## 3 Results
### Wound Areas' Comparison  
The first step in AIM's validation was the comparison of the average wound extension recorded over time with the different methods (Figure 2). For this analysis, the extension of each wound was normalized with respect to the area of the corresponding cell-free region at time T = 0. This procedure must be preferred to consider the average initial wound area as a normalizer, as it minimizes the effect of the width of the initial scratch on the results.  
In Figure 2a, the decrease in average wound extension in the control condition is reported. While showing a limited dynamic range when compared with the TGF-\(\beta\)1-treated population (Figure 2b), it is possible to notice how all the considered methods show comparable results. Specifically, untreated A549 cells exhibit limited invasive capabilities that are associated with a decrease in wound area of only about 10% after 48 h. The supplementation of TGF-\(\beta\)1, on the other hand, leads to a marked increase in invasiveness and thus to a final wound extension that is approximately 60% smaller than the one at T = 0.  
Notably, the wound area reduction is also associated with the increase in variability among the different methods. This is particularly accentuated for the ImageJ macro, shown in green, which has an average wound area at the end of the experiment that is almost 1/3 larger than the one obtained by the other techniques. In Panel (c) of Figure 2, the ratio between the areas reported in (b) and (a) is shown. This parameter, often considered when evaluating the differential invasiveness of two conditions, has a behavior similar to the one reported in (b), due to the modest changes in wound area of the control condition. It, however, assumes a greater importance when both tested conditions exhibit a significant variation with respect to the initial one. These considerations are also supported by the analysis of the percentage difference between each of the considered methods and the ground truth (Figure 3).  
This quantity (Equation (3)) is a measure of the distance between the result of each method and the true wound area and thus was computed only considering the images for which this result was available (about 40% of the total). Again, we can notice that all the methods are equivalent for the control condition (Figure 3a), as both their average value and standard error are coherent with the intrinsic variability of the considered dataset. This was quantified as the standard deviation of the ground truth and is reported in Figure 3 as the shaded area. On the other hand, the TGF-\(\beta\)1 condition  
Figure 2: Time course of the percentage of wound area over time. In (**a**), the control condition is reported; while (**b**) shows the data relative to the transforming growth factor \(\beta\)1 (TGF-\(\beta\)1) treated cells; finally in (**c**), the ratio between the treatment and control condition is shown.  
(Figure 3b) is associated with an increase in variability both within each method and among them. In particular the mean percentage difference between the ImageJ macro and the ground truth exits the shaded area 8 h after the beginning of the assay, and 34 h later, the average wound extension recorded by this method is almost 1.5-fold larger than its true value.  
With the other methods, the average remains within the shaded area throughout the whole experiment, and thus, the percentage difference from the ground truth remains below 10%. AIM, in particular, is associated with the \(\Delta\) ground truth closer to zero for all the time points except the last one (T = 48 h), suggesting that, on average, the wound area obtained with AIM is the most reliable and represents a closer approximation of the ground truth.