This study aimed to determine the effect of added noise, filtering and time series length on the largest Lyapunov exponent (LyE) value calculated for time series obtained from a passive dynamic walker. The simplest passive dynamic walker model comprising of two massless legs connected by a frictionless hinge joint at the hip was adopted to generate walking time series. The generated time series was used to construct a state space with the embedding dimension of 3 and time delay of 100 samples. The LyE was calculated as the exponential rate of divergence of neighboring trajectories of the state space using Rosenstein's algorithm. To determine the effect of noise on LyE values, seven levels of Gaussian white noise (SNR=55-25dB with 5dB steps) were added to the time series. In addition, the filtering was performed using a range of cutoff frequencies from 3Hz to 19Hz with 2Hz steps. The LyE was calculated for both noise-free and noisy time series with different lengths of 6, 50, 100 and 150 strides. Results demonstrated a high percent error in the presence of noise for LyE. Therefore, these observations suggest that Rosenstein's algorithm might not perform well in the presence of added experimental noise. Furthermore, findings indicated that at least 50 walking strides are required to calculate LyE to account for the effect of noise. Finally, observations support that a conservative filtering of the time series with a high cutoff frequency might be more appropriate prior to calculating LyE.
BACKGROUND: Rheumatoid arthritis is a chronic inflammatory joint disease which affects the joints and soft tissues of the foot and ankle. Rocker shoes may be prescribed for the symptomatic foot in rheumatoid arthritis; however, there is a limited evidence base to support the use of rocker shoes in these patients.
OBJECTIVES: The aim of this study was to evaluate the effectiveness of heel-to-toe rocker shoes on pain, disability, and activity limitation in patients with rheumatoid arthritis.
STUDY DESIGN: Clinical trial.
METHODS: Seventeen female patients with rheumatoid arthritis of 1 year or more duration, disease activity score of less than 2.6, and foot and ankle pain were recruited. Heel-to-toe rocker shoe was made according to each patient's foot size. All the patients were evaluated immediately, 7 and 30 days after their first visit. Foot Function Index values were recorded at each appointment.
RESULTS: With the use of rocker shoes, Foot Function Index values decreased in all subscales. This reduction was noted in the first visit and was maintained throughout the trials.
CONCLUSION: Rocker shoe can improve pain, disability, and activity limitation in patients with rheumatoid foot pain. All the subjects reported improved comfort levels.
CLINICAL RELEVANCE: The results of this study showed that high-top, heel-to-toe rocker shoe with wide toe box was effective at reducing foot and ankle pain. It was also regarded as comfortable and acceptable footwear by the patients with rheumatoid foot problems.
KEYWORDS: Foot Function Index questionnaire; Rheumatoid arthritis; pain; rocker shoes
Study site: Biomechanics Lab, Iran University of Medical Sciences, Tehran, Iran