# Foot Contact Dynamics and Fall Risk among Children Diagnosed with Idiopathic Toe Walking
## 2 Materials and Methods
Parameters from Vertical Ground Reaction Forces (GRF): vertical GRF was obtained when the participants walked over a forceplate that was embedded in the 10-m long walkway center. The vertical GRF was divided into a sequence of events (i) Foot initial Contact (FIC), (ii) Peak Loading Response (PLR), (iii) mid-stance (MS), (iv) peak push off (PPO), and (v) foot off (FO). Loading rate is defined as the slope of vertical GRF from FIC to PLR. COM ascending rate is defined as the slope of vertical GRF from PLR to MS. COM descending rate is defined as the slope of vertical GRF from MS to PPO. Push off rate is defined as the slope of vertical GRF from PPO to FO. The times taken to reach these events are shown in Figure 1. Similarly, force impulses were computed as area under the GRF-time curve and defined as loading impulse, COM ascending impulse, and push-off impulse. The impulses were calculated, as shown by Equation (1) below. Where Vertical RF(t) is GRF at time t.  
\[\text{Force Impulse}=\int_{\text{t1}}^{\text{t2}}\text{Vertical GRF(t).dt} \tag{1}\]  
Joint angles were evaluated at the hip, knee, and ankle. Each segment was represented with three strategically placed markers to compute embedded vector basis (EVB) [22]. EVB was constructed using the Gram-Schmidt Orthogonalization method and embedded axes were aligned to be anatomically meaningful, as per ISB recommendations [22]. In the neutral position, joint angles are zero and they are quantified as segments reposition [23]. The foot segment angle was computed as the angle made by the line adjoining heel and toe markers with the horizontal axis (as shown in Figure 2). Gait Assessments: foot contact was defined when the vertical force exceeded more than 7 N after the foot contacted the ground. In pilot trials, we placed heel and toe markers on lateral sides of the foot, such that foot initial contact determination (forceplate versus motion capture camera system) was consistently at about 7 N of vertical force. This could be due to signal noise from forceplate, which could not consistently detect force less than 7 N. The foot contact velocity was computed while utilizing the foot position marker at toe or heel, whichever impacts the ground surface during foot landing. The foot contact velocity was evaluated for horizontal and vertical directions through foot lowest marker displacement of 1/100 s before and after the foot contact phase of gait cycle using instantaneous foot velocity formula [24; 25], as shown in Equation (2). \[\text{Foot velocity}=\frac{\left(\text{Foot Marker Position}(\text{i}+1)- \text{Foot Marker Position}(\text{i}-1)\right.}{2\Delta\text{t}} \tag{2}\]  
Minimum Toe Clearance (MTC): it is the minimum vertical distance between the toe marker of the swing foot and the walking surface during swing. MTC is associated with trip-related falls during over ground walking [26; 27; 28; 29]. Stride Time: it is the time taken from foot initial contact (FIC) to the next FIC of the same foot [30]. Stride Length: the distance that is covered during a stride time is stride  
Figure 1: Stance vertical ground reaction force with events (i) foot initial contact (FIC), (ii) Peak Loading Response (PLR), (iii) mid-stance (MS), (iv) peak push off (PPO), and (v) foot off (FO). Slopes from FIC to PLR was defined as loading rate; PLR to MS as COM ascending rate; MS to PPO as COM descending rate; PPO to FO as Push off rate. Figure 2: Foot segment angles during foot initial contact for (**i**) healthy typical walking, (**ii**) toe walking, and (**iii**) Idiopathic Toe Walking (ITW) typical walking. Dorsiflexion angles are taken as positive and plantar flexion as negative. length [30]. Transitional acceleration of COM is defined as the acceleration of COM during the foot initial contact [31], and it is represented in Equation (3) (Figure 3a).