Development of a two-dimensional dynamic model of the foot-ankle system exposed to vibration

Workers in mining, mills, construction and some types of manufacturing are exposed to vibration that enters the body through the feet. Exposure to foot-transmitted vibration (FTV) is associated with an increased risk of developing vibration-induced white foot (VIWFt). VIWFt is a vascular and neurological condition of the lower limb, leading to blanching in the toes and numbness and tingling in the feet, which can be disabling for the worker. This paper presents a two-dimensional dynamic model describing the response of the foot-ankle system to vibration using four segments and eight Kelvin-Voigt models. The parameters of the model have been obtained by minimizing the quadratic reconstruction error between the experimental and numerical curves of the transmissibility and the apparent mass of participants standing in a neutral position. The average transmissibility at five locations on the foot has been optimized by minimizing the difference between experimental data and the model prediction between 10 and 100 Hz. The same procedure has been repeated to fit the apparent mass measured at the driving point in a frequency range between 2 and 20 Hz. Monte Carlo simulations were used to assess how the variability of the mass, stiffness and damping matrices affect the overall data dispersion. Results showed that the 7°-of-freedom model correctly described the transmissibility: the average transmissibility modulus error was 0.1. The error increased when fitting the transmissibility and apparent mass curves: the average modulus error was 0.3. However, the obtained values were reasonable with respect to the average inter-participant variability experimentally estimated at 0.52 for the modulus. Study results can contribute to the development of materials and equipment to attenuate FTV and, consequently, lower the risk of developing VIWFt.