Fig 1.
Schematic of the lower leg and force plate, showing coordinate systems and heel point.
A global coordinate system XYZ is defined, where the origin O is situated in a corner of the force plate. The direction X is lateral, Y is anterior and Z is vertical up. A local coordinate system xyz is defined, where the origin L is situated at an LED kinematic marker. This is the lower of two markers placed directly on the skin over the medial surface of the tibia. The local z direction points to the second LED marker, the y direction is perpendicular to the z axis and lies in the plane of progression (defined as a plane parallel to the global YZ-plane), the x direction is defined orthogonal to the yz-plane to complete the local right-handed orthogonal coordinate system. The position of the heel point H is derived from the location of the center of pressure as obtained from the force plate data during heel strike, as measured in the global coordinate system XYZ. These global center of pressure points are transformed to the local coordinate system xyz. The median xyz-position of these transformed local center of pressure points is taken as the position of the heel point rH, which is a time-invariant vector in the local lower-leg coordinate system xyz. The global position of the heel point RH is time variant, due to the movement of the local coordinate system in the global coordinate system.
Fig 2.
Schematic zoomed in on heel-pad-ground contact, showing foot-ankle deformation definition.
The global position of the heel point H, defined with position vector RH with respect to the global coordinate system XYZ as shown in Fig 1, is shown at the instant of initial heel contact t0 and at a time t during heel strike. Due to deformation of the heel pad, foot and ankle, the heel point H(t) will effectively move through the ground during heel strike. The movement of the heel point during heel strike is taken as a measure for the foot-ankle deformation S(t)(= RH(t) − RH(t0)).
Table 1.
Energy absorption, foot-ankle deformation and other experimental results.
Fig 3.
A typical example of the measured ground reaction force acting on the right foot defined in the global coordinate system XYZ as a percentage of body weight (727 N) as a function of time, where the subscript X corresponds to mediolateral, Y to anterior-posterior and Z to vertical component of the force.
A dotted rectangle is shown to indicate the initial part of the stance phase where heel strike takes place. The ground reaction forces of this initial part is shown in Fig 4.
Fig 4.
A typical example of the measured ground reaction force acting on the heel (top) and foot-ankle deformation (bottom) as a function of time defined in the global coordinate system XYZ (shown in Fig 1), where the subscript X corresponds to mediolateral, Y to anterior-posterior and Z to vertical component (same measurement as in Fig 3).
The start of heel strike is shown by a vertical dotted line indicated by t0, the instant of the vertical force peak is indicated by tp and the end of heel strike, which is defined as zero vertical heel velocity, by te.
Fig 5.
A typical example of the location in the local xyz coordinate system of the center of pressure (COP) points during the impact phase used to define the heel point H.
The COP point at each instant is transformed to the local xyz coordinate system (see Fig 1), where the mean of these points are used to define the heel point H. The progression of the COP points as a function of time is indicated by the arrow. A point Q is defined in order to perform a parameter sensitivity analysis. This point lies 1 cm away from H in lateral (x), posterior (−y) and inferior (−z) direction. The gray areas are drawn to roughly indicate the boundaries of the undeformed heel.
Fig 6.
Subject specific scatter plot of maximal compressive foot-ankle deformation |SZe| as a function of corresponding energy absorption due to heel strike WZ, which is estimated using force-integral method (integral of vertical ground reaction force over vertical foot-ankle deformation).
Each marker represents a single measurement, where the marker style is participant specific and the body mass is shown in the legend for comparison. Previous results from in vivo tests on the human barefoot constrained lower legs collected by [26] are shown.
Fig 7.
A typical example of the vertical heel point acceleration in the same figure as vertical ground reaction force FZ as reference (same measurement as in Figs 3 and 4).
As in Fig 4 the start of impact is shown by a vertical dotted line indicated by t0, the instant of the vertical force peak is indicated by tp and the end of heel strike, which is defined as zero vertical heel velocity, by te. Here also the gravitational acceleration g is shown.