The neural network model chosen for this problem is based on the U-Net architecture, which has previously shown promising results in the tasks of segmentation, particularly for medical images (15 (link),22 –25 ), and has fewer trainable parameters than the other popular segmentation architecture, SegNet (26 ). The U-Net architecture can be viewed in Figure E1 (online) . The network takes a full image section as input and then, through a series of trainable weights, creates the corresponding section segmentation mask (22 ).
Our U-Net model uses a weighted cross-entropy loss function between the true segmentation value and the output for our model. The weighted cross-entropy function was used to account for the class imbalance of the volume that cartilage and meniscus compartments make up compared with the entire MR imaging volume. Details on this equation can be viewed inAppendix E1 (online) .
To build the U-Net models, data in subjects from both the T1ρ-weighted and the DESS sets were divided into training, validation, and time-point testing sets with a 70/20/10 split and were then broken down into their respective two-dimensional (2D) sections to be used as inputs for the two sequence models. The time-point testing set for both data sets consisted of only follow-up studies corresponding to baseline studies in the training and validation data sets. This time-point hold-out data set was used as validation for the precision of the automatic segmentation longitudinally. A full breakdown of the T1ρ-weighted and DESS training, validation, and time-point testing data according to diagnostic group (ACL, OA, control) can be viewed inTable 2 . The full 3D segmentation map was then generated by stacking the predicted 2D sections for a subject and then taking the largest 3D-connected component for each compartment class.
All U-Net models were implemented in Native TensorFlow, version 1.0.1 (Google, Mountain View, Calif). Model selection was made by using the 1-standard-error rule on the validation data set (27 ) (B.N., with 3 years of experience). For full learning specifications and learning curves of the U-Net, seeTable E1 and Figure E2 (both online).
Our U-Net model uses a weighted cross-entropy loss function between the true segmentation value and the output for our model. The weighted cross-entropy function was used to account for the class imbalance of the volume that cartilage and meniscus compartments make up compared with the entire MR imaging volume. Details on this equation can be viewed in
To build the U-Net models, data in subjects from both the T1ρ-weighted and the DESS sets were divided into training, validation, and time-point testing sets with a 70/20/10 split and were then broken down into their respective two-dimensional (2D) sections to be used as inputs for the two sequence models. The time-point testing set for both data sets consisted of only follow-up studies corresponding to baseline studies in the training and validation data sets. This time-point hold-out data set was used as validation for the precision of the automatic segmentation longitudinally. A full breakdown of the T1ρ-weighted and DESS training, validation, and time-point testing data according to diagnostic group (ACL, OA, control) can be viewed in
All U-Net models were implemented in Native TensorFlow, version 1.0.1 (Google, Mountain View, Calif). Model selection was made by using the 1-standard-error rule on the validation data set (27 ) (B.N., with 3 years of experience). For full learning specifications and learning curves of the U-Net, see
