Landmark-free Assessment of Lower-limb Alignment with Implicit Neural Shape Functions from Knee Radiographs

Technical Summary: Landmark-free Assessment of Lower-limb Alignment with Implicit Neural Shape Functions from Knee Radiographs

Problem Statement
The accurate radiographic assessment of lower-limb alignment (LLA) is critical for predicting joint health and surgical outcomes in total knee arthroplasty (TKA). Traditional measurement methods are manual and time-consuming. While recent machine learning approaches have automated this process, they predominantly rely on point-based models that predict a fixed set of anatomical landmarks to compute clinical angles (e.g., anatomical tibio-femoral angle [aTFA], anatomical medial proximal tibial angle [aMPTA], and joint line convergence angle [JLCA]). This reliance on explicit landmarks limits flexibility, requires dense and consistent annotation, and necessitates re-annotation if clinical definitions change. The authors propose a landmark-free approach that encodes anatomy into a compact latent space to regress clinical alignment measurements directly, thereby offering a more flexible shape representation.

Methodology
The proposed framework utilizes Implicit Neural Shape Functions (INSF) to model bone morphology from X-ray images. The workflow consists of four main stages:

1. Pre-alignment: An Hourglass-based CNN detects two reference points at the corners of the tibial plateau to align all images into a canonical space.
2. SDF Prediction: A U-Net predicts the Signed Distance Functions (SDFs) for the aligned knee images. The predicted SDF contains two channels, representing separate signed distance maps for the femur and tibia outlines. To address truncated shafts in radiographs, the authors manually extended truncated shaft contours toward image margins during training, allowing the model to learn consistent shaft geometry.
3. Implicit Shape Representation Learning: The authors employ a SIREN-based auto-decoder to learn compact latent shape representations. The decoder takes 2D normalized spatial coordinates and a latent vector as input, outputting the signed distance to the shape surface. The network parameters and latent embeddings are optimized jointly using a Signed Focal L1 loss to capture high-frequency geometric details.
4. Test-time Optimization and LLA Regression: For each test image, the latent vector is optimized via test-time optimization to minimize the focal loss between the generated SDF and the U-Net’s predicted SDF. Finally, a compact 4-layer Multilayer Perceptron (MLP) directly regresses the angular LLA measurements from these latent shape codes, bypassing explicit landmark computation.

Key Contributions

• First Application of INSF to Knee Radiographs: This is the first study to apply implicit neural representations for automated LLA assessment from knee radiographs.
• Landmark-free Architecture: The method encodes global anatomical structure into a continuous latent space, enabling direct regression of clinical angles without predefined landmark definitions.
• Flexible Representation: The architecture allows for rapid extendability to new tasks without altering the backbone representation, addressing the rigidity of discrete landmark-based models.

Results
The method was trained on an internal dataset of 566 knee radiographs and evaluated on an internal test set (50 patients) and an external dataset (402 cases from the MRKR dataset).

• Internal Dataset Performance: The proposed method achieved performance comparable to state-of-the-art landmark-based methods ([10, 12]) and manual inter-rater agreement. For aTFA, the Mean Absolute Difference (MAD) was 1.2° and Intraclass Correlation Coefficient (ICC) was 0.97 when compared to orthopaedic surgeon measurements.
• Impact of Shaft Extension: Incorporating shaft extension preprocessing improved accuracy, reducing MAD from 1.8° to 1.2° and increasing ICC from 0.94 to 0.97 compared to surgeon measurements.
• External Dataset Generalization: On the external MRKR dataset, the method performed comparably to landmark-based methods for aTFA. However, it showed marginally lower numerical performance for aMPTA and JLCA compared to both the landmark-based method and manual intra-rater agreement.
• Latent Space Analysis: Correlation analysis revealed strong associations between specific latent dimensions and clinical angles (e.g., latent dimension 116 correlated strongly with aTFA and JLCA). Visualizations indicated that these dimensions capture pose-related information, such as the relative positioning of femoral and tibial shafts.

Significance and Limitations
The paper claims that implicit neural representations effectively capture variations associated with LLA, offering a flexible alternative to landmark-based models. This flexibility is particularly valuable when landmarks are difficult to detect or when clinical definitions evolve.

However, the authors note several limitations:

• Generalizability: Performance declined slightly on the external dataset, potentially due to population differences (the internal dataset was predominantly White and older, while the external dataset included diverse ethnicities and was younger).
• Evaluation Constraints: Training targets were derived from landmark-based annotations, which may inherently favor landmark-driven approaches and constrain the full evaluation of the landmark-free advantage.
• Preprocessing Dependency: The method currently relies on a separate pre-alignment step, though the authors note this could be integrated into a single U-Net model.

The authors conclude that while the method is statistically equivalent to ground truth and existing automated methods within a ±1° difference threshold, future work should focus on regressing measurements not readily derived from landmarks to more comprehensively demonstrate the extendability of the implicit representation.