Symmetry and regularity of walking are two important aspects in gait analysis. Symmetry is related to similarity of contralateral steps, whereas regularity is related to similarity of consecutive strides. Both symmetry and regularity of gait are usually impaired in subjects wearing lower limb prostheses 123. The optimal use of a lower limb prosthesis is a challenging task, often requiring a long training for the amputee to achieve a nearly physiological pattern of movement 456. In this context, a fundamental clinical issue is to verify whether the correct gait pattern learned during the physiotherapy sessions is maintained during autonomous walking. The presence or development of gait anomalies resulting in gait asymmetries 7 are known to be the cause of important comorbidities, such as low-back pain 8, osteoarthritis 9 and risk of falls 10, which can highly affect the quality of life of the subject. For these reasons, the restoration and persistence of a symmetric gait is one of the main targets in the rehabilitation of amputees.

In such a perspective, the availability of an easy-to-use, portable system capable of measuring the degree of gait symmetry and regularity may provide important contributions for the treatment of lower limb amputees, both in the clinical practice supporting professional caregivers (for reporting and decision-making in hospital or in out-clinics environment), and for home-care practice to support the patient for self-rating (for example in the home environment or during activities of daily life).

In this scenario, to facilitate the use of the system by both practitioners and patients, both in the hospital and in independent life, the device must implement the following features: low-cost, high-comfort, easy-mounting and low-maintenance requirements. For this purpose, the use of inertial sensors appears the most convenient choice, similarly to what has been done in other contexts, and only partially for lower-limb amputees 1112131415, with only Robinson and colleagues 11 partially addressing the problem of gait symmetry and regularity.

From the on-board intelligence viewpoint, the development of a portable system for automatic detection of gait symmetry and regularity requires the selection of signal processing algorithms optimized for moderate processing resources consumption.

The aim of this study was therefore to assess the suitability of a method based on a single accelerometer and on the computation of the acceleration autocorrelation function 16, to measure the gait symmetry and regularity of unilateral transfemoral amputees (AMPs). For this purpose, we evaluated the correlation, sensitivity and specificity of the proposed approach with respect to reference indices computed from foot pressure measurements, together with their discriminative ability of detecting differences between AMPs and able-bodied subjects. To the best of our knowledge, this is the first study assessing gait regularity with inertial sensors in a group of transfemoral amputees.

Representative patterns of the autocorrelation function computed from the three components of the acceleration signals in an AMP and in a CTRL are shown in Figure 2. As represented in the figure, Ad1_ML values are always negative, both in AMP and in CTRL, since they correspond to the lateral trunk acceleration along the right-left directions (with opposite sign of the acceleration values when left stepping vs. right stepping). However, the absolute values were considered for the analyses. The patterns for the two subjects also show that the AMP's values for Ad1 and Ad2 are generally lower than CTRL's, for all the directions. Ad1 seems in general more different between the two subjects than Ad2.

Figures 3 and 4 report the results of the univariate regression analysis between accelerometry-based and pressure-based indices. When considering all the test sessions for all the subjects (AMPs+CTRLs) we found a good level of association between the indices. In particular, the highest correlations were found between SI1 and Ad1_AP (R² = 0.735, P < 0.0001), and between SI2 and Ad2_V (R² = 0.524, P < 0.0001). Therefore, any one of the three Ad1 indices may be considered a good surrogate of SI1 for the assessment of step regularity, and the same states for Ad2 indices for the assessment of stride regularity. Values of R² (and corresponding P) for all the indices are listed in captions of Figures 3 and 4.

Analysis of covariance showed that, for each index, there was no difference in the regression lines related to the three different walking speeds. Through the multivariate regression analysis, we found that any one of the three Ad1 indices contributes to explain the variability of SI1, i.e. all three indices were significant covariates (P < 0.016), with R² reaching the value of 0.776. As for Ad2 indices, in multivariate regression analysis only Ad2_V was a significant covariate of SI2, whereas Ad2_ML and Ad2_AP were not.

Regression analyses were carried out, with AMPs and CTRLs treated separately in the analysis. In AMPs, no significant correlation was found between Ad1_V and SI1, and the same for Ad1_ML. Conversely, a significant correlation was found between Ad1_AP and SI1 (R² = 0.401, P < 0.0001; regression line: Y = 0.83+0.17·X). Furthermore a significant correlation in SI2 was found with all the accelerometry-based indices, the best correlation being with Ad2_V (R² = 0.570, P < 0.0001; regression line: Y = 0.960+0.035·X). Similarly, in CTRLs, no significant correlation was found between Ad1_V or Ad1_ML and SI1. For Ad1_AP a significant though weak correlation was found with SI1 (R² = 0.127, P = 0.0052; regression line: Y = 0.93+0.05·X). Again, SI2 was significantly correlated with all the accelerometry-based indices, the best correlation being with Ad2_V (R² = 0.326, P < 0.0001; regression line: Y = 0.974+0.019·X).

Mean values of all the indices in the two groups are shown in the bar graphs of Figure 5. As for the regularity of step (i.e. symmetry between consecutive steps), all the Ad1 indices, as well as SI1, were significantly different between AMPs and CTRLs (P < 0.0001). Similarly, in terms of regularity of stride, all the Ad2 indices (P < 0.0001), as well as SI2, (P = 0.0005) were different in the two groups.

By means of ROC analysis, two subjects among CTRLs were found having impaired walking tests in terms of gait symmetry assessed by SI1. Conversely, three subjects among AMPs had some normal walking tests. As for gait regularity assessed by SI2, only one CTRL had one impaired walking test, whereas all the AMPs had one or more normal walking tests. Table 2 reports the results of the sensitivity and specificity analysis of the various Ad1 and Ad2 indices. An exemplary ROC plot is shown in Figure 6. It can be noted that indices related to step had higher sensitivity and specificity than those related to stride.

Since the time of use of the C-leg varied within a wide range (2 months to 7 years), the presence of a correlation between the duration of use and the gait performance was investigated, but no significant correlation was detected.

The aim of this study was to evaluate the appropriateness of a method based on the use of a single triaxial trunk accelerometer for the assessment of symmetry and regularity of gait in unilateral, transfemoral amputees. The interest for such measures is justified by their potential role in developing a portable automated device that may be able to evaluate the patient's gait features. In fact, one of the main characteristic that a portable, easy to use device to monitor gait features should have, is unobtrusive sensing units. Inertial sensors, such are accelerometers, are ideal candidate for such purpose. In this view, the methods and results presented in this study represent a step forward in the development of a potentially stand-alone portable system, that may act as a "virtual gait trainer" with the potentials of providing a summary score of walking ability in terms of gait symmetry and regularity during training, and, possibly, of alerting the therapist or the patient in the case of worsening of these gait features (biofeedback approach). The system could then be used even out of the clinics or rehabilitation institutes, allowing more frequent and prolonged training and rehabilitative therapy.

To these purposes, it was important to select a method for gait symmetry/regularity estimation that is particularly simple, both in terms of equipment and of computational requirements. In fact, if many approaches are possible for the estimation of gait regularity or gait variability 2223, the main characteristic of the method based on the autocorrelation function proposed by Moe-Nilssen and Helbostad 16 is that it is extremely uncomplicated, thus adequate for possible implementation even on portable devices with limited computational resources (as a palmtop computer or a dedicated microprocessor-based unit, than can be worn by the user during unconstrained training of gait).

The proposed algorithm may provide information to the user regarding the overall gait performance, in terms of symmetry and regularity, since it requires a large number of consecutive steps to supply a reliable estimate of performance. This approach is indeed in accordance with the concept of task-oriented training, which has been recently confirmed as more appropriate than, e.g., single muscle or single body segment rehabilitation, when a specific motor function needs to be restored 242526. A device based on a single accelerometer is light, inexpensive, and easy to wear over the patient's clothes. On the contrary more established methods to estimate gait symmetry or regularity are often based on pressure insoles 27 or optical movement analysis systems 28. Such systems are indeed reliable and widely described in the literature, but they are usually expensive, cumbersome, delicate in terms of maintenance, with a complex set-up, hence limited for a pervasive diffusion in the clinical practice or for home-based rehabilitation. In addition, Ad1 or Ad2 instead of temporal instants are preferable: they include information also on the morphology of the acceleration signals, not only on temporal features. Accelerometric data can potentially provide further information such as activity monitor functions and estimation of spatial parameters of gait. On the other side, systems based on pressure insoles have several drawbacks. In fact, the use of insoles is not comfortable for many patients, especially those using plantar supports, and a considerable amount of time may be necessary for some patients to wear them without help, as it may happen in the daily life; moreover, the insoles need to be of the specific patient's size; finally, systems based on insoles are usually very expensive and require an accurate calibration. Potential development of our approach toward a portable automatic device for gait training in subjects with lower limb prostheses will include further considerations, such as definition of the processing unit, identification of a simple and possibly wireless accelerometric unit, energy efficiency for long-lasting batteries. All these implementation issues are essential and will be arguments of further studies.

The analysis of gait symmetry and regularity in subjects wearing lower limb prostheses has been performed in previous studies. However, only few studies included healthy control subjects 12. In 1, 11 unilateral transfemoral amputees and 2 control subjects were studied. The amputees were found to have an asymmetrical gait compared to control subjects, and the amount of asymmetry was related to the stump length. In 2, 9 unilateral transfemoral amputees and 18 control subjects were studied. The amputees showed asymmetry in their gait: for instance, the single support phase on the amputated side was shorter than on the intact side, whereas, as expected, no difference between the two sides was observed in control subjects. Our results are hence in agreement with both studies 12, since we found that gait indices computed from both the insole pressure measurement and from the accelerometer are lower in amputees than in control subjects.

As far as cross-validation of the two measurement systems is concerned, we found that Ad1 and Ad2 indices computed from the acceleration signals were well correlated with SI1 and SI2, hence the simple and inexpensive approach based on the use of a single accelerometer may be adequate to estimate gait symmetry and regularity in transfemoral amputees. To our knowledge, only a few studies used inertial sensors to evaluate gait in subjects with lower limb prosthesis 1112131415, and only one of these studies addressed the issue of gait symmetry and regularity 11, but the study focused on below knee amputees and no control subjects were included. Of note, reliability of measures from accelerometers, in particular mounted on the trunk, was previously assessed with satisfactory results 29.

In the regression analysis, a possible limitation might be due to the inclusion of the data from all the repetitions for each subject. However, since the regression was performed on two measures both acquired during different tests, the independency between the samples remained despite the fact than more than one test resulted from the same subject.

As for the computation of Ad1 and Ad2 indices, comparison with other studies was possible only in relation to the control group. In 16, where the use of the autocorrelation function for gait analysis purposes was proposed for the first time, the authors found values for Ad1 and Ad2 very similar to the ones we estimated here (for instance, Ad1 = 0.89 and Ad2 = 0.91 from the vertical acceleration with a sensor at the L3 vertebra).

It is worth noting that the difference in Ad1 between AMPs and CTRLs was more marked than in Ad2 (absolute difference between the mean values equal to 0.27 and 0.10, respectively), and this is in agreement with what the physiotherapist expects. In fact, Ad1 represents the regularity of consecutive steps, and most likely in a subject wearing a unilateral prosthesis the right and left steps are different. Thus, it is reasonable that the differences compared with the CTRLs are more evident in the step regularity rather than in the stride regularity that may be still quite regular even in the amputees. As evidence, differences in SI2 between and AMPs and CTRLs were found statistically different, but appear clinically irrelevant.

In the analysis of AMPs and CTRLs grouped together, we found that each component of Ad1 (V, ML, AP) correlates with SI1, even if the degree of correlation (see R² values) differs between components. Similar results were found for Ad2 and SI2. However, no significant correlation was found between Ad1_V or Ad1_ML and SI1 in the single AMP and CTRL groups. In AMPs, that may indicate the existence of compensatory trunk asymmetry to regain some degree of gait symmetry, and that may reflect in relatively high SI1 values, differently to Ad1 values that are generally low. In CTRLs, a relation between Ad1 indices and SI1 may not be possible to demonstrate, because of lack of dispersion in the data. In all the subjects, it must also be noted that the correlation between Ad1 and SI1 (and similarly for Ad2 and SI2), even if significant, showed a slope of the regression line far from 1, i.e. they have much different range: SI1 and SI2 have in fact much narrower ranges compared to Ad indices. This was particularly observed in SI1 for the control subjects.

Even if there is not a standard reference method for the calculation of the symmetry indices 21 our results are robust to different formulation of the symmetry indices, since we tested some expressions (such as min(T_{STEP_R}, T_{STEP_L})/mean(T_{STEP_R}, T_{STEP_L}) for the step, and similarly for the stride), and the main findings of the study were confirmed.

The sensitivity and specificity of Ad1 and Ad2 further support their use in the clinical practice. In particular, Ad1_AP and Ad2_v appear to be the best compromise between specificity and sensitivity for general uses, even though the 100% specificity for Ad2_AP may be appealing when the amount of false positives is a major concern.

We studied gait performance in a homogeneous group of prosthesis-aided patients, and we compared the symmetry and regularity of their gait with that of a population of control subjects. We found that a simple accelerometer, placed on the thorax at the xiphoid process may be adequate for the assessment of gait symmetry and regularity. Symmetry can be best assessed by the autocorrelation coefficient at the first dominant period computed from the acceleration along the anteroposterior axis (Ad1_AP), and regularity by the coefficient at the second dominant period computed along the vertical axis (Ad2_v). The use of the simple, low-cost accelerometry-based system will allow for early detection of asymmetric and irregular walking patterns; it will possibly be beneficial in the correction of these alterations to prevent related comorbidities, with potential wide penetration of this approach both in the clinical practice, and, on a future perspective, for home-based rehabilitation.

The authors declare that they have no competing interests.

AT has made substantial contributions to analysis and interpretation of data and has been involved in drafting the manuscript. MR has made substantial contributions to acquisition, analysis and interpretation of data. LR has made substantial contributions to analysis and interpretation of data and has been involved in revising the manuscript. AGC has made substantial contributions to conception and design, analysis and interpretation of data, and has been involved in revising the manuscript. LC has made substantial contributions to conception and design of the study and has been involved in revising the manuscript.

All authors read and approved the final manuscript.