Mechanical Modeling of Tibial Axial Accelerations Following Impulsive Heel Impact

A fourth order mass/spring/damper (MSD) mechanical model with linear coefficients was used to estimate axial tibial accelerations following impulsive heel impacts. A generic heel pad with constant stiffness was modeled to improve the temporal characteristics of the model. Subjects ( n = 14) dropped (~5 cm) onto a force platform (3 trials), landing on the right heel pad with leg fully extended at the knee. A uni-axial accelerometer was mounted over the skin on the anterior aspect of the medial tibial condyle inferior to the tibial plateau using a Velcro™ strap (normal preload ~45 N). Model coefficients for stiffness (k 1 , k 2 ) and damping (c 1 , c 2 ) were varied systematically until the minimum difference in peak tibial acceleration (%PTA min ) plus maximum rate of tibial acceleration (%RTA max ) between the estimated and measured curves was achieved for each trial. Model responses to mean subject and mean group model coefficients were also determined. Subject PTA and RTA magnitudes were reproduced well by the model (%PTA min = 1.4 ± 1.0 %, %RTA min = 2.2 ± 2.7%). Model estimates of PTA were fairly repeatable for a given subject despite generally high variability in the model coefficients, for subjects and for the group (coefficients of variation: CV k1 = 57; CV k2 = 59; CV c1 = 48; CV c2 = 85). Differences in estimated parameters increased progressively when subject and group mean coefficients (%PTA sub = 8.4 ± 6.3%, %RTA sub = 18.9 ± 18.6%, and %PTA grp = 19.9 ± 15.2 %, %RTA grp = 30.2 ± 30.2%, respectively) were utilized, suggesting that trial specific calibration of coefficients for each subject is required. Additional model refinement seems warranted in order to account for the large intra-subject variability in coefficients.