# A Novel Wearable Foot and Ankle Monitoring System for the Assessment of Gait Biomechanics
## 2 Materials and Methods
### Correlation of the Plantar Pressure with Muscular Activity
Cross-correlation of the FSR to the lower-limb muscular activity accounts for a local maximum in the origin provided that the FSR and muscular activation are interdependent. For exemplification, cross-correlation of the binarized FSR readings with the EMG activation from Figure 13 is illustrated in Figure 14. Indeed, since the FSR readings and EMG activations exhibit simultaneity--with the physiological delay in-between FSR\({}_{0}\) and the gastrocnemius, their cross-correlation exhibits a maximum in the origin. If on the other hand the FSR and the EMG activation are not interdependent, as illustrated in Figure 15a for FSR\({}_{1}\) and tibialis anterior and in Figure 15b for FSR\({}_{5}\) and gastrocnemius, their cross-correlation maxima will not be found in the origin, as illustrated in Figure 16.  
Figure 14: Illustration of the FSR and EMG interdependency via the cross-correlation of the binarized FSR reading and EMG activation which exhibits a maximum in the origin: (**a**) FSR\({}_{5}\) and tibialis anterior at heel strike, and (**b**) FSR\({}_{0}\) and gastrocnemius at toe-off. Another aspect which must pe pointed out at this stage is that, provided the cross-correlation maxima of physiologically unrelated plantar pressures and muscular activities are still found in the origin, this is a clear indicator of non-physiological gait. To be able to discriminate physiological from non-physiological gait respectively, we have further defined a gait map as the binary matrix representation of the interdependency between the FSRs and muscle activity. The matrix columns correspond to the gait phases as prescribed in Table 1. The matrix rows correspond to the cross-correlation of each FSR deployed onto the shoe insole with the tibialis anterior and the gastrocnemius respectively. Then, using Table 1, we were able to formulate the gait map template of the physiological gait cycle, namely which FSR is correlated to which muscle during the gait cycle. Accordingly, a logical '1' element in the gait map-stemming from the FSR-EMG cross-correlation maximum in the origin for the corresponding gait phase, accounts for the interdependency of the FSR with the muscular activity. A logical '0' on the other hand-stemming from the  
Figure 16: Illustration of the FSR and EMG lack of interdependency via the cross-correlation of the binarized FSR reading and EMG activation which does not have a maximum in the origin: (**a**) FSR\({}_{1}\) and tibialis anterior at heel strike, and (**b**) FSR\({}_{5}\) and gastrocnemius at toe-off. Figure 15: Time-domain plots of the FSR and EMG signals lack of interdependency during the gait phases: (**a**) FSR\({}_{1}\) and tibialis anterior at heel strike, (**b**) FSR\({}_{5}\) and gastrocnemius at toe-off. absence of a cross-correlation local maximum in the origin, states that the respective FSR and EMG are not interdependent. The gait map template of physiological walking, according to the proposed definition, is illustrated in Table 5. Physiological gait is then decided based on the bi-dimensional cross-correlation of the gait map \(G\) [12 \(\times\) 5] to the physiological gait map template \(G_{template}\) [1.2 \(\times\) 5], defined by:  
\[R_{gaitmap}(k,l)=\sum_{m=0}^{11}\sum_{n=0}^{4}G(m,n)G_{template}^{*}(m-k,n-l), \tag{7}\]  
where  
\[ \begin{array}{c}k=[-11,11]\\ l=[-4,4]\end{array} , \tag{8}\]  
and \((. )^{*}\) denotes complex conjugation [52]. As such, it can be decided upon physiological gait provided the bi-dimensional cross-correlation function exhibits a maximum in the origin.