## 5 Discussion  
Toe-activity analysis: Using videos, various toe movements were observed during walking. Some participants without stumbling history showed noticeable toe movements in the swing phase. Preservation of posture in the swing phase by participants with stumbling experiences was observed. These factors monitored by our proposed system are difficult to measure with conventional pressure sheet sensors. These factors also explain why we focused on the first and second peaks (contact areas at the start and end of the swing phase) and the difference between them to evaluate toe activity. Effects of toe activity on stumbling: All the evaluation values shown in Figure 7 and Table 3 exhibit the same tendency--that is, higher toe activity decreased the stumbling risk. This tendency was particularly clear at the mean and maximum NDPCAs, as the statistically significant differences were evident. [PERSON] et al. [38] assessed the effects of restricting the flexion-extension motion of the first metatarsophalangeal (MTP) joint on the walking gait of humans, and found a high risk of slipping and falling when the MTP joint is constrained. They also found that the flexion-extension motion of the MTP joint is important for normal walking. This supports our finding that low toe activity was associated with high stumbling risk. [PERSON] et al. [24] and [PERSON] et al. [25] investigated the relationship between the risk of falling and toe flexor strength of middle-aged and elderly individuals. Their results showed that toe flexor strength is related to the incidence of falls. Given that high toe activity corresponds to high flexion-extension ability, it was assumed that the risk of stumbling and falling could be estimated by the NDPCA. [PERSON] et al. [39] reported a strong correlation between maximum isometric toe flexor strength and the cross-sectional area of intrinsic and extrinsic plantar muscles. [PERSON] et al. [40] reported a moderate correlation between toe flexor strength and ankle dorsiflexion range of motion (DF ROM). [PERSON] et al. [41] reported correlations between ankle ROM and balance among community-dwelling elderly women. The aforementioned studies show that toe flexor strength is closely related to balance in walking because the ankle DF ROM can reflect toe flexor strength. We believe that high NDPCA corresponds to high ankle mobility, which means that individuals with high NDPCA have better walking dynamics than those with low NDPCA. Furthermore, low NDPCA indicates that the flexion-extension motion of the MTP joint is not working properly, and that the DF ROM is low, which increases the risk of falling and stumbling. A well-known criterion for evaluating stumbling is the minimum toe clearance (MTC), which is the minimum distance between the toe and the floor. [PERSON] et al. [42] investigated the sensitivity of MTC to the hip, knee, and ankle joint angles of the swing leg, and found that MTC was most sensitive to the ankle joint \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Young** & **Elderly** & \(p\)**-Value** \\ \hline
**Mean NDPCA** & & & \\ Without stumbling experience & \(0.339\pm 0.064\) & \(0.335\pm 0.054\) & 0.451 \\ With stumbling experience & \(0.269\pm 0.041\) & \(0.278\pm 0.019\) & 0.348 \\ \(p\)**-value** & **0.020 * & **0.039 * & / \\
**Maximum NDPCA** & & & \\ Without stumbling experience & \(0.454\pm 0.065\) & \(0.564\pm 0.053\) & **0.012 * \\ With stumbling experience & \(0.385\pm 0.041\) & \(0.471\pm 0.043\) & **0.038 * \\ \(p\)**-value** & **0.089** & **0.017 * & / \\
**Minimum NDPCA** & & & \\ Without stumbling experience & \(0.207\pm 0.112\) & \(0.123\pm 0.104\) & 0.101 \\ With stumbling experience & \(0.171\pm 0.087\) & \(0.113\pm 0.023\) & 0.110 \\ \(p\)**-value** & & & \\
**NDPCA Standard Deviation** & & & \\ Without stumbling experience & \(0.098\) & \(0.128\) & **0.067** \\ With stumbling experience & \(0.063\) & \(0.109\) & **0.048 * \\ \(p\)**-value** & **0.096** & \(0.151\) & / \\ \hline \hline \end{tabular}  
* * Significant at \(p<0.05\).  
\end{table}