The disagreement between ground truth and calculation was higher when the measured walk ratio differed from the pre-assessed walk ratio (first 3 walks). The results are shown in detail in Table 2.

Fig. 1
figure 1

Scatter plot of gait speed calculated using pre-assessed walk ratio and measured by GAITRite walk-way of all 20 community-dwelling older persons walking with normal gait speed, a bit slower and a bit faster (n = 60)

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Table 2 Measured ground truth (GAITRite) and calculated (using pre-assessed walk ratio) gait speed of slow, habitual and fast walking of all participating community-dwelling older persons (n = 20)
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The coefficient of correlation between gait speed and step-frequency, both measured by GAITRite (slow, habitual, fast), was r = 0.85 and was r = 0.93 when step-frequency was adjusted to body height. A linear regression including step-frequency and body height as independent variables explained 85% of variation of gait speed. The resulting formula (1) of gait speed calculation was:

$$V = \left(0.018745 *\text{SF}\right)+ \left(1.246501 * H \right) - 2.904699$$
(1)

with V = gait speed, SF = step-frequency and H = body height.

Discussion

In this study, a healthy group of community-dwelling older adults with an unimpaired walking performance was investigated. The proper walking performance is based on an appropriate gait speed [23,24,25] and walk ratio [26], a low stride-length variability [25] and a small step-length difference [26], in total reflecting high capacity and quality of walking [22].

The general agreement between ground truth and gait speed calculated using the persons’ walk ratio was very high demonstrating the proof-of-concept of this method. The results are comparable to a study including younger persons [13]. Our suggested approach outperforms the method using step-frequency for gait speed calculation in our study. So far, the method appears valid for community-dwelling older adults with an unimpaired walking performance. The method should be confirmed in other clinical and multi-morbid geriatric cohorts to be applied in clinical studies.

If a gait analysis in a laboratory is included in a study protocol, the persons’ walk ratio can be used to calculate the mean gait speed of single walking bouts during activity monitoring. The added value would be that additional parameters, such as the median mean gait speed of all walking bouts, the range of gait speeds or the complexity of gait speed can be calculated and may provide further insight into real-world activity monitoring [22]. The predictive validity of these gait speed parameters concerning health-related parameters, such as mortality, hospital admission, mobility decline or others has to be shown in future studies. Furthermore, the results of these studies have to be compared to the existing literature with results gained by gait speed measurements in the laboratory. With regard to future falls, the predictive validity of gait quality parameters has already been shown [27].

There was a small, but considerable range of the walk ratio across target gait speeds negatively affecting the accuracy of gait speed calculation. A possible explanation could be that the test persons were advised to walk a bit slower or faster in the laboratory. This is supported by other studies [14, 15] with differing walk ratios at fixed advised gait speeds or step-frequencies and dual tasks. Since an instruction of walking speed during real-world activity monitoring is not likely, the accuracy of gait speed estimation by the proposed method might be even higher than in our study.

The method of gait speed calculation using step-frequency does not need an accompanying gait analysis. Agreement with ground truth was very high but was lower than the method using the walk ratio. Only body height is needed and can be asked from the person to be included into the gait speed calculation. For existing activity monitor systems, this method could easily be integrated to provide additional parameters, such as median, minimum, and maximum gait speed of walking bouts. Further accuracy may be obtained by measuring leg length instead of asking body height.

For this proof-of-concept study with intra-individual comparisons only, a normalization of the results to anatomical characteristics was not necessary. Nevertheless, a normalization is necessary for inter-individual comparison or when comparing different cohorts [28]. An example is a comparison between men and women, because gait kinematics are different in both groups [29].

It is a limitation that our results are valid only for healthy community-dwelling older adults with an unimpaired walking performance. Future studies should test this method in larger patient cohorts and in geriatric patients representing lower, mid and upper level gait disorders and multifactorial gait disorders. Relevant examples are hip fracture and osteoarthritis patients with a potentially higher step-length difference [26] or Parkinson`s disease and normal pressure hydrocephalus where a lower walk ratio might be expected [30, 31] and persons with higher stride-length variability. Although the walking performance is likely impaired in these cohorts, our proposed method of gait speed calculation might still be acceptable, because of lower resources to change/adapt walking in these cohorts and so affecting the walk ratio. Another limitation is the fact that only the mean gait speed can be calculated by this method suggesting steady-state walking. Our method might be still acceptable, because longer walking bouts, characterized by lower variability of step-frequency/gait intensity and reflecting “purposeful walking”, are more interesting in this context [12]. These longer walking bouts are less affected by acceleration and deceleration of walking. Furthermore, this method of gait speed estimation is intended to be used in the real-world environment (activity monitoring) with wearable sensors but was tested for the “proof-of-concept” in a laboratory setting. Thus, the accuracy of gait speed estimation with wearable sensors relies on the accuracy of these sensors to detect the duration of walking and the number of steps. Unfortunately, there is no gold standard of gait speed measurement during daily life to compare with the proposed method. Therefore, the development of an accurate and continuous measurement of gait speed during a walking bout is desirable.

Conclusion

After confirmation in larger cohorts of healthy community-dwelling older adults, the mean gait speed of single walking bouts during activity monitoring can be estimated using the person’s pre-assessed walk ratio. Furthermore, the mean gait speed can be calculated using the step-frequency and body height and can be an additional parameter in stand-alone activity monitoring.