## 3 Experiment and Results
### Experiment 1: Cartilage Change Prediction at the Bottom Horizontal Line  
Experiment 1 was designed to study the changing pattern of cartilage at the lower position of the medial tibia compartment. When we chose CDI as the quantification method, CDI points (# 1, #2, and #3 in Figure 2) were used to represent cartilage thickness; when we chose manual segmentation to quantify cartilage volume, we used X1 slice (see Figure 2) at the bottom horizontal line to represent cartilage thickness information. We first described the feature space for CDI. For each CDI location, we used the thickness values of the baseline year at the location itself as well as its two neighbors, forming a 3-dimensional feature vector as an input to the ANN, to predict 'changed' or 'no change' class label. Specifically, to predict change at CDI # 2, we used CDI values at locations #1, #2, and #3 to form the feature vector. To predict change at CDI #1, we used #2, #1, and #2 to form the feature vector, by a mirror padding at the right side of #1. The same procedure was implemented to generate the feature vector for CDI location #3. The output is 'changed' if there is a change of thickness value at that CDI location at 12-month follow-up and 'no-change' otherwise, indicating the OA disease has 'progression' or 'no progression'. In terms of the manual segmentation to quantify cartilage thickness, for each pixel, similarly, we have a neighborhood thickness vector as input and 'changed' and 'no-change' as output. To match the CDI method, we found the corresponding MR slice (such as X1 in Figure 2) that contained the corresponding CDI locations. Unlike CDI using only three locations on one MR slice, all the locations along the cartilage layer on the MR slice were included in the analysis when using manual segmentation to quantify the cartilage. Take X1 slice for example, a thickness vector was obtained to represent the thickness value of each pixel along with cartilage on X1 slice. We treated every single pixel as a sample and used the thickness of itself and its surrounding neighborhood pixels to predict the change of thickness at this particular position one year later. We tested various sizes of neighborhood including three neighbors (the pixel itself plus immediate left and right pixels) to 149 neighbors (the pixel itself plus 74 pixels on the left and 74 pixels on right) to find the best prediction performance using manual segmentation. The best AUC of ANN was using 75 neighbors (37 left and 37 right, mirror padding for pixels near the two ends). The general methodology to study the manual segmentation and CDI is the same, i.e., they both use neighborhood thickness vector as input to ANN, and use 'changed' or 'no-change' as output for each sample pixel. The difference is at the input dimension for each sample and the number of samples. The manual segmentation has a much larger sample pool since every pixel along the cartilage boundary is considered as a sample while the CDI has limited sample locations. This is the potential advantage of CDI that we only need to measure a few representative locations, but we can still, or even better, track the change of cartilage. We used the same training and testing data separation (as discussed in Section 2.6) for the two quantification methods. Because we noticed the data distribution had severed unbalance between 'changed' and 'no-change' categories (much more 'no-change' than 'changed'), we conducted resampling on the training dataset to balance the two categories. Table 1 shows the distribution of the two categories on the original dataset and rebalanced dataset. The performance of ANN model on both datasets was summarized in Table 2. As the results showed, the CDI generated a better performance (AUC = 0.651) than manual segmentation (AUC = 0.496) using raw data. For the rebalanced dataset, the CDI also showed a better prediction performance than manual segmentation (AUC = 0.669 VS AUC = 0.521).