Stability Limits for Vertical Vibrations of Paraplegic Subjects while Using Passive Orthosis

Spinal cord injury (SCI) subjects use passive orthosis to assist them with the postural balance in daily life. Vertical vibrations are used to improve the postural balance of theses patients, mainly in terms of whole-body-vibrations, as in therapies. It is noteworthy to understand in what situation these patients are able to tolerate vertical vibrations while wearing orthosis. The main focus of this paper is to model vertical vibrations in the postural balance of arm free standing of the paraplegic subjects who use passive orthosis, and, mathematically understand the stability limits for these vibrations. To find the stable amplitudes and frequencies, equations of motions of the system are translated into non-homogeneous Mathieu equations, which are then analytically solved and the results are numerically plotted. In addition, the effect of shoe stiffness on the amplitude and frequency of the vibrations which violate stability are studied. The results show to be sure of the stability of the paraplegics in vertical vibrations, the shoe sole of the orthosis should have high values of stiffness, and this will guarauntee bigger ranges of stable vibrations and safer stance for the patients. Using the results, one can interpret how a paraplegic subject with passive orthosis may react to vertical perturbations, meaning, what ranges of frequencies and amplitudes of perturbations is tolerable without losing stability. This study is one of the necessities in designing new passive orthosis with more stability when exposed to perturbations.