# Treadmill Deck Performance Optimization Design Based on Muscle Activity during Running
## 3 Results  
Similar to the results of [PERSON] and [PERSON] [29], there is a specific region in the \(k_{ti}\)-\(\zeta_{ti}\) plane where the optimal value of the objective function is close to zero. The region where the optimal value of the objective function is less than 0.07 is called the safe region, as shown in Figure 3a,b, and is identified by two dotted lines in each subgraph of Figure 3. It can be seen that with the generation of fatigue, the size of the safe area is obviously reduced. This occurred due to the reduction in muscle capability while modifying its viscoelastic properties to align with the two underlying physiological hypotheses.  
Figure 3: _Cont_.  
In Figure 3c-f, the adjustment parameters \(k_{2}\) and \(c_{2}\) of lower-limb stiffness and damping are shown, respectively. It can be observed that higher damping and stiffness coefficients of the treadmill deck increase the lower-limb stiffness parameter \(k_{2}\) and decrease the lower-limb damping parameter \(c_{2}\). For the pre-fatigue state or post-fatigue state, the value of \(k_{2}\) does not reach the upper bound, which means that the leg muscles do not need to be very stiff in order to minimize the objective function. We note that the stiffness and damping values of the lower-limb muscles also increase as fatigue arises within the safe area. This finding is consistent with the findings of [PERSON] et al. (2018), who observed that an increase in damping coefficient is observed when runners tire during running.  
In Figure 3g-j, the GRF's first and second peak values acquired through each optimization are depicted. These outcomes show that by reducing the hardness of the treadmill deck, the first peak is decreasing, and conversely the second peak is increasing. However, within the safe area, there was no significant change in the values of the first and second peaks. This shows that when the hardness parameters of the treadmill deck are within a safe range, the CNS can keep the GRF peak stable, reducing the impact of shoe and movement surface changes. This is also consistent with the findings of [PERSON] et al. (2017) and [PERSON] (2018), who determined that GRF peaks remain constant over the appropriate range of parameters.  
The vibration amplitudes that may be noticed on the calf muscles during the landing support phase are depicted in Figure 3k,l. Within the hardness range of the treadmill deck, the vibration amplitude changes only very slightly (less than 5%) and is almost constant. This is because leg muscles have high stiffness and damping. This fact should also be attributed to the CNS, although it contributes less to CNS function than keeping GRF spikes constant.  
Figure 3: Simulation outcomes for the target function described by Equation (3). The first column is for pre-fatigueed condition (t/\(\tau\) = 0) and the second column is for post-fatigueed condition (t/\(\tau\) = 3). The identified safe area is shown between two black dotted lines. The variables expressed in the sub-graphs are as follows: (**a,b**) optimal value of the objective function; (**c–f**) stiffness and damping characteristics of the LLST that yield the optimal solution for the objective function; (**g–j**) the first and the second peaks of the GRF; (**k,l**) amplitude of the LLST oscillation.